Energy-Efficient Multichannel Cooperative Sensing Scheduling With Heterogeneous Channel Conditions...

2690 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 62, NO. 6, JULY 2013

Energy-Efficient Multichannel Cooperative SensingScheduling With Heterogeneous Channel Conditions

for Cognitive Radio NetworksSalim Eryigit, Student Member, IEEE, Suzan Bayhan, Member, IEEE, and Tuna Tugcu, Member, IEEE

Abstract—Spectrum sensing is an important aspect of cognitiveradio networks (CRNs). Secondary users (SUs) should periodi-cally sense the channels to ensure primary-user (PU) protection.Sensing with cooperation among several SUs is more robust andless error prone. However, cooperation also increases the energyspent for sensing. Considering the periodic nature of sensing,even a small amount of savings in each sensing period leadsto considerable improvement in the long run. In this paper, weconsider the problem of energy-efficient (EE) spectrum sensingscheduling with satisfactory PU protection. Our model exploitsthe diversity of SUs in their received signal-to-noise ratio (SNR)of the primary signal to determine the sensing duration for eachuser/channel pair for higher energy efficiency. We model the givenproblem as an optimization problem with two different objectives.The first objective is to minimize the energy consumption, and thesecond objective is to minimize the spectrum sensing duration tomaximize the remaining time for data transmission. We solve bothproblems using the outer linearization method. In addition, wepresent two suboptimal but efficient heuristic methods. We pro-vide an extensive performance analysis of our proposed methodsunder various numbers of SUs, average channel SNR, and channelsampling frequency. Our analysis reveals that all proposals withan energy minimization perspective provide significant energysavings compared with a pure transmission-time maximization(TXT) technique.

Index Terms—Cooperative sensing scheduling (CSS), energy-efficient (EE) sensing, heterogeneous sensing, sensing taskassignment.

I. INTRODUCTION

THE increasing demand for wireless communications callsfor better spectrum utilization. One of the most promising

solutions is the dynamic spectrum access (DSA) paradigm,which allows the opportunistic access of a spatiotemporal un-used wireless spectrum by cognitive radio networks (CRNs). Ina CRN, a secondary user (SU) transmits through a frequencychannel that is licensed to primary users (PUs) but is currently

Manuscript received August 30, 2012; revised November 26, 2012 andJanuary 28, 2013; accepted February 4, 2013. Date of publication February 13,2013; date of current version July 10, 2013. This work was supported inpart by the State Planning Organization of Turkey under Grant 07K120610,in part by the Scientific and Technical Research Council of Turkey underGrant 108E101, and in part by the COST Action IC0902. The review of thispaper was coordinated by Dr. E. K. S. Au.

S. Eryigit and T. Tugcu are with the Department of Computer Engineering,Bogazici University, Istanbul 34342, Turkey (e-mail: [email protected];[email protected]).

S. Bayhan is with Helsinki Institute for Information Technology, AaltoUniversity, 00076 Espoo, Finland (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2013.2247070

unoccupied. However, DSA has the challenge to guaranteethat SUs vacate the spectrum whenever a PU simultaneouslytransmits at the band of SU transmission. Hence, SUs mustperform spectrum sensing. The accuracy of spectrum sens-ing is paramount for both finding the spectral voids and forprotecting the PU communications. Hence, a sensing periodis reserved at the beginning of each frame for the spectrumsensing task.

Previous works showed the increase in sensing accuracy withthe increase in sensing time [1]. On the other hand, SUs thatare mostly mobile devices should be energy-efficient (EE)1

as they use their battery power. Therefore, from the energy(throughput) efficiency perspective, the more time is spent onsensing, the more energy is consumed for overhead, and lesstime remains for transmission. On the other hand, the through-put of the network is a function of the detection accuracy (i.e.,probability of detection Pd and probability of false alarm Pf ).Hence, there is a tradeoff between sensing and transmissionduration for both throughput and EE.

In addition, it is shown that cooperation among the SUsincreases the detection reliability of spectrum sensing at theexpense of additional communication overhead that increaseswith the number of cooperating SUs [2]. Different from cooper-ative sensing in a single channel, cooperative sensing schedul-ing (CSS) has to balance the tradeoff between the detectionaccuracy of a single channel and the number of channels beingsensed in a multichannel CRN. That is, if there are more SUsassigned to sense a single channel, there will be a higher prob-ability of detection for that channel at the expense of leavingsome channels being unexplored. While cooperative sensinghas been well investigated, CSS still remains unexplored. Itis shown in previous works that CSS is NP-hard [3]. Takingthe EE concerns into account makes this problem even morecomplicated.

In this paper, we focus on the EE of cooperative spectrumsensing in a multichannel CRN with heterogeneous PU chan-nels in terms of received SNRs. Since scheduling the SUs tosense a number of channels in a CRN is a difficult task [3], wepropose three schemes for EE CSS. The first scheme uses outerlinearization to find the optimal solution, whereas the latter twoare efficient heuristic methods. Apart from these three, we alsoanalyze the problem from the transmission-time point of viewas time spent for sensing is also the time lost for transmission.

1We use EE for both energy efficiency and energy-efficient throughout thepaper. The exact meaning can be derived from the context.

