Dynamic Resource Allocation in OFDMA Uplinkfor MAI Mitigation and Throughput Improvement

Hieu LeTelecommunincation DepartmentTechnical University of Berlin

Berlin 10587, GermanyEmail: le@tkn.tu-berlin.de

Arash BehboodiTelecommunincation DepartmentTechnical University of Berlin

Berlin 10587, GermanyEmail: arash.beboohdi@tkn.tu-berlin.de

Adam WoliszTelecommunincation DepartmentTechnical University of Berlin

Berlin 10587, GermanyEmail: awo@ieee.org

Abstract—In OFDMA uplink, Multiple Access Interference(MAI) caused by synchronization offsets in user signals can con-siderably degrade user throughputs. In this paper, we investigatethe problem of applying Dynamic Resource Allocation (DRA)to mitigate MAI and simultaneously improve user throughputs.Firstly, we introduce a novel solvable optimization problem (OP)based on DRA to maximize the minimum user throughput. Usingthis proposed OP, we show the optimal RA schemes can increaseminimum user throughput up to 300% compared to earliersolutions following DRA, and to 25% compared to the estimationand correction based approach. Secondly, by investigating theassignment of frequency sub-bands, we show an insight aboutthe advantage of DRA in uplink, where better exploitationof frequency and multiuser diversities leads to efficient MAImitigation and significant throughput gain. Finally, we introducesuboptimal OPs to reduce the complexity, among that the onebased on chunking can significantly reduce the complexity andstill provide comparable throughput gain.

I. INTRODUCTION

Orthogonal Frequency Division Multiple Access (OFDMA)has been adopted in the fourth generation (4G) of mobilecommunication standards (i.e. LTE-A and WiMAX) for bothdownlink and uplink, due to several favorable characteristicssuch as spectral efficiency, robustness against multi-path inter-ference, and the flexibility of Resource Allocation (RA).

Unlike OFDMA downlink, there are still several open issuesin OFDMA uplink. One primary challenge in uplink stemsfrom synchronization offsets between the User Terminals(UTs) and the Base Stations (BS). The problem arises as signalarriving BS is superposition of components sent simultane-ously by several UTs. Lack of perfect synchronization both intime and frequency causes Multiple Access Interference (MAI)and severely degrades user throughputs [1].

The common approach to deal with MAI is based onprinciple of estimating time and frequency offsets on eachUT’s signal, and then subtracting the estimated offsets torecover orthogonality. In this paper, that approach is referredto as the Estimation and Correction Based Approach (ECBA).Numerous techniques following ECBA have been proposed,and one well-known example based on the concept of multiuser detection can be found in [2]. (See [3] for a thoroughsurvey about ECBA’s techniques.) One of the main disad-vantages of ECBA lies in the large overhead including long

Cyclic Prefix (CP) and pilot frequency sub-bands, and, thus,the reduction in throughput [4].

Alternatively, to avoid the large overhead of ECBA, onecan apply Dynamic Resource Allocation (DRA) instead. Inthis approach, the overhead is reduced through shortened CPand less pilot frequency sub-bands, and therefore residualtime and frequency offsets exist, causing mutual MAI onuser signals. However, since MAI and throughput stronglydepend on several factors such as assignment and relativeoffsets, a proper RA scheme can help mitigating MAI andsimultaneously increase user throughput [5]. Particularly, it issupposed to assign each frequency sub-band to a UT, that canachieve high throughput without causing too much MAI onother UTs. In other words, DRA improves user throughputsby taking advantages of the frequency and multiuser diversitiesoffered by OFDMA. Moreover, we introduce frequency guardbands (GB) into DRA to add another degree of freedom.Unlike CP, whose length is static and identical for all UTs,GBs can be dynamically used as needed or re-assigned tocarry user data as MAI is not severe. The main challenge ofthis approach is to deal with two trade-offs affecting MAI[4]. First, assigning a good frequency sub-bands to a badly-synchronized UT u improves throughput of u, but at the sametime increases MAI caused by UT u on all other UTs (i.e.∀u′ 6= u). Second, the mitigation of MAI using GBs comeswith the cost of frequency resource losses. In general, anoptimization problem is needed to solve the trade-offs andoffer optimal RA schemes subject to the desired throughputgoal. However, to the best of our knowledge, no such optimalsolutions based on DRA to mitigate MAI and to improveuser throughput have been formulated and successfully solvedeither analytically or numerically. As a matter of fact, onlysuboptimal solutions have been numerically solved in [4], [5].

