Resource Allocation for Throughput Enhancement in Cellular Shared Relay Networks

Transcription

1 Resource Allocaton for Throughput Enhancement n Cellular Shared Relay Networs Mohamed Fadel, Ahmed Hndy, Amr El-Key, Mohammed Nafe, O. Ozan Koyluoglu, Antona M. Tulno Wreless Intellgent Networs Center (WINC), Nle Unversty, Caro, Egypt Wreless Communcaton Theory Research, Bell Laboratores, Holmdel, NJ 7733, USA Department of Electrcal and Computer Engneerng, The Unversty of Texas at Austn, Austn, TX 7871, USA Emal: {mohamed.fadel,ahmed.hndy}@nleu.edu.eg, {aeley,mnafe}@nleunversty.edu.eg, ozan@austn.utexas.edu, a.tulno@alcatel-lucent.com Abstract The downln frame of a cellular relay networ s consdered, where a shared MIMO decode-and-froward relayng s used to serve the users at the edge of the cell. The relay employs zero-forcng beamformng to manage the nterference among the moble statons (MSs) at the edge of the cell. A non-cooperatve scheme s consdered where there s no coordnaton between the base statons (BSs) and the relay staton (RS), and a power control algorthm for the RS s developed that maxmzes the rate of the relayed users. A cooperatve settng whch allows the coordnaton of a power allocaton between BSs and RSs s also consdered. For ths settng, based on the proposed achevable scheme, an optmzaton formulaton s derved to maxmze the total throughput of the MSs subject to a constrant on the total power of the system. The problem s solved teratvely as a sequence of geometrc programs. Smulaton results are provded showng that a sgnfcant ncrease n the networ throughput can be acheved va the proposed schemes compared to a conventonal cellular system wth no relays. Index Terms MIMO decode-and-forward relayng, cellular systems, power control, convex optmzaton. I. INTRODUCTION Wreless relayng s a promsng technque to enhance the capabltes of cellular wreless networs va ncreasng the data rate and/or robustness aganst channel mparments [1]. Relays are cost-effectve devces that employ only a fracton of the base staton (BS) functons and are not connected to the wred nfrastructure of the cellular networ. In addton, when a shared relay uses multple antennas t can manage the multuser nterference va beamformng leadng to an ncrease n the total throughput of the cellular networ. Several strateges for the deployment of relays n wreless cellular networs have been consdered n the lterature, e.g. one-way, two-way, twopath, and shared relayng []. The shared relay concept was proposed n [3] where a relay s placed at the ntersecton of two transmtters. The shared relay s used to serve the users at the edge of these cells. Snce the RS s n close proxmty to these users, t can satsfy ther data rate demands effcently. Furthermore, the RS can manage the mult-user nterference due to the presence of multple MSs. Several technques have been proposed for managng the mult-user nterference usng relays. For example, a soft frequency reuse-based ntercell nterference coordnaton scheme The wor at Nle Unversty was supported by a grant from the Egyptan Natonal Telecommuncatons Regulatory Authorty. was proposed n [4]. In [5], Kaneo et al. consdered a subchannel allocaton algorthm that s performed at the BS and the RS. A genetc algorthm for optmzng the system parameters was proposed n [6] n order to maxmze the system spectral effcency. These parameters nclude the number of RSs and ther locatons, the frequency-reuse pattern, and the allocated system resources. Furthermore, a dstrbuted power allocaton algorthm usng the framewor of game theory was proposed n [7]. In ths wor, the relays were modeled as ratonal agents engagng n a non-cooperatve game where each relay node tres to maxmze ts ndvdual rate whle treatng the sgnals from the other users as addtve nose. In [8], Chae et al. consdered MIMO relayng wth a sngle MIMO source, a MIMO relay, and multple sngle-antenna destnatons, where the relay smply amplfes and forwards the receved sgnal to