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ERYIGIT et al.: EE MULTICHANNEL CSS WITH HETEROGENEOUS CHANNEL CONDITIONS FOR CRNS 2691

The rest of this paper is organized as follows. In Section II,we revise the related work on EE in spectrum sensing and stateour contributions to the literature. In Section III, we definethe cooperative sensing system model and introduce the basictheorems used in the formulated EE CSS scheme. Section IVfirst formulates the problem and presents the methodology forfinding the optimal solution. Proposed heuristic schemes aredescribed in Section V, and their performances are evaluatedin Section VI. Finally, Section VI concludes this paper.

II. RELATED WORK AND CONTRIBUTIONS

EE of CRNs has recently gained interest, and most of theinitial works focus on the EE of spectrum sensing [4]–[9] andcooperative sensing [10]–[14]. Su and Zhang minimized thesensing energy consumption while meeting the constraint onundiscovered spectrum opportunities [5], and they adapted theperiod of spectrum sensing to attain a balance between energyconsumption and missed spectrum opportunities for a randomaccess CRN [7]. Optimal sensing duration and transmissionduration for an SU under both high and low SU power capacityare analytically derived in [8]. The effect of transmission,idling, and sensing power consumption are analyzed in thatwork. Pei et al. devised an optimal policy for a single SU todecide on the order of channels to be sensed and when to stopsensing and start transmission [9]. While all these previousworks have valuable contributions, they fall short of practi-cality. In practical CRNs, there are multiple and most likelyheterogenous primary channels. In this setting, one of the majorconcern of the operator is to explore as many PU channels aspossible, meeting the PU detection and false alarm constraints.Therefore, in this paper, we enforce the SUs to sense allPU channels collaboratively to maximize the discovered spec-trum opportunities.

In [12] and [13], the communication cost for determiningthe number of cooperating SUs is considered. Maleki et al.found the minimum number of cooperating SUs that attainsthe required detection and false alarm probability performance[12]. If fewer SUs are engaged in sensing, less time will bespent reporting the sensing outcomes; thereby, more time willbe spent for transmission. Moreover, sensing reports from unre-liable SUs may decrease the sensing performance. SUs with un-reliable sensing information are refrained from reporting theirsensing results to save energy in [13]. In addition, a cluster-based decision collection instead of a high power-consumingbroadcasting scheme is also proposed in [13]. The cluster-basedscheme adapts the transmission power considering the mostdistant node. The decision fusion rule (i.e., how the collectedsensing information is processed to give the final decision onthe existence of PU) at the fusion center also affects the EE.Peh et al. [14] tuned the k parameter in k-out-of-N fusion ruleat each frame and the threshold for energy detection schemeat the fusion center. Heterogeneity of PU channels and SU linkconditions were ignored in these works, making the investigatedscenarios less realistic. In addition, assigning the same sensingduration for all SUs, regardless of their link conditions, mayresult in wasted energy at SUs with good link conditions. Incontrast to these works, we incorporate the effect of SNRs of

SUs into our scheme to calculate appropriate sensing durationfor each SU and frequency pair.

In [15]–[17], various solutions for improving the EE ofCSS are presented. Sensing scheduling is modeled as a utilitymaximization problem subject to a certain cooperative detec-tion probability in [15]. In addition, a constraint on minimumdiscovered transmission time is imposed to ensure a certainquality-of-service, together with heterogeneous detection prob-ability requirements. Similarly, Zhang and Tsang determinedthe number of SUs to sense each channel and the sensingduration in a slot [16], whereas Hao et al. study the optimalpartition of the SUs into coalitions, such that the total EE of allcoalitions are maximized [17]. In [16], a partially observableMarkovian decision process framework is utilized, and thepunishment parameter for higher EE is tuned. A distributedsolution using coalition formation is proposed in [17].

Apart from these works, the main contributions of this papercan be summarized as follows.

• We consider a scenario in which the number of SUs islarger than the number of primary channels. Therefore, ourmain concern is to select the SUs to sense all channels,whereas in [15]–[17], a subset of primary channels to besensed by all SUs is selected. In addition, in the previousworks, an SU can sense at most one channel, whereas inthis paper, SUs can sense multiple channels, as long asthey finish sensing in the dedicated time.

• Unlike these works, we account for the heterogeneity ofthe SU link conditions (i.e., received SNR of the PUsignal at the SU). Therefore, our CSS solution additionallydetermines which SUs should sense a channel. This paperdiverges from the previous works, which only determinethe number of SUs to sense a specific primary channel.

• Moreover, sensing duration associated with an SU isadjusted according to the link SNR as opposed to theprior works, which consider identical sensing duration forall SUs. Simply, our approach is based on the fact thatchannels with high SNRs require less sensing time for arequired detection probability and false alarm probability.Hence, an SU can save energy by sensing one of thechannels with a higher SNR, as opposed to the fixedsensing duration scheme.

