Power Control for Full-Duplex Relay-Enhanced Cellular Networks With QoS Guarantees

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1 SPECIAL SECTION ON FUTURE NETWORKS: ARCHITECTURES, PROTOCOLS, AND APPLICATIONS Receved January 9, 07, accepted February, 07, date of publcaton March 5, 07, date of current verson Aprl 4, 07. Dgtal Object Identfer 0.09/ACCESS Power Control for Full-Duplex Relay-Enhanced Cellular Networks Wth QoS Guarantees XIAOYAN HUANG, KUN YANG, Senor Member, IEEE, FAN W, AND SUPENG LENG, Member, IEEE Unversty of Electronc Scence and Technology of Chna, Chengdu 673, Chna Unversty of Essex, Colchester, CO4 3SQ, U.K. Correspondng author: X. Huang Ths work was supported n part by the Natonal Natural Scence Foundaton of Chna under Grant and n part by the Fundamental Research Funds for the Central Unverstes under Grant ZYGX05J004. ABSTRACT Full-duplex FD has emerged as a new communcaton paradgm wth the potental advantage of enhancng the capacty of the wreless communcaton systems. In ths paper, we consder an FD relay-enhanced cellular network, wheren the resdual self-nterference, the uplnk downlnk nterference, as well as the relay-access-lnk nterference are the vtal restrctons to network performance. To ths end, we nvestgate power control desgn for the FD relay-enhanced cellular networks, so as to maxmze the system spectral effcency whle fulfllng the qualty of servce QoS requrements of both the uplnk and downlnk user equpments UEs. We characterze the propertes of the optmal transmt power allocaton, and propose a power control algorthm based on sgnomal programmng to coordnate the transmt power of the uplnk UE, base staton, and relay statons to mtgate the nterference. Meanwhle, we also derve the closed-form optmal transmt power allocaton for the conventonal half-duplex HD transmsson mode. Moreover, we conduct extensve smulaton experments to study the network-level gan of the FD mode over the HD mode n the relay-enhanced cellular networks. Smulaton results demonstrate that FD relayng outperforms HD relayng on mprovng the spectral and energy effcency, as well as provsonng QoS guarantees for both the uplnk and downlnk users. INDEX TERMS Wreless networks, full duplex, relayng, power control, spectral effcency. I. INTRODUCTION Wreless full-duplex FD communcaton allows a node to transmt and receve smultaneously on the same frequency band, such that the lnk capacty can be doubled compared to the conventonal half-duplex HD communcaton. Meanwhle, wreless relayng has evolved from the early theoretc analyses to a practcal stage n cellular networks. Deployng relay statons RSs n cellular networks can acheve sgnfcant performance mprovement, ncludng cell capacty enhancement, cell coverage extenson, and transmt power savng. Therefore, the combned applcaton of the two technologes n cellular networks should be a promsng way to acheve hgh spectral effcency. In the new FD relayenhanced cellular network archtecture, the base staton BS and nfrastructure RSs work n FD mode, whle the user equpments UEs stll work n HD mode wth the consderaton of ther capabltes n practcal systems. To mprove the qualty of users experence, the UEs wth good channel condtons, e.g., the cell-center users, can be served by the BS drectly, whle the ones wth unfavorable channel condtons, e.g., the cell-edge users, can be served va the assstance of RSs. It s worthwhle to pont out that there exsts three types of nterference n the FD relay-enhanced cellular networks, whch are the vtal restrctons to network performance. Frst of all, wreless FD communcaton brngs n the self-nterference between the smultaneous transmsson and recepton paths at each FD node, henceforth self-nterference cancellaton s a key challenge n realzng the FD nodes. In addton, another key challenge for the FD cellular networks s the uplnk-downlnk nterference [] between the concurrent uplnk and downlnk transmssons takng place wthn a sngle cell or multple neghborng cells. Takng a sngle cell wth a FD BS and several HD UEs for nstance, the FD BS can communcate wth an uplnk UE and a downlnk UE smultaneously on each frequency band. In ths case, the uplnk UE nterferes wth the recepton of the downlnk UE, potentally nullfyng the benefts from FD communcaton. The uplnk-downlnk nterference becomes more severe VOLUME 5, IEEE. Translatons and content mnng are permtted for academc research only. Personal use s also permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton. 4859

