Proportional Fair Scheduling in Relay EnhancedCellular OFDMA Systems

Woo-Geun Ahn and Hyung-Myung Kim, Senior Member, IEEE

Department of Electrical Engineering and Computer ScienceKorea Advanced Institute of Science and Technology, Daejeon, Republic of Korea

E-mail: {wgahn.hmkim}@csplab.kaist.ac.kr

Fig. 1. Cell structure and resource allocation of the fixed RS based system.

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RH B&+ BHMS MS MS

B&+ Bs-+ RHMS MS MS

BH RS'+ BHMS MS MS

SedDr (a) SedDr (b) SedDr (c)

Let us assume the MQAM systems, then the instantaneous datarate of the user k on subcarrier n can be written as Tk n ==log2{1 + ,~n), where r == -In{5BER)/1.5 [3]. Instantan'eousdata rate of user k is represented by

N

Rk = L wk,n1og2 ( 1 + ')'~n)n=l

and only two-hop link is taken into account as shown in Fig.1. Each RS is located in the outer region of cell area andconnected to BS with a wireless link. It is assumed that threeorthogonal subcarrier sets are defined for the communicationsof users in the outer region. In order to mitigate the inter­RS interference, the subcarrier set to be used in each RS isorthogonally defined as Fig. 1. In other words, three adjacentRSs select the subcarrier set for RS transmission orthogonally,respectively. The subcarriers included in the selected subcarrierset among the three ones are used for RS users and theremained subcarriers are used for BS users.

In practical environments, there may be some interferencefrom the adjacent BSs and/or RSs. In this paper, we use thesignal to noise ratio (SNR) as an information about link qualityunder the assumption that the interference can be included inthe additive white Gaussian noise term.

We define Hk,n as the channel gain of the user k onb · 2su carner n. Let ak,n denote the noise power and Pk,n the

allocated transmit power of the user k on subcarrier n. Then,the SNR is expressed as

I. INTRODUCTION

In mobile communication systems, customers want to usevarious services at a high data rate. However, in currentwireless systems, severe limitations exist in the coverage andin the capacity. Recently, relay station (RS) enhanced cellularsystems have gained many attentions as a method to extend theservice area and increase the throughput of cell-edge users atlow complexity. In this paper, we consider a system employingfixed RSs.

In cellular relaying networks, the user can be communicatewith the base-station (BS) directly or RS relaying can beused for more efficient communications. Most of existingworks for cellular relaying networks concentrate on findingout the routing path of mobile-station (MS) based on themetric corresponding to the effective throughput of the end­to-end link [1], [2]. It is important to determine a properrouting strategy in employing scheduling paradigm since it hasa great amount of effect on the performance such as systemthroughput or fairness of the user throughput.

In this paper, a proportional fair (PF) scheduler in cellularOFDMA system is considered to achieve throughput gainand to guarantee fairness at the same time. The optimizationproblem of the sum of logarithmic user data rate is formulatedin downlink OFDMA systems with fixed relays. Based onthe proposed user routing, we provide an efficient resourceallocation algorithm in PF sense at relaying networks.

The remainder of this paper is as follows. First, we introducea system model and formulate a PF maximization problem inrelaying networks in Section II. In Section ITI, we provide aPF scheduling algorithm based on the user routing. Simulationresults are given in Section IV and some concluding remarksare presented in Section V.

Abstract-We propose an efficient proportional fair (PF)~cheduling algorithm for multi-user OFDMA systems employ­Ing fixed relays. An PF metric maximization problem is firstformulated for relay enhanced OFDMA cellular systems. A two­step.algorithm is then proposed to solve the problem; the userroutIng step and the resource allocation step. The simulationresults confirm the near-optimal performance of the proposedalgorithm in PF sense.

II. SYSTEM MODEL AND PROBLEM FORMULATION

We consider OFDMA based cellular networks employingfixed relays. Three RSs are deployed at each hexagonal cell

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where UB and UR are the user set of BS and RS, respectively.In this subsection, we find out the user set UB and UR whichmaximize the PF metric in (3) and maximally exploit themultiuser diversity gain.

In order to reflect the functionality of the PF scheduling,in the first step, we further assume that the same number ofsubcarriers are assigned to all users belonging to the sameserving station. It is a reasonable assumption since the PFscheduler tends to allocate a fair portion of subcarriers tothe users although the PF scheduling is not a frequency fairscheduling in the strict sense [4]. Let the K B (== n (UB)) bethe number of users in set UB. Then, we set the number ofthe subcarriers allocated for the user k belonging to the BS toNB/KB.