III. SYSTEM MODEL

We assume an infrastructure-based CRN with N SUs,M channels, and a cognitive-radio base station (CBS). Ourconsideration is a specific case where the number of channels isless than the number of SUs, i.e., N � M . We believe that, ina cellular network, this assumption generally holds as there aremany users within the coverage area of the base station. If thatis not the case, the CBS may select a subset of the channelsbased on their past data, such as availability, capacity, etc.,such that there are enough SUs to sense all selected channels.This selection procedure has the potential to reduce energyconsumption by eliminating the less-favorable channels. SUsoperate in a time-synchronized manner within a frame-basedcommunication protocol. Each frame starts with a fixed-lengthquiet sensing period of duration T s during which SUs sense the


Fig. 1. Frame starts with a sensing period followed by reporting and transmis-sion periods.

channel(s) assigned to them. An SU may sense multiple chan-nels during the quiet period as long as the total time dedicatedto sensing by the SU does not exceed T s. Then, all SUs thatsense at least one channel report their hard decisions about thesechannels (0 or 1, indicating the absence or presence of PU) tothe CBS. We assume that the secondary network has a dedicatedcommon control channel that is used for this reporting taskand other control messages. The CBS combines the decisionsusing OR rule. The remaining time is used for transmission. Wealso assume that the SUs and the channels are heterogeneous.That is, the SNR of each SU over each channel is differentdue to different proximity from the PUs and different channelconditions (shadowing, fading, etc.). We assume the existenceof a receiver block at each SU to estimate the SNR level and tofeed it back to the CBS through the error-free feedback channel[18]. With the help of the receiver block, we assume that theinstantaneous SNRs are known. However, if that is not the case,long-term SNRs can also be used. This time, the techniquesdiscussed in this paper can also be applied. However, the mainobjective becomes the minimization of expected energy, insteadof the actual energy. The frame structure is shown in Fig. 1where T , T rep, and τm,n are the total frame length, the timededicated for reporting sensing results, and the time that SUn

senses channel m, respectively.Our main goal is to sense all M channels with minimum

energy and sufficient accuracy, such that cooperative detectionprobability of each channel is greater than some predefinedthreshold value (denoted by thQ

d), and cooperative false alarmprobability is smaller than another threshold (denoted by thQ

f ).Since channel sensing consumes energy, an SU may not utilizeall of the quiet period duration for sensing if not necessary.On the other hand, it is desirable to sense a channel witha couple of SUs instead of a single SU (although, it maysatisfy the thresholds) to increase robustness. Hence, there isa tradeoff between energy consumption and sensing reliability.The problem includes the assignment of SUs to channel(s) forthe sensing task, together with the decision of the sensing timefor the channel(s) to be sensed by each SU.

Let P fm,n, P d

m,n, and γm,n denote the probability of falsealarm, probability of detection, and SNR for SUn over channelm, respectively. If we assume that P f

m,n is fixed, then for acomplex-valued PSK channel with circularly symmetric com-plex Gaussian noise, P d

m,n is given by [1]

P dm,n = Q

(Q−1

(P fm,n

)−√

τm,nfsγm,n√2γm,n + 1

)(1)

where fs is the sampling frequency, and Q is the complemen-tary cumulative distribution of a standard Gaussian.

Theorem 1: P dm,n is an increasing function of τm,n. Further-

more, it is also concave if

− 1√τm,n

+γm,n

√fs

(2γm,n+1)

(Q−1

(P fm,n

)−√

τm,nfsγm,n

)<0.

(2)

This theorem is well known, and its proof is given inAppendix A.

Lemma 1: P dm,n is a concave function of τm,n if P d

m,n>0.5.Lemma 1 is a straightforward application of Theorem 1. The

proof can be found in Appendix B.Lemma 2: 1 − P d

m,n is a nonnegative decreasing function ofτm,n. It is also convex if the condition in (2) is satisfied.

Let Sm and Qdm denote the set of SUs sensing channel

m, and the cooperative detection probability for channel m,respectively. Using OR rule for decision combining gives

Qdm=1−

∏n∈Sm

(1−P d

m,n

)

=1−∏

n∈Sm

(1−Q

(Q−1 (P f

m,n

)−√

τm,nfsγm,n√2γm,n+1

)).

Theorem 2: Qdm is an increasing function of τm,n. More-

over, it is also concave if the condition in (2) is satisfied∀n ∈ Sm.

The proof of this theorem is given in Appendix C.

IV. OPTIMIZATION MODEL AND

SOLUTION METHODOLOGY

A. Energy Consumption Model

Let P s and Esm,n be the power consumed during channel

sensing and energy dissipated by SUn for sensing channel m,respectively. Es

m,n is equal to P sτm,n. Then, energy consump-tion for channel sensing (denoted by Es) can be written as

Es =M∑

m=1

N∑n=1

P sτm,n.

In addition to channel sensing, SUs also consume energyby transmitting their local results to the CBS. We assume thatSU transmits its sensing report as a single packet, regardlessof the number of channels sensed, and the reporting period islong enough such that all SUs can send their packets. Let Erep

n

denote the energy consumed for reporting the sensing result toCBS, which depends on the location of SUn relative to the CBS.In addition, let Srep denote the set of SUs that perform sensingin this frame and are required to report their local decisions tothe CBS. Then, the total energy consumption for reporting isgiven by

Erep =∑

n∈Srep

Erepn .

