Research Article Joint Bandwidth and Power Allocation for...

Research ArticleJoint Bandwidth and Power Allocation for LTE-BasedCognitive Radio Network Based on Buffer Occupancy

Alia Asheralieva and Yoshikazu Miyanaga

Laboratory of Information Communication Networks Hokkaido University Kita 14 Nishi 9 Kita-kuSapporo Hokkaido 060-0814 Japan

Correspondence should be addressed to Alia Asheralieva aasheralievagmailcom

Received 17 August 2015 Accepted 23 November 2015

Academic Editor Yuh-Shyan Chen

Copyright copy 2016 A Asheralieva and Y Miyanaga This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

We investigate the problem of resource allocation in a cognitive long-term evolution (LTE) network where the available bandwidthresources are shared among the primary (licensed) users (PUs) and secondary (unlicensed) users (SUs) Under such spectrumsharing conditions the transmission of the SUs should have minimal impact on quality of service (QoS) and operating conditionsof the PUs To achieve this goal we propose to assign the network resources based on the buffer sizes of the PUs and SUs in theuplink (UL) and downlink (DL) directions To ensure that the QoS requirements of the PUs are satisfied we enforce some upperbound on the size of their buffers considering two network usage scenarios In the first scenario PUs pay full price for accessingthe spectrum and get full QoS protection the SUs access the network for free and are served on a best-effort basis In the secondscenario PUs pay less in exchange for sharing the bandwidth and get the reduced QoS guarantees SUs pay some price for theiraccess without any QoS guarantees Performance of the algorithms proposed in the paper is evaluated using simulations in OPNETenvironment The algorithms show superior performance when compared with other relevant techniques

1 Introduction

The traditional fixed spectrum allocation policy has beencharacterized by a very ineffective spectrum utilizationresulting in an artificial scarcity of the network resources[1] which stimulated a surge of interest to an alternativespectrumusage concept known as cognitive radio (CR) [2] Ina CR network (CRN) the available bandwidth resources canbe shared among the PUs (paying some price for accessingspectrum) and the SUs (who can get the wireless accessfor free) Needless to say under such spectrum sharingconditions the transmission of the SUs should have minimalimpact on QoS and operating conditions of the PUs [2]

Among existingwireless standards considered for deploy-ment in CRNs LTE is considered to be the most favourabledue to such appealing features as spectrum flexibility fastadaptation to time-varying channel conditions high spectralefficiency and robustness against interference [3] A detaileddescription of the LTE radio interface can be found forinstance in [4] In short LTE is based on the universal

terrestrial radio access (UTRA) and a high-speed downlinkpacket access (HSDPA) In the DL LTE uses an orthogonalfrequency division multiple access (OFDMA) which hashigh spectral efficiency and robustness against the interfer-ence A single carrier frequency divisionmultiple access (SC-FDMA) is applied in the UL direction due to its lower(compared to OFDM) peak-to-average power ratio (PAPR)[5] The numerology of LTE includes a subcarrier spacingof 15 kHz support for scalable bandwidth of up to 20MHzand a resource allocation granularity of 180 kHz times 1ms(called a resource block) Available transmission resourcesare distributed among the users by the medium accesscontrol (MAC) schedulers located in enhanced NodeBs(eNBs) Depending on the implementation the schedulingcan be done based on queuing delay instantaneous channelconditions fairness and so forth [6 7]

Due to existence of two types of users (primary andsecondary) with different QoS requirements the problems ofdynamic spectrum access (DSA) and resource allocation forCRNs are more complex than those considered in traditional

Hindawi Publishing CorporationMobile Information SystemsVolume 2016 Article ID 6306580 23 pageshttpdxdoiorg10115520166306580

2 Mobile Information Systems

wireless networks The majority of the works on resourceallocation in LTE-based CRNs focus on various lower layertechniques for spectrum sensing and spectrummobility (seeeg [8ndash10])These techniques are very effective in identifyingand reducing the interference in the physical channels butdo not improve the overall user-perceived QoS which ismainly expressed in terms of the packet end-to-end delay andloss for the network users Consequently the results of theseworks are applicable only in combination with the techniquesdesigned for MAC and higher layers [11]

The QoS protection for the PUs and the admissibility ofthe SUs have been studied using the theoretical analysis ofuser behaviour For instance in [12] the authors propose astatistical traffic control for the LTE-based CRNs To satisfythe timing constraints of all packets belonging to differentstreams (with diverse QoS characteristics and requirements)and achieve the statistical QoS guarantees the authorsdeploy admission control and coordinated transmissions ofthe constant-bit-rate (CBR) and the variable-bit-rate (VBR)streams Dynamic channel selection for autonomous wirelessusers transmitting delay-sensitive multimedia applicationsover a CRN has been studied in [13] Unlike prior workswhere the application-layer requirements of the users havenot been considered here the rate and delay requirements ofheterogeneous multimedia users are taken into account Theauthors propose a novel priority based virtual queue interfaceto efficiently manage the available spectrum resources Thisinterface is used to (i) determine the required informationexchanges (ii) evaluate the expected delays experiencedby various priority traffics (iii) design a dynamic strategylearning (DSL) algorithm deployed at each user that exploitsthe expected delay and (iv) adapt to the channel selectionstrategies to maximize the userrsquos utility function

The authors of [5] present a delay-power control (DPC)exploiting the trade-off between the transmission delayand transmission power in wireless networks In a pro-posed resource allocation procedure each wireless linkautonomously updates its power based on the interferenceobserved at its receiver (without any crosslink communi-cation) The DPC scheme has been proved to convergeto a unique equilibrium point and contrasted to the well-known Foschini-Miljanic (FM) formulation Some theoreti-cal underpinnings of DPC and their practical implications forefficient protocol design have also been established In [14]the problem of allocating the network resources (channelsand transmission power) in a multihop CRN is modeledas a multicommodity flow problem with the dynamic linkcapacity resulting from dynamic resource allocation Basedon such queue-balancing the authors propose a distributedscheme for optimal resource allocation without exchangingthe spectrum dynamics between remote nodes Consideringthe power masks each node makes resource allocationdecisions based on current or past local information fromneighboring nodes to satisfy the throughput requirement ofeach flow and maintain the network stability

In this paper we suggest an alternative strategy forresource allocation in a LTE-based CRN and propose toassign the network resources (bandwidth and transmissionpower) to the UL and DL of LTE system based on buffer

size of user equipment (UE) pieces Note that in manypreviously proposed algorithms (eg [8ndash13]) the bandwidthand transmission power are assigned without considering thebuffer occupancy of UE pieces which may lead to a ratherunfair resource allocation (when users with lower demandsare allocated larger bandwidth than the users with higherdemands)

To ensure that the QoS requirements of the PUs aresatisfied we put the constraints on the sizes of their buffersTwo network usage scenarios are considered In the firstscenario the PUs pay full price for accessing the spectrumand get the full QoS protection whereas the SUs access thenetwork for free and are served on a best-effort basis In thesecond scenario the PUs pay less in exchange for sharingthe bandwidth and get the reduced QoS guarantees SUs paysome price for their usage without any QoS guarantees Theproposed resource allocation algorithm is derived based on adiscrete spectrum assumption with the spectrum resourcescounted in terms of LTE resource blocks (RBs) Note thata continuous spectrum assumption (used in all past works)is not applicable for a practical LTE realization since thenumber of RBs comprising the bandwidth is relatively small(6 10 20 50 and 100 RBs corresponding to 14 3 5 10and 100MHzwidebands resp [15]) Unlike existing researchcontributions the transmission rates of SUs and DUs arecalculated using the modified Shannon expression whichaccounts for the adaptive modulation and coding (AMC)used in LTE

The rest of the paper is organized as follows In Section 2we describe the network model and formulate the resourceallocation problems in two network usage scenarios InSection 3 we provide the solution methodology and dis-cuss the implementation of a presented resource allocationapproach in a real LTE system In Section 4 we outline asimulation model and evaluate performance of the proposedresource allocation algorithms in two network usage scenar-ios The paper is finalized in Conclusion

2 Problem Statement

21 NetworkModel Assumptions and Notation In this workthe problem of joint power and bandwidth allocation forthe LTE-based CRN is investigated for both the UL and theDL directions Similarly the discussion through the rest ofthe paper is applicable (if not stated otherwise) to eitherdirection

Consider a basic LTE-based CRN architecture whichconsists of one eNB providing wireless access to 119899 PUs num-bered PU

1 PU

119899 and 119898 SUs numbered SU

1 SU

119898

Two spectrum usage scenarios are considered in this paperIn the first scenario PUs are the licensed network users whopay some price for accessing the spectrum and thereforemustbe provided with the certain guaranteed QoS levels SUs arethe unlicensed network users who can access the spectrumfor free and therefore they are served on a best-effort basis Inthe second scenario the PUs pay less in exchange for sharingthe spectrum the SUs have to pay some price for the sharedspectrum to compensate for the income losses of a serviceprovider

Mobile Information Systems 3

The considered network operates on a slotted-time basiswith the time axis partitioned into mutually disjoint timeintervals (slots) 119879

119904 (119905+1)119879

119904 119905 = 0 1 2 with 119879

119904denoting

the slot length and 119905 being the slot indexThenumber of activePUs and SUs can be tracked using an LTE random accesschannel (RACH) procedure [15] which is used for initialaccess to the network (ie for originating terminating orregistration calls)

In the UL direction the user-generated traffic (in bits perslot or bps) is enqueued in the buffers of UE pieces and thentransmitted to the eNB using a standard packet schedulingprocedure [15] In this procedure the information about theamount of data (in bps) enqueued in the buffers of UE piecesis constantly transmitted to the eNB so that the eNB ldquoknowsrdquothe exact amount of data generated by the users at any slot 119905This information is then used by the eNB to allocate the ULtransmission resources to UE pieces In the DL direction thetransmission resources are allocated based on the amount ofdata transmitted by eNB to the users

In LTE system the transmission resources are allocatedto the users in terms of RBs Each user can be allocatedonly the integer number of RBs and these RBs should notbe adjacent to each other [7 15] Another important featureof both the SC-FDMA (applied in the UL direction) andOFDMA (applied in the DL direction) is the orthogonal-ity of resource allocation which allows achieving minimallevel of cochannel interference between different transmitter-receiver pairs located within one cell (ie when no frequencyreuse is considered)

It is assumed that the bandwidth of the eNB is fixed andequal to 119861 RBs For any 119894 in I = 1 119899 and any 119895 in J =1 119898 consider the following

(i) The channel between the eNB and PU119894is character-

ized by the noise and interference coefficient 0 lt

ℎ119875119894

le 1 which is known to the eNB and PU119894 The

channel between the eNB and SU119895is characterized by

the noise and interference coefficient 0 lt ℎ119878119895le 1

which is known to the eNB and SU119895 The values of ℎ

119875119894

and ℎ119878119895in the UL and DL directions can be obtained

from the channel state information (CSI) through theuse of the LTE reference signals (RSs) [16 17]

(ii) The size of the buffers and the arrival rates (in bits) ofPU119894and SU

119895can be observed at any slot 119905 in the UL

and DL directions

The following notations are used throughout the paper

(i) 119887119875119894(119905) and 119887

119878119895(119905) denote the number of RBs allocated

at slot 119905 to PU119894and SU

119895 respectively

(ii) 119901119875119894(119905) and 119901

119878119895(119905) denote the transmission power

allocated at slot 119905 to PU119894and SU

119895 respectively

(iii) 119886119875119894(119905) and 119886

119878119895(119905) denote the arrival rate (in bps) at slot

119905 in PU119894and SU

119895 respectively

(iv) 119902119875119894(119905) and 119902

119878119895(119905) denote the buffer size (in bits) at slot

119905 of PU119894and SU

119895 respectively

(v) 119903119875119894(119905) and 119903

119878119895(119905) denote the transmission rate (in bps)

at slot t in the channels of PU119894and SU

119895 respectively

(vi) 119875eNB 119875119875119894 and 119875119878119895denote the maximal transmission

power of the eNB PU119894 and SU

119895 respectively

22 Scenario 1 The objective of this paper is to devise asustainable algorithm for joint bandwidth and transmissionpower allocation based on two goals

(1) QoS Protection for the PUs PUs should maintain theirtarget QoS irrespective of how many SUs enter thenetwork and how much load they are generating

(2) Admissibility of the SUs SUs should be able to utilizethe spare capacity of the eNB (if left) to maximizetheir QoS

These goals however cannot be achieved without pro-viding the quantified measures for the user-perceived QoSNote that because of the orthogonality of the RB allocationthe need for interference mitigation in a considered CRNis eliminated In this case the use of such physical layercharacteristics as signal-to-noise ratio (SNR) is not well-reasoned More practical QoS measures can be obtainedfrom the higher layers network information For instancesuch metrics as round-trip latency and loss are traditionallyused for performance evaluation in wireless networks [5]Unfortunately in LTE system the direct estimation of delayand loss is rather complex For instance the end-to-endlatency consists of various delay components includingtransmission and queuing delays propagation andprocessingdelays the UL delay due to scheduling and delay due tohybrid automatic repeat request (HARQ) [18] The accurateanalysis of these delay components requires knowledge ofmany system parameters which may be not available duringresource allocation

Consequently in this paper we argue in favour of usingthe buffer size of UE pieces as a QoS measure The buffersize of PUs and SUs can be easily estimated from the knownparameters 119902

119875119894(119905) 119886119875119894(119905) and 119902

119878119895(119905) 119886119878119895(119905) using well-known

Lindleyrsquos equation [19]

119902119875119894(119905 + 1) = lceil119902

119875119894(119905) + 119886

119875119894(119905) minus 119903

119875119894(119905)rceil+

forall119894 isin I (1a)

119902119878119895(119905 + 1) = lceil119902

119878119895(119905) + 119886

119878119895(119905) minus 119903

119878119895(119905)rceil

+

forall119895 isin J (1b)

where lceil119909rceil+ = max0 119909 whereas the transmission rates119903119875119894(119905) 119903119878119895(119905) depend on the unknown bandwidth and trans-

mission power allocation vectors given by (relationshipbetween the transmission rate transmission power and thebandwidth will be established in the next section)

p119875= [1199011198751(119905) 119901

119875119899(119905)]119879

b119875= [1198871198751(119905) 119887

119875119899(119905)]119879

(2a)

p119878= [1199011198781(119905) 119901

119878119898(119905)]119879

b119878= [1198871198781(119905) 119887

119878119898(119905)]119879

(2b)

Note that the average round-trip latency of any primaryUE can be retained below some upper bound level by


restricting its buffer size to be less than a certain target buffersize The only information which is necessary in this case isthe desired upper bound on delay and the average arrival ratein PUs during some interval 119879 gt 0 Then we can find thetarget buffer size by deploying Littlersquos formula [20]

119863119894sdot 119886119875119894(119905) = 119871

119894 forall119894 isin I (3a)

where119863119894is the upper bound on delay for PU

119894 119871119894is the target

buffer size for PU119894 119886119875119894(119905) is the average arrival in PU

119894during

time interval [119905 minus 119879 + 1 119905] given by

119886119875119894(119905) =

119905

sum

120591=119905minus119879+1

119886119875119894(119905) forall119894 isin I (3b)

To maintain the desired upper bound on the end-to-enddelay the buffer size of PUs should be constrained as follows

119902119875119894(119905 + 1) le 119871

119894 forall119894 isin I (4)

or equivalently using (1a)

119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894le 119903119875119894(119905) le 119902

119875119894(119905) + 119886

119875119894(119905)

forall119894 isin I(5)

If added to an optimization problem constraint (5) canguarantee the QoS protection for PUs Except some (veryrare) cases when constraint (5) is not feasible the buffersize will always stay below the target level irrespective ofhow many SUs are in the network and how much load theyare generating The setting of the parameters 119871

119894 as well as

the cases when constraint (5) is unfeasible is discussed inSection 3

Note that at any slot 119905 the number of RBs allocatedfor data transmissions of PUs and SUs in the UL and DLdirections should not exceed 119861 RBs That is

sum

119894isinI119887119875119894(119905) + sum

119895isinJ119887119878119895(119905) le 119861 (6a)

where

119887119875119894(119905) isin Z+

119887119878119895(119905) isin Z+

forall119894 isin I forall119895 isin J

(6b)

where Z+ represents the set of all nonnegative integersAdditionally the transmission power allocated to the

users at any slot 119905 should be nonnegative and cannot exceedthe maximal transmission power levels Hence

119901119875119894(119905) le 119875

119875119894

119901119878119895(119905) le 119875

119878119895


(7a)

for the UL direction and

sum

119894isinI119901119875119894(119905) + sum

119895isinJ119901119878119895(119905) le 119875eNB (7b)

for the DL direction where119901119875119894(119905) ge 0

119901119878119895(119905) ge 0


(7c)

We are now ready to show how to attain the second goalof resource allocation As in case with QoS protection of PUswe use the buffer sizes of SUs as ameasure of the SUsrsquoQoSWesay that the admissibility of SUs in the network is preserved ifthey are allocated the bandwidth that is not used by the PUsThis can be done for instance byminimizing the sum (or thelogarithmic sum) of the buffer sizes of SUs or minimizing themaximal buffer size of SUs subject to the constraints listedabove

For the UL direction this gives us the following problem(to simplify notation we skip the index t below)

minimize max119895isinJ

lceil119902119878119895+ 119886119878119895minus 119903119878119895rceil

+

(8a)

subject to 119902119875119894+ 119886119875119894minus 119871119894le 119903119875119894le 119902119875119894+ 119886119875119894 forall119894 isin I (8b)

sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (8c)

119887119875119894isin Z+

119887119878119895isin Z+


(8d)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(8e)

119901119875119894ge 0

119901119878119895ge 0


(8f)

For the DL direction constraint (8e) should be replaced by

sum

119894isinI119901119875119894+sum

119895isinJ119901119878119895le 119875eNB (8g)

In above formulation each PU is guaranteed a certaintarget QoS level and the optimal allocations for PUs are suchthat

119902119875119894+ 119886119875119894minus 119903119875119894= 119871119894 forall119894 isin I (9)