the destnatons. The authors of [9] have proposed a scheme that consders both the farness of resource allocaton and the system effcency. Furthermore, the scheme taes nto account that users mght have dfferent servce requrements. In ths paper, we consder a cellular networ wth halfduplex decode-and-forward shared relayng at the ntersecton of each three cells as shown n Fg. 1. Each cell s dvded nto 3 sectors where the BS employs a sngle drectve antenna per sector. The shared relays are equpped wth multple antennas at the ntersecton of the sectors of the three cells, and are used to serve the users at the cell edge. The users n each sector are assgned ether to the BS servng ths sector or to the shared RS based on ther proxmty to the BS or the RS. We focus on the downln frame whch s splt nto two subframes. In the frst subframe, the 3 BSs send the sgnal desred by the users served by relay to the MIMO relay. The shared relay employs zero-forcng (or MMSE) beamformng to decode the sgnals transmtted by the BSs. In the second subframe, the RS also employs zero-forcng transmt beamformng to re-transmt the decoded sgnals to the users at the cell edge. In addton, each BS transmts to ts drect-mode user n the second subframe. Our objectve s to allocate the BSs and RS powers n order to maxmze the total throughput of the system subject to total power constrant on the frame. We frst consder a noncooperatve scheme where there s no coordnaton between the BSs and RS. In ths case, the optmzaton problem reduces

2 Fg. 1. System model. Blac crcles are BSs, green crcles are users, and the blue crcle s a relay node. to a constraned waterfllng power allocaton problem on the RS n order to maxmze the throughput of the relayed users. We also consder a cooperatve scheme where the powers of the BSs and the RS can be jontly allocated subject to a total power constrant on the frame. We derve an teratve algorthm that allocates the power to the BSs and the RS n order to maxmze the total throughput of the MSs. The algorthm depends on solvng a sequence of geometrc programs teratvely. We show through numercal smulatons that the cooperatve scheme outperforms the non-cooperatve one. Nevertheless, both schemes provde sgnfcant performance gans n terms of the total throughput of the networ compared to a conventonal cellular system that does not use relays. Unle [5] and [8], our proposed schemes are pecular n the sense that they requre no more than one resource bloc for all transmssons, nor do they requre spatal dversty or hgh complexty at the end termnals. II. SYSTEM MODEL AND PROPOSED SCHEME Let us consder a sngle hexagonal cluster of a cellular relayng system as shown n Fg. 1. The cluster s dvded nto 3 sectors where each sector s served by a sngle antenna BS,.e., the 3 BSs are placed at the alternate vertces of the hexagon. A sngle MIMO relay wth M r antennas s placed at the center of the hexagon. The MSs n each sector are served by the BS (drect users) or the RS (outer users) based on ther proxmty to the two statons. We consder a cellular system wth frequency reuse factor of 1 and focus on one resource bloc. Ths resource bloc s utlzed by 3 drect mode users (one assocated wth each BS) and 3 outer users that are served by the relay. Hence, each cluster has a total number of 6 sngle antenna MSs, where the th sector contans two MSs; a drect MS, denoted by u, served by the BS of sector, and an outer MS, denoted by e, served by the RS. It s worth mentonng that the scheduler can be optmzed to provde mult-user dversty gan that taes nto account the multuser nterference. However, ths s outsde the scope of ths paper where we focus on nterference management for cellular relay networs. We assume that the cellular system employs tme-dvson duplexng where the upln and downln transmssons occur over the same bandwdth but n dfferent tme slots. Hence, the shared RS can estmate the channel to all the MSs n the cluster wth enough accuracy. For the outer