This model assumes that all reporting packets are success-fully transmitted. If that is not the case, the model can be


modified as follows. Let p denote the probability of successfulpacket transmission that is geometrically distributed. Then, theexpected number of transmission attempts for an SU is givenby 1/p, and Erep is given by Erep = 1/p

∑n∈Srep Erep

n .

B. Optimization Model for EE Sensing

We first define the decision variables that are used in theoptimization model. Let

τm,n = time spent by SUn for sensing channel m

xm,n =

{1, if channel m is sensed by SUn

0, otherwise

yn =

{1, if SUn transmits sensing result to CBS0, otherwise.

From (1), for a given P dm,n value, the required τm,n can be

written as

τm,n =

(Q−1

(P fm,n

)−Q−1

(P dm,n

)√2γm,n + 1

γm,n

√fs

)2

.

(3)

In addition, let τminm,n denote the sensing time required for SUn

to achieve a P dm,n value of 0.5. It can be calculated from (3) as

τminm,n =

(Q−1

(P fm,n

)γm,n

√fs

)2

.

We assume that a channel should be sensed by at least δmin

SUs. δmin defines the minimum number of cooperating SUs fora channel. The selection of δmin value is a design criterion. Toencourage cooperation and improve robustness, a δmin valuegreater than 1 is preferred. On the other hand, regarding EEconcern, δmin should not be high as each additional SU usedfor sensing incurs sensing energy consumption and, maybe,reporting energy.

If we assume that P fm,n = P f ∀m, n, then Qf

m is given by

Qfm = 1 −

∏n∈Sm

(1 − P f ).

Since Qfm ≤ thQ

f , then the maximum number of cooperatingSUs, which is denoted by δmax, can be calculated as

δmax =

⌊log (1 − thQ

f )

log (1 − P f )

⌋. (4)

In other words, δmax is the maximum number of cooperatingSUs that satisfy the cooperative false alarm constraint. Thesolution methodology that we apply can also be used for thecase where P f

m,n values differ. We discuss this case in detailat the end of Section IV-C. The optimization model can bewritten as

P1 : minw =

M∑m=1

N∑n=1

P sτm,n +

N∑n=1

Erepn yn (5)

subject to

τm,n ≥ τminm,nxm,n ∀m ∈ M ; ∀n ∈ N (6)

M∑m=1

τm,n ≤T syn ∀n ∈ N (7)

N∑n=1

xm,n ≥ δmin ∀m ∈ M (8)

N∑n=1

xm,n ≤ δmax ∀m ∈ M (9)

M∑m=1

xm,n ≤Myn ∀n ∈ N (10)

thQd −Qd

m ≤ 0 ∀m ∈ M (11)

xm,n, yn ∈{0, 1} ∀m ∈ M ; ∀n ∈ N (12)

τm,n ≥ 0 ∀m ∈ M ; ∀n ∈ N (13)

where, this time, Qdm is defined as

Qdm=1−

N∏n=1

(1−Q

(Q−1(P f )−

√τm,nfsγm,n√

2γm,n+1

)xm,n

).

Hence, SUs with xm,n value of 0 contribute 1 to the givenmultiplication, whereas those with xm,n value of 1 contribute(1 − P d

m,n).The objective in (5) minimizes the total energy consumption

associated with sensing for a frame. Constraint (6) specifiesthat, if SUn senses channel m, the sensing duration shouldbe at least τmin

m,n. This way, we guarantee that the concavitycondition always holds. Constraint (7) denotes that total timespent by an SU for sensing should be less than or equal tothe sensing duration of a frame. It also forces all τm,n valuesassociated with SUn to 0 if yn = 0. Constraint (8) requiresthat each channel should be sensed by at least δmin SUs.Similarly, Constraint (9) limits the number of cooperating SUsfor a channel to satisfy the false alarm probability threshold.Constraint (10) forces yn value for an SU to 1 if that SUsenses any channels. The requirement for cooperative detectionprobability being greater than the threshold for each channel isexpressed by constraint (11). Finally, constraints (12) and (13)specify the types of variables.

The given problem is a mixed-integer nonlinear program-ming problem because of constraint (11), although its objectiveis linear. We resort to the outer linearization algorithm to solvethe given problem.

C. Outer Linearization

As proven before, once the xm,n values are fixed, Qdm

value is concave in terms of τm,n. Thus, constraint (11) isconvex, and the outer linearization procedure can be used tofind the optimal solution [19]. Outer linearization works by firstignoring the mixed-integer nonlinear constraints to obtain aninitial solution. If the solution satisfies all previously ignoredconstraints, then it is optimal. On the other hand, if it does not,then the most violated constraint is linearized using the current


solution and is added to the current problem as a new constraintto obtain another solution. The linearization process goes onuntil all constraints are satisfied with an ε tolerance. Since theconstraints are convex, the procedure is guaranteed to terminatein finite number of steps [20]. The steps of the procedure areas follows.

Step 1: Initialize the iteration counter, i.e., k = 1. Solve theinitial mixed-integer linear programming problem (P2)formed by ignoring constraint (11), and obtain the initialsolution τ1m,n, x1

m,n, and y1n.Step 2: Identify the most violated constraint gm among the M

constraints of (11) with the current solution (τkm,n, xkm,n,

and ykn). That is, gm is the cooperative detection probabilityconstraint corresponding to the channel that deviates fromthe threshold value most. Let vm denote the correspondingdeviation.