The spare bandwidth (if left) is distributed among the SUsto minimize the size of their buffer which means that thetwo goals of resource allocation are achieved However thisformulation works well only if the aggregated traffic demandof the SUs is greater than that of the PUs Otherwise theremight be a situationwhen the optimal solution for SUs is suchthat

max119895isinJ


+

le 119871119894 forall119894 isin I (10)


which is apparently not fair since the PUs have larger buffersizes than the SUs and therefore they will experience longerdelays than the SUs

To avoid such situation we propose to modify problem(8a)ndash(8g) by replacing its objective (8a) with

minimize max119894isinI

lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+

+max119895isinJ


+

(11)

Objective (11) guarantees that PUs are served with max-imal QoS even if the aggregated traffic demand of SUs isgreater than that of the PUs

23 Scenario 2 We now consider a different scenario inwhich the PUs will benefit (by paying less in exchange) fromsharing their bandwidth with the SUs Let us assume that inthe network without price benefits (ie in Scenario 1) theprice for accessing the licensed spectrum of the PUs equals1 In this case all the PUs get the full QoS protection (ieguaranteed target buffer size 119871

119894and the average end-to-end

latency 119863119894) Suppose that each PU can define the portion of

allocated spectrum that it is willing to share with the SUsThedelay in turn is related to lceil119902

119875119894+ 119886119875119894minus 119903119875119894rceil+

Let us denote by 120572119894 0 le 120572

119894lt 1 the price for the portion

of spectrum that PU119894is willing to share with the SUs So

120572119894represents the willingness of PU

119894to trade off its QoS for

money Subsequently the guaranteed QoS level of PU119894will

reduce and instead of the QoS protection constraint (8b) wewill have

119903119875119894ge 119902119875119894+ 119886119875119894minus (1 + 120572

119894) 119871119894 forall119894 isin I (12)

Now to compensate for the income losses of a serviceprovider the SUs will have to pay the price for the sharedspectrum Let 120573 denote the price that each SU will pay foraccessing the shared spectrum The amount that SU

119895pays in

this case is 120573119903119878119895 whereas the revenue of the service provider

is

sum

119895isinJ120573119903119878119895minussum

119894isinI120572119894lceil119902119875119894+ 119886119875119894minus 119903119875119894rceil+

(13)

Assuming that a service provider does not incur loss byallowing the secondary users to use the spectrum we have toincorporate the constraint

sum

119895isinJ120573119903119878119895minussum


ge V (14)

where V is the profit that a service provider would like tomakeby allowing the SUs into the network

Note that in such formulation the SUs get no QoSguarantee and therefore we have to minimize the price that

the SUs pay for their usage Thus the optimization problemis

minimize 120573 (15a)

subject to 119902119875119894+ 119886119875119894minus (1 + 120572

119894) 119871119894le 119903119875119894

le 119902119875119894+ 119886119875119894

forall119894 isin I

(15b)

sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (15c)

119887119875119894isin Z+

119887119878119895isin Z+


(15d)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(15e)

119901119875119894ge 0

119901119878119895ge 0


(15f)

sum

119895isinJ120573119903119878119895minussum


ge V (15g)

for the UL direction For the DL direction constraint (15e) isreplaced by constraint (8g)The value of120573 obtained by solving(15a)ndash(15g) is then broadcasted by a service provider to theSUs that will have to pay a determined price

We note in passing that there are many other ways inwhich the pricing problem could be addressed For instancethe numbers 120572

119894may be negotiated between the PUs and a

service provider One can also think of a scenario wheredifferent SUs may be able to express their willingness to payvia bidding the prices 120573

119895 The options are numerous but they

are beyond the scope of this paper

3 Implementation Issues

31 Rate as a Function of Bandwidth and Power Note thatthe transmission rates in the UL and DL channels of a LTEsystem can be found using the modified Shannon equation[21] expressed as

119903119875119894(b119875 p119875) = 120596120595

119875119894119887119875119894log (1 + 120585

119875119894SNR119875119894)

= 120596120595119875119894119887119875119894log (1 + 120585

119875119894ℎ119875119894119901119875119894)

0 lt 120595119875119894 120585119875119894le 1 forall119894 isin I

(16a)


119903119878119895(b119878 p119878) = 120596120595

119878119895119887119878119895log (1 + 120585

119878119895SNR119878119895)

= 120596120595119878119895119887119878119895log (1 + 120585

119878119895ℎ119878119895119901119878119895)

0 lt 120595119878119895 120585119878119895le 1 forall119895 isin J

(16b)

where SNR119875119894and SNR

119878119895are the SNRs in the channels of PU

119894

and SU119895 respectively 120595

119875119894and 120595

119878119895are the system bandwidth

efficiencies for PU119894and SU

119895 respectively 120585

119875119894and 120585

119878119895are

the SNR efficiencies for PU119894and SU

119895 respectively 120596 is the

bandwidth of one RB (120596 = 180 kHz) [21]In real LTE networks the system bandwidth efficiency

is strictly less than 1 due to the overheads on the link andsystem levels The bandwidth efficiency is fully determinedby the design and internal settings of the system and doesnot depend on the physical characteristics of the wirelesschannels between the user and the eNB [21 22] Hence it isreasonable to assume that

120595119875119894= 120595119878119895= 120595 forall119894 isin I forall119895 isin J (17)

The SNR efficiency is mainly limited by the maximumefficiency of the supported modulation and coding scheme(MCS) [16] In LTE MCS is chosen using AMC to maximizethe data rate by adjusting the transmission parameters to thecurrent channel conditions AMC is one of the realizations ofa dynamic link adaptation In AMC algorithm the appropri-ate MCSs for packet transmissions are assigned periodically(within short fixed time interval usually equal to one slot)by the eNB based on the instantaneous channel conditionsreported by the usersThe higherMCS values are allocated tothe high-quality channels to achieve higher transmission rateThe lower MCS values are assigned to the channels of poorquality to decrease the transmission rate and consequentlyensure the transmission quality [16 17]

The method for choosing MCS can be expressed asfollows Based on the instantaneous radio channel conditionsthe SNR is calculated for the DL wireless channels betweenthe eNB and the users A supported MCS index is chosenusing expression [16 17]

MCS =

MCS1 SNR lt 120574

1

MCS2 1205741le SNR lt 120574

2

MCS119897 120574119897minus1

le SNR lt 120574119897

(18)

where 1205741

lt 1205742

lt sdot sdot sdot lt 120574119897are the SNR thresholds

corresponding to minus10 dB bit error ratio (BER) given by theAdditive White Gaussian Noise (AWGN) curves for eachMCS (the standard AWGN curves can be found in [17]) TheLTE standard allows 119897 = 15 MCS levels (description of MCSlevels their code rate and efficiency is shown in Table 1) [17]

Table 1 Allowed MCS values in LTE standard [17]

MCS index Modulation Code rate Efficiency0 No transmission1 QPSK 78 015232 QPSK 120 023443 QPSK 193 037704 QPSK 308 060165 QPSK 449 087706 QPSK 602 117587 16 QAM 378 147668 16 QAM 490 191419 16 QAM 616 2406310 64 QAM 466 2730511 64 QAM 567 3322312 64 QAM 666 3902313 64 QAM 772 4523414 64 QAM 873 5115215 64 QAM 948 55547

Based on the above the SNR efficiency depends onthe SNR of the DL wireless channel and therefore can berepresented by a function

119892 (SNR) =

1205851 SNR lt 120574

1

1205852 1205741le SNR lt 120574

2

120585119897 120574119897minus1

le SNR lt 120574119897

(19)

where 0 lt 1205851lt 1205852lt sdot sdot sdot lt 120585

119897are the values of the SNR

efficiency corresponding to the supported MCSUsing (17) and (19) the transmission rates of the users can

be expressed as

119903119875119894(b119875 p119875) = 120596120595119887

119875119894log (1 + 119892 (SNR

119875119894) sdot SNR

119875119894)

= 120596120595119887119875119894log (1 + 119892 (119901

119875119894) sdot ℎ119875119894119901119875119894)

forall119894 isin I

(20a)

119903119878119895(b119878 p119878) = 120596120595119887

119878119895log (1 + 119892 (SNR

119878119895) sdot SNR

119878119895)

= 120596120595119887119878119895log (1 + 119892 (119901

119878119895) ℎ119878119895119901119878119895)

forall119895 isin J

(20b)

32 Solution Methodology In this subsection we describe asolution methodology for the resource allocation problemin Scenario 1 in the UL direction (with the objective givenby (11) and the constraints defined in (8b)ndash(8f)) A resourceallocation problem for the DL direction as well as problem(15a)ndash(15g) for Scenario 2 can be solved analogously


Note that in Scenario 1 a resource allocation problem inthe UL direction is equivalent to

minimize Ω + Φ (21a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (21b)

119887119875119894isin Z+

119887119878119895isin Z+


(21c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(21d)

119901119875119894ge 0

119901119878119895ge 0


(21e)

Ω ge 0

Φ ge 0

(21f)

1198911

119894(b119875 p119875) = 119903119875119894(b119875 p119875) minus (119902

119875119894+ 119886119875119894)

le 0

forall119894 isin I

(21g)

1198912

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894minus 119871119894) minus 119903119875119894(b119875 p119875)

le 0

forall119894 isin I

(21h)

1198913

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894) minus 119903119875119894(b119875 p119875) minus Ω

le 0

forall119894 isin I

(21i)

1198914

119895(b119878 p119878)

= (119902119878119895+ 119886119878119895) minus 119903119878119895(b119878 p119878) minus Φ

le 0

forall119895 isin J

(21j)

In above problem some of the optimization variables(particularly the components of b

119875and b

119878) can take only

integer values whereas the other variables (the componentsof p119875and p

119878) are real-valued ones In addition constraints

(21g)ndash(21j) are represented by the nonsmooth nonlinear

functions of (b119875 p119875) and (b

119875 p119875) Hence (21a)ndash(21j) is a

nonlinear mixed integer programming (MINLP) problemwhich is Nondeterministic Polynomial-time (NP) hard Forimmediate proof of NP-hardness note that MINLP includesmixed integer linear programming (MILP) problem which isNP-hard [23]

Before applying any MINLP method for solving (21a)ndash(21j) the nonsmooth function 119892(sdot) in (19) included in theexpressions of 119903

119875119894(b119875 p119875) and 119903

119878119895(b119875 p119875) should be replaced

by its smooth approximation To construct a smooth approx-imation of 119892(119909) note that this function is equivalent to thesum of the shifted and scaled versions of a Heaviside stepfunction119867(119909) [24] That is

119892 (119909) =

15

sum

119897=1

(120577119897minus 120577119897minus1)119867 (119909 minus 120574

119897)

119867 (119909) =

1 if 119909 ge 0

0 otherwise

(22)

where 1205770= 0

Recall that a smooth approximation for a step function119867(119909) is given by a logistic sigmoid function [25]

119902(119909) =

1

1 + 119890minus2119902119909

(23)

where 119902 gt 0 119909 is in range of real numbers from minusinfin to +infinIf we take 119867(0) = 12 then larger 119902 corresponds to a closertransition to119867(119909) that is

lim119902rarrinfin

119902(119909) = 119867 (119909) (24)

The above holds because for 119909 lt 0 we have

119890minus2119902119909

997888rarr +infin

119902(119909) asymp 119867 (119909) = 1

(25)

for 119909 gt 0

119890minus2119902119909

997888rarr 0

119902(119909) asymp 119867 (119909) = 1

(26)

for 119909 = 0

119890minus2119902119909

= 1

119902(119909) = 119867 (119909) =

1

2

(27)

Consequently an approximation for a shifted Heavisidefunction is represented by a shifted logistic function

119902(119909 minus 120574

119897) =

1

1 + 119890minus2119902(119909minus120574119897)

(28)

defined for 119902 gt 0 with real 119909 in range from minusinfin to +infin


Based on (28) we can construct a smooth approximationfor 119892(119909) as

119902(119909) =

15

sum

119897=1

(120577119897minus 120577119897minus1) 119902(119909 minus 120574

119897) =

15

sum

119897=1

120577119897minus 120577119897minus1

1 + 1198902119902(119909minus120574119897)

(29)

Then it is rather straightforward to verify that

lim119902rarrinfin

119902(119909) = 119892 (119909) (30)

and the approximations for 119903119875119894(b119875 p119875) and 119903

119878119895(b119875 p119875) will

take the form

119875119894(b119875 p119875) = 120596120595119887

119875119894log (1 + (119901

119875119894) sdot ℎ119875119894119901119875119894)

forall119894 isin I(31a)

119878119895(b119878 p119878) = 120596120595119887

119878119895log (1 + (119901

119878119895) ℎ119878119895119901119878119895)

forall119895 isin J(31b)

With the approximations given by (31a) and (31b) prob-lem (21a)ndash(21j) can be solved using a sequential optimizationapproach as

(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (32a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (32b)

119887119875119894isin Z+

119887119878119895isin Z+


(32c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(32d)

119901119875119894ge 0

119901119878119895ge 0


(32e)

Ω ge 0

Φ ge 0

(32f)

119891

1

119894(b119875 p119875)

= 119875119894(b119875 p119875)

minus (119902119875119894+ 119886119875119894) le 0

forall119894 isin I

(32g)

119891

2

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894minus 119871119894)

minus 119875119894(b119875 p119875) le 0

forall119894 isin I

(32h)

119891

3

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894)

minus 119875119894(b119875 p119875) minus Ω

le 0

forall119894 isin I

(32i)

119891

4

119895(b119878 p119878)

= (119902119878119895+ 119886119878119895)

minus 119878119895(b119878 p119878) minus Φ

le 0

forall119895 isin J

(32j)

The above problem is smooth MINLP which can besolved using some fast and effective MINLP method Notethat most of the MINLP techniques involve constructionof the following relaxations to the considered problem thenonlinear programming (NLP) relaxation (original problemwithout integer restrictions) and the MILP relaxation (origi-nal problem where nonlinearities are replaced by supportinghyperplanes) In our case a smooth MILP relaxation to(32a)ndash(32j) in a given point (b0

119875 p0119875 b0119878 p0119878) is given by

(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (33a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (33b)

119887119875119894isin Z+

119887119878119895isin Z+


(33c)


119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(33d)

119901119875119894ge 0

119901119878119895ge 0


(33e)

Ω ge 0

Φ ge 0

(33f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33i)

119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

]

le 0

forall119895 isin J

(33j)

The NLP relaxation to (32a)ndash(32j) is

(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (34b)

119887119875119894ge 0

119887119878119895ge 0


(34c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(34d)

119901119875119894ge 0

119901119878119895ge 0


(34e)

Ω ge 0

Φ ge 0

(34f)

119891

1

119894(b119875 p119875) le 0

forall119894 isin I(34g)

119891

2

119894(b119875 p119875) le 0

forall119894 isin I(34h)

119891

3

119894(b119875 p119875) le 0

forall119894 isin I(34i)

119891

4

119895(b119878 p119878) le 0

forall119895 isin J(34j)

Note that theMINLP problems can be solved using eitherdeterministic technique or an approximation A typical exact


method for solving MINLPs is a well-known branch-and-bound algorithmand its variousmodifications [26] examplesof heuristic approaches include local branching [27] largeneighborhood search [28] and feasibility pump [29] to namea few Since we are interested in a reasonably simple and fastalgorithm it is more convenient to use heuristics for solvingthe problem In this paper a Feasibility Pump (FP) heuristic[29 30] is applied to solve (32a)ndash(32j) FP is perhaps the mostsimple and most effective method for producing more andbetter solutions in a shorter average running time For theproblems with nonbinary integer variables the complexity ofFP is exponential in size of a problem [31]

A fundamental idea of FP algorithm is to decomposethe problem into two parts integer feasibility and constraint

feasibility The former is achieved by rounding (solvinga NLP relaxation to the original problem) and the latterby projection (solving a MILP relaxation) Consequentlytwo sequences of points are generated The first sequence(b119875 p119875 b119878 p119878)119896119870

119896=1 119870 = 1 2 contains the integral

points that may violate the nonlinear constraintsThe secondsequence (b

119875 p119875 b119878 p119878)119896119870

119896=1contains the points which are

feasible for a continuous relaxation to the original problembut might not be integral

More specifically with input (b119875 p119875 b119878 p119878)1being a

solution to the NLP relaxation given by (34a)ndash(34j) thealgorithm generates two sequences by solving the followingproblems for 119896 = 1 119870

(b119875 p119875 b119878 p119878)119896= argmin

100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b

119875 p119875 b119878 p119878)119896

1003817100381710038171003817100381710038171

(35a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (35b)

119887119875119894isin Z+

119887119878119895isin Z+


(35c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(35d)

119901119875119894ge 0

119901119878119895ge 0


(35e)

Ω ge 0

Φ ge 0

(35f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35i)


119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

] le 0

forall119895 isin J

(35j)

(b119875 p119875 b119878 p119878)119896+1

= argmin 10038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b

119875 p119875 b119878 p119878)119896

100381710038171003817100381710038172

(36a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (36b)

119887119875119894ge 0

119887119878119895ge 0


(36c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(36d)

119901119875119894ge 0

119901119878119895ge 0


(36e)

Ω ge 0

Φ ge 0

(36f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0


where sdot1and sdot

2are 1198971norm and 119897

2norm respectivelyThe

rounding step is carried out by solving (35a)ndash(35j) whereasthe projection is the solution to (36a)ndash(36j) A suggested FPalgorithm alternates between the rounding and projectionsteps until (b

119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896(which implies

feasibility) or the number of iterations 119896 has reached thepredefined limit 119870 The workflow of a corresponding FPalgorithm is illustrated in the following part

FP Algorithm for Non-Convex MINLP(0) INITIALIZATION input119870 set 119896 = 1

solve (34a)ndash(34j) to obtain (b119875 p119875 b119878 p119878)119896

(1) WHILE (119896 lt 119870) do

(2) ROUNDING solve (35a)ndash(35j) to obtain(b119875 p119875 b119878 p119878)119896