In OFDMA systems, the channel gains of stibcarriers arefluctuated over frequency domains by the multipath fading,which means that the obtainable data rate in each subcarrieris different form each other. By using the SNR averaged outover subcarriers, we can approximate the data rate of user kas

where Ck denotes the set of subcarriers allocated for the userk, Tk ( = log2 ( 1 + '¥' )) the average transmittable rate persubcarrier, and 'Yk the average SNR of user k.

It is required to express the data rate of each user accordingto the routing path. In the systems adopted the multiuserscheduling, the data rate of user can be expressed in termsof the multiuser diversity gain. The multiuser diversity gainis varied according to the number of users to be scheduled.Therefore, it needs to consider the expression of the user datarate taken into account the multiuser diversity gain accordingto the number of users routed to BS or RS.

For the case of the K B BS users, the multiuser diversitygain is given by

KB 1G(KB) = LT'

l=l

From the multiuser diversity gain, the SNR of user k belongingto BS is improved as 'YkG(KB) [5]. Then, from the objectiveof optimization problem (3), PF metric based on the usergrouping can be expressed as

k~/n (;:IOg2 (1 + 'YkG~KB»))

+k~R In (;:IOg2 (1 + 'YkG~KR»)) (7)

where N R (== N - N B) denotes the number of subcarriers forRS and K R ( == n(UR) == K - K B) the number of users in setUR. The user SNR 'Yk is defined as

- _{ 'YkBM' ifkEUB'Yk - r (2TkBRTkRM/(TkBR+TkRM) - 1), otherwise

(8)where the effective SNR of BS-RS-MS link by using theharmonic mean of the per-link throughput is defined for the

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III. AN EFFICIENT PF SCHEDULING FOR RS ENHANCEDCELLULAR SYSTEMS

Achieving the optimal solution of problem (3) is NP-hard.Therefore, in this paper, we propose an efficient sub-optimalsolution to the problem. To make the problem tractable, wedivide the problem into two steps: user routing and resourceallocation. In the first step, serving station of the users isdetermined by considering the link metrics and the multiuserdiversity gain resulted from the scheduling. In the next step, PFscheduling is performed in each serving station. By using thetwo step approach, we simplify the original PF maximizationproblem.

where assignment indicator Wk,n is used. It takes 1 if the nthsubcarrier is allocated to the user k, while 0, otherwise.

It is assumed that the users select the only one servingstation among the BS and RS. We assume that the first N B

subcarriers among the total N subcarriers are used for thetransmissions of users belonging to the BS.

For a relay employing system, an PF metric maximizationproblem can be formulated as

~ax t Pk,lln (~Wk,nrk,n)Pk, k,n,Pk,n k=l n=l

+ Pk,2 ln ( t Wk,nrk,n) (3)n=NB+1

s. 1. Pk == [Pk,l Pk,2] E {[I 0], [0 I]}K ~ K N

L Pk,l L Pk,n ~ PB & L Pk,2 L Pk,n ~ PR

k=l n=l k=l n=NB+1

Pk,n ~ 0 tI k and tI nK

L Wk,n ~ 1 tI n and Wk,n E {O, I} tI k and tj nk=l

where total K users are used. In order to indicate the servingstation of the user k, Pk is introduced. Pk,l is 1 if the userk belongs to the BS, while Pk,2 is 1, otherwise. PB and PR

are the total transmit power of BS and RS, respectively. Thefirst constraint guarantees the only one routing path of eachuser. The second and third conditions are the limited transmitpower constraints of BS and RS. The fourth constraint ensuresthe disjoint allocation of subcarrier.

A. User Routing

It is shown that the optimal power allocation and theequal power allocation have similar performance in OFDMAsystems [3]. This is because the data rate is a logarithmicfunction of the user SNR and the throughput improvement byoptimal approach such as water-filling method is negligibleexcept the low SNR case.

Therefore, for simplicity, we assume that the equal power isallocated for the subcarriers belonging to each serving station.That is

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RS users. The sub-subscripts B, R, and M denote that thevariable is associated with BS, RS, and MS, respectively. Thedouble sub-subscript notation is used to indicate the wirelesslink between two stations. As an example, rkRM denotes theaverage transmittable rate of the link between the RS and theuser k.

In order to maximize the PF metric (7), we need to findout the user set UB and UR. In order to find out the user setoptimally, it is required to search for all possible combinationsof user sets. But, it requires heavy complexity.