Step 3: If the maximum violation is smaller than ε, then stop;the current solution is optimal with ε feasibility tolerance.Otherwise, proceed with Step 4.

Step 4: Linearize the most violated constraint by adding thefollowing linear constraint to P2:

∇gm(. . . xkm, i, . . . τ

km, i, . . .)

T

⎡⎢⎢⎢⎢⎢⎢⎢⎣

...xm, i − xk

m, i

...τm, i − τkm, i

...

⎤⎥⎥⎥⎥⎥⎥⎥⎦+ vm ≤ 0

where ∇gm(. . . xkm, i, . . . τ

km, i, . . .) is the gradient of gm

evaluated at the current solution. Its individual entries aregiven by

∂gm∂xm, i

= −Q(Q−1(P f )−

√τm, ifsγm, i√

2γm, i + 1

)Bm, i

∂gm∂τm, i

= − xm, iγm, i

√fs

2√τm, i

√2π

√2γm, i + 1

Am, iBm, i

where Bm, i is given by

N∏n=1, n=i

[1 −Q

(Q−1(P f )−

√τm,nfsγm,n√

2γm,n + 1

)xm,n

].

Set k = k + 1, and solve the current problem to obtainτkm,n, xk

m,n, and ykn values. Proceed with Step 2.

In the remainder of this paper, we refer to the application ofouter linearization to Problem P1 as EE.

For the case where P fm,n values differ, the false alarm

constraint assumes the following form:

1 −N∏

n=1

(1 − P f

m,nxm,n

)− thQ

f ≤ 0.

The outer linearization procedure can still be applied in thiscase, but this time, 2M constraints (cooperative false alarmprobability constraint in addition to cooperative detection prob-

ability constraint for each channel) need to be checked forfeasibility. The other steps of the procedure are the same.

D. TXT

The model mentioned previously optimizes the total en-ergy dedicated to the sensing task while achieving satisfactorysensing performance in terms of detection and false alarmprobabilities. However, in this approach, sensing duration ofa frame (denoted by T s) is constant. Hence, if we denote theframe duration by T and reporting time of the sensing outcomesby T rep, which are also constant, then the transmission time fordata packets is given by T − T s − T rep. Another approach is tomaximize the data transmission duration of a frame. This time,we treat T s as a decision variable. Assuming a quiet sensingperiod, T s is given by maxn{

∑Mm=1 τm,n}. In other words,

T s is the maximum of total sensing times for all SUs as thenetwork should wait for the SU with the longest total sensingtime before moving on the next phase of a frame. Then, the ob-jective becomes max z1 = T − T rep −maxn{

∑Mm=1 τm,n}.

Since T and T rep are constants, this objective is equivalent tomin z2 = maxn{

∑Mm=1 τm,n} subject to constraints (6)–(13).

To solve this problem, we resort to the outer linearizationprocedure again as the constraints are almost the same.

V. HEURISTIC APPROACHES

Here, we propose two suboptimal but fast heuristic ap-proaches for the EE sensing problem. The first one focuseson greedily minimizing sensing energy while disregarding thereporting energy. On the other hand, the second heuristic ini-tially considers the reporting energy, and then, it considers thesensing energy.

Unlike the previous two approaches that support differentdetection probabilities for different channel and user pairs,these heuristics require a fixed detection probability P d forall channels and users for the sake of simplicity and quickexecution time. This approach is frequently applied in theliterature [4], [12], [14]. For both heuristics, we sense eachchannel with δmin SUs. Thus, the required P d value can becalculated as

P d = max{

1 −(1 − thQ

d)1/δmin

, P dmin

}which guarantees a minimum detection probability of P d

min. Asthe P f

m,n values are assumed to be the same for all SU–channelpairs as before, the goal of the heuristics is to find the bestSU/channel assignment.

A. SEM Heuristic

This heuristic minimizes the sensing energy by selecting SUswith high SNRs for a channel while disregarding reportingenergy. Initially, the remaining sensing time of all SUs are equalto T s. The heuristic starts with the first channel, sorts the SUsin descending order based on their γm,n values, and selects thefirst SU in the list. Then, it calculates the required τm,n valuefor the selected SU to obtain a detection probability of P d. If theremaining sensing time of the selected SU is greater than τm,n,


the selected SU is assigned to sense channel m. Otherwise, wemove on to the next SU. The algorithm runs until δmin SUs areassigned to all channels. The pseudocode for this heuristic isgiven in Algorithm 1.

Algorithm 1 Sensing Energy Minimization (SEM) Heuristic

Require:P d, δminM , N , γm,n, T s

1: remainingT ime[n] = T s ∀n2: for m = 1 to M do3: Sort SUs in descending order of γm,n and let index

be the list of indices of the sorted entries such thatindex[1] corresponds to the index of SU with thehighest γm,n and index[N ] corresponds to the indexof SU with the lowest γm,n.