(3) IF ((b119875 p119875 b119878 p119878)119896= (b119875 p119875 b119878 p119878)119896) THEN goto

step (6)(4) PROJECTION solve (36a)ndash(36j) to obtain

(b119875 p119875 b119878 p119878)119896+1

(5) Set 119896 = 119896 + 1


(6) OUTPUT solution (b119875 p119875 b119878 p119878)lowast

=

(b119875 p119875 b119878 p119878)119896

Note that in order to retain the convergence of thealgorithm both problems (35a)ndash(35j) and (36a)ndash(36j) needto be solved exactly Problem (36a)ndash(36j) (and consequentlyproblem (34a)ndash(34j)) can be solved using any standard NLPmethod In this paper an interior point algorithm (describedeg in [32]) with polynomial complexity is applied to solve(36a)ndash(36j) and (34a)ndash(34j) MILP problem (35a)ndash(35j) isrelatively simple and therefore can be solved efficiently foroptimality by any technique from the family of the branch-and-bound methods (eg [26])

33 Target Buffer Size for PUs and Feasibility Issues Recallthat 119871

119894represents the target buffer size for PU

119894 which

indicates that the QoS requirements of PU119894are satisfied By

limiting the buffer size of PUs we restrict the QoS of PUs(measured in terms of their buffer size) to be higher (or atleast not smaller) than the required minimum From thispoint of view constraints (5) and (12) guarantee the QoSprotection of PUs in Scenario 1 and Scenario 2 respectivelyApparently one can always restrict the target buffer size ofPUs to be equal to zero so that after each subsequent dataarrival the buffer of each PU is fully cleared This approachrepresents a ldquogreedyrdquo policy which ensures that the PUs arealways served with the best possible QoS but does not guar-antee that some spare capacity will be left to serve the SUs

A ldquoless greedyrdquo strategy would be to establish somelower bound on QoS for the PUs which will provide anldquoopportunityrdquo for SUs to be served To establish this lowerbound recall that the growing delay and loss indicate thata buffer of a corresponding node is congested whereas inan uncongested node the packet delay and loss are alwaysminimal [33] On the other hand it has been reported in[33 34] that in an uncongested node the buffer size 119902(119905) isincreasing very slowly that is 119902(119905 + 1)119902(119905) asymp 1 whereas ina congested node the buffer size is growing very fast so that119902(119905+1)119902(119905) ≫ 1 Hence to serve the PUs withminimal delayand loss it is enough to prevent the growth of their buffersthat is for each PU set

119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)

where 120576 ge 0 is some small value such that

120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)

More sophisticated approach to find the lowerQoS boundcan be deployed if information about the past buffer size isavailable at any time slot 119905 In this case one can set the targetbuffer size based on past T observations 119902(119905) 119902(119905 minus 119879 + 1)as

119871119894= min120591isinT

119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38a)

or

119871119894=

1

119879

sum

120591isinT119902119875119894(119905 minus 120591 + 1) + 120576 forall119894 isin I (38b)

where T = 1 119879

UBADPC MBC

60

70

80

90

100

110

120

130

140

Alg

orith

m it

erat

ions

10020 8040 50 60 7030 90100Number of SUs m

120572i = 1 v = m lowast 1Mbps

Figure 1 Average number of iterations before convergence as afunction of number of SUs in simulations with 119899 = 100 PUs andaverage SNR = 0 dB

MBC

070

075

080

085

090

095

100

120572i=0

v=0

120572i=1

v=0

120572i=0

v=m

lowast1

Mbp

s

120572i=1

v=m

lowast1

Mbp

s

Fairness among SUs FSU

Fairness among PUs FPU

Fairness among all users F

Figure 2 Jainrsquos index of fairness119865SU119865PU and119865 for the PUs SUs andall users in simulations with 119899 = 100 PUs119898 = 100 SUs and averageSNR = 0 dB

In some (very rare) cases (when the service capacity of theeNB is not enough to guarantee that the buffer sizes in all PUsdo not exceed the target buffer size) constraints (5) and (12)in Scenarios 1 and 2 may be not feasible In the following weshow how to identify such situation and what should be theoptimal resource allocation strategy in this case

Note that the service capacity of LTE system greatlydepends on physical characteristics (eg SINR and MCS) of


UBADPCGBC

NBCMBCABC

780

800

820

840

860

880

900

920

940

960Th

roug

hput

for P

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r PU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for P

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

Figure 3 Mean throughput packet delay and loss for PUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB

the wireless channels between the eNB and the users Henceat the moment preceding the bandwidthpower allocation itis rather difficult to estimate the service capacity of a systemNevertheless it is possible to find the average service capacityand to determine the upper and lower bounds on servicecapacity of the eNB in the UL and DL directions such that

119877min le sum119894isinI119903119875119894(119905) asymp 119877ave le 119877max (39)

where119877min119877ave and119877max are the lower bound upper boundand average service capacity of the eNB respectively

In our case the upper bound on service capacity of theeNB is given by

119877max = 120596120595119861 log (1 + 119892 (SNRmax) sdot SNRmax) (40a)

where SNRmax is the maximal possible SNR value

The lower bound on service capacity of eNB is

119877min = 120596120595119861 log (1 + 119892 (SNRmin) sdot SNRmin) (40b)

where SNRmin is the minimal possible SNR valueThe average service capacity of the eNB equals

119877ave = 120596120595119861 log (1 + 119892 (SNRave) sdot SNRave) (40c)

where SNRave is the average SNR valueIf SNR information is available then the values SNRmax

SNRmin and SNRave can be set as

SNRmax = max119894isinI

SNR119894 (41a)


0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r SU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for S

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

Figure 4 Mean throughput packet delay and loss for SUs as a function of number of SUs in simulations with 119899 = 100 PUs and average SNR= 0 dB

SNRmin = min119894isinI

SNR119894 (41b)

SNRave =1

119899

sum

119894isinISNR119894 (41c)

Otherwise (ie if SNR information is not available) thevalues are set arbitrarily

Now we can identify the situation when constraints (5)and (12) cannot be satisfied For this we should perform thefollowing test For Scenario 1 if

119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894) (42)

then constraint (5) is feasible Otherwise condition (5)cannot be satisfiedHence all the SUs receive zero allocations

andwe assign the bandwidthpower resources only to the PUsby solving the following optimization problem


lceil119902119875119894+ 119886119875119894minus 119903119875119894(b119875 p119875)rceil+

(43a)

subject to 119903119875119894(b119875 p119875) le 119902119875119894+ 119886119875119894 forall119894 isin I (43b)

sum

119894isinI119887119875119894le 119861 (43c)

119887119875119894isin Z+ forall119894 isin I (43d)

119901119875119894le 119875119875119894 forall119894 isin I (43e)

119901119875119894ge 0 forall119894 isin I (43f)


725

750

775

800

825

850

875

900

925

950Th

roug

hput

for P

Us (

kbits

s)

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC

10

20

30

40

50

60

70

Dela

y fo

r PU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

Loss

for P

Us (

)

0

005

01

015

02

025

03

035

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC

Figure 5 Mean throughput packet delay and loss for PUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB

for the UL direction For the DL directions constraint (43e)should be replaced by

sum

119894isinI119901119875119894le 119875eNB (43g)

For Scenario 2 if

119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus (1 + 120572

119894) 119871119894) (44)

then constraint (12) is feasible Otherwise inequality (12)cannot be satisfied and the bandwidthpower resources areassigned only to the PUs (according to (43a)ndash(43g)) whereasthe SUs receive zero allocations

4 Performance Evaluation

41 Simulation Model A simulation model of the networkconsisting of one eNB 119899 PUs and 119898 SUs randomly locatedin a service area with 3 km radius has been developed upona standard LTE platform using the OPNET package [35]Thebandwidth of the eNB equals 119861 = 50RBs (which is equivalentto 10MHz) The slot duration in the algorithm equals 119879

119904=

1msThemaximal number of iterations in FP algorithm is set119870 = 200Themaximal transmission power of the eNB equals119875eNB = 46 dBm and the maximal transmission power of eachPUSU equals 119875

1198751= sdot sdot sdot = 119875

119875119899= 1198751198781= sdot sdot sdot = 119875

119878119898= 23 dBm

Other simulation settings of the model are listed in Table 2(all the parameters are based on LTE specifications [36])


Table 2 Simulation parameters of the model

Parameter ValueRadio network model

Pass loss 119871 = 40log10119877 + 30log

10119891 + 49 119877 distance (km) 119891

carrier frequency (Hz)

Shadow fading Log-normal shadow fading with a standard deviation of1012 dB for outdoorindoor users

Penetration loss The average building penetration loss is 12 dB with astandard deviation of 8 dB

Multipath fading Spatial Channel Model (SCM) Suburban macroUE velocity 0 kmsTransmitterreceiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver antenna gain 10 dBi (pedestrian) 2 dBi (indoor)Receiver noise figure 5 dBThermal noise density minus174 dBmHzCableconnectorcombiner losses 2 dB

Physical profileOperation mode FDDCyclic prefix type Normal (7 symbols per slot)Evolved packet core (EPC) bearer definitions 348 kbits (nonguaranteed bit rate)Subcarrier spacing 15 kHz

Admission control parametersPhysical downlink control channel (PDCCH) symbols per subframe 3UL loading factor 1DL loading factor 1Inactive bearer timeout 20 sec

Buffer status report parametersPeriodic timer 5 subframesRetransmission timer 2560 subframes

L1L2 control parametersReserved size 2 RBsCyclic shifts 6Starting RB preserver for Format 1 messages 0Allocation periodicity 5 subframes

Random access (RA) parametersNumber of preambles 64Preamble format Format 0 (1-subframe long)Number of RA resources per frame 4Preamble retransmission limit 5 subframesRA response timer 5 subframesContention resolution timer 40 subframes

HARQ parametersMaximal number of retransmissions 3 (UL and DL)HARQ retransmission timer 8 subframes (UL and DL)Maximal number of HARQ processes 8 per UE (UL and DL)

A radio model of the network corresponds to the require-ments of ITU-T Recommendation M1225

The algorithms proposed in the paper are denoted asfollows

(i) GBC (greedy buffer Control) where the target buffersize equals 0 for all the PUs

(ii) NBC (nongreedy buffer control) with the target buffersize calculated according to (37a) and (37b)

(iii) MBC (Minimal Buffer Control) with 119879 = 10 slots andthe target buffer size given by (38a)

(iv) ABC (Average Buffer Control) with 119879 = 10 slots andthe target buffer size equaling (38b)

Two previously proposed schemes used to benchmark theperformance of the algorithms proposed in this paper are

(i) UBA (Utility Based Allocation) presented in [11]where the network resources (bandwidth and trans-mission power) are allocated to the UL channels tomaximize the total transmission rate of the userssubject to the capacity and transmission power con-straints


0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)

Figure 6 Mean throughput packet delay and loss for SUs as a function of SNR in simulations with 119899 = 100 PUs and average SNR = 0 dB

(ii) DPC (Delay Power Control) derived in [5] whichis used to balance the transmission delay againsttransmission power in wireless channels between theeNB and the users

We also gather simulation results for a proposed resourceallocation approach in Scenario 2 with different settings ofthe parameters120572

119894and V and benchmark its performancewith

the performance of the algorithm in Scenario 1All algorithms are simulated using identical settings

The data traffic in simulations is represented by voice overInternet Protocol (VoIP) video and Hypertext TransferProtocol (HTTP) applications mixed in proportion 2 3 5using the models defined in [37]

42 Complexity and Fairness Issues Let us first evaluatethe complexity and the fairness of resource allocation indifferent algorithms Figure 1 shows the average numberof iterations before convergence for UBA DPC and theproposed algorithms in Scenario 1 (denoted as MBC) andScenario 2 gathered in simulations with 119899 = 100 PUs andaverage SNR = 0 dB Note that the target buffer size for thePUs is calculated according to (38a) with T = 10 slots (inScenarios 1 and 2) and 120572

119894= 1 V = 119898 lowast 1Mbps (for

Scenario 2) Results demonstrate that the complexity of FPmethod deployed for resource allocation in Scenarios 1 and2 is exponential in size of the problem (which correspondsto the findings reported in [31]) and is comparable to thecomplexities of other techniques (UBA and DPC)


915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0

v = m lowast 1kbpsv = m lowast 10kbps

v = m lowast 100 kbpsv = m lowast 1MbpsMBC

080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i

Figure 7 Mean throughput packet delay and loss for the PUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average

SNR = 0 dB

Figure 2 shows the fairness of different methods calcu-lated according to Jainrsquos equation [38] as

119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =

(sum119894isinI 119903119875119894 + sum119895isinJ 119903119878119895)

2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)

where 119865PU 119865SU and 119865 stand for Jainrsquos index of fairness forthe PUs SUs and all of the users respectively 119903

119875119894 119903119878119895

arethe mean throughputs for PU

119894and SU

119895 respectively Results

have been gathered for 119899 = 100 PUs 119898 = 100 SUs average


v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i

Figure 8 Mean throughput packet delay and loss for the SUs as a function of the parameter 120572119894with 119899 = 100 PUs 119898 = 50 SUs and average

SNR = 0 dB

SNR = 0 dB and target buffer size for the PUs calculatedaccording to (38a) (Scenarios 1 and 2) with different settingsof 120572119894and V in Scenario 2

It follows from these graphs that the fairness index amongall of the users (denoted as 119865) is higher in Scenario 2 with120572119894= 1 and lower in Scenario 1 and Scenario 2 with 120572

119894= 0

Such results are rather expectable in Scenario 1 and Scenario2 with 120572

119894= 0 the SUs are served for free on a best-effort

basis whereas the PUs enjoy full QoS guarantees Hence thenetwork resources are shared nonequally between the PUs

and the SUs with most of the RBs allocated to the PUs andthe rest of the bandwidth distributed among the SUs Onthe other hand the fairness index for the PUs and SUs (ie119865PU and 119865SU) is rather high in both scenarios with differentsettings of 120572

119894and V which indicates that the users of the same

type are treated equally during resource allocation

43 Simulation Results in Scenario 1 Let us evaluate theperformance of a resource allocation algorithm in Scenario1 in terms of mean throughput packet end-to-end delay and


MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



Figure 9 Mean throughput packet delay and loss for the PUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB

loss for different user types Figures 3ndash6 show results obtainedin simulations with 119899 = 100 PUs and average SNR = 0 dBResults demonstrate that aUBA scheme has the largest packetdelay and loss and the lowest throughput for both the PUs andthe SUs A poor performance of this scheme is explained asfollows

(i) QoS protection of PUs is not considered in UBAHence the throughput delay and loss are the samefor PUs and SUs

(ii) Buffer sizes of individual users are not consideredin resource allocation and therefore the QoS for


0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



Figure 10 Mean throughput packet delay and loss for the SUs as a function of number of SUs with 119899 = 100 PUs 119898 = 50 SUs and averageSNR = 0 dB

different users varies significantly (since differentusers have different traffic demands)

(iii) Although widely used the choice of transmission rateas an individual user utility is not very rational someusers may have very low demand and small buffer

size and therefore there is no need to maximize theirtransmission rate and spend the network resources

Performance of the DPC scheme is a little better than thatofUBANote thatDPC takes into account transmission delaywhich is balanced against the transmission power in wireless


channels and therefore performance of DPC for PUs and SUsis better than performance of UBA However the queuingdelay related to usersrsquo buffer size and the QoS requirementsof PUs are not considered and therefore the delay and lossfor PUs are much greater in UBA than those in GBC NMCMBC and ABC

GBC NBC MBC and ABC show very consistent perfor-mance for the users All of these techniques take into accountthe usersrsquo buffer size whichmakes it possible tominimize theaverage delay and loss in the network for both the PUs andthe SUs Additionally the QoS for the PUs is guaranteed byrestricting the buffer size of each PU to stay below the targetbuffer size level which ensures that the packet delays for PUsdo not exceed the average target delays

The best performances for the PUs and the SUs areachieved by GBC andNBC respectively Such results providegood demonstration of trade-off between delay and loss forthe SUs and the target buffer size of the PUs In particulara ldquogreedyrdquo strategy shows good throughput delay and lossresults for the PUs but poor performance for the SUs Onthe other hand it is possible to achieve some compromisebetween holding the QoS guarantees of the PUs and provid-ing a reasonable performance for the SUs by using the lessstrict target buffer size settings (eg NBC ABC and MBC)

44 Simulations Results in Scenario 2 We now presentsimulation results in Scenario 2 with different settings of theparameters 120572

119894and V and the target buffer size of the PUs

calculated according to (38a) for 119879 = 10 and benchmark theseresults with the performance of the MBC algorithm in Sce-nario 1 Figures 7 and 8 show mean throughput packet end-to-end delay and loss in simulations with 119899 = 100 PUs 119898 =50 SUs and average SNR = 0 dB

Results demonstrate that QoS of the PUs and the SUsdepends to a great extent on the settings of 120572

119894and V The

parameter 120572119894has negative impact on service performance for

the PUs andpositive impact on performance for the SUsNotethat the target buffer size of the PUs increases with 120572

119894 which

leads to decreased throughput and increased delay and lossfor these users

We also observe that a service providerrsquos revenue V hasnegative impact on QoS of the SUs and positive impacton performance of the PUs Such results are due to themore strict constraints on the network usage for differenttypes of users Consequently the cases when the targetQoS of PUs cannot be satisfied (and problem (15a)ndash(15g)is unfeasible) happen more frequently and the QoS forthese users degrades On the other hand the SUs utilizemore bandwidth in response to the revenue constraints andtherefore their QoS improves

45 Comparison between Scenario 1 and Scenario 2 Resultsbelow show performance of the algorithms in Scenario 1 andScenario 2 with the target buffer size for the PUs calculatedaccording to (38a) with 119879 = 10 slots (in Scenarios 1 and 2)and different settings of the parameters 120572

119894and V in Scenario 2

Figures 9 and 10 show mean throughput packet end-to-enddelay and loss in simulations with 119899 = 100 PUs 119898 = 50 SUsand average SNR = 0 dB

Results demonstrate that theQoS of the PUs ismaximal inScenario 1 and Scenario 2 with 120572

119894= 0 because in this case the

PUs are provided with full QoS guarantees whereas the SUsare served on a best-effort basis On the other hand the ser-vice performance for the SUs is better in Scenario 2 with 120572

119894=

1 since the target buffer size for the PUs increased leading todegraded throughput and increased delay and loss for theseusers and improved performance for the SUs that pay for theshared resources