users that communcate wth the RS, ths nformaton can be obtaned by the RS through the plots n the sgnal of the outer users. Also, the RS can overhear the plots transmtted by the drect MSs to ther servng BSs, and hence, can use t to estmate the channel to these termnals. We consder the downln of the cellular system where each frame s dvded nto two subframes. In the frst subframe, the BSs transmt to the RS. The receved sgnal by the RS s gven by y r (t) = h w e (t) + z r (t) (1) =1 where w e (t) s the sgnal transmtted by the th BS to the RS contanng the data for the outer MS e, s the transmt power of the th BS n the frst subframe, h s the M r 1 channel vector between the th BS and the RS, and z r (t) s the relay nose vector. The relay nose s assumed to be Gaussan zero-mean and spatally whte,.e., E { z r (t)z H r (t) } = σri. Here, the notaton A H denotes the conjugate transposton of the matrx A. The relay operates n half-duplex decode-and-forward mode. It employs the 3 M r receve beamformng matrx V (1) to decode the sgnals transmtted by the three BSs. The sgnal to nterference-plus-nose rato (SINR) of the output of the beamformer for the th relayed user n the frst subframe can be wrtten as v (1)H h SINR r = () j v (1)H h j + σ r j=1,j where v (1)H s the th row of the matrx V (1). Although each outer user mght be able to overhear ts desred sgnal w e n the 1 st phase whle beng transmtted to the RS, explotng the overheard message for example va rate splttng or sgnal combnng wll add addtonal complexty to the MS recever. In addton, the SINR of the ln between the BSs and the outer users s expected to be sgnfcantly lower than that of the ln between the RSs and the outer users. As a result, the throughput gan that can be acheved by overhearng the messages durng the frst phase s very small. Consequently, no form of sgnal combnng or successve decodng at the MSs s adopted n the proposed scheme. In the second subframe, the relay transmts to the outer MSs and the BSs transmt to the drect-mode MSs. Let V () = [v () 1, v(), v() 3 ] denote the transmt beamfomng matrx of the RS n the second subframe. Note that the transmt beamformng vectors are normalzed such that v () = 1. Therefore, the sgnal transmtted from the RS n the second subframe can be expressed as x r (t) = =1 v () w e (t) (3) where s the power used by the RS to transmt the message of the th outer MS, e. Concurrently, each BS transmts the

3 sgnal ntended to ts drect user. The sgnal transmtted by the th BS to ts drect user s gven by x u (t) = w u (t) (4) where w u (t) s the sgnal carryng the data for the drect MS of the th BS and s the power transmtted by the th BS n the second subframe. As a result, the sgnal receved at the th outer user s gven by y e (t) = g H (e x,r) r(t) + g H (e x,s) u(t) + z e (t) (5) where x u (t) s the vector contanng all the sgnals transmtted from the 3 BSs n the second subframe,.e., x u (t) = [x u1 (t), x u (t), x u3 (t)] T, g (e,r) s the M r 1 channel vector between the relay and the th outer user, g (e,s) s the channel vector between the BSs and the th outer user, and z e (t) s the zero-mean Gaussan nose generated at the th relayed user whose varance s gven by σe = E { z e (t) }. As a result, the receved SINR of the th outer MS can be expressed as SINR e = j g H (e,r)v () j j=1,j g H (e,r) v() + =1 g(e,s ) (6) + σe where g (e,s ) s the th element of g (e,s). On the other hand, the sgnal receved at the th drect user s gven by y u (t) = g H (u x,s) u(t) + g H (u x,r) r(t) + z u (t) (7) where g (u,s) s the channel vector between the BSs and the th drect user, g (u,r) s the M r 1 channel vector between the relay and the th drect user and z u (t) s the nose generated at the th drect user whch s also assumed to be zero-mean Gaussan wth varance σu. As a result, the receved SINR at the th drect user can be expressed as SINR u = j g H (u,r) v() j j=1 + g (u,s ) g(u,s ) =1, (8) + σu where g (u,s ) s the th element of the g H (u,s) row