In this paper, we investigate the problem of mitigating MAIand maximizing the minimum user throughput using DRA.• We propose a novel optimization problem (OP), which

is numerically solvable and thus able to provide theoptimal RA scheme subject to the desired throughputgoal. In addition, we investigate suboptimal cases toreduce computational complexity.

• Via simulations, we quantify and analyze the utilizationof the frequency and multiuser diversities, and the usage

of GBs in order to provide an insight about the source ofthroughput gain and the advantage of DRA in uplink.

• Finally, we study the complexity of the proposed OPswith regard to the solving time.

Our results show DRA can efficiently mitigate MAI andsimultaneously improve minimum user throughput, due toshortened overhead and the better exploitation of frequencyand multiuser diversities. In addition, among proposed OPs,the suboptimal OP based on chunking scheme can significantlyreduce complexity and provide comparable throughput gain.

II. SYSTEM MODEL

A. Overview and assumptions

In this paper, we consider one cell using OFDMA withTime Division Duplexing (OFDMA/TDD) as data transmis-sion scheme. Total Nsca subcarriers are shared among MUTs. In addition, every G adjacent subcarriers are groupedinto one subchannel to reduce computation load and overheadfor addresses. Let Si be the set of subcarriers in subchanneli. In this work, G is defined equal to the channel coherencebandwidth, thus the frequency diversity is efficiently exploited[4]. Hence, there are total Nsch = Nsca/G subchannels.

Let f0 be the frequency spacing; the OFDMA symbolduration then equals Tsym = 1/f0. Prior to OFDMA symbol,a CP with the length of v is added, then one OFDMA symbolwith CP included has the length of T = Tsym + v. Besides,total number of OFDMA symbols during the uplink frame isdenoted by Nsym.

The smallest addressable resource unit takes one subchannelin frequency and Nsym symbols in time (i.e. the whole uplinkframe). In uplink, UTs can take several subchannels to sendtheir data simultaneously to BS over different wireless chan-nels. Particularly, slow fading channels between UTs and BSare modeled including 3 components of path loss, shadowingand multi-path. In addition, due to the coherence bandwidth,channel gain Hk,i,u of all subcarriers k belonging to the samesubchannel i are equal. We define the channel gain Hi,u ofsubchannel i of UT u as Hi,u = Hk,i,u, ∀k ∈ Si.

The power generated on subcarrier k ∈ Si by UT u isdenoted by PTXk,i,u, then the corresponding received power takesthe form PRXk,i,u = PTXk,i,u×Hk,i,u. For simplicity’s sake, a staticand equal power allocation is assumed, i.e. PTXk,i,u = PTX ,∀k, i, u. Consequently, we define the received power of thesubchannel i of UT u as PRXi,u = PRXk,i,u = PTX ×Hi,u.

Due to synchronization errors, signals sent by UT u isshifted by τu in time and ∆fu in frequency relatively to BS.

It is important to mention that our system model makesthe following assumptions. First, unlike ECBA, CP here isrelatively short and only enough to deal with the delay spread.MAI caused by (a) residual frequency offsets (includingDoppler shift and clock errors in frequency) and (b) residualtime offsets (including propagation delay and clock errorsin time) would be mitigated via an appropriate RA scheme.Second, during the downlink, in order to receive correctly thesignals sent from BS, UTs need to estimate channel quality

and offsets. We assume these estimations are sent to BS, thusBS has perfect knowledge of the channel quality, time offsets,and frequency offsets in uplink. Third, signaling is assumablysent on a separate channel and overhead information is notconsidered.