5 Conclusion

Theproblemconsidered in this paper relates to the problemoftransmission power and bandwidth allocation in a cognitiveLTE network where the bandwidth is shared among thePUs and SUs To guarantee that the QoS requirementsof the PUs are satisfied we enforce some upper boundon their buffer size Unlike previously proposed resourceallocation techniques our algorithm is derived based onrealistic assumptions such as discrete spectrum resourcesand consideration of AMC deployed in LTE systems Per-formance of the algorithm is evaluated using simulationsin OPNET environment Results show that the proposedresource allocation strategy performs significantly better thanother relevant resource allocation techniques

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] FCC Spectrum Policy Task Force ldquoReport of the spectrumefficiency working grouprdquo Tech Rep 2002

[2] S Haykin ldquoCognitive radio brain-empowered wireless com-municationsrdquo IEEE Journal on Selected Areas in Communica-tions vol 23 no 2 pp 201ndash220 2005

[3] 3GPP ldquoRequirements for evolved UTRA (E-UTRA) andevolved UTRAN (E- UTRAN)rdquo 3GPP TR 25913 2008

[4] E Dahlman S Parkvall and J Skod 3G Evolution HSPA andLTE for Mobile Broadband Academic Press Oxford UK 2007

[5] F Baccelli N Bambos and N Gast ldquoDistributed delay-powercontrol algorithms for bandwidth sharing in wireless networksrdquoIEEEACM Transactions on Networking vol 19 no 5 pp 1458ndash1471 2011

[6] C Y Wong R S Cheng K B Letaief and R D MurchldquoMultiuser OFDM with adaptive subcarrier bit and powerallocationrdquo IEEE Journal on Selected Areas in Communicationsvol 17 no 10 pp 1747ndash1758 1999

[7] A Larmo M Lindstrom M Meyer G Pelletier J Torsner andH Wiemann ldquoThe LTE link-layer designrdquo IEEE Communica-tions Magazine vol 47 no 4 pp 52ndash59 2009

[8] V Osa C Herranz J F Monserrat and X Gelabert ldquoImple-menting opportunistic spectrum access in LTE-advancedrdquoEURASIP Journal onWireless Communications and Networkingvol 2012 article 99 2012

[9] A Alizadeh S M-S Sadough and S A Ghorashi ldquoRelay selec-tion and resource allocation in LTE-advanced cognitive relay


networksrdquo International Journal on Communications Antennaand Propagation vol 1 no 4 pp 303ndash310 2011

[10] Y Chen C Cho I You and H Chao ldquoA cross-layer protocol ofspectrum mobility and handover in cognitive LTE networksrdquoSimulation Modelling Practice and Theory vol 19 no 8 pp1723ndash1744 2011

[11] J Acharya and R D Yates ldquoDynamic spectrum allocation foruplink users with heterogeneous utilitiesrdquo IEEE Transactions onWireless Communications vol 8 no 3 pp 1405ndash1413 2009

[12] S Y Lien andK C Chen ldquoStatistical traffic control for cognitiveradio empowered LTE-advanced with network MIMOrdquo in Pro-ceedings of the IEEE Conference on Computer CommunicationsWorkshops (INFOCOM WKSHPS rsquo11) pp 80ndash84 ShanghaiChina April 2011

[13] H-P Shiang and M van der Schaar ldquoQueuing-based dynamicchannel selection for heterogeneous multimedia applicationsover cognitive radio networksrdquo IEEE Transactions on Multime-dia vol 10 no 5 pp 896ndash909 2008

[14] W Wang K G Shin and W Wang ldquoDistributed resourceallocation based on queue balancing in multihop cognitiveradio networksrdquo IEEEACM Transactions on Networking vol20 no 3 pp 837ndash850 2012

[15] E-UTRA ldquoMAC protocol specificationrdquo 3GPP TS 36321(Release 8) 2007

[16] 3GPP ldquoPhysical channels and modulationrdquo 3GPP TS 362112011

[17] 3GPP ldquoMultiplexing and channel codingrdquo 3GPP TS 362122008

[18] H Holma and A Toskala LTE for UMTS Evolution to LTE-Advanced John Wiley and Sons 2011

[19] D V Lindley ldquoThe theory of queues with a single serverrdquoMath-ematical Proceedings of the Cambridge Philosophical Society vol48 no 2 pp 277ndash289 1952

[20] J D C Little ldquoA proof for the queuing formula 119871 = 120582119882rdquoOperations Research vol 9 no 3 pp 383ndash387 1961

[21] P MogensenW Na I Z Kovaes et al ldquoLTE capacity comparedto the shannon boundrdquo inProceedings of the IEEE 65thVehicularTechnologyConference (VTC-Spring rsquo07) pp 1234ndash1238DublinIreland April 2007

[22] P Vieira M P Queluz and A Rodrigues ldquoMIMO antennaarray impact on channel capacity for a realistic macro-cellularurban environmentrdquo in Proceedings of the IEEE 68th VehicularTechnology Conference (VTC-Fall rsquo08) pp 1ndash5 Calgary CanadaSeptember 2008

[23] R Kannan and C Monma ldquoOn the computational complex-ity of integer programming problemsrdquo in Optimization andOperations Research vol 157 of Lecture Notes in Economics andMathematical Systems pp 161ndash172 Springer 1978

[24] R Bracewell ldquoHeavisidersquos unit step function H(x)rdquo in TheFourier Transform and Its Applications pp 61ndash65McGraw-HillNew York NY USA 3rd edition 2000

[25] M O SearcoidMetric Spaces Springer Undergraduate Mathe-matics Series Springer Berlin Germany 2006

[26] S Leyffer ldquoIntegrating SQP and branch-and-bound for mixedinteger nonlinear programmingrdquo Computational Optimizationand Applications vol 18 no 3 pp 295ndash309 2001

[27] M Fischetti and A Lodi ldquoLocal branchingrdquo MathematicalProgramming vol 98 no 1ndash3 pp 23ndash47 2003

[28] A Lodi ldquoThe heuristic (dark) side of MIP solversrdquo HybridMetaheuristics vol 434 pp 273ndash284 2013

[29] C DrsquoAmbrosio A Frangioni L Liberti and A Lodi ldquoA stormof feasibility pumps for nonconvex MINLPrdquo MathematicalProgramming vol 136 no 2 pp 375ndash402 2012

[30] T Berthold Heuristic Algorithms in Global MINLP SolversVerlag Dr Hut 2014

[31] M Fischetti and D Salvagnin ldquoFeasibility pump 20rdquo Mathe-matical Programming Computation vol 1 no 2-3 pp 201ndash2222009

[32] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004

[33] V Jacobson ldquoCongestion avoidance and controlrdquo ACM SIG-COMM Computer Communication Review vol 18 no 4 pp314ndash329 1988

[34] J Mo and J Walrand ldquoFair end-to-end window-based conges-tion controlrdquo IEEEACMTransactions on Networking vol 8 no5 pp 556ndash567 2000

[35] OPNET website httpwwwopnetcom[36] E-UTRA and E-UTRAN ldquoOverall descriptionrdquo 3GPP TS

36300 Stage 2 (Release 8) 2008[37] IPOGUE Internet study 2007 and 20082009 research report

httpwwwcsucsbedusimalmerothclassesW10290Fpapersipoque-internet-study-08-09pdf

[38] R Jain W Hawe and D Chiu ldquoA quantitative measure offairness and discrimination for resource allocation in sharedcomputer systemsrdquo Tech Rep DEC-TR-301 Eastern ResearchLaboratory 1984

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



wireless networks The majority of the works on resourceallocation in LTE-based CRNs focus on various lower layertechniques for spectrum sensing and spectrummobility (seeeg [8ndash10])These techniques are very effective in identifyingand reducing the interference in the physical channels butdo not improve the overall user-perceived QoS which ismainly expressed in terms of the packet end-to-end delay andloss for the network users Consequently the results of theseworks are applicable only in combination with the techniquesdesigned for MAC and higher layers [11]

The QoS protection for the PUs and the admissibility ofthe SUs have been studied using the theoretical analysis ofuser behaviour For instance in [12] the authors propose astatistical traffic control for the LTE-based CRNs To satisfythe timing constraints of all packets belonging to differentstreams (with diverse QoS characteristics and requirements)and achieve the statistical QoS guarantees the authorsdeploy admission control and coordinated transmissions ofthe constant-bit-rate (CBR) and the variable-bit-rate (VBR)streams Dynamic channel selection for autonomous wirelessusers transmitting delay-sensitive multimedia applicationsover a CRN has been studied in [13] Unlike prior workswhere the application-layer requirements of the users havenot been considered here the rate and delay requirements ofheterogeneous multimedia users are taken into account Theauthors propose a novel priority based virtual queue interfaceto efficiently manage the available spectrum resources Thisinterface is used to (i) determine the required informationexchanges (ii) evaluate the expected delays experiencedby various priority traffics (iii) design a dynamic strategylearning (DSL) algorithm deployed at each user that exploitsthe expected delay and (iv) adapt to the channel selectionstrategies to maximize the userrsquos utility function

The authors of [5] present a delay-power control (DPC)exploiting the trade-off between the transmission delayand transmission power in wireless networks In a pro-posed resource allocation procedure each wireless linkautonomously updates its power based on the interferenceobserved at its receiver (without any crosslink communi-cation) The DPC scheme has been proved to convergeto a unique equilibrium point and contrasted to the well-known Foschini-Miljanic (FM) formulation Some theoreti-cal underpinnings of DPC and their practical implications forefficient protocol design have also been established In [14]the problem of allocating the network resources (channelsand transmission power) in a multihop CRN is modeledas a multicommodity flow problem with the dynamic linkcapacity resulting from dynamic resource allocation Basedon such queue-balancing the authors propose a distributedscheme for optimal resource allocation without exchangingthe spectrum dynamics between remote nodes Consideringthe power masks each node makes resource allocationdecisions based on current or past local information fromneighboring nodes to satisfy the throughput requirement ofeach flow and maintain the network stability

In this paper we suggest an alternative strategy forresource allocation in a LTE-based CRN and propose toassign the network resources (bandwidth and transmissionpower) to the UL and DL of LTE system based on buffer

size of user equipment (UE) pieces Note that in manypreviously proposed algorithms (eg [8ndash13]) the bandwidthand transmission power are assigned without considering thebuffer occupancy of UE pieces which may lead to a ratherunfair resource allocation (when users with lower demandsare allocated larger bandwidth than the users with higherdemands)

To ensure that the QoS requirements of the PUs aresatisfied we put the constraints on the sizes of their buffersTwo network usage scenarios are considered In the firstscenario the PUs pay full price for accessing the spectrumand get the full QoS protection whereas the SUs access thenetwork for free and are served on a best-effort basis In thesecond scenario the PUs pay less in exchange for sharingthe bandwidth and get the reduced QoS guarantees SUs paysome price for their usage without any QoS guarantees Theproposed resource allocation algorithm is derived based on adiscrete spectrum assumption with the spectrum resourcescounted in terms of LTE resource blocks (RBs) Note thata continuous spectrum assumption (used in all past works)is not applicable for a practical LTE realization since thenumber of RBs comprising the bandwidth is relatively small(6 10 20 50 and 100 RBs corresponding to 14 3 5 10and 100MHzwidebands resp [15]) Unlike existing researchcontributions the transmission rates of SUs and DUs arecalculated using the modified Shannon expression whichaccounts for the adaptive modulation and coding (AMC)used in LTE

The rest of the paper is organized as follows In Section 2we describe the network model and formulate the resourceallocation problems in two network usage scenarios InSection 3 we provide the solution methodology and dis-cuss the implementation of a presented resource allocationapproach in a real LTE system In Section 4 we outline asimulation model and evaluate performance of the proposedresource allocation algorithms in two network usage scenar-ios The paper is finalized in Conclusion

2 Problem Statement

21 NetworkModel Assumptions and Notation In this workthe problem of joint power and bandwidth allocation forthe LTE-based CRN is investigated for both the UL and theDL directions Similarly the discussion through the rest ofthe paper is applicable (if not stated otherwise) to eitherdirection

Consider a basic LTE-based CRN architecture whichconsists of one eNB providing wireless access to 119899 PUs num-bered PU

1 PU

119899 and 119898 SUs numbered SU

1 SU

119898

Two spectrum usage scenarios are considered in this paperIn the first scenario PUs are the licensed network users whopay some price for accessing the spectrum and thereforemustbe provided with the certain guaranteed QoS levels SUs arethe unlicensed network users who can access the spectrumfor free and therefore they are served on a best-effort basis Inthe second scenario the PUs pay less in exchange for sharingthe spectrum the SUs have to pay some price for the sharedspectrum to compensate for the income losses of a serviceprovider



119904 (119905+1)119879

119904 119905 = 0 1 2 with 119879

119904denoting







ℎ119875119894





119875119894





and DL directions


(i) 119887119875119894(119905) and 119887



119895 respectively

(ii) 119901119875119894(119905) and 119901



119895 respectively

(iii) 119886119875119894(119905) and 119886


119905 in PU119894and SU

119895 respectively

(iv) 119902119875119894(119905) and 119902


119905 of PU119894and SU

119895 respectively

(v) 119903119875119894(119905) and 119903



119895 respectively



119895 respectively






119875119894(119905) 119886119875119894(119905) and 119902

119878119895(119905) 119886119878119895(119905) using well-known


119902119875119894(119905 + 1) = lceil119902

119875119894(119905) + 119886

119875119894(119905) minus 119903

119875119894(119905)rceil+


119902119878119895(119905 + 1) = lceil119902

119878119895(119905) + 119886

119878119895(119905) minus 119903

119878119895(119905)rceil

+




p119875= [1199011198751(119905) 119901

119875119899(119905)]119879

b119875= [1198871198751(119905) 119887

119875119899(119905)]119879

(2a)

p119878= [1199011198781(119905) 119901

119878119898(119905)]119879

b119878= [1198871198781(119905) 119887

119878119898(119905)]119879

(2b)




119863119894sdot 119886119875119894(119905) = 119871

119894 forall119894 isin I (3a)


119894 119871119894is the target


119894during


119886119875119894(119905) =

119905

sum

120591=119905minus119879+1

119886119875119894(119905) forall119894 isin I (3b)


119902119875119894(119905 + 1) le 119871

119894 forall119894 isin I (4)


119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894le 119903119875119894(119905) le 119902

119875119894(119905) + 119886

119875119894(119905)



119894 as well as



sum

119894isinI119887119875119894(119905) + sum

119895isinJ119887119878119895(119905) le 119861 (6a)

where

119887119875119894(119905) isin Z+

119887119878119895(119905) isin Z+


(6b)



119901119875119894(119905) le 119875

119875119894

119901119878119895(119905) le 119875

119878119895


(7a)


sum

119894isinI119901119875119894(119905) + sum

119895isinJ119901119878119895(119905) le 119875eNB (7b)


119901119878119895(119905) ge 0


(7c)





+

(8a)


sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (8c)

119887119875119894isin Z+

119887119878119895isin Z+


(8d)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(8e)

119901119875119894ge 0

119901119878119895ge 0


(8f)


sum

119894isinI119901119875119894+sum

119895isinJ119901119878119895le 119875eNB (8g)




max119895isinJ


+

le 119871119894 forall119894 isin I (10)






+max119895isinJ


+

(11)






119875119894+ 119886119875119894minus 119903119875119894rceil+








119903119875119894ge 119902119875119894+ 119886119875119894minus (1 + 120572

119894) 119871119894 forall119894 isin I (12)


119895pays in


is

sum

119895isinJ120573119903119878119895minussum


(13)


sum

119895isinJ120573119903119878119895minussum


ge V (14)





subject to 119902119875119894+ 119886119875119894minus (1 + 120572

119894) 119871119894le 119903119875119894

le 119902119875119894+ 119886119875119894

forall119894 isin I

(15b)

sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (15c)

119887119875119894isin Z+

119887119878119895isin Z+


(15d)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(15e)

119901119875119894ge 0

119901119878119895ge 0


(15f)

sum

119895isinJ120573119903119878119895minussum


ge V (15g)









119903119875119894(b119875 p119875) = 120596120595

119875119894119887119875119894log (1 + 120585

119875119894SNR119875119894)

= 120596120595119875119894119887119875119894log (1 + 120585

119875119894ℎ119875119894119901119875119894)


(16a)


119903119878119895(b119878 p119878) = 120596120595

119878119895119887119878119895log (1 + 120585

119878119895SNR119878119895)

= 120596120595119878119895119887119878119895log (1 + 120585

119878119895ℎ119878119895119901119878119895)


(16b)



119894


119875119894and 120595




119875119894and 120585

119878119895are








MCS =

MCS1 SNR lt 120574

1

MCS2 1205741le SNR lt 120574

2

MCS119897 120574119897minus1

le SNR lt 120574119897

(18)

where 1205741

lt 1205742






119892 (SNR) =

1205851 SNR lt 120574

1

1205852 1205741le SNR lt 120574

2

120585119897 120574119897minus1

le SNR lt 120574119897

(19)




be expressed as

119903119875119894(b119875 p119875) = 120596120595119887

119875119894log (1 + 119892 (SNR

119875119894) sdot SNR

119875119894)

= 120596120595119887119875119894log (1 + 119892 (119901

119875119894) sdot ℎ119875119894119901119875119894)

forall119894 isin I

(20a)

119903119878119895(b119878 p119878) = 120596120595119887

119878119895log (1 + 119892 (SNR

119878119895) sdot SNR

119878119895)

= 120596120595119887119878119895log (1 + 119892 (119901

119878119895) ℎ119878119895119901119878119895)

forall119895 isin J

(20b)





subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (21b)

119887119875119894isin Z+

119887119878119895isin Z+


(21c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(21d)

119901119875119894ge 0

119901119878119895ge 0


(21e)

Ω ge 0

Φ ge 0

(21f)

1198911

119894(b119875 p119875) = 119903119875119894(b119875 p119875) minus (119902

119875119894+ 119886119875119894)

le 0

forall119894 isin I

(21g)

1198912

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894minus 119871119894) minus 119903119875119894(b119875 p119875)

le 0

forall119894 isin I

(21h)

1198913

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894) minus 119903119875119894(b119875 p119875) minus Ω

le 0

forall119894 isin I

(21i)

1198914

119895(b119878 p119878)