vector. III. OPTIMIZATION FORMULATION In ths secton, we consder the problem of desgnng the relay beamformng matrces,.e., V (1) and V (), and allocatng the power to the BSs and the RS n the two subframes. The desgn objectve s to maxmze the sum rate of the MSs. Snce we compare the performance of the proposed algorthms wth a conventonal cellular system wth no relays, for the sae of farness, we assume that the total power budget consumed per cell n each frame s gven by P 1 max. Hence, we can wrte the relay beamformng and power allocaton problem as { max,, } =1 =1 mn {R e,1, R e,} + R u + + P max (9) where R e,1 and R e, are the rates of the th outer user n the frst and the second subframes, respectvely, whereas R u 1 In the non-cooperatve scheme, we assume that each transmttng termnal has an nstantaneous power constrant and the total power P max s dvded equally between the transmttng termnals. s the rate of the th drect-mode user and P max denotes the total power budget of the system per frame. We propose two schemes to solve ths optmzaton problem. The frst scheme assumes that there s no coordnaton between the transmttng termnals (BSs and RS) whle the other scheme consders the case when the shared relay can coordnate ts transmsson power wth the BSs. A. Non-cooperatve scheme In ths scheme, we assume that there s no coordnaton among the BSs and/or the RS. As a result, the power s dvded equally between the transmttng termnals n the two subframes. Hence, n the frst subframe the transmsson power of the th BS s gven by = P max /9. In the next subframe, the transmsson power of the th BS s also gven by = P max /9, whereas, the maxmum transmsson power of the RS s constraned such that P max 3. (1) =1 Frst, we consder the desgn of the beamformng vectors of the RS. In order to enable the shared relay to handle the mult-user nterference of the three cells, we assume that the number of RS antennas s larger than or equal to the number of spatally-multplexed MSs n the three cells,.e., M r 6. Assumng that the BSs employ Gaussan codeboos, the rate of transmsson from the th BS to the RS n the frst subframe s gven by R e,1 = log (1 + SINR r ). Hence, ths rate can be maxmzed by selectng the receve beamformng vectors of the RS such that the output SINR s maxmzed [1] by settng v (1) = j=1,j j h j h H j + σri 1 h. (11) In the second subframe, the relay beamformng vectors are selected accordng ( to the zero-forcng (ZF) crteron. Let ṽ () = I G ( ) ) 1 H GH G G g (e,r) (1) { where the columns of the } M r 5 matrx G are gven by {g(e,r)}, {g (u,r)} 3 =1, the relay beamformng vector for the th MS s then gven by v () = ṽ () / ṽ () (13) and hence, the relay does not cause any nterference to the outer MS or drect MSs nsde the cluster. Our objectve now s to determne the power allocated to the streams transmtted by the RS durng the second subframe n order to maxmze the sum rate of the outer MSs subject to a power constrant on the RS. Hence, the optmzaton problem n (9) reduces to max { } 3 =1 =1 =1 R e, Pmax 3 R e, R e,1 = 1,..., 3 (14) where R e, = log(1 + SINR e ). Note that the last constrant n (14) s due to the fact that the maxmum rate that can

4 be acheved by the outer MSs s constraned by the rate transmtted from the BS to the RS n the frst subframe. Substtutng wth (13) n (6), we can wrte (14) as max { } 3 =1 log 1 + =1 log 1+ =1 =1 =1 g H (e,r) v() g (e,s ) g H (e,r)v () g (e,s ) + σe + σe Re,1 Pmax 3. (15) Note that the rates R e,1 are fxed as they are determned by the powers allocated to the BSs durng the frst subframe. The above problem s a constraned waterfllng problem [1] that can be solved effcently usng nteror-pont methods [11]. B. Cooperatve scheme Due to the absence of any form of coordnaton between the RS and the BSs, the transmsson powers of dfferent statons are determned ndependently. Ths leads to a loss of performance, e.g., snce the rates of the outer MSs are completely determned by the transmsson power