4: assignmentNo = 0, k = 15: while assignmentNo < δmin do6: n = index[k]7: Select SUn as a candidate and calculate the τm,n value

to achieve P d using (3).8: if τm,n ≤ remainingT ime[n] then9: remainingT ime[n] = remainingT ime[n]−

τm,n

10: assignmentNo = assignmentNo+ 111: end if12: k = k + 113: end while14: end for

Starting with the first channel, the heuristic selects δmin

SUs with the best γm,n values and enough remaining sens-ing time for the sensing task. The outer loop takes O(M)steps. Sorting SUs based on their γm,n values is O(N logN),whereas the inner loop is O(N). Hence, the total running timeis O(MN logN).

B. REM Heuristic

The main difference between the reporting energy mini-mization (REM) heuristic and SEM heuristic is that REM firstconsiders SUs that are already assigned to sense a channel. LetSrep be the set of SUs that are going to perform sensing andtransmit their reports for this frame. Similarly, Snrep is the setof SUs that are not assigned to sense a channel yet. Initially,Srep = ∅, Snrep = {SU1,SU2, . . . ,SUN}. The heuristic firstlooks for SUs among those in Srep to save reporting energy.If enough SUs are not found, then it moves on to Snrep. Asin the previous case, SUs in Srep and Snrep are processed indecreasing order of γm,n values for the considered channel.The pseudocode of REM heuristic is given in Algorithm 2.

Algorithm 2 Reporting Energy Minimization Heuristic

Require:P d, δmin, M , N , γm,n, T s

1: remainingT ime[n] = T s ∀n2: Srep = ∅, Snrep = {SU1,SU2, . . . ,SUN}

3: for m = 1 to M do4: Sort SUs in Srep in descending order of γm,n, and let

indexRep be the list of indices of the sorted entries.5: assignmentNo = 0, k = 16: while (assignmentNo < δmin) && (k ≤ |Srep|) do7: n = indexRep[k]8: Select SUn ∈ Srep as a candidate, and calculate τm,n

value to achieve P d using (3).9: if τm,n ≤ remainingT ime[n] then10: remainingT ime[n] = remainingT ime[n]−

τm,n

11: assignmentNo = assignmentNo+ 112: end if13: k = k + 114: end while15: if assignmentNo < δmin then16: Sort SUs in Snrep in descending order of γm,n, and

let indexNrep be the list of indices of the sortedentries.

17: k = 118: while assignmentNo < δmin do19: n = indexNrep[k]20: Select SUn ∈ Snrep as a candidate and calculate

τm,n value to achieve P d using (3).21: if τm,n ≤ remainingT ime[n] then22: remainingT ime[n] = remainingT ime[n]−

τm,n

23: assignmentNo=assignmentNo+1,Srep =Srep ∪ {SUn},Snrep = Snrep \ {SUn}

24: end if25: k = k + 126: end while27: end if28: end for

This time, both inner WHILE loops (lines 6 and 18) takeO(N), and the sorting operations are still O(N logN). As inthe previous case, the total running time is O(MN logN).

VI. RESULTS

We assume that the received SNR at SU (γm,n) follows anexponential distribution with mean μSNR. To be consistent, weuse the same γm,n values for a given μSNR across differentruns. For a given parameter set, we first run the transmission-time maximization (TXT) method to obtain the ideal sensingtime denoted by T s

opt. For the other methods, we scale this valuewith an α value (α > 1), and use αT s

opt as the sensing time forthe other methods. The values for the other parameters are givenin Table I.

By using (4), we obtain δmax = 10 for the given P f andthQ

f values. Note that the presented results are for a singleframe. Hence, the cumulative effect will be much higher ifmultiple frames are considered. Furthermore, the processingorder of the channels is important for the given heuristics asthey converge to local optimal solutions. Although the channelsare ordered naturally in the given pseudocode, we also run bothheuristics with randomly ordered channels 20 times. The results


TABLE IPARAMETERS VALUES

Fig. 2. Energy consumption profiles with N = 200, δmin = 3, and α = 2.(a) Low SNR: μSNR = −5 dB. (b) High SNR: μSNR = 2 dB.

given in the following for the heuristics are the best of the21 runs in terms of energy consumption.

We first observe the total energy consumption and its individ-ual components in Fig. 2(a) and (b) for μSNR values of −5 and2 dB, respectively. For low μSNR, the sensing component of theenergy consumption is more dominant. On the other hand, thereporting energy consumption becomes the major componentwhen μSNR is higher. As we can see, the reporting energy

Fig. 3. Effect of μSNR on total sensing energy consumption with N = 200,δmin = 3, and α = 2. (a) μSNR between −10 and 5 dB. (b) μSNR between−2 and 3 dB.

consumption is similar in both cases. Hence, the differencestems from the sensing energy consumption. With high μSNR,the time required to achieve a particular detection probabilitydecreases, which in turn decreases the required sensing time.In both cases, TXT achieves the worst performance since itsobjective does not consider the energy consumption at all.On the other hand, the performance of EE is always superiorcompared with other methods. Furthermore, SEM is slightlysuperior compared with REM for low SNRs because it prior-itizes the sensing energy. On the contrary, REM achieves lowertotal energy for high SNR since it first considers the reportingenergy component.