B. Calculation of MAI and SINR

The instantaneous Signal to Interference plus Noise Ratio(SINR) γi,u of subchannel i of UT u takes the following form.

γi,u =PRXi,u

σ2 +∑∀u′ 6=u

∑∀j 6=iMAI

j,u′

i,u

, (1)

where σ2 is the thermal noise power, and we formulateMAI

j,u′

i,u as below to represent the average MAI caused bysubchannel j of UT u′ on subchannel i of UT u.

MAIj,u′

i,u =1

G

∑k∈Si

∑r∈Sj

MAIr,u′

k,u . (2)

The MAIr,u′

k,u in (2) is MAI caused by subcarrier r ∈ Sj ofUT u′ on subcarrier k ∈ Si of UT u (u′ 6= u). The calculationof MAIr,u

′

k,u is formally derived in [1] and briefly review asfollows:

MAIr,u′

k,u =PRXr,u′

N2sca

× A(k − r,∆fu′ −∆fu, τu′ − τu)

sin2[ πNsca

(k − r +∆fu′ −∆fu)], (3)

where A(.) is a function of the relative time and frequencyoffsets between UT u′ and UT u as well as the frequencydistance (i.e. k − r). The detailed calculation of A(.) ispresented in [1].

C. Calculation of throughput

In this paper, to come up with a detailed model, the adap-tive coding and modulation (ACM) is adopted. Particularly,based on the instantaneous SINR value γi,u, an appropriatecoding and modulation scheme is chosen subject to the tol-erable error rate Perr. The monotonically increasing functionFsinr2rate(γi,u, Perr) is used to represent the ACM mecha-nism. In practice, Fsinr2rate(γi,u, Perr) returns the number ofbits sent on subchannel i of UT u corresponding to the chosenACM scheme divided by T . In total, L schemes are available.Let Thl and Bl be the required SINR and the instantaneousthroughput as ACM scheme l is chosen, respectively. Forexample, the 64-QAM with coding rate 2/3 scheme allows tosend total 6 bits and ,thus , 4 data bits per OFDMA symbol;the throughput B then equals 4/T [bps].

III. DYNAMIC RESOURCE ALLOCATION FOR MAIMITIGATION AND THROUGHPUT IMPROVEMENT

Based on the system model in Section II, we describe twomain trade-offs, and apply DRA in order to mitigate MAI andimprove user throughputs.• Trade-off of assignment: Assigning a good/bad subchan-

nel i to UT u obviously increases/decreases the u-th UT’sthroughput (as shown in (1)), but increases/decreases

MAIi,u

j,u′ causing on all other subchannel j of all otherUT u′ (see (3)).

• Trade-off of GB: Taking some subchannels from a badly-synchronized UT u′ and setting them as GBs obviouslyavoid MAI caused by those subchannels on all othersubchannels of all UTs u 6= u′. However, that mitigationof MAI comes at the cost of frequency wastage and, thus,throughput losses. Therefore, considering only channelquality without consideration of MAI might actuallyincrease MAI, and thus lead to wrong RA schemes.

In general, a RA scheme should efficiently exploit thefrequency and multiuser diversities to solve these two trade-offs, and thus improve the system performance. In this section,we formulate OPs to provide optimal RA schemes subject tothe goal of maximization of minimum (shortly max-min) userthroughput (i.e. the fairness is under consideration).