= (119902119878119895+ 119886119878119895) minus 119903119878119895(b119878 p119878) minus Φ

le 0

forall119895 isin J

(21j)


119875and b









119875119894(b119875 p119875) and 119903



119892 (119909) =

15

sum

119897=1


119897)

119867 (119909) =

1 if 119909 ge 0

0 otherwise

(22)

where 1205770= 0


119902(119909) =

1

1 + 119890minus2119902119909

(23)


lim119902rarrinfin

119902(119909) = 119867 (119909) (24)


119890minus2119902119909

997888rarr +infin

119902(119909) asymp 119867 (119909) = 1

(25)

for 119909 gt 0

119890minus2119902119909

997888rarr 0

119902(119909) asymp 119867 (119909) = 1

(26)

for 119909 = 0

119890minus2119902119909

= 1

119902(119909) = 119867 (119909) =

1

2

(27)


119902(119909 minus 120574

119897) =

1

1 + 119890minus2119902(119909minus120574119897)

(28)




119902(119909) =

15

sum

119897=1


119897) =

15

sum

119897=1

120577119897minus 120577119897minus1

1 + 1198902119902(119909minus120574119897)

(29)


lim119902rarrinfin

119902(119909) = 119892 (119909) (30)


119878119895(b119875 p119875) will

take the form

119875119894(b119875 p119875) = 120596120595119887

119875119894log (1 + (119901

119875119894) sdot ℎ119875119894119901119875119894)


119878119895(b119878 p119878) = 120596120595119887

119878119895log (1 + (119901

119878119895) ℎ119878119895119901119878119895)



(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (32a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (32b)

119887119875119894isin Z+

119887119878119895isin Z+


(32c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(32d)

119901119875119894ge 0

119901119878119895ge 0


(32e)

Ω ge 0

Φ ge 0

(32f)

119891

1

119894(b119875 p119875)

= 119875119894(b119875 p119875)

minus (119902119875119894+ 119886119875119894) le 0

forall119894 isin I

(32g)

119891

2

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894minus 119871119894)

minus 119875119894(b119875 p119875) le 0

forall119894 isin I

(32h)

119891

3

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894)

minus 119875119894(b119875 p119875) minus Ω

le 0

forall119894 isin I

(32i)

119891

4

119895(b119878 p119878)

= (119902119878119895+ 119886119878119895)

minus 119878119895(b119878 p119878) minus Φ

le 0

forall119895 isin J

(32j)


119875 p0119875 b0119878 p0119878) is given by

(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (33a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (33b)

119887119875119894isin Z+

119887119878119895isin Z+


(33c)


119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(33d)

119901119875119894ge 0

119901119878119895ge 0


(33e)

Ω ge 0

Φ ge 0

(33f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33i)

119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

]

le 0

forall119895 isin J

(33j)


(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (34b)

119887119875119894ge 0

119887119878119895ge 0


(34c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(34d)

119901119875119894ge 0

119901119878119895ge 0


(34e)

Ω ge 0

Φ ge 0

(34f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0









119875 p119875 b119878 p119878)119896119870





(b119875 p119875 b119878 p119878)119896= argmin

100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b

119875 p119875 b119878 p119878)119896

1003817100381710038171003817100381710038171

(35a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (35b)

119887119875119894isin Z+

119887119878119895isin Z+


(35c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(35d)

119901119875119894ge 0

119901119878119895ge 0


(35e)

Ω ge 0

Φ ge 0

(35f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35i)


119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

] le 0

forall119895 isin J

(35j)

(b119875 p119875 b119878 p119878)119896+1


119875 p119875 b119878 p119878)119896

100381710038171003817100381710038172

(36a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (36b)

119887119875119894ge 0

119887119878119895ge 0


(36c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(36d)

119901119875119894ge 0

119901119878119895ge 0


(36e)

Ω ge 0

Φ ge 0

(36f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0


where sdot1and sdot

2are 1198971norm and 119897







(1) WHILE (119896 lt 119870) do




(b119875 p119875 b119878 p119878)119896+1

(5) Set 119896 = 119896 + 1



=

(b119875 p119875 b119878 p119878)119896




119894 which




119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)


120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)


119871119894= min120591isinT


or

119871119894=

1

119879

sum


where T = 1 119879

UBADPC MBC

60

70

80

90

100

110

120

130

140

Alg

orith

m it

erat

ions

10020 8040 50 60 7030 90100Number of SUs m



MBC

070

075

080

085

090

095

100

120572i=0

v=0

120572i=1

v=0

120572i=0

v=m

lowast1

Mbp

s

120572i=1

v=m

lowast1

Mbp

s








UBADPCGBC

NBCMBCABC

780

800

820

840

860

880

900

920

940

960Th

roug

hput

for P

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r PU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for P

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m















SNR119894 (41a)


0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r SU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for S

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC



SNR119894 (41b)

SNRave =1

119899

sum

119894isinISNR119894 (41c)



119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894) (42)





(43a)


sum

119894isinI119887119875119894le 119861 (43c)


119901119875119894le 119875119875119894 forall119894 isin I (43e)

119901119875119894ge 0 forall119894 isin I (43f)


725

750

775

800

825

850

875

900

925

950Th

roug

hput

for P

Us (

kbits

s)

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC

10

20

30

40

50

60

70

Dela

y fo

r PU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

Loss

for P

Us (

)

0

005

01

015

02

025

03

035

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC



sum

119894isinI119901119875119894le 119875eNB (43g)

For Scenario 2 if

119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus (1 + 120572

119894) 119871119894) (44)




119904=


1198751= sdot sdot sdot = 119875

119875119899= 1198751198781= sdot sdot sdot = 119875

119878119898= 23 dBm





Pass loss 119871 = 40log10119877 + 30log

10119891 + 49 119877 distance (km) 119891




















0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)








119894= 1 V = 119898 lowast 1Mbps (for



915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





119904 (119905+1)119879

119904 119905 = 0 1 2 with 119879

119904denoting







ℎ119875119894





119875119894





and DL directions


(i) 119887119875119894(119905) and 119887



119895 respectively

(ii) 119901119875119894(119905) and 119901



119895 respectively

(iii) 119886119875119894(119905) and 119886


119905 in PU119894and SU

119895 respectively

(iv) 119902119875119894(119905) and 119902


119905 of PU119894and SU

119895 respectively

(v) 119903119875119894(119905) and 119903



119895 respectively



119895 respectively






119875119894(119905) 119886119875119894(119905) and 119902

119878119895(119905) 119886119878119895(119905) using well-known


119902119875119894(119905 + 1) = lceil119902

119875119894(119905) + 119886

119875119894(119905) minus 119903

119875119894(119905)rceil+


119902119878119895(119905 + 1) = lceil119902

119878119895(119905) + 119886

119878119895(119905) minus 119903

119878119895(119905)rceil

+




p119875= [1199011198751(119905) 119901

119875119899(119905)]119879

b119875= [1198871198751(119905) 119887

119875119899(119905)]119879

(2a)

p119878= [1199011198781(119905) 119901

119878119898(119905)]119879

b119878= [1198871198781(119905) 119887

119878119898(119905)]119879

(2b)




119863119894sdot 119886119875119894(119905) = 119871

119894 forall119894 isin I (3a)


119894 119871119894is the target


119894during


119886119875119894(119905) =

119905

sum

120591=119905minus119879+1

119886119875119894(119905) forall119894 isin I (3b)


119902119875119894(119905 + 1) le 119871

119894 forall119894 isin I (4)


119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894le 119903119875119894(119905) le 119902

119875119894(119905) + 119886

119875119894(119905)



119894 as well as



sum

119894isinI119887119875119894(119905) + sum

119895isinJ119887119878119895(119905) le 119861 (6a)

where

119887119875119894(119905) isin Z+

119887119878119895(119905) isin Z+


(6b)



119901119875119894(119905) le 119875

119875119894

119901119878119895(119905) le 119875

119878119895


(7a)


sum

119894isinI119901119875119894(119905) + sum

119895isinJ119901119878119895(119905) le 119875eNB (7b)


119901119878119895(119905) ge 0


(7c)





+

(8a)


sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (8c)

119887119875119894isin Z+

119887119878119895isin Z+


(8d)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(8e)

119901119875119894ge 0

119901119878119895ge 0


(8f)


sum

119894isinI119901119875119894+sum

119895isinJ119901119878119895le 119875eNB (8g)




max119895isinJ


+

le 119871119894 forall119894 isin I (10)






+max119895isinJ


+

(11)






119875119894+ 119886119875119894minus 119903119875119894rceil+








119903119875119894ge 119902119875119894+ 119886119875119894minus (1 + 120572

119894) 119871119894 forall119894 isin I (12)


119895pays in


is

sum

119895isinJ120573119903119878119895minussum


(13)


sum

119895isinJ120573119903119878119895minussum


ge V (14)





subject to 119902119875119894+ 119886119875119894minus (1 + 120572

119894) 119871119894le 119903119875119894

le 119902119875119894+ 119886119875119894

forall119894 isin I

(15b)

sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (15c)

119887119875119894isin Z+

119887119878119895isin Z+


(15d)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(15e)

119901119875119894ge 0

119901119878119895ge 0


(15f)

sum

119895isinJ120573119903119878119895minussum


ge V (15g)









119903119875119894(b119875 p119875) = 120596120595

119875119894119887119875119894log (1 + 120585

119875119894SNR119875119894)

= 120596120595119875119894119887119875119894log (1 + 120585

119875119894ℎ119875119894119901119875119894)


(16a)


119903119878119895(b119878 p119878) = 120596120595

119878119895119887119878119895log (1 + 120585

119878119895SNR119878119895)

= 120596120595119878119895119887119878119895log (1 + 120585

119878119895ℎ119878119895119901119878119895)


(16b)



119894


119875119894and 120595




119875119894and 120585

119878119895are








MCS =

MCS1 SNR lt 120574

1

MCS2 1205741le SNR lt 120574

2

MCS119897 120574119897minus1

le SNR lt 120574119897

(18)

where 1205741

lt 1205742






119892 (SNR) =

1205851 SNR lt 120574

1

1205852 1205741le SNR lt 120574

2

120585119897 120574119897minus1

le SNR lt 120574119897

(19)




be expressed as

119903119875119894(b119875 p119875) = 120596120595119887

119875119894log (1 + 119892 (SNR

119875119894) sdot SNR

119875119894)

= 120596120595119887119875119894log (1 + 119892 (119901

119875119894) sdot ℎ119875119894119901119875119894)

forall119894 isin I

(20a)

119903119878119895(b119878 p119878) = 120596120595119887

119878119895log (1 + 119892 (SNR

119878119895) sdot SNR

119878119895)

= 120596120595119887119878119895log (1 + 119892 (119901

119878119895) ℎ119878119895119901119878119895)

forall119895 isin J

(20b)





subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (21b)

119887119875119894isin Z+

119887119878119895isin Z+


(21c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(21d)

119901119875119894ge 0

119901119878119895ge 0


(21e)

Ω ge 0

Φ ge 0

(21f)

1198911

119894(b119875 p119875) = 119903119875119894(b119875 p119875) minus (119902

119875119894+ 119886119875119894)

le 0

forall119894 isin I

(21g)

1198912

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894minus 119871119894) minus 119903119875119894(b119875 p119875)

le 0

forall119894 isin I

(21h)

1198913

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894) minus 119903119875119894(b119875 p119875) minus Ω

le 0

forall119894 isin I

(21i)

1198914

119895(b119878 p119878)

= (119902119878119895+ 119886119878119895) minus 119903119878119895(b119878 p119878) minus Φ

le 0

forall119895 isin J

(21j)


119875and b









119875119894(b119875 p119875) and 119903



119892 (119909) =

15

sum

119897=1


119897)

119867 (119909) =

1 if 119909 ge 0

0 otherwise

(22)

where 1205770= 0


119902(119909) =

1

1 + 119890minus2119902119909

(23)


lim119902rarrinfin

119902(119909) = 119867 (119909) (24)


119890minus2119902119909

997888rarr +infin

119902(119909) asymp 119867 (119909) = 1

(25)

for 119909 gt 0

119890minus2119902119909

997888rarr 0

119902(119909) asymp 119867 (119909) = 1

(26)

for 119909 = 0

119890minus2119902119909

= 1

119902(119909) = 119867 (119909) =

1

2

(27)


119902(119909 minus 120574

119897) =

1

1 + 119890minus2119902(119909minus120574119897)

(28)




119902(119909) =

15

sum

119897=1


119897) =

15

sum

119897=1

120577119897minus 120577119897minus1

1 + 1198902119902(119909minus120574119897)

(29)


lim119902rarrinfin

119902(119909) = 119892 (119909) (30)


119878119895(b119875 p119875) will

take the form

119875119894(b119875 p119875) = 120596120595119887

119875119894log (1 + (119901

119875119894) sdot ℎ119875119894119901119875119894)


119878119895(b119878 p119878) = 120596120595119887

119878119895log (1 + (119901

119878119895) ℎ119878119895119901119878119895)



(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (32a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (32b)

119887119875119894isin Z+

119887119878119895isin Z+


(32c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(32d)

119901119875119894ge 0

119901119878119895ge 0


(32e)

Ω ge 0

Φ ge 0

(32f)

119891

1

119894(b119875 p119875)

= 119875119894(b119875 p119875)

minus (119902119875119894+ 119886119875119894) le 0

forall119894 isin I

(32g)

119891

2

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894minus 119871119894)

minus 119875119894(b119875 p119875) le 0

forall119894 isin I

(32h)

119891

3

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894)

minus 119875119894(b119875 p119875) minus Ω

le 0

forall119894 isin I

(32i)

119891

4

119895(b119878 p119878)

= (119902119878119895+ 119886119878119895)

minus 119878119895(b119878 p119878) minus Φ

le 0

forall119895 isin J

(32j)


119875 p0119875 b0119878 p0119878) is given by

(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (33a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (33b)

119887119875119894isin Z+

119887119878119895isin Z+


(33c)


119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(33d)

119901119875119894ge 0

119901119878119895ge 0


(33e)

Ω ge 0

Φ ge 0

(33f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33i)

119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

]

le 0

forall119895 isin J

(33j)


(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (34b)

119887119875119894ge 0

119887119878119895ge 0


(34c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(34d)

119901119875119894ge 0

119901119878119895ge 0


(34e)

Ω ge 0

Φ ge 0

(34f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0









119875 p119875 b119878 p119878)119896119870





(b119875 p119875 b119878 p119878)119896= argmin

100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b

119875 p119875 b119878 p119878)119896

1003817100381710038171003817100381710038171

(35a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (35b)

119887119875119894isin Z+

119887119878119895isin Z+


(35c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(35d)

119901119875119894ge 0

119901119878119895ge 0


(35e)

Ω ge 0

Φ ge 0

(35f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35i)


119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

] le 0

forall119895 isin J

(35j)

(b119875 p119875 b119878 p119878)119896+1


119875 p119875 b119878 p119878)119896

100381710038171003817100381710038172

(36a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (36b)

119887119875119894ge 0

119887119878119895ge 0


(36c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(36d)

119901119875119894ge 0

119901119878119895ge 0


(36e)

Ω ge 0

Φ ge 0

(36f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0


where sdot1and sdot

2are 1198971norm and 119897







(1) WHILE (119896 lt 119870) do




(b119875 p119875 b119878 p119878)119896+1

(5) Set 119896 = 119896 + 1



=

(b119875 p119875 b119878 p119878)119896




119894 which




119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)


120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)


119871119894= min120591isinT


or

119871119894=

1

119879

sum


where T = 1 119879

UBADPC MBC

60

70

80

90

100

110

120

130

140

Alg

orith

m it

erat

ions

10020 8040 50 60 7030 90100Number of SUs m



MBC

070

075

080

085

090

095

100

120572i=0

v=0

120572i=1

v=0

120572i=0

v=m

lowast1

Mbp

s

120572i=1

v=m

lowast1

Mbp

s








UBADPCGBC

NBCMBCABC

780

800

820

840

860

880

900

920

940

960Th

roug

hput

for P

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r PU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for P

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m















SNR119894 (41a)


0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r SU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for S

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC



SNR119894 (41b)

SNRave =1

119899

sum

119894isinISNR119894 (41c)



119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894) (42)





(43a)


sum

119894isinI119887119875119894le 119861 (43c)


119901119875119894le 119875119875119894 forall119894 isin I (43e)

119901119875119894ge 0 forall119894 isin I (43f)


725

750

775

800

825

850

875

900

925

950Th

roug

hput

for P

Us (

kbits

s)

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC

10

20

30

40

50

60

70

Dela

y fo

r PU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

Loss

for P

Us (

)

0

005

01

015

02

025

03

035

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC



sum

119894isinI119901119875119894le 119875eNB (43g)

For Scenario 2 if

119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus (1 + 120572

119894) 119871119894) (44)




119904=


1198751= sdot sdot sdot = 119875

119875119899= 1198751198781= sdot sdot sdot = 119875

119878119898= 23 dBm





Pass loss 119871 = 40log10119877 + 30log

10119891 + 49 119877 distance (km) 119891




















0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)








119894= 1 V = 119898 lowast 1Mbps (for



915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





119863119894sdot 119886119875119894(119905) = 119871

119894 forall119894 isin I (3a)


119894 119871119894is the target


119894during


119886119875119894(119905) =

119905

sum

120591=119905minus119879+1

119886119875119894(119905) forall119894 isin I (3b)


119902119875119894(119905 + 1) le 119871

119894 forall119894 isin I (4)


119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894le 119903119875119894(119905) le 119902

119875119894(119905) + 119886

119875119894(119905)



119894 as well as



sum

119894isinI119887119875119894(119905) + sum

119895isinJ119887119878119895(119905) le 119861 (6a)

where

119887119875119894(119905) isin Z+

119887119878119895(119905) isin Z+


(6b)



119901119875119894(119905) le 119875

119875119894

119901119878119895(119905) le 119875

119878119895


(7a)


sum

119894isinI119901119875119894(119905) + sum

119895isinJ119901119878119895(119905) le 119875eNB (7b)


119901119878119895(119905) ge 0


(7c)





+

(8a)


sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (8c)

119887119875119894isin Z+

119887119878119895isin Z+


(8d)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(8e)