The effect of changing μSNR on the total sensing energyconsumption is shown in Fig. 3. Fig. 3(a) shows a broaderrange, whereas Fig. 3(b) shows the high-SNR regime. Initially,increasing μSNR values have a significant impact on the totalenergy consumption for all methods, whereas beyond a certainpoint, the benefits are minimal. In this case, EE provides 7%improvement over the next best method, namely SEM heuristic,when μSNR is −10 dB. Moreover, the improvement over othermethods is much better when μSNR assumes higher values, asshown in Fig. 3(b). As an example, using EE results in 22%


Fig. 4. Effect of the number of SUs on the total sensing energy consumptionwith μSNR = −5 dB, δmin = 3, and α = 2.

Fig. 5. Energy consumption profiles with N = 200, δmin = 3, α = 2, fs =10 kHz, and μSNR = −5 dB.

reduction in total energy consumption compared with the nextbest method, which is REM this time, when μSNR is 0 dB.In addition, both figures support our previous claim that SEMachieves better performance than REM for low SNRs, whereasthe reverse is true for high SNRs.

Fig. 4 shows the change in total energy consumption withrespect to the increase in the number of SUs. Apart fromTXT method, all schemes yield better results as N increases.The main reason for this performance improvement is thediversity brought by the added SUs. That is, with more SUs, theprobability of finding an SU with a high γm,n value increasesfor a given channel m. On the other hand, the TXT methodshows slight variations since its goal is not related to energyconsumption.

The total energy consumption and its individual componentsfor fs = 10 kHz case are presented in Fig. 5. In comparisonwith Fig. 2, increasing fs has a similar effect as increasing SNR.However, the effect of SNR is more prominent. For instance,with all other factors constant, increasing μSNR from −5 to2 dB (almost a fivefold increase) results in nearly 83% reductionin energy consumption for EE. On the other hand, increasing fs

tenfold from 1 to 10 kHz gives a 76% decrease for EE. Theseobservations are in accordance with (3). In addition, similar tothe case in Fig. 3(b), with a higher sampling rate, the REMheuristic provides lower energy consumption than the SEMheuristic.

The energy consumption values for various values of α aregiven in Fig. 6(a) and (b) for μSNR values of −5 and 2 dB,respectively. As α is not a parameter for TXT, it is not affectedby the change in α. For low α values, the results for SEM andREM are not shown because both heuristics fail to provide afeasible solution. For the low-SNR regime, both EE and SEMproduce lower energy consumption with increasing α, but thedecrease is marginal. Unlike SEM and EE, the results for REMfirst decrease and then start to increase. The rationale behindthis pattern can be explained as follows: Since REM prefersSUs that are already assigned with a channel for sensing whenselecting SUs for channel m, long sensing duration causes SUswith low γm,n to be assigned to channel m. We observe thatsensing energy component dominates in the low-SNR regime;therefore, this causes an increase in total energy consumptionfor REM. On the contrary, for high-SNR regime, REM pro-duces lower energy consumption values as the reporting energycomponent is the dominating factor. Both figures show that withonly a small amount of additional sensing time, great energysavings are possible.

To sum up, all three energy minimization methods (EE, SEM,and REM) provide significant energy savings compared with apure TXT technique. In all cases, EE achieves the best energyvalues, whereas the performance of SEM and REM dependson the parameter values. On one hand, a low μSNR or high αfavors SEM. On the other hand, a high μSNR or high fs supportsREM. As both heuristics have very low complexity, both canbe executed in a short amount of time, and one can select themethod with the better energy consumption.

VII. CONCLUSION

In this paper, we have formulated the EE CSS problem fora CRN and presented various approaches for this problem.Each scheme ensures the minimum detection probability con-straint as a PU protection criterion and the maximum falsealarm probability constraint as a CRN operability criterion ineach channel. EE, SEM, and REM aim to minimize energyexpenditure for sensing, whereas TXT minimizes time spent forthe sensing task to leave more time for data transmission. Wehave investigated the performance of our proposals with variousparameters. To find the optimal solution, we have employedthe outer linearization method. Numerical evaluations haveshown that by sacrificing very little data transmission time, asignificant amount of energy can be saved. Furthermore, re-porting energy is an important factor in energy consumption,particularly when the SNR or sampling frequency is high.

As future work, we plan to incorporate different fusion rules,e.g., AND, MAJORITY, etc., into our model. Moreover, we alsowould like to analyze the impact of channel switching delay andenergy consumption of channel switching on sensing energyconsumption. Another point to pursue is to treat false alarmprobabilities as decision variables and jointly optimize themtogether with sensing times.


Fig. 6. Effect of sensing duration (Ts) under low and high SNRs with N = 200, δmin = 3. (a) Low SNR: μSNR = −5 dB. (b) High SNR: μSNR = 2 dB.

APPENDIX APROOF OF THEOREM 1

The first derivative of P dm,n with respect to τm,n is

dP dm,n

dτm,n=

γm,n

√fs

2√τm,n

√2π

√2γm,n + 1

Am,n

where

Am,n = exp

⎛⎝−1

2

(Q−1

(P fm,n

)−√


)2⎞⎠ .