A. Basic max-min user throughput OP

To form the OP, the assignment of subchannel i to UT uis represented by a binary optimization variables xi,u, whichtakes 1 if UT u takes subchannel i and 0 if not. Consequently,the basic max-min user throughput OP, which is based directlyon system model in Section II, has the following formulation.

max ε

s.t. a)

Nsch−1∑i=0

xi,uFsinr2rate(γi,u, Perr) ≥ ε, ∀u

b)

M−1∑u=0

xi,u ≤ 1, ∀i

(4)

Essentially, the first constraint in (4) assures all userthroughputs, which are functions of channel quality as well asMAI, are higher than ε which to be maximized. In addition,constraint (b) allows each subchannel be assigned at most toone UT, or left unmodulated and thus set as a GB. Note thatthe instant SINR γi,u now takes the following form.

γi,u =PRXi,u

σ2 +∑∀u′ 6=u

∑∀j 6=iMAI

j,u′

i,u xj,u′

(5)

As it can be seen, two aforementioned trade-offs are bothtackled in (4), therefore this OP can theoretically offer theoptimal solution. However, due to several mathematical dif-ficulties (including the quadratic term, non-linear functionFsinr2rate(.), xj,u′ in the denominator), the basic OP isconsidered as non-continuous (integer), non-linear, non-convexand NP-hard (see [10] for the mathematical proof for asimilar case). To the best of our knowledge, this complicatedOP has never been successfully solved either analytically ornumerically.

B. Advanced max-min user throughput OP

In this subsection, we propose a novel max-min userthroughput OP in (4), which is numerically solvable. To dothat, apart from xi,u, we introduce new auxiliary optimizationvariables, which are continuous variable Ωi,u standing for the

throughput of subchannel i of UT u, and binary variables zi,u,lindicating if the ACM scheme is chosen (true) or not (false).Then, OP in (4) can be transformed into (6).

max ε

s.t. a)

Nsch−1∑i=0

xi,uΩi,u ≥ ε , ∀u

b)Ωi,u ≤L∑l=0

zi,u,lBl ,∀i, u

c)

L∑l=0

zi,u,lT hi,u,l ≥(∑

j

∑u′

MAIj,u′

i,u xj,u′)

,∀i, u

d)

L∑l=0

zi,u,l = 1 ,∀i, u

e)∑u

xi,u ≤ 1 ,∀i

(6)

where T hi,u,l = (10(γi,u−Thl)/10 − 1) and γi,u is the signalto noise (SNR) of subchannel i of UT u.

Proposition 1: The OP of (6) is equivalent to the OP of (4).

Proof The proof is presented in Appendix.

The advanced max-min user throughput OP shown in (6),which is referred as OP1, is a non-convex Mixed Inte-ger Quadratically Constrained Problem (MIQCP). Since thequadratical term xi,uΩi,u involves binary variable xi,u, OP1is supposed to be transformed to a convex MIQCP and, thus,solved by an optimizer such as ILOG CPlex or Gurobi.

The problem is solvable but computationally complex. Tosee this, consider that in general, since total number ofsubchannel is Q and each subchannel can be assigned to oneof M UTs or set as GB, the total number of possibilities ofallocation is computed as (M + 1)Nsch . Let us consider atypical IEEE802.16m system as an example, where there aretotal 16 subchannels (i.e. Nsch = 16). Hence, even with asmall number of UTs, the searching space is still extremelylarge. There are about 152 billions possibilities as M = 4.Roughly speaking, OP1 might require a brutal computation.

C. Suboptimal solutions

In this subsection, we investigate there suboptimal OPsin order to reduce the complexity. The first suboptimal OP(referred as OP11) is based on the chunking scheme, whereNck adjacent subchannels are grouped into a chunk. Con-sequently, the formulation of OP11 is similar to (6) exceptthat number of frequency sub-bands equals Nsch/Nck and i, jare now replaced by chunk indices. Although, chunking canonly provide suboptimal solutions, the searching space nowis greatly reduced to (M + 1)Nsch/Nck . The second way isto relax some variables in OP1. To relax OP1, we introduceOP12, in which zi,u,l is now defined as continuous variable,instead of integer in (6). This might alleviate the difficulty ofOP1 but leads to the sub-optimal resource allocation. Finally,

we come up with the concurrent optimization model (OP13),where a timeout value is defined as the maximum solvingtime available for solver to solve OP1. If the instance of OP1cannot be solved in time, simple heuristics shown in [5], inwhich MAI is not considered, is used.