119901119875119894ge 0

119901119878119895ge 0


(8f)


sum

119894isinI119901119875119894+sum

119895isinJ119901119878119895le 119875eNB (8g)




max119895isinJ


+

le 119871119894 forall119894 isin I (10)






+max119895isinJ


+

(11)






119875119894+ 119886119875119894minus 119903119875119894rceil+








119903119875119894ge 119902119875119894+ 119886119875119894minus (1 + 120572

119894) 119871119894 forall119894 isin I (12)


119895pays in


is

sum

119895isinJ120573119903119878119895minussum


(13)


sum

119895isinJ120573119903119878119895minussum


ge V (14)





subject to 119902119875119894+ 119886119875119894minus (1 + 120572

119894) 119871119894le 119903119875119894

le 119902119875119894+ 119886119875119894

forall119894 isin I

(15b)

sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (15c)

119887119875119894isin Z+

119887119878119895isin Z+


(15d)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(15e)

119901119875119894ge 0

119901119878119895ge 0


(15f)

sum

119895isinJ120573119903119878119895minussum


ge V (15g)









119903119875119894(b119875 p119875) = 120596120595

119875119894119887119875119894log (1 + 120585

119875119894SNR119875119894)

= 120596120595119875119894119887119875119894log (1 + 120585

119875119894ℎ119875119894119901119875119894)


(16a)


119903119878119895(b119878 p119878) = 120596120595

119878119895119887119878119895log (1 + 120585

119878119895SNR119878119895)

= 120596120595119878119895119887119878119895log (1 + 120585

119878119895ℎ119878119895119901119878119895)


(16b)



119894


119875119894and 120595




119875119894and 120585

119878119895are








MCS =

MCS1 SNR lt 120574

1

MCS2 1205741le SNR lt 120574

2

MCS119897 120574119897minus1

le SNR lt 120574119897

(18)

where 1205741

lt 1205742






119892 (SNR) =

1205851 SNR lt 120574

1

1205852 1205741le SNR lt 120574

2

120585119897 120574119897minus1

le SNR lt 120574119897

(19)




be expressed as

119903119875119894(b119875 p119875) = 120596120595119887

119875119894log (1 + 119892 (SNR

119875119894) sdot SNR

119875119894)

= 120596120595119887119875119894log (1 + 119892 (119901

119875119894) sdot ℎ119875119894119901119875119894)

forall119894 isin I

(20a)

119903119878119895(b119878 p119878) = 120596120595119887

119878119895log (1 + 119892 (SNR

119878119895) sdot SNR

119878119895)

= 120596120595119887119878119895log (1 + 119892 (119901

119878119895) ℎ119878119895119901119878119895)

forall119895 isin J

(20b)





subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (21b)

119887119875119894isin Z+

119887119878119895isin Z+


(21c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(21d)

119901119875119894ge 0

119901119878119895ge 0


(21e)

Ω ge 0

Φ ge 0

(21f)

1198911

119894(b119875 p119875) = 119903119875119894(b119875 p119875) minus (119902

119875119894+ 119886119875119894)

le 0

forall119894 isin I

(21g)

1198912

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894minus 119871119894) minus 119903119875119894(b119875 p119875)

le 0

forall119894 isin I

(21h)

1198913

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894) minus 119903119875119894(b119875 p119875) minus Ω

le 0

forall119894 isin I

(21i)

1198914

119895(b119878 p119878)

= (119902119878119895+ 119886119878119895) minus 119903119878119895(b119878 p119878) minus Φ

le 0

forall119895 isin J

(21j)


119875and b









119875119894(b119875 p119875) and 119903



119892 (119909) =

15

sum

119897=1


119897)

119867 (119909) =

1 if 119909 ge 0

0 otherwise

(22)

where 1205770= 0


119902(119909) =

1

1 + 119890minus2119902119909

(23)


lim119902rarrinfin

119902(119909) = 119867 (119909) (24)


119890minus2119902119909

997888rarr +infin

119902(119909) asymp 119867 (119909) = 1

(25)

for 119909 gt 0

119890minus2119902119909

997888rarr 0

119902(119909) asymp 119867 (119909) = 1

(26)

for 119909 = 0

119890minus2119902119909

= 1

119902(119909) = 119867 (119909) =

1

2

(27)


119902(119909 minus 120574

119897) =

1

1 + 119890minus2119902(119909minus120574119897)

(28)




119902(119909) =

15

sum

119897=1


119897) =

15

sum

119897=1

120577119897minus 120577119897minus1

1 + 1198902119902(119909minus120574119897)

(29)


lim119902rarrinfin

119902(119909) = 119892 (119909) (30)


119878119895(b119875 p119875) will

take the form

119875119894(b119875 p119875) = 120596120595119887

119875119894log (1 + (119901

119875119894) sdot ℎ119875119894119901119875119894)


119878119895(b119878 p119878) = 120596120595119887

119878119895log (1 + (119901

119878119895) ℎ119878119895119901119878119895)



(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (32a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (32b)

119887119875119894isin Z+

119887119878119895isin Z+


(32c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(32d)

119901119875119894ge 0

119901119878119895ge 0


(32e)

Ω ge 0

Φ ge 0

(32f)

119891

1

119894(b119875 p119875)

= 119875119894(b119875 p119875)

minus (119902119875119894+ 119886119875119894) le 0

forall119894 isin I

(32g)

119891

2

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894minus 119871119894)

minus 119875119894(b119875 p119875) le 0

forall119894 isin I

(32h)

119891

3

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894)

minus 119875119894(b119875 p119875) minus Ω

le 0

forall119894 isin I

(32i)

119891

4

119895(b119878 p119878)

= (119902119878119895+ 119886119878119895)

minus 119878119895(b119878 p119878) minus Φ

le 0

forall119895 isin J

(32j)


119875 p0119875 b0119878 p0119878) is given by

(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (33a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (33b)

119887119875119894isin Z+

119887119878119895isin Z+


(33c)


119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(33d)

119901119875119894ge 0

119901119878119895ge 0


(33e)

Ω ge 0

Φ ge 0

(33f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33i)

119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

]

le 0

forall119895 isin J

(33j)


(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (34b)

119887119875119894ge 0

119887119878119895ge 0


(34c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(34d)

119901119875119894ge 0

119901119878119895ge 0


(34e)

Ω ge 0

Φ ge 0

(34f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0









119875 p119875 b119878 p119878)119896119870





(b119875 p119875 b119878 p119878)119896= argmin

100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b

119875 p119875 b119878 p119878)119896

1003817100381710038171003817100381710038171

(35a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (35b)

119887119875119894isin Z+

119887119878119895isin Z+


(35c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(35d)

119901119875119894ge 0

119901119878119895ge 0


(35e)

Ω ge 0

Φ ge 0

(35f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35i)


119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

] le 0

forall119895 isin J

(35j)

(b119875 p119875 b119878 p119878)119896+1


119875 p119875 b119878 p119878)119896

100381710038171003817100381710038172

(36a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (36b)

119887119875119894ge 0

119887119878119895ge 0


(36c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(36d)

119901119875119894ge 0

119901119878119895ge 0


(36e)

Ω ge 0

Φ ge 0

(36f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0


where sdot1and sdot

2are 1198971norm and 119897







(1) WHILE (119896 lt 119870) do




(b119875 p119875 b119878 p119878)119896+1

(5) Set 119896 = 119896 + 1



=

(b119875 p119875 b119878 p119878)119896




119894 which




119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)


120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)


119871119894= min120591isinT


or

119871119894=

1

119879

sum


where T = 1 119879

UBADPC MBC

60

70

80

90

100

110

120

130

140

Alg

orith

m it

erat

ions

10020 8040 50 60 7030 90100Number of SUs m



MBC

070

075

080

085

090

095

100

120572i=0

v=0

120572i=1

v=0

120572i=0

v=m

lowast1

Mbp

s

120572i=1

v=m

lowast1

Mbp

s








UBADPCGBC

NBCMBCABC

780

800

820

840

860

880

900

920

940

960Th

roug

hput

for P

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r PU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for P

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m















SNR119894 (41a)


0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r SU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for S

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC



SNR119894 (41b)

SNRave =1

119899

sum

119894isinISNR119894 (41c)



119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894) (42)





(43a)


sum

119894isinI119887119875119894le 119861 (43c)


119901119875119894le 119875119875119894 forall119894 isin I (43e)

119901119875119894ge 0 forall119894 isin I (43f)


725

750

775

800

825

850

875

900

925

950Th

roug

hput

for P

Us (

kbits

s)

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC

10

20

30

40

50

60

70

Dela

y fo

r PU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

Loss

for P

Us (

)

0

005

01

015

02

025

03

035

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC



sum

119894isinI119901119875119894le 119875eNB (43g)

For Scenario 2 if

119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus (1 + 120572

119894) 119871119894) (44)




119904=


1198751= sdot sdot sdot = 119875

119875119899= 1198751198781= sdot sdot sdot = 119875

119878119898= 23 dBm





Pass loss 119871 = 40log10119877 + 30log

10119891 + 49 119877 distance (km) 119891




















0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)








119894= 1 V = 119898 lowast 1Mbps (for



915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








+max119895isinJ


+

(11)






119875119894+ 119886119875119894minus 119903119875119894rceil+








119903119875119894ge 119902119875119894+ 119886119875119894minus (1 + 120572

119894) 119871119894 forall119894 isin I (12)


119895pays in


is

sum

119895isinJ120573119903119878119895minussum


(13)


sum

119895isinJ120573119903119878119895minussum


ge V (14)





subject to 119902119875119894+ 119886119875119894minus (1 + 120572

119894) 119871119894le 119903119875119894

le 119902119875119894+ 119886119875119894

forall119894 isin I

(15b)

sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (15c)

119887119875119894isin Z+

119887119878119895isin Z+


(15d)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(15e)

119901119875119894ge 0

119901119878119895ge 0


(15f)

sum

119895isinJ120573119903119878119895minussum


ge V (15g)









119903119875119894(b119875 p119875) = 120596120595

119875119894119887119875119894log (1 + 120585

119875119894SNR119875119894)

= 120596120595119875119894119887119875119894log (1 + 120585

119875119894ℎ119875119894119901119875119894)


(16a)


119903119878119895(b119878 p119878) = 120596120595

119878119895119887119878119895log (1 + 120585

119878119895SNR119878119895)

= 120596120595119878119895119887119878119895log (1 + 120585

119878119895ℎ119878119895119901119878119895)


(16b)



119894


119875119894and 120595




119875119894and 120585

119878119895are








MCS =

MCS1 SNR lt 120574

1

MCS2 1205741le SNR lt 120574

2

MCS119897 120574119897minus1

le SNR lt 120574119897

(18)

where 1205741

lt 1205742






119892 (SNR) =

1205851 SNR lt 120574

1

1205852 1205741le SNR lt 120574

2

120585119897 120574119897minus1

le SNR lt 120574119897

(19)




be expressed as

119903119875119894(b119875 p119875) = 120596120595119887

119875119894log (1 + 119892 (SNR

119875119894) sdot SNR

119875119894)

= 120596120595119887119875119894log (1 + 119892 (119901

119875119894) sdot ℎ119875119894119901119875119894)

forall119894 isin I

(20a)

119903119878119895(b119878 p119878) = 120596120595119887

119878119895log (1 + 119892 (SNR

119878119895) sdot SNR

119878119895)

= 120596120595119887119878119895log (1 + 119892 (119901

119878119895) ℎ119878119895119901119878119895)

forall119895 isin J

(20b)





subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (21b)

119887119875119894isin Z+

119887119878119895isin Z+


(21c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(21d)

119901119875119894ge 0

119901119878119895ge 0


(21e)

Ω ge 0

Φ ge 0

(21f)

1198911

119894(b119875 p119875) = 119903119875119894(b119875 p119875) minus (119902

119875119894+ 119886119875119894)

le 0

forall119894 isin I

(21g)

1198912

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894minus 119871119894) minus 119903119875119894(b119875 p119875)

le 0

forall119894 isin I

(21h)

1198913

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894) minus 119903119875119894(b119875 p119875) minus Ω

le 0

forall119894 isin I

(21i)

1198914

119895(b119878 p119878)

= (119902119878119895+ 119886119878119895) minus 119903119878119895(b119878 p119878) minus Φ

le 0

forall119895 isin J

(21j)


119875and b









119875119894(b119875 p119875) and 119903



119892 (119909) =

15

sum

119897=1


119897)

119867 (119909) =

1 if 119909 ge 0

0 otherwise

(22)

where 1205770= 0


119902(119909) =

1

1 + 119890minus2119902119909

(23)


lim119902rarrinfin

119902(119909) = 119867 (119909) (24)


119890minus2119902119909

997888rarr +infin

119902(119909) asymp 119867 (119909) = 1

(25)

for 119909 gt 0

119890minus2119902119909

997888rarr 0

119902(119909) asymp 119867 (119909) = 1

(26)

for 119909 = 0

119890minus2119902119909

= 1

119902(119909) = 119867 (119909) =

1

2

(27)


119902(119909 minus 120574

119897) =

1

1 + 119890minus2119902(119909minus120574119897)

(28)




119902(119909) =

15

sum

119897=1


119897) =

15

sum

119897=1

120577119897minus 120577119897minus1

1 + 1198902119902(119909minus120574119897)

(29)


lim119902rarrinfin

119902(119909) = 119892 (119909) (30)


119878119895(b119875 p119875) will

take the form

119875119894(b119875 p119875) = 120596120595119887

119875119894log (1 + (119901

119875119894) sdot ℎ119875119894119901119875119894)


119878119895(b119878 p119878) = 120596120595119887

119878119895log (1 + (119901

119878119895) ℎ119878119895119901119878119895)



(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (32a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (32b)

119887119875119894isin Z+

119887119878119895isin Z+


(32c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(32d)

119901119875119894ge 0

119901119878119895ge 0


(32e)

Ω ge 0

Φ ge 0

(32f)

119891

1

119894(b119875 p119875)

= 119875119894(b119875 p119875)

minus (119902119875119894+ 119886119875119894) le 0

forall119894 isin I

(32g)

119891

2

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894minus 119871119894)

minus 119875119894(b119875 p119875) le 0

forall119894 isin I

(32h)

119891

3

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894)

minus 119875119894(b119875 p119875) minus Ω

le 0

forall119894 isin I

(32i)

119891

4

119895(b119878 p119878)

= (119902119878119895+ 119886119878119895)

minus 119878119895(b119878 p119878) minus Φ

le 0

forall119895 isin J

(32j)


119875 p0119875 b0119878 p0119878) is given by

(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (33a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (33b)

119887119875119894isin Z+

119887119878119895isin Z+


(33c)


119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(33d)

119901119875119894ge 0

119901119878119895ge 0


(33e)

Ω ge 0

Φ ge 0

(33f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33i)

119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

]

le 0

forall119895 isin J

(33j)


(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (34b)

119887119875119894ge 0

119887119878119895ge 0


(34c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(34d)

119901119875119894ge 0

119901119878119895ge 0


(34e)

Ω ge 0

Φ ge 0

(34f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0









119875 p119875 b119878 p119878)119896119870





(b119875 p119875 b119878 p119878)119896= argmin

100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b

119875 p119875 b119878 p119878)119896

1003817100381710038171003817100381710038171

(35a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (35b)

119887119875119894isin Z+

119887119878119895isin Z+


(35c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(35d)

119901119875119894ge 0

119901119878119895ge 0


(35e)

Ω ge 0

Φ ge 0

(35f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35i)


119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

] le 0

forall119895 isin J

(35j)

(b119875 p119875 b119878 p119878)119896+1


119875 p119875 b119878 p119878)119896

100381710038171003817100381710038172

(36a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (36b)

119887119875119894ge 0

119887119878119895ge 0


(36c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(36d)

119901119875119894ge 0

119901119878119895ge 0


(36e)

Ω ge 0

Φ ge 0

(36f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0


where sdot1and sdot

2are 1198971norm and 119897







(1) WHILE (119896 lt 119870) do




(b119875 p119875 b119878 p119878)119896+1

(5) Set 119896 = 119896 + 1



=

(b119875 p119875 b119878 p119878)119896




119894 which




119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)


120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)


119871119894= min120591isinT


or

119871119894=

1

119879

sum


where T = 1 119879

UBADPC MBC

60

70

80

90

100

110

120

130

140

Alg

orith

m it

erat

ions

10020 8040 50 60 7030 90100Number of SUs m



MBC

070

075

080

085

090

095

100

120572i=0

v=0

120572i=1

v=0

120572i=0

v=m

lowast1

Mbp

s

120572i=1

v=m

lowast1

Mbp

s








UBADPCGBC

NBCMBCABC

780

800

820

840

860

880

900

920

940

960Th

roug

hput

for P

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r PU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for P

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m















SNR119894 (41a)


0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r SU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for S

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC



SNR119894 (41b)

SNRave =1

119899

sum

119894isinISNR119894 (41c)



119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894) (42)





(43a)


sum

119894isinI119887119875119894le 119861 (43c)


119901119875119894le 119875119875119894 forall119894 isin I (43e)

119901119875119894ge 0 forall119894 isin I (43f)


725

750

775

800

825

850

875

900

925

950Th

roug

hput

for P

Us (

kbits

s)

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC

10

20

30

40

50

60

70

Dela

y fo

r PU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

Loss

for P

Us (

)

0

005

01

015

02

025

03

035

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC



sum

119894isinI119901119875119894le 119875eNB (43g)

For Scenario 2 if

119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus (1 + 120572

119894) 119871119894) (44)




119904=


1198751= sdot sdot sdot = 119875

119875119899= 1198751198781= sdot sdot sdot = 119875

119878119898= 23 dBm





Pass loss 119871 = 40log10119877 + 30log

10119891 + 49 119877 distance (km) 119891




















0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)








119894= 1 V = 119898 lowast 1Mbps (for



915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




119903119878119895(b119878 p119878) = 120596120595

119878119895119887119878119895log (1 + 120585

119878119895SNR119878119895)

= 120596120595119878119895119887119878119895log (1 + 120585

119878119895ℎ119878119895119901119878119895)


(16b)