If the end-to-end throughput of a RS link is larger than thatof a BS link, it is better to use a RS link to improve the spectralefficiency. Otherwise, a BS link is preferred. If the end-to-endthroughputs of the two links are similar, it could be arguedthat there is no significant performance difference by servingstation selection.

Based on the above descriptions, we simply the optimizationproblem of PF metric (7) as a simple problem of grouping ofusers based on the throughput difference between the BS linkand the RS link. Without loss of generality, we arrange thethroughput difference between BS-MS link and BS-RS-MSlink in a nonincreasing order, which is given by

B. PF Scheduling of BS and RS

After the user sets are determined, PF scheduling is per­formed for the users included in each serving station. Sinceour goal is to present a low complexity PF algorithm in relayenhanced cellular networks, as in step 1, the equal powerallocation for the subcarriers belonging to each serving stationis assumed [6], [7].

In order to maximize the PF metric, subcarrier n is allocatedto user k~ whose achievable rate normalized by the averageuser rate is the best [6], where

k* - Tk,nn - argmax-

R.

k k

Then, the subcarrier allocation indicator, Wk,n, becomes asfollows:

_ {I, if k = k~Wk,n - 0, if k f k~.

After subcarrier n is allocated to user k~, data rate of user k~,

Rk~, is updated as

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Then, based on the throughput difference factors and theobtained K'B, the routing path indicator of the user k, Pk,is given by

where the user index k denotes the k-th largest value amongthe throughput difference factor ~k for 1 ~ k ~ K.

The modified problem (11) is much easier to solve than themaximization problem of (7) since it is reduced to a simple 1­dimensional maximization problem. As a result, the first K Busers among the users ordered by the throughput differencesuch as (10) are selected as BS users and the others RS userswhere

where

ti.k = log2 (1 + "'Yk;M) - log2 (1 + ;Yk;M ) (10)

where ;YkRM is the effective SNR of BS-RS-MS link,r (2rkBRrkRM/(rkBR+rkRM) - 1). In here, if the throughputdifference of the user is negative, it implies that the user isrecommended to communicate via RS relaying.

Under the assumption of K B BS users, let us define'Fk(KB ) = log2 (1 + 'YkG~KB»). Then, the maximizationproblem of (7) can be modified as

maxU(KB ) =KB

KB (N ) K (N )rw;xLIn K: 'Fk(KB ) + L In K:'Fk(KR )k=l k=KB+l

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Until all of the subcarriers are assigned to the users, the abovesubcarrier allocation based on the (13) and (14) is iterativelyperformed.

Computer simulation is based on the OFDMA system withthe radius of lkm. The fixed-RS is located at the 2/3 positionof cell radius. Users are assumed to be uniformly distributedin overall region.

It is assumed that the channel gains of different linksare independent of each other and that the channel gain isinfluenced by the path-loss, shadowing, and multipath fading.For path-loss model, we adopt the typical urban macro-cellscenario of 1ST-WINNER [8]. Then, it is given by

IV. SIMULATION RESULTS

38.4 + 3510g10 (d) + 2010g10(le/5) (16)

where d is the distance from the serving station and the Ieis the operating frequency. We use the Ie of 2.3GHz in thissimulation. ITU pedestrian model-A with 3 km/h is employed.Shadowing is assumed to be lognormally distributed withmean 0 dB and standard deviation 8 dB. We assume thatthe BS-RS link is line-of sight and its SINR is 30 dB. It isassumed that the total transmit power PB and PR are 43 dBmand 40 dBm, respectively. We use the system bandwidth of10 MHz, BER of 10-3 , frame duration of 5 msec, and noisepower spectral density of -174 dBmlHz. In this study, it isassumed that 960 subcarriers among the 1024 subcarriers and25 DL symbols in a frame are used for transmission. After thesubcarriers are allocated in a frame, average user data rate isupdated by a window of 5 frames.

The proposed algorithm is compared with two algorithms,link-optimal routing based PF scheduling algorithm and ex­haustive full-search based PF scheduling algorithm. The rout­ing path of the user k in link-optimal routing based algorithm

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~l ~ ~2 ~ ••• ~ ~K

_ _ { [1 0], if k ~ K nPk - [Pk,! Pk,2] - [0 1], otherwise.

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4

161410 12Total number of users

-e- Link optimal scheme-e- Proposed scheme

. . ... . . . . .. . . .. .. .. ... . ... . .... .. ... .... . .. _ Exhausitive search

0.56L...-..------oL-------L-------I..------L...---.....&.------'4

161410 12

Total number of users

f ( ·1 -e- Link optimal scheme .-e- Proposed scheme 0.58..... Exhausitive search

12,....---~------r------r----r----~---.....,

11 r· · .. ········:-········· .. ·,,.··:-· ·:./: ·-:-·· ···· ·;· : ~~~

11.5t-··,,······························.·········~,·· ..,., .