of the BSs n the frst subframe. In ths subsecton, we assume that the RS and the BSs can coordnate ther transmsson powers jontly n order to maxmze the total throughput of the networ. The RS taes over the tas of coordnatng wth the BSs n order to effcently utlze the power budget. It s worth mentonng that the only requrement of the cooperatve scheme over the non-cooperatve one s the capablty of the RS to obtan the gans of the channels between the drect users and the BSs. Ths nformaton s avalable n the feedbac nformaton (such as the channel qualty ndcator (CQI)) sent by each drect user to ts BS n control messages. Thereby, f the RS successfully overhears these control messages, the cooperatve scheme can be appled wthout the need of any addtonal feedbac messages between the RS and the BSs. Snce the man functon of the shared relay s to manage the mult-user nterference, the RS employs ZF receve beamformng n the frst subframe by selectng the beamformng vectors as v (1) = ( I H ( ) ) 1 H HH H H h, (16) where H s the M r matrx whose columns are {h }. Also, n the second subframe, the RS employs the ZF transmt beamformng vectors of (13). Usng (13) and (16), we can wrte the optmzaton problem n (9) as max Π 3 =1 (1 + τ ) (1 + SINR u ) v (1)H σr h τ, =1 =1, =1 g H (e,r) v() g(e,s ) τ, + σe g(u,s ) g(u,s ) + + SINR u, + σu P max (17) where we have used the auxlary optmzaton varables {τ, SINR u } 3 =1 n addton to the orgnal varables {,, } 3 =1. Note that on tang the exponentaton for the orgnal optmzaton problem n (9), the log terms are removed and wll result n the multplcaton form shown above. Now, the constrants n the problem can be wrtten n the form of posynomal nequalty constrants,.e., f (z) 1 where z s a vector contanng the optmzaton varables. However, the objectve functon s not a monomal [11], and hence, the optmzaton problem n (17) s not an extended Geometrc Program. Hence, n order to be able to solve (17) effcently, we approxmate the objectve functon as [1] 3 3 (1 + τ ) (1 + SINR u ) c (τ ) λe (SINR u ) λu (18) =1 =1 where c > and {λ u, λe }3 =1 are constants and are gven by λ e τ =, 1 + τ λ u SINR u =, 1 + SINR u 3 =1 c = (τ + 1) (SINR u + 1) 3 =1 (τ. (19) ) λe (SINR u ) λu Usng the above approxmaton n (18), the optmzaton problem n (17) s solved wth a sequence of GPs va the followng teratve procedure: Intalze c and {λ u, λe }3 =1 randomly. whle target accuracy s not reached do solve (17) usng the approxmaton n (18). Update c and {λ u, λe }3 =1 from (19). end Note that as proven n [1], the objectve functon n (17) ncreases after every teraton and the algorthm s guaranteed to converge to a local optmum pont. However, convergence to a global optmum pont s not guaranteed as the problem s not convex. IV. NUMERICAL SIMULATIONS In ths secton, we present some numercal results to demonstrate the performance of the proposed schemes. Smulaton results are averaged over 1 runs. In each run, each channel coeffcent s gven by A G S G P L G H F where H F denotes the

5 1 4 CDF Cooperatve Scheme (Drect User Rates) Noncooperatve Scheme (Drect User Rates) System wthout relays (Drect User Rates) Cooperatve Scheme (Edge User Rates) Noncooperatve Scheme (Edge User Rates) System wthout relays (Edge User Rates) Throughput (bts) Cooperatve Scheme Noncooperatve Scheme System Wthout Relays Sum Rates P max (db) Fg.. Emprcal CDF of the throughput of one cluster at P max = 4 db. Fg. 3. Total throughput of one cluster versus frame power budget P max. fast fadng coeffcent of the channel, whle A G, S G and P L G represent the antenna pattern gan, the shadowng gan and the pathloss gan, respectvely. The relay has omn-drectonal antennas whose gan s unty,.e, A G = 1, whle the BS employs a drectonal antenna n each { sector wth gan (n decbels) gven by A L ( θ) = mn 1 ( θ ) }, θ 3dB where θ 3dB = 7 corresponds to the 3dB beamwdth of the BS antenna, and θ s the angular drecton of the MS wth respect to the md-sector drecton. The shadowng