119894


119875119894and 120595




119875119894and 120585

119878119895are








MCS =

MCS1 SNR lt 120574

1

MCS2 1205741le SNR lt 120574

2

MCS119897 120574119897minus1

le SNR lt 120574119897

(18)

where 1205741

lt 1205742






119892 (SNR) =

1205851 SNR lt 120574

1

1205852 1205741le SNR lt 120574

2

120585119897 120574119897minus1

le SNR lt 120574119897

(19)




be expressed as

119903119875119894(b119875 p119875) = 120596120595119887

119875119894log (1 + 119892 (SNR

119875119894) sdot SNR

119875119894)

= 120596120595119887119875119894log (1 + 119892 (119901

119875119894) sdot ℎ119875119894119901119875119894)

forall119894 isin I

(20a)

119903119878119895(b119878 p119878) = 120596120595119887

119878119895log (1 + 119892 (SNR

119878119895) sdot SNR

119878119895)

= 120596120595119887119878119895log (1 + 119892 (119901

119878119895) ℎ119878119895119901119878119895)

forall119895 isin J

(20b)





subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (21b)

119887119875119894isin Z+

119887119878119895isin Z+


(21c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(21d)

119901119875119894ge 0

119901119878119895ge 0


(21e)

Ω ge 0

Φ ge 0

(21f)

1198911

119894(b119875 p119875) = 119903119875119894(b119875 p119875) minus (119902

119875119894+ 119886119875119894)

le 0

forall119894 isin I

(21g)

1198912

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894minus 119871119894) minus 119903119875119894(b119875 p119875)

le 0

forall119894 isin I

(21h)

1198913

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894) minus 119903119875119894(b119875 p119875) minus Ω

le 0

forall119894 isin I

(21i)

1198914

119895(b119878 p119878)

= (119902119878119895+ 119886119878119895) minus 119903119878119895(b119878 p119878) minus Φ

le 0

forall119895 isin J

(21j)


119875and b









119875119894(b119875 p119875) and 119903



119892 (119909) =

15

sum

119897=1


119897)

119867 (119909) =

1 if 119909 ge 0

0 otherwise

(22)

where 1205770= 0


119902(119909) =

1

1 + 119890minus2119902119909

(23)


lim119902rarrinfin

119902(119909) = 119867 (119909) (24)


119890minus2119902119909

997888rarr +infin

119902(119909) asymp 119867 (119909) = 1

(25)

for 119909 gt 0

119890minus2119902119909

997888rarr 0

119902(119909) asymp 119867 (119909) = 1

(26)

for 119909 = 0

119890minus2119902119909

= 1

119902(119909) = 119867 (119909) =

1

2

(27)


119902(119909 minus 120574

119897) =

1

1 + 119890minus2119902(119909minus120574119897)

(28)




119902(119909) =

15

sum

119897=1


119897) =

15

sum

119897=1

120577119897minus 120577119897minus1

1 + 1198902119902(119909minus120574119897)

(29)


lim119902rarrinfin

119902(119909) = 119892 (119909) (30)


119878119895(b119875 p119875) will

take the form

119875119894(b119875 p119875) = 120596120595119887

119875119894log (1 + (119901

119875119894) sdot ℎ119875119894119901119875119894)


119878119895(b119878 p119878) = 120596120595119887

119878119895log (1 + (119901

119878119895) ℎ119878119895119901119878119895)



(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (32a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (32b)

119887119875119894isin Z+

119887119878119895isin Z+


(32c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(32d)

119901119875119894ge 0

119901119878119895ge 0


(32e)

Ω ge 0

Φ ge 0

(32f)

119891

1

119894(b119875 p119875)

= 119875119894(b119875 p119875)

minus (119902119875119894+ 119886119875119894) le 0

forall119894 isin I

(32g)

119891

2

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894minus 119871119894)

minus 119875119894(b119875 p119875) le 0

forall119894 isin I

(32h)

119891

3

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894)

minus 119875119894(b119875 p119875) minus Ω

le 0

forall119894 isin I

(32i)

119891

4

119895(b119878 p119878)

= (119902119878119895+ 119886119878119895)

minus 119878119895(b119878 p119878) minus Φ

le 0

forall119895 isin J

(32j)


119875 p0119875 b0119878 p0119878) is given by

(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (33a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (33b)

119887119875119894isin Z+

119887119878119895isin Z+


(33c)


119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(33d)

119901119875119894ge 0

119901119878119895ge 0


(33e)

Ω ge 0

Φ ge 0

(33f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33i)

119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

]

le 0

forall119895 isin J

(33j)


(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (34b)

119887119875119894ge 0

119887119878119895ge 0


(34c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(34d)

119901119875119894ge 0

119901119878119895ge 0


(34e)

Ω ge 0

Φ ge 0

(34f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0









119875 p119875 b119878 p119878)119896119870





(b119875 p119875 b119878 p119878)119896= argmin

100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b

119875 p119875 b119878 p119878)119896

1003817100381710038171003817100381710038171

(35a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (35b)

119887119875119894isin Z+

119887119878119895isin Z+


(35c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(35d)

119901119875119894ge 0

119901119878119895ge 0


(35e)

Ω ge 0

Φ ge 0

(35f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35i)


119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

] le 0

forall119895 isin J

(35j)

(b119875 p119875 b119878 p119878)119896+1


119875 p119875 b119878 p119878)119896

100381710038171003817100381710038172

(36a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (36b)

119887119875119894ge 0

119887119878119895ge 0


(36c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(36d)

119901119875119894ge 0

119901119878119895ge 0


(36e)

Ω ge 0

Φ ge 0

(36f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0


where sdot1and sdot

2are 1198971norm and 119897







(1) WHILE (119896 lt 119870) do




(b119875 p119875 b119878 p119878)119896+1

(5) Set 119896 = 119896 + 1



=

(b119875 p119875 b119878 p119878)119896




119894 which




119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)


120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)


119871119894= min120591isinT


or

119871119894=

1

119879

sum


where T = 1 119879

UBADPC MBC

60

70

80

90

100

110

120

130

140

Alg

orith

m it

erat

ions

10020 8040 50 60 7030 90100Number of SUs m



MBC

070

075

080

085

090

095

100

120572i=0

v=0

120572i=1

v=0

120572i=0

v=m

lowast1

Mbp

s

120572i=1

v=m

lowast1

Mbp

s








UBADPCGBC

NBCMBCABC

780

800

820

840

860

880

900

920

940

960Th

roug

hput

for P

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r PU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for P

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m















SNR119894 (41a)


0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r SU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for S

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC



SNR119894 (41b)

SNRave =1

119899

sum

119894isinISNR119894 (41c)



119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894) (42)





(43a)


sum

119894isinI119887119875119894le 119861 (43c)


119901119875119894le 119875119875119894 forall119894 isin I (43e)

119901119875119894ge 0 forall119894 isin I (43f)


725

750

775

800

825

850

875

900

925

950Th

roug

hput

for P

Us (

kbits

s)

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC

10

20

30

40

50

60

70

Dela

y fo

r PU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

Loss

for P

Us (

)

0

005

01

015

02

025

03

035

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC



sum

119894isinI119901119875119894le 119875eNB (43g)

For Scenario 2 if

119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus (1 + 120572

119894) 119871119894) (44)




119904=


1198751= sdot sdot sdot = 119875

119875119899= 1198751198781= sdot sdot sdot = 119875

119878119898= 23 dBm





Pass loss 119871 = 40log10119877 + 30log

10119891 + 49 119877 distance (km) 119891




















0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)








119894= 1 V = 119898 lowast 1Mbps (for



915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (21b)

119887119875119894isin Z+

119887119878119895isin Z+


(21c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(21d)

119901119875119894ge 0

119901119878119895ge 0


(21e)

Ω ge 0

Φ ge 0

(21f)

1198911

119894(b119875 p119875) = 119903119875119894(b119875 p119875) minus (119902

119875119894+ 119886119875119894)

le 0

forall119894 isin I

(21g)

1198912

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894minus 119871119894) minus 119903119875119894(b119875 p119875)

le 0

forall119894 isin I

(21h)

1198913

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894) minus 119903119875119894(b119875 p119875) minus Ω

le 0

forall119894 isin I

(21i)

1198914

119895(b119878 p119878)

= (119902119878119895+ 119886119878119895) minus 119903119878119895(b119878 p119878) minus Φ

le 0

forall119895 isin J

(21j)


119875and b









119875119894(b119875 p119875) and 119903



119892 (119909) =

15

sum

119897=1


119897)

119867 (119909) =

1 if 119909 ge 0

0 otherwise

(22)

where 1205770= 0


119902(119909) =

1

1 + 119890minus2119902119909

(23)


lim119902rarrinfin

119902(119909) = 119867 (119909) (24)


119890minus2119902119909

997888rarr +infin

119902(119909) asymp 119867 (119909) = 1

(25)

for 119909 gt 0

119890minus2119902119909

997888rarr 0

119902(119909) asymp 119867 (119909) = 1

(26)

for 119909 = 0

119890minus2119902119909

= 1

119902(119909) = 119867 (119909) =

1

2

(27)


119902(119909 minus 120574

119897) =

1

1 + 119890minus2119902(119909minus120574119897)

(28)




119902(119909) =

15

sum

119897=1


119897) =

15

sum

119897=1

120577119897minus 120577119897minus1

1 + 1198902119902(119909minus120574119897)

(29)


lim119902rarrinfin

119902(119909) = 119892 (119909) (30)


119878119895(b119875 p119875) will

take the form

119875119894(b119875 p119875) = 120596120595119887

119875119894log (1 + (119901

119875119894) sdot ℎ119875119894119901119875119894)


119878119895(b119878 p119878) = 120596120595119887

119878119895log (1 + (119901

119878119895) ℎ119878119895119901119878119895)



(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (32a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (32b)

119887119875119894isin Z+

119887119878119895isin Z+


(32c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(32d)

119901119875119894ge 0

119901119878119895ge 0


(32e)

Ω ge 0

Φ ge 0

(32f)

119891

1

119894(b119875 p119875)

= 119875119894(b119875 p119875)

minus (119902119875119894+ 119886119875119894) le 0

forall119894 isin I

(32g)

119891

2

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894minus 119871119894)

minus 119875119894(b119875 p119875) le 0

forall119894 isin I

(32h)

119891

3

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894)

minus 119875119894(b119875 p119875) minus Ω

le 0

forall119894 isin I

(32i)

119891

4

119895(b119878 p119878)

= (119902119878119895+ 119886119878119895)

minus 119878119895(b119878 p119878) minus Φ

le 0

forall119895 isin J

(32j)


119875 p0119875 b0119878 p0119878) is given by

(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (33a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (33b)

119887119875119894isin Z+

119887119878119895isin Z+


(33c)


119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(33d)

119901119875119894ge 0

119901119878119895ge 0


(33e)

Ω ge 0

Φ ge 0

(33f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33i)

119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

]

le 0

forall119895 isin J

(33j)


(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (34b)

119887119875119894ge 0

119887119878119895ge 0


(34c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(34d)

119901119875119894ge 0

119901119878119895ge 0


(34e)

Ω ge 0

Φ ge 0

(34f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0









119875 p119875 b119878 p119878)119896119870





(b119875 p119875 b119878 p119878)119896= argmin

100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b

119875 p119875 b119878 p119878)119896

1003817100381710038171003817100381710038171

(35a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (35b)

119887119875119894isin Z+

119887119878119895isin Z+


(35c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(35d)

119901119875119894ge 0

119901119878119895ge 0


(35e)

Ω ge 0

Φ ge 0

(35f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35i)


119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

] le 0

forall119895 isin J

(35j)

(b119875 p119875 b119878 p119878)119896+1


119875 p119875 b119878 p119878)119896

100381710038171003817100381710038172

(36a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (36b)

119887119875119894ge 0

119887119878119895ge 0


(36c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(36d)

119901119875119894ge 0

119901119878119895ge 0


(36e)

Ω ge 0

Φ ge 0

(36f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0


where sdot1and sdot

2are 1198971norm and 119897







(1) WHILE (119896 lt 119870) do




(b119875 p119875 b119878 p119878)119896+1

(5) Set 119896 = 119896 + 1



=

(b119875 p119875 b119878 p119878)119896




119894 which




119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)


120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)


119871119894= min120591isinT


or

119871119894=

1

119879

sum


where T = 1 119879

UBADPC MBC

60

70

80

90

100

110

120

130

140

Alg

orith

m it

erat

ions

10020 8040 50 60 7030 90100Number of SUs m



MBC

070

075

080

085

090

095

100

120572i=0

v=0

120572i=1

v=0

120572i=0

v=m

lowast1

Mbp

s

120572i=1

v=m

lowast1

Mbp

s








UBADPCGBC

NBCMBCABC

780

800

820

840

860

880

900

920

940

960Th

roug

hput

for P

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r PU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for P

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m















SNR119894 (41a)


0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r SU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for S

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC



SNR119894 (41b)

SNRave =1

119899

sum

119894isinISNR119894 (41c)



119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894) (42)





(43a)


sum

119894isinI119887119875119894le 119861 (43c)


119901119875119894le 119875119875119894 forall119894 isin I (43e)

119901119875119894ge 0 forall119894 isin I (43f)


725

750

775

800

825

850

875

900

925

950Th

roug

hput

for P

Us (

kbits

s)

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC

10

20

30

40

50

60

70

Dela

y fo

r PU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

Loss

for P

Us (

)

0

005

01

015

02

025

03

035

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC



sum

119894isinI119901119875119894le 119875eNB (43g)

For Scenario 2 if

119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus (1 + 120572

119894) 119871119894) (44)




119904=


1198751= sdot sdot sdot = 119875

119875119899= 1198751198781= sdot sdot sdot = 119875

119878119898= 23 dBm





Pass loss 119871 = 40log10119877 + 30log

10119891 + 49 119877 distance (km) 119891




















0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)








119894= 1 V = 119898 lowast 1Mbps (for



915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





119902(119909) =

15

sum

119897=1


119897) =

15

sum

119897=1

120577119897minus 120577119897minus1

1 + 1198902119902(119909minus120574119897)

(29)


lim119902rarrinfin

119902(119909) = 119892 (119909) (30)


119878119895(b119875 p119875) will

take the form

119875119894(b119875 p119875) = 120596120595119887

119875119894log (1 + (119901

119875119894) sdot ℎ119875119894119901119875119894)


119878119895(b119878 p119878) = 120596120595119887

119878119895log (1 + (119901

119878119895) ℎ119878119895119901119878119895)



(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (32a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (32b)

119887119875119894isin Z+

119887119878119895isin Z+


(32c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(32d)

119901119875119894ge 0

119901119878119895ge 0


(32e)

Ω ge 0

Φ ge 0

(32f)

119891

1

119894(b119875 p119875)

= 119875119894(b119875 p119875)

minus (119902119875119894+ 119886119875119894) le 0

forall119894 isin I

(32g)

119891

2

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894minus 119871119894)

minus 119875119894(b119875 p119875) le 0

forall119894 isin I

(32h)

119891

3

119894(b119875 p119875)

= (119902119875119894+ 119886119875119894)

minus 119875119894(b119875 p119875) minus Ω

le 0

forall119894 isin I

(32i)

119891

4

119895(b119878 p119878)

= (119902119878119895+ 119886119878119895)

minus 119878119895(b119878 p119878) minus Φ

le 0

forall119895 isin J

(32j)


119875 p0119875 b0119878 p0119878) is given by

(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (33a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (33b)

119887119875119894isin Z+

119887119878119895isin Z+


(33c)


119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(33d)

119901119875119894ge 0

119901119878119895ge 0


(33e)

Ω ge 0

Φ ge 0

(33f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33i)

119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

]

le 0

forall119895 isin J

(33j)


(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (34b)

119887119875119894ge 0

119887119878119895ge 0


(34c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(34d)

119901119875119894ge 0

119901119878119895ge 0


(34e)

Ω ge 0

Φ ge 0

(34f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0









119875 p119875 b119878 p119878)119896119870





(b119875 p119875 b119878 p119878)119896= argmin

100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b

119875 p119875 b119878 p119878)119896

1003817100381710038171003817100381710038171

(35a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (35b)

119887119875119894isin Z+

119887119878119895isin Z+


(35c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(35d)

119901119875119894ge 0

119901119878119895ge 0


(35e)

Ω ge 0

Φ ge 0

(35f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35i)


119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

] le 0

forall119895 isin J

(35j)

(b119875 p119875 b119878 p119878)119896+1


119875 p119875 b119878 p119878)119896

100381710038171003817100381710038172

(36a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (36b)

119887119875119894ge 0

119887119878119895ge 0


(36c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(36d)

119901119875119894ge 0

119901119878119895ge 0


(36e)

Ω ge 0

Φ ge 0

(36f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0


where sdot1and sdot

2are 1198971norm and 119897







(1) WHILE (119896 lt 119870) do




(b119875 p119875 b119878 p119878)119896+1

(5) Set 119896 = 119896 + 1



=

(b119875 p119875 b119878 p119878)119896




119894 which




119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)


120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)


119871119894= min120591isinT


or

119871119894=

1

119879

sum


where T = 1 119879

UBADPC MBC

60

70

80

90

100

110

120

130

140

Alg

orith

m it

erat

ions

10020 8040 50 60 7030 90100Number of SUs m



MBC

070

075

080

085

090

095

100

120572i=0

v=0

120572i=1

v=0

120572i=0

v=m

lowast1

Mbp

s

120572i=1

v=m

lowast1

Mbp

s








UBADPCGBC

NBCMBCABC

780

800

820

840

860

880

900

920

940

960Th

roug

hput

for P

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r PU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for P

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m















SNR119894 (41a)


0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r SU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for S

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC



SNR119894 (41b)

SNRave =1

119899

sum

119894isinISNR119894 (41c)



119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894) (42)





(43a)


sum

119894isinI119887119875119894le 119861 (43c)


119901119875119894le 119875119875119894 forall119894 isin I (43e)

119901119875119894ge 0 forall119894 isin I (43f)


725

750

775

800

825

850

875

900

925

950Th

roug

hput

for P

Us (

kbits

s)

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC

10

20

30

40

50

60

70

Dela

y fo

r PU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

Loss

for P

Us (

)

0

005

01

015

02

025

03

035

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC



sum

119894isinI119901119875119894le 119875eNB (43g)