10.5t-· :.. ····f

Fig. 2. Performance in terms of average PF metric. Fig. 3. System fairness vs. number of users.

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TABLE IGAIN OF THE 5% THROUGHPUT OVER LINK-OPTIMAL ROUTING BASED

SCHEME

Num. of users 4 6 8 10 12 14 16Gain (%) 20.5 23.8 25.8 26.9 26.4 22.8 23.5

is determined as the path having the minimum end-to-end linkmetric in [2], which is given by

. [1 1 1]mIn -- --+-- .TkBM ' TkBR TkRM

In the exhaustive full-search based PF algorithm, all the usercombinations are searched for the best user grouping in step1.

Fig. 2 shows the PF metric versus the number of users.The number of users is the total number of users per cell. Weuse the long-term throughput averaged out over simulationtime. It can be observed that the proposed scheme has nearoptimal PF and outperforms than link-optimal routing basedPF algorithm. Note that the PF metric is decreased when thetotal number of users is large. This is because the throughput ismeasured in Mbps (If the user throughput is below the IMbps,its logarithmic value is negative).

Fig. 3 shows the performance in terms of system fairnesswith respect to the number of users. As a measure of thefairness of resource allocation, we used the Jain's fairnessindex (JFI), which is defined as [9]

JFI = (~Rk) 2 / (K~R~). (18)

From the figure, the proposed algorithm and the exhaustivesearch based PF scheduling scheme have almost similar per­formance. Meanwhile, JF [ for the link-optimal routing basedPF scheduling is lower than the others, which means that thelink-optimal routing based PF scheduler degrades the fairnessof the resource allocation in relay enhanced systems.

The 5th percentile throughput can be regarded as a repre­sentative performance of cell-edge users and is the average

of the lowest 5% throughput of users. In Table 1, the 5thpercentile throughput gain over the link-optimal routing basedallocation scheme is shown. The proposed scheme improvesthe throughput of cell-edge users nearly 25%. Therefore, it canbe said that the proposed algorithm is a good PF scheduler forRS enhanced cellular systems.

V. CONCLUSIONS

In this paper, an efficient PF scheduling algorithm forfixed-RS enhanced OFDMA systems is proposed. The routingpath of each user is first determined in a PF sense andan PF scheduling scheme for users belonging to the sameserving station is performed. The simulation results show thatthe proposed algorithm provides a near-optimal proportionalfairness.

REFERENCES

[1] J. w. Son, w. Y. Jung, and D. H. Cho., "Serving node selection inwireless multi-hop cellular system," in Proc. IEEE Vehicular TechnologyConference (VTC-2006), Sept. 2006, pp. 1-5.

[2] E. Kwon, J. Lee, M. Do, and K. Jung, "Comparison of symmetric andasymmetric routing for fixed two-hop cellular relaying network," IEEECommun. Lett., vol. 11, no. 5, pp. 378-380, May 2007.

[3] J. Jang and K. B. Lee, "Transmit power adaptation for multiuser OFDMsystems," IEEE 1. Select. Areas Commun., vol. 21, no. 3, pp. 171-178,Feb. 2003.

[4] W. Anchun, Shexiaoming, Z. S. X. Xibin, and Y. Yan, "Asymptoticanalysis of fair scheduling in the OFDM systems," in Proc. IEEE PIMRC,Sept. 2003, pp. 1186-1191.

[5] F. Berggren and R. Jantti, "Asymptotically fair transmission schedulingover fading channels," IEEE Trans. Wireless Commun., vol. 3, no. 1, pp.326-336, Jan. 2004.

[6] S. Yoon, Y. Cho, C. Chae, and H. Lee, "System level performance ofOFDMA forward link with proportional fair scheduling," in Proc. IEEEPIMRC, Sept. 2004, pp. 1384-1388.

[7] H. Kim and Y. Han, "A proportional fair scheduling for multicarriertransmission systems," IEEE Commun. Lett., vol. 9, no. 3, pp. 210-212,Mar. 2005.

[8] D. S. Baum et aI., "Final report on link level and system level channelmodel," IST-2003-507581, D5.4 v 1.4 available at <http://www.ist­winner.org/ >.

[9] R. Jain, D.-M. Chiu, and W. Hawe, "A quantitative measure of fairnessand discrimination for resource allocation inshared computer systems,"Technocal Report TR-301, DEC Research Report, 1984.

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