gan, S G, s modelled as log-normal wth standard devaton 8 db for the channel between a BS and MS and the channel between the RS and the MS, whereas the standard devaton of the shadowng loss for the channel between the BS and the RS s 6 db. The path loss, P L G, s calculated accordng to the IEEE 8.16j model [13], where we assume the BS and relay antennas are 3 m and 15 m hgh, respectvely, and the MS antennas are located at a heght of 1 m. The fast fadng coeffcent, H F, s modelled as zero-mean complex Gaussan random varable wth unt varance. In ths smulaton, we assume the cell radus s 1 m. The relay has M r = 6 antennas. The nose varances, σr, σe and σu, are assumed to be 144 db. In each run, we generate 6 users randomly n each hexagonal cell such that 1 MS exsts n each subsector of Fg. 1. We compare the proposed schemes wth a conventonal cellular system that uses tme-dvson multplexng and does not employ any relays. For ths system, each BS serves an MS n one subframe and the power s dvded equally between the 3 BSs. Hence, = = Pmax 6. The frst subframe s assgned to serve the 3 users n the subsectors close to the BSs whle n the second subframe the three outer users are served. Frst, we consder a system composed of only one cluster. Fg. shows the cumulatve dstrbuton functon (CDF) of the total drect and outer users throughput acheved usng the proposed schemes for a total power budget per frame gven by P max = 4 db, where 4 channel realzatons are used. We note that, for outer users, there s a crossng n the CDF acheved by the two proposed schemes. Ths can Throughput (bts) Cooperatve Scheme (Total Throughput) Noncooperatve Scheme (Total Throughput) System Wthout Relays (Total Throughput) Cooperatve Scheme (Outer Users Throughput) Noncooperatve Scheme (Outer Users Throughput) System Wthout Relays (Outer Users Throughput) P max (db) Fg. 4. Total throughput of one cluster versus frame power budget P max for a system composed of 19 clusters. be explaned that for outer users, the cooperatve scheme has hgher varaton n throughput wth respect to the channel condtons. Ths s because the cooperatve scheme jontly optmzes the transmtted power for the outer users n the two phases. Hence, t s relatvely more senstve to channel varatons than the non-cooperatve scheme, whch optmzes the nd phase power only, resultng n a hgher varance of the acheved rates. Fg. 3 shows the sum rates of the system obtaned by the cooperatve and the non-cooperatve schemes versus dfferent values of frame power constrant P max. We can see from the two fgures that the cooperatve scheme outperforms the non-cooperatve one and that both schemes yeld sgnfcant performance mprovements over a conventonal system wthout relays. Next, we consder a system consstng of 19 clusters n a wrap around arrangement where all the clusters use the same frequency,.e., a unty frequency reuse factor s employed. Note that the proposed schemes allocate the power to the termnals of each cluster ndependently and do not tae nto account the out-of-cluster nterference. Fg. 4 shows the total throughput of the central cluster versus P max. It also shows the throughput of the outer MSs. We can see from ths fgure

6 Objectve Functon Objectve functon of problem (17) Approxmated Objectve functon usng (18) Iteraton ndex Fg. 5. The orgnal and approxmated objectve functons versus teraton ndex of the proposed teratve algorthm at P max = 5 db. Number of Iteratons P max (db) Fg. 6. Average number of teratons of the proposed teratve algorthm versus frame power budget P max. that the out-of-cluster nterference reduces the throughput of the networ. Nevertheless, the performance of the proposed schemes s sgnfcantly superor to that of a conventonal system whch does not employ any relays. We can also see from ths fgure that the cooperatve scheme enhances the rates of the outer users sgnfcantly. Fnally, we nvestgate the convergence of the teratve algorthm. Fg. 5 shows the orgnal objectve functon