IV. PERFORMANCE EVALUATION

We numerically evaluate the performance of the proposedapproach via simulations based on the OMNeT++ framework.The parameterization selection shown in Table I is chosenbased on recommendations in [8] for the IEEE802.16m stan-dard. Besides, UTs locates uniformly in the cell.

TABLE ISYSTEM PARAMETERS.

Parameters ValuesNumber of UTs 4Number of subcarriers 128Subcarrier spacing 10940HzNumber of subcarriers per subchannel 8Number of subchannels 16Number of subchannels per chunk 2Power per subcarrier 1mWMS maximal time offset 25µs (See page 803 in [6])MS maximal frequency offset 2000Hz (See page 803 in [6])Cell radius 250mPath loss model COST231 Walfish-IkegamiLog normal shadowing std. dev. 10dBMultipath fading model Jakes’s/Clarke’s modelThermal noise density (as used in [6]) −174dBm/HzPenetration and other losses 10dBDelay spread (rms) 0.251µsReceive Antenna Gain 14dB

Apart from our proposed OPs, we also simulate the heuristicOPs introduced in [5] (referred as OP2) and [4] (referred asOP3) for a comparison with earlier work similarly applyingDRA. While the objective function in OP2 is based on theSNR instead of SINR (i.e. MAI is not considered), OP3 aimsto minimize the maximum of normalized MAI.

Fig. 1. Avg. minimum user throughput

Especially, a simple system (based on IEEE802.16m stan-dard) adopting ECBA to deal with MAI is also simulated.By doing that, we further compare two different approachesdealing with MAI subject to the minimum user throughput.In this ECBA system, the CP is long enough to deal withdelay spread, propagation delay and clock errors. In addition,one third of total subcarriers are for pilots as specified inthe Partially Used Sub-Channelization (PUSC) method in theIEEE 802.16m. Finally, the block-wise strategy is adopted to

Fig. 2. Quartiles of solving time (in second)

statically assign subchannels to UTs. Consequently, we furtherevaluate two cases, referred as ECBA1 and ECBA2. First, theestimation and correction is assumed to be perfect in ECBA1,thus no residual time and frequency offsets exist. Second, thereis however always a chance that estimation is not perfect [9],which leads to a residual frequency offset. Thus, in ECBA2,we assume the residual frequency offset is 10Hz. (Note thatthe Doppler shift for the velocity of 30km/h is about 70Hz.)

We simulate in total 20 runs, and total 100 uplink frames perrun are conducted. For each uplink frame, at identical systemstatus, the ECBA systems are simulated, and instances of OPsare formed and sent to optimization solvers. Particularly, allOPs are solved by Gurobi except for OP2, which is solved byILOG CPLex due to the existence of logical expressions. RAschemes achieved at the output of the optimization solvers areused to calculate user throughputs.

Figure 1 shows the minimum user throughput achieved bydifferent OPs as well as the simple system based on ECBA.The two most left columns illustrates the comparison of OP1and ECBA1 in the idealized scenario. As it can be seen, OP1provides a significant gain (about 26%) compare to ECBT1.On the right, under the assumption of the residual offsetaccording to the literature, novel DRA approach offers thepotential to improve the minimum user throughput by 25%compared to ECBA2. Furthermore, among proposed OPs, theOP1 provides a great improvement compared to OP2 and OP3equivalent to about 300% and 129%, respectively. Thereforeby using optimal RA schemes, the system performance canbe greatly improved subject to the desired throughput goal.In addition, the chunking approach OP11 and the concurrentOP13 also provide improvement (190% and 115% comparedto OP2 and OP3, respectively) but the relaxation of OPvariables in OP12 leads to poorer performances.