The first derivative is always positive; hence, P dm,n is an

increasing function of τm,n.The second derivative of P d

m,n with respect to τm,n isgiven as

d2P dm,n

dτ2m,n

=γm,n

√fsAm,n

4√

2π√

2γm,n+1

⎡⎣− 1√

τ3m,n

+γm,n

√fs

τm,n(2γm,n+1)

×(Q−1 (P f

m,n

)−√

τm,nfsγm,n

)⎤⎥⎦.

The second derivative is negative if

−1√τ3m,n

+γm,n

√fs

τm,n(2γm,n + 1)

×(Q−1

(P fm,n

)−√

τm,nfsγm,n

)< 0.

Reducing the τm,n term leads to

− 1√τm,n

+γm,n

√fs

(2γm,n + 1)

(Q−1

(P fm,n

)−√

τm,nfsγm,n

)<0.

Thus, P dm,n is a concave function of τm,n if the condition in

(2) is satisfied.

APPENDIX BPROOF OF LEMMA 1

By combining (1) and (2), we get

− 1√τm,n

+γm,n

√fsQ−1

(P dm,n

)√

2γm,n + 1< 0.

The first term is always negative, whereas the second term isnegative if P d

m,n > 0.5. Since it is reasonable to assume a P dm,n

value greater than 0.5, we can safely say that P dm,n is a concave

function of τm,n most of the time.

APPENDIX CPROOF OF THEOREM 2

Let τn denote the τ vector with n entries that consists of τm,n

values for channel m. Moreover, let fm,k and hm,k denote (1 −P dm,k), and fm,1fm,2, . . . , fm,k, respectively. The proof is by

induction on the number of elements in Sm denoted by |Sm|.• |Sm| = 2: Without loss of generality, assume that SUs 1

and 2 are in Sm. We can rewrite Qdm as 1 − hm,2.

The gradient of hm,2 is given by

∂hm,2

∂τ2=

[− γm,1

√fsAm,1

2√τm,1

√2π

√2γm,1 + 1

fm,2,

− γm,2

√fsAm,2

2√τm,2

√2π

√2γm,2 + 1

fm,1

]

where

Am,n = exp

⎛⎝−1

2

(Q−1

(P fm,n

)−√


)2⎞⎠ .

Both terms are always negative; thus, hm,2 is a decreasingfunction of τ2. Therefore, Qd

m is an increasing functionof τ2 since (∂Qd

m/∂τ2) = −(∂hm,2/∂τ2). In addition,as shown in Lemma 2, both fm,1 and fm,2 are nonneg-ative, decreasing, and convex functions; therefore, their


multiplication hm,2 is also convex [21], which leads to theconcavity of Qd

m.• Let us assume that the theorem holds for |Sm| = k and

show that it also holds for |Sm| = k + 1. This time, Qdm

can be written as

Qdm = 1 − hm,k+1 = 1 − hm,kfm,k+1.

The gradient of hm,k+1 is given by

∂hm,k+1

∂τk+1=

[∂hm,k

∂τk+1fm,k+1, hm,k

∂fm,k+1

∂τk+1

].

Let us focus on the first term. Since (∂hm,k/∂τk+1) isnegative by induction and fm,k+1 is nonnegative, thentheir multiplication is negative. For the second term, hm,k

is a nonnegative function, and (∂fm(k+1)/∂τk+1) is neg-ative by Lemma 2. Thus, their multiplication is also nega-tive. Since both terms are negative, hm,k+1 is a decreasingfunction of τk+1.

We apply the same logic as in the previous step toprove the convexity of hm,k+1. Both hm,k and fm,k+1

are decreasing convex functions (convexity of hm,k comesfrom induction); then, their multiplication hm,k+1 is alsoconvex. Thus, Qd

m is a concave and increasing functionof τk+1.

Proving both the base step and the induction step leads to theconclusion that Qd

m is an increasing concave function of τm,n

if (2) is satisfied.

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Salim Eryigit (S’12) received the B.S. degreein industrial engineering and the M.S. degree incomputer engineering from Bogazici University,Istanbul, Turkey, in 2003 and 2008, respectively.He is currently working toward the Ph.D. degree incomputer engineering with Bogazici University.

His research interests include network optimiza-tion, cognitive radio networks, green communica-tions, and scheduling.

Suzan Bayhan (M’13) received the B.S., M.S.,and Ph.D. degrees in computer engineering fromBogazici University, Istanbul, Turkey, in 2003, 2006,and 2012, respectively.

She is currently a Postdoctoral Researcher withthe Helsinki Institute for Information Technology,Aalto University, Espoo, Finland. Her current re-search interests include cognitive radio networks,small cells, green communications, and mobile op-portunistic networks.

Tuna Tugcu (M’00) received the B.S. and Ph.D.degrees in computer engineering from BogaziciUniversity, Istanbul, Turkey, in 1993 and 2001,respectively, and the M.S. degree in computer andinformation science from the New Jersey Institute ofTechnology, Newark, NJ, USA, in 1994.

He worked as a Postdoctoral Fellow and as a Vis-iting Professor with the Georgia Institute of Technol-ogy, Atlanta, GA, USA. He is currently an AssociateProfessor with the Department of Computer Engi-neering, Bogazici University. His research interests

include cognitive radio networks, WiMAX, and molecular communications.

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