n (17) and the approxmated one n (18) at each teraton of the teratve algorthm. The value of P max s chosen as 5. We can notce that both functons ncrease wth each teraton tll the approxmate functon, whch s consdered a lower bound, becomes wthn.1 tolerance from the orgnal one, and hence, the algorthm termnates provdng the soluton of the approxmated problem whch s very close to the soluton of the problem n (17). Fg. 6 shows the average number of teratons requred for convergence of the teratve algorthm versus the dfferent values of frame power constrant P max. The algorthm termnates and convergence s declared when the approxmaton n (18) becomes wthn.1 tolerance. Smulaton results are averaged over 1 channel realzatons. We can see from ths fgure that the number of requred teratons does not ncrease sgnfcantly wth ncreasng P max and that at most 7 teratons are suffcent for convergence. V. CONCLUSION We have nvestgated the use of shared relayng n cellular networs n order to maxmze the system throughput by managng the nterference among the users of the cell. We have consdered a non-cooperatve scheme where there s no coordnaton between the BSs and/or the relay. For ths scheme, we have proposed a power allocaton algorthm for the relay that can be consdered a constraned waterfllng algorthm. We have also proposed a jont power allocaton algorthm for the BSs and the RS, where ths coordnaton does not mply the use of the networ bachaul. The proposed algorthm obtans the power allocaton by solvng a sequence of Geometrc Programs that s guaranteed to converge. In addton, the complexty of the proposed schemes s not prohbtvely hgh. We have shown through numercal smulatons that the performance of the cooperatve scheme s superor to that of the non-cooperatve one. We have also shown that addng relays to the system enhances the system performance n terms of total throughput by ncreasng the cell-edge user rates. REFERENCES [1] A. J. Paulraj, D. A. Gore, R. U. Nabar, and H. Bölcse, An overvew of MIMO communcatons A ey to Ggabt wreless, Proc. IEEE, vol. 9, pp , Feb. 4. [] S. W. Peters, A. Y. Panah, K. T. Truong, and R. W. Heath, Relay archtectures for 3GPP LTE-advanced, EURASIP Journal on Wreless Communcaton and Networng, vol. 9, pp. 1 14, March 9. [3] A. Tajer and A. Nosratna, A broadcastng relay for orthogonal multuser channels, IEEE Globecom, Nov. 6. [4] J. Lu, D. Wang, J. Pang, J. Wang, and G. Shen, Inter-cell nterference coordnaton based on soft frequency reuse for relay enhanced cellular networ, Proc. IEEE Personal, Indoor and Moble Rado Communcatons, 1. [5] M. Kaneo and P. Popovs, Rado resource allocaton algorthm for relay-aded cellular OFDMA system, n Proceedngs of the IEEE Internatonal Conference on Communcatons (ICC 7), Glasgow, Scotland, UK, June 7. [6] W-H Sheen, S-J Ln, and C-C Huang, Downln optmzaton and performance of relay-asssted cellular networs n multcell envronments, IEEE Trans. Veh. Technol., vol. 59, no. 5, June 1. [7] S. Ren and M. van der Schaar, Dstrbuted power allocaton n multuser mult-channel cellular relay networs, IEEE Transactons on Wreless Communcaton, vol. 9, no. 6, June 1. [8] C. Chae, T. Tang, R. W. Heath, and S. Cho, Mmo relayng wth lnear processng for multuser transmsson n fxed relay networs, IEEE Transactons on Sgnal Processng, vol. 56, no., pp , 8. [9] K. Chen, B. Zhang, D. Lu, J. L, and G. Yue, Far resource allocaton n OFDMA two-hop cooperatve relayng cellular networs, Proc. IEEE Vehcular Technology Conference, Sept 9. [1] D. Tse and P. Vswanath, Fundamental of Wreless Communcaton, Cambrdge Unversty Press, Cambrdge, UK, 5. [11] S. Boyd and L. Vandenberghe, Convex Optmzaton, Cambrdge Unversty Press, Cambrdge, UK, 4. [1] J. Tadrous, A. Sultan, M. Nafe, and A. El-Key, Power control for constraned throughput maxmzaton n spectrum shared networs, IEEE Globecom, Dec. 1. [13] Mult-hop relay system evaluaton methodology (Channel model and performance metrc), IEEE 8.16j-6/13r3 Std., Feb. 7.