We further investigate the complexity of OPs with regard tothe average solving time as shown in Figure 2. In general, thedistribution of solving time have heavy tails, thus the quartileis used instead of mean values with confidence intervals. Asa result, OP11 might be a good suboptimal solution, since itcould be solved much faster than OP1 (i.e. the median valueof OP11 is less than 0.1s equal 10% of the one of OP1) asstill able to provide comparable throughput gain.

To have an insight about DRA’s performance, we investigatethe utilization of the frequency and multiuser diversities byquantizing the number of GBs and the number of heteroge-neous junctions (HJ), which is defined as the border between

OP1 OP11 OP12 OP13 OP2 OP3 0

1

2

3

4

Avg. num

ber

of G

B

(a) Avg. no. of GBs

OP1 OP11 OP12 OP13 OP2 OP3 0

2

4

6

8

10

12

Avg. num

ber

of H

Js

(b) Avg. no. of HJs

0 5 10 150

200

400

600

800

1000

1200

His

togra

m o

f num

ber

of G

B

(c) Hist. of GB in OP1

Fig. 3. Analyis of frequency and multiuser diversities

2 data blocks assigned to 2 different UTs. Figures 3a and3b show the average number of GBs and HJs used by OPs.Furthermore, the histogram of number of GBs of OP1 is shownin Figure 3c. As it can be seen from Figure 3, our proposedOP1 as well as its suboptimal cases OP11 and OP13 exploitbetter frequency and multiuser diversities.

V. CONCLUSION

In this paper, the problem of using dynamic resourceallocation to deal with MAI and simultaneously improveuser throughput is investigated. It was shown that, insteadof large overhead for estimation and correction offsets asused in the common approach ECBA, one can use properRA scheme with shortened overhead and frequency guardbands to mitigate MAI more efficiently. To this purpose, wecome up with an advanced max-min user throughput OP,which can be numerically solved, along with correspondingsimplifications to reduce the complexity. It was shown vianumerical results that the minimum user throughput can besignificantly improved by a better utilization of frequency andmultiuser diversities as well as by the assignment of GBs.Future works involves the extension to multi-cell scenario.

ACKNOWLEDGEMENTS

The authors would like to thank Mr. Chien-Chi Kao forsome useful discussion and a valuable revising work.

APPENDIX

The function Fsinr2rate(γi,u, Perr) is essentially equivalentto Algorithm 1 described as follows:

Algorithm 1 Algorithm for AMC selectionfor (1 ≤ l ≤ L) do

if (Thl[dB] < γi,u[dB]) thenΩi,u = Bl

end ifend for

Furthermore, we have

Thl ≤ γi,u ⇔ Thl ≤ 10log10( PRXi,u

σ2 +∑j,u′ MAI

j,u′

i,u

)⇔ T hi,u,l ≥

∑j,u′

MAIj,u′

i,u

σ2, (7)

where T hi,u,l = 10(PRXi,u /σ2−Thl)/10 − 1.

To make the mathematical reformulation valid, it is neces-sary to add one virtual ACM scheme (the first one) represent-ing the case when γi,u is too small for any ACM schemes,i.e. B0 = 0 as Th0 ≤ γi,u < Th1. Th0 is a sufficientlysmall constant; it has to be smaller than all possible valuesof γi,u. Obviously, only one ACM scheme is chosen foreach subchannel. Consequently, Algorithm 1 can be furthertransformed into two following equivalent equations.

Ωi,u ≤L∑l=0

zi,u,lBl (8)

together with

L∑l=0

zi,u,lT hi,u,l ≥∑j,u′

MAIj,u′

i,u

σ2(9)

Finally, we have the formulation as shown in (6).

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