For Scenario 2 if

119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus (1 + 120572

119894) 119871119894) (44)




119904=


1198751= sdot sdot sdot = 119875

119875119899= 1198751198781= sdot sdot sdot = 119875

119878119898= 23 dBm





Pass loss 119871 = 40log10119877 + 30log

10119891 + 49 119877 distance (km) 119891




















0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)








119894= 1 V = 119898 lowast 1Mbps (for



915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(33d)

119901119875119894ge 0

119901119878119895ge 0


(33e)

Ω ge 0

Φ ge 0

(33f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(33i)

119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

]

le 0

forall119895 isin J

(33j)


(b119875 p119875 b119878 p119878) = argmin (Ω + Φ) (34a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (34b)

119887119875119894ge 0

119887119878119895ge 0


(34c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(34d)

119901119875119894ge 0

119901119878119895ge 0


(34e)

Ω ge 0

Φ ge 0

(34f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0









119875 p119875 b119878 p119878)119896119870





(b119875 p119875 b119878 p119878)119896= argmin

100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b

119875 p119875 b119878 p119878)119896

1003817100381710038171003817100381710038171

(35a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (35b)

119887119875119894isin Z+

119887119878119895isin Z+


(35c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(35d)

119901119875119894ge 0

119901119878119895ge 0


(35e)

Ω ge 0

Φ ge 0

(35f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35i)


119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

] le 0

forall119895 isin J

(35j)

(b119875 p119875 b119878 p119878)119896+1


119875 p119875 b119878 p119878)119896

100381710038171003817100381710038172

(36a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (36b)

119887119875119894ge 0

119887119878119895ge 0


(36c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(36d)

119901119875119894ge 0

119901119878119895ge 0


(36e)

Ω ge 0

Φ ge 0

(36f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0


where sdot1and sdot

2are 1198971norm and 119897







(1) WHILE (119896 lt 119870) do




(b119875 p119875 b119878 p119878)119896+1

(5) Set 119896 = 119896 + 1



=

(b119875 p119875 b119878 p119878)119896




119894 which




119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)


120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)


119871119894= min120591isinT


or

119871119894=

1

119879

sum


where T = 1 119879

UBADPC MBC

60

70

80

90

100

110

120

130

140

Alg

orith

m it

erat

ions

10020 8040 50 60 7030 90100Number of SUs m



MBC

070

075

080

085

090

095

100

120572i=0

v=0

120572i=1

v=0

120572i=0

v=m

lowast1

Mbp

s

120572i=1

v=m

lowast1

Mbp

s








UBADPCGBC

NBCMBCABC

780

800

820

840

860

880

900

920

940

960Th

roug

hput

for P

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r PU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for P

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m















SNR119894 (41a)


0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r SU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for S

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC



SNR119894 (41b)

SNRave =1

119899

sum

119894isinISNR119894 (41c)



119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894) (42)





(43a)


sum

119894isinI119887119875119894le 119861 (43c)


119901119875119894le 119875119875119894 forall119894 isin I (43e)

119901119875119894ge 0 forall119894 isin I (43f)


725

750

775

800

825

850

875

900

925

950Th

roug

hput

for P

Us (

kbits

s)

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC

10

20

30

40

50

60

70

Dela

y fo

r PU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

Loss

for P

Us (

)

0

005

01

015

02

025

03

035

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC



sum

119894isinI119901119875119894le 119875eNB (43g)

For Scenario 2 if

119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus (1 + 120572

119894) 119871119894) (44)




119904=


1198751= sdot sdot sdot = 119875

119875119899= 1198751198781= sdot sdot sdot = 119875

119878119898= 23 dBm





Pass loss 119871 = 40log10119877 + 30log

10119891 + 49 119877 distance (km) 119891




















0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)








119894= 1 V = 119898 lowast 1Mbps (for



915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in









119875 p119875 b119878 p119878)119896119870





(b119875 p119875 b119878 p119878)119896= argmin

100381710038171003817100381710038171003817(b119875 p119875 b119878 p119878) minus (b

119875 p119875 b119878 p119878)119896

1003817100381710038171003817100381710038171

(35a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (35b)

119887119875119894isin Z+

119887119878119895isin Z+


(35c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(35d)

119901119875119894ge 0

119901119878119895ge 0


(35e)

Ω ge 0

Φ ge 0

(35f)

119891

1

119894(b0119875 p0119875) + nabla

119891

1

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35g)

119891

2

119894(b0119875 p0119875) + nabla

119891

2

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35h)

119891

3

119894(b0119875 p0119875) + nabla

119891

3

119894(b0119875 p0119875)

119879

[

b119875minus b0119875

p119875minus p0119875

] le 0

forall119894 isin I

(35i)


119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

] le 0

forall119895 isin J

(35j)

(b119875 p119875 b119878 p119878)119896+1


119875 p119875 b119878 p119878)119896

100381710038171003817100381710038172

(36a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (36b)

119887119875119894ge 0

119887119878119895ge 0


(36c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(36d)

119901119875119894ge 0

119901119878119895ge 0


(36e)

Ω ge 0

Φ ge 0

(36f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0


where sdot1and sdot

2are 1198971norm and 119897







(1) WHILE (119896 lt 119870) do




(b119875 p119875 b119878 p119878)119896+1

(5) Set 119896 = 119896 + 1



=

(b119875 p119875 b119878 p119878)119896




119894 which




119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)


120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)


119871119894= min120591isinT


or

119871119894=

1

119879

sum


where T = 1 119879

UBADPC MBC

60

70

80

90

100

110

120

130

140

Alg

orith

m it

erat

ions

10020 8040 50 60 7030 90100Number of SUs m



MBC

070

075

080

085

090

095

100

120572i=0

v=0

120572i=1

v=0

120572i=0

v=m

lowast1

Mbp

s

120572i=1

v=m

lowast1

Mbp

s








UBADPCGBC

NBCMBCABC

780

800

820

840

860

880

900

920

940

960Th

roug

hput

for P

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r PU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for P

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m















SNR119894 (41a)


0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r SU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for S

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC



SNR119894 (41b)

SNRave =1

119899

sum

119894isinISNR119894 (41c)



119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894) (42)





(43a)


sum

119894isinI119887119875119894le 119861 (43c)


119901119875119894le 119875119875119894 forall119894 isin I (43e)

119901119875119894ge 0 forall119894 isin I (43f)


725

750

775

800

825

850

875

900

925

950Th

roug

hput

for P

Us (

kbits

s)

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC

10

20

30

40

50

60

70

Dela

y fo

r PU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

Loss

for P

Us (

)

0

005

01

015

02

025

03

035

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC



sum

119894isinI119901119875119894le 119875eNB (43g)

For Scenario 2 if

119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus (1 + 120572

119894) 119871119894) (44)




119904=


1198751= sdot sdot sdot = 119875

119875119899= 1198751198781= sdot sdot sdot = 119875

119878119898= 23 dBm





Pass loss 119871 = 40log10119877 + 30log

10119891 + 49 119877 distance (km) 119891




















0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)








119894= 1 V = 119898 lowast 1Mbps (for



915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




119891

4

119895(b0119878 p0119878) + nabla

119891

4

119895(b0119878 p0119878)

119879

[

b119878minus b0119878

p119878minus p0119878

] le 0

forall119895 isin J

(35j)

(b119875 p119875 b119878 p119878)119896+1


119875 p119875 b119878 p119878)119896

100381710038171003817100381710038172

(36a)

subject to sum

119894isinI119887119875119894+sum

119895isinJ119887119878119895le 119861 (36b)

119887119875119894ge 0

119887119878119895ge 0


(36c)

119901119875119894le 119875119875119894

119901119878119895le 119875119878119895


(36d)

119901119875119894ge 0

119901119878119895ge 0


(36e)

Ω ge 0

Φ ge 0

(36f)

119891

1

119894(b119875 p119875) le 0


119891

2

119894(b119875 p119875) le 0


119891

3

119894(b119875 p119875) le 0


119891

4

119895(b119878 p119878) le 0


where sdot1and sdot

2are 1198971norm and 119897







(1) WHILE (119896 lt 119870) do




(b119875 p119875 b119878 p119878)119896+1

(5) Set 119896 = 119896 + 1



=

(b119875 p119875 b119878 p119878)119896




119894 which




119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)


120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)


119871119894= min120591isinT


or

119871119894=

1

119879

sum


where T = 1 119879

UBADPC MBC

60

70

80

90

100

110

120

130

140

Alg

orith

m it

erat

ions

10020 8040 50 60 7030 90100Number of SUs m



MBC

070

075

080

085

090

095

100

120572i=0

v=0

120572i=1

v=0

120572i=0

v=m

lowast1

Mbp

s

120572i=1

v=m

lowast1

Mbp

s








UBADPCGBC

NBCMBCABC

780

800

820

840

860

880

900

920

940

960Th

roug

hput

for P

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r PU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for P

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m















SNR119894 (41a)


0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r SU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for S

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC



SNR119894 (41b)

SNRave =1

119899

sum

119894isinISNR119894 (41c)



119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894) (42)





(43a)


sum

119894isinI119887119875119894le 119861 (43c)


119901119875119894le 119875119875119894 forall119894 isin I (43e)

119901119875119894ge 0 forall119894 isin I (43f)


725

750

775

800

825

850

875

900

925

950Th

roug

hput

for P

Us (

kbits

s)

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC

10

20

30

40

50

60

70

Dela

y fo

r PU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

Loss

for P

Us (

)

0

005

01

015

02

025

03

035

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC



sum

119894isinI119901119875119894le 119875eNB (43g)

For Scenario 2 if

119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus (1 + 120572

119894) 119871119894) (44)




119904=


1198751= sdot sdot sdot = 119875

119875119899= 1198751198781= sdot sdot sdot = 119875

119878119898= 23 dBm





Pass loss 119871 = 40log10119877 + 30log

10119891 + 49 119877 distance (km) 119891




















0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)








119894= 1 V = 119898 lowast 1Mbps (for



915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





=

(b119875 p119875 b119878 p119878)119896




119894 which




119871119894= 119902119875119894(119905) + 120576 forall119894 isin I (37a)


120576 ≪ 119902119875119894(119905) forall119894 isin I (37b)


119871119894= min120591isinT


or

119871119894=

1

119879

sum


where T = 1 119879

UBADPC MBC

60

70

80

90

100

110

120

130

140

Alg

orith

m it

erat

ions

10020 8040 50 60 7030 90100Number of SUs m



MBC

070

075

080

085

090

095

100

120572i=0

v=0

120572i=1

v=0

120572i=0

v=m

lowast1

Mbp

s

120572i=1

v=m

lowast1

Mbp

s








UBADPCGBC

NBCMBCABC

780

800

820

840

860

880

900

920

940

960Th

roug

hput

for P

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r PU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for P

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m















SNR119894 (41a)


0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r SU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for S

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC



SNR119894 (41b)

SNRave =1

119899

sum

119894isinISNR119894 (41c)



119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894) (42)





(43a)


sum

119894isinI119887119875119894le 119861 (43c)


119901119875119894le 119875119875119894 forall119894 isin I (43e)

119901119875119894ge 0 forall119894 isin I (43f)


725

750

775

800

825

850

875

900

925

950Th

roug

hput

for P

Us (

kbits

s)

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC

10

20

30

40

50

60

70

Dela

y fo

r PU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

Loss

for P

Us (

)

0

005

01

015

02

025

03

035

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC



sum

119894isinI119901119875119894le 119875eNB (43g)

For Scenario 2 if

119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus (1 + 120572

119894) 119871119894) (44)




119904=


1198751= sdot sdot sdot = 119875

119875119899= 1198751198781= sdot sdot sdot = 119875

119878119898= 23 dBm





Pass loss 119871 = 40log10119877 + 30log

10119891 + 49 119877 distance (km) 119891




















0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)








119894= 1 V = 119898 lowast 1Mbps (for



915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




UBADPCGBC

NBCMBCABC

780

800

820

840

860

880

900

920

940

960Th

roug

hput

for P

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r PU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for P

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m















SNR119894 (41a)


0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r SU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for S

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC



SNR119894 (41b)

SNRave =1

119899

sum

119894isinISNR119894 (41c)



119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894) (42)





(43a)


sum

119894isinI119887119875119894le 119861 (43c)


119901119875119894le 119875119875119894 forall119894 isin I (43e)

119901119875119894ge 0 forall119894 isin I (43f)


725

750

775

800

825

850

875

900

925

950Th

roug

hput

for P

Us (

kbits

s)

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC

10

20

30

40

50

60

70

Dela

y fo

r PU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

Loss

for P

Us (

)

0

005

01

015

02

025

03

035

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC



sum

119894isinI119901119875119894le 119875eNB (43g)

For Scenario 2 if

119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus (1 + 120572

119894) 119871119894) (44)




119904=


1198751= sdot sdot sdot = 119875

119875119899= 1198751198781= sdot sdot sdot = 119875

119878119898= 23 dBm





Pass loss 119871 = 40log10119877 + 30log

10119891 + 49 119877 distance (km) 119891




















0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)








119894= 1 V = 119898 lowast 1Mbps (for



915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

10

30

50

70

90

110

130

150

170

Dela

y fo

r SU

s (m

s)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC

0

01

02

03

04

05

06

07

08

Loss

for S

Us (

)

10 20 30 40 50 60 70 80 90 1000Number of SUs m

UBADPCGBC

NBCMBCABC



SNR119894 (41b)

SNRave =1

119899

sum

119894isinISNR119894 (41c)



119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus 119871

119894) (42)





(43a)


sum

119894isinI119887119875119894le 119861 (43c)


119901119875119894le 119875119875119894 forall119894 isin I (43e)

119901119875119894ge 0 forall119894 isin I (43f)


725

750

775

800

825

850

875

900

925

950Th

roug

hput

for P

Us (

kbits

s)

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC

10

20

30

40

50

60

70

Dela

y fo

r PU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

Loss

for P

Us (

)

0

005

01

015

02

025

03

035

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC



sum

119894isinI119901119875119894le 119875eNB (43g)

For Scenario 2 if

119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus (1 + 120572

119894) 119871119894) (44)




119904=


1198751= sdot sdot sdot = 119875

119875119899= 1198751198781= sdot sdot sdot = 119875

119878119898= 23 dBm





Pass loss 119871 = 40log10119877 + 30log

10119891 + 49 119877 distance (km) 119891




















0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)








119894= 1 V = 119898 lowast 1Mbps (for



915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




725

750

775

800

825

850

875

900

925

950Th

roug

hput

for P

Us (

kbits

s)

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC

10

20

30

40

50

60

70

Dela

y fo

r PU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

Loss

for P

Us (

)

0

005

01

015

02

025

03

035

200 5 10 15 25 30minus5minus10

Average SNR (dB)

UBADPCGBC

NBCMBCABC



sum

119894isinI119901119875119894le 119875eNB (43g)

For Scenario 2 if

119877min ge sum119894isinI(119902119875119894(119905) + 119886

119875119894(119905) minus (1 + 120572

119894) 119871119894) (44)




119904=


1198751= sdot sdot sdot = 119875

119875119899= 1198751198781= sdot sdot sdot = 119875

119878119898= 23 dBm





Pass loss 119871 = 40log10119877 + 30log

10119891 + 49 119877 distance (km) 119891




















0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)








119894= 1 V = 119898 lowast 1Mbps (for



915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






Pass loss 119871 = 40log10119877 + 30log

10119891 + 49 119877 distance (km) 119891




















0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)








119894= 1 V = 119898 lowast 1Mbps (for



915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0 10 20 30 40 50 60 70 80Average SNR (dB)

UBADPCGBC

NBCMBCABC

30

35

40

45

50

55

60

65

70

Dela

y fo

r SU

s (m

s)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

012

015

018

021

024

027

03

033

Loss

for S

Us (

)

250 5 10 15 20 30minus10 minus5

Average SNR (dB)

UBADPCGBC

NBCMBCABC

250

300

350

400

450

500Th

roug

hput

for S

Us (

kbits

s)








119894= 1 V = 119898 lowast 1Mbps (for



915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

v = 0



080020 090070050 060 100000 030010 040120572i

10

20

30

40

50

60

70

80

90

100

110

Dela

y fo

r PU

s (m

s)

v = 0



040030 090000 080060010 020 050 100070120572i

005

010

015

020

025

030

035

040

045

050

Loss

for P

Us (

)

v = 0



030020 040 090010 060 070 080 100000 050120572i


SNR = 0 dB


119865PU =

(sum119894isinI 119903119875119894)

2

119899 sdot sum119894isinI 1199032

119875119894

119865SU =

(sum119895isinJ 119903119878119895)

2

119898 sdot sum119895isinJ 1199032

119878119895

119865 =


2

(119899 + 119898) sdot (sum119894isinI 1199032

119875119894+ sum119895isinJ 1199032

119878119895)

(45)


119875119894 119903119878119895


119894and SU




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




v = 0



410

420

430

440

450

460

470

480

490

500

510Th

roug

hput

for S

Us (

kbits

s)

010 020 080 090050 060 070030 100000 040120572i

v = 0



15

20

25

30

35

40

45

50

Dela

y fo

r SU

s (m

s)

070 090030 040 050 080000 020010 100060120572i

v = 0



007

009

011

013

015

017

019

021

023

Loss

for S

Us (

)

080070 090020 050 060030 100040010000120572i


SNR = 0 dB



119894= 0









MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




MBC

915

920

925

930

935

940

945

950Th

roug

hput

for P

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

120572i = 0 v = 0

120572i = 1 v = 0



10

20

30

40

50

60

70

80

90

Dela

y fo

r PU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



005

010

015

020

025

030

035

040

045

Loss

for P

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0








0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0

100

200

300

400

500

600

700

800

900

1000Th

roug

hput

for S

Us (

kbits

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



10

30

50

70

90

110

130

Dela

y fo

r SU

s (m

s)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0



000

010

020

030

040

050

060

Loss

for S

Us (

)

20 40 60 80 1000Number of SUs m

MBC120572i = 0 v = 0

120572i = 1 v = 0
















119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in











119894and V The



119894 which









119894=


5 Conclusion




References
















































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in









































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Research Article Joint Bandwidth and Power Allocation for...

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