2 n multcell networks or when the UEs also work n FD mode. Furthermore, when wreless FD relayng s appled, there also exsts the relay-access-lnk nterference between the concurrent relay-lnk and access-lnk transmssons due to the smultaneous transmsson and recepton at the FD RS, whch drectly affects the achevable end-to-end data rate of the two-hop relayng communcaton. More mportantly, wth both the BS and RSs workng n FD mode, the relayaccess-lnk nterference and the uplnk-downlnk nterference nterweave wth each other, thus resultng n an extremely complcated nterference envronment for the FD relayenhanced cellular networks. Apparently, the overall performance of the FD relayenhanced cellular networks could be degraded sgnfcantly f the aforementoned three types of nterference are not managed properly. The self-nterference at each FD node may be easly addressed snce the nterference nformaton s locally avalable at the node. So far, substantal works have focused on addressng the self-nterference through both analog [] [3] and dgtal [4] cancellaton schemes. On the contrary, mtgatng the uplnk-downlnk nterference and the relay-access-lnk nterference s much more challengng, as t nvolves the coordnaton among dstrbuted nodes who couldn t share data nformaton wthout damagng ther nformaton securty or sacrfcng bandwdth resource. Therefore, effcent nterference mtgaton scheme especally addressng the uplnk-downlnk nterference and the relay-accesslnk nterference n network scale plays an essental role n reapng the potental benefts of wreless FD communcatons and wreless relayng n practcal systems. In the lterature, wth the development of the selfnterference cancellaton technology, research focus has shfted to addressng the ssues related to the wreless FD systems. The authors n [5] and [6] nvestgated the throughput of the wreless networks wth FD rados usng stochastc geometry. The authors n [7] studed the network-level capacty gan of FD communcaton over HD communcaton. The authors n [8] desgned a FD capable meda access control MAC protocol based on the IEEE 80. MAC protocol. The authors n [9] proposed to use spatal nterference algnment to address the uplnk-downlnk nterference and characterzed the scalng of FD s multplexng gan n multcell FD networks. The authors n [0] devsed a queue-length based carrer sense multple access CSMA-type schedulng algorthm for the wreless networks wth FD cut-through transmsson. Meanwhle, wreless FD relayng has also attracted consderable research attentons n both academa and ndustry. The authors n [] nvestgated the end-to-end capacty of the two-hop FD relayng channels wth decodeand-forward and amplfy-and-forward relay, respectvely. The authors n [] studed the outage probablty of the end-to-end communcaton lnk n the multhop FD relayng systems wth decode-and-forward relays. The authors n [3] nvestgated the outage probablty and ergodc capacty of the FD two-way amplfy-and-forward relayng channels. Then the authors n [4] developed an opportunstc mode selecton scheme for the two-hop relayng systems, wheren the relay swtches opportunstcally between FD and HD modes so as to optmze the spectral effcency. The authors n [5] studed the optmal and suboptmal relay selecton schemes for the two-hop FD amplfy-and-forward relayng systems. The authors n [6] proposed a hybrd relay selecton strategy for the two-hop FD decode-and-forward relayng systems to mnmze the total power consumpton, where the selected relay can work n FD or HD mode accordng to the channel condtons. The authors n [7] proposed a jont relay and antenna selecton scheme for the two-hop FD amplfyand-forward relayng systems, so as to maxmze the end-toend sgnal-to-nterference and nose rato. The authors n [8] proposed the best-worst-channel relay selecton scheme for the FD two-way amplfy-and-forward relayng systems. The authors n [9] derved the upper and lower bounds on the end-to-end achevable rate of the FD MIMO decode-andforward relayng systems wth the assumpton that the selfnterference can be cancelled completely. Note that these exstng works mostly concentrate on the theoretcal analyss of system performance, mode selecton, and relay selecton n the FD systems, as well as power control n the two-hop FD relayng lnks. However, network-level nterference mtgaton for the FD relayng networks has been rarely dscussed. Motvated by the precedng works, we focus on QoSaware nterference mtgaton for the FD relay-enhanced cellular networks. In partcular, we nvestgate power control desgn for the system spectral effcency maxmzaton problem wth QoS guarantees n the FD relay-enhanced cellular networks. Then man contrbutons of ths paper are as follows. We consder a FD relay-enhanced cellular network, wheren both the BS and nfrastructure RSs enable smultaneous transmsson and recepton on the same frequency band. In ths scenaro, the nterference envronment s exceptonally complcated. The resdual self-nterference, the uplnk-downlnk nterference, and the relay-access-lnk nterference are the vtal essental restrctons to the network performance. We jontly optmze the transmt power of the uplnk UE, BS, and RSs, so as to maxmze the system spectral effcency whle fulfllng the QoS requrements of the uplnk and downlnk UEs. We characterze the propertes of the optmal transmt power allocaton, and propose a sgnomal programmng SP based power control algorthm to obtan the globally or at least locally optmal power allocaton. For comparson, we also derve the closed-form optmal transmt power allocaton for the conventonal HD transmsson mode. We conduct extensve smulaton experments to study the effects of dfferent factors on system performance, and demonstrate the network-level gan of FD relayng over HD relayng. The rest of ths paper s organzed as follows. In Secton II, we present the system model and formulate the power 4860 VOLUME 5, 07

3 control optmzaton problem. In Secton III, we elaborate the optmal QoS-aware power control desgn for the FD relayenhanced cellular networks. In Secton IV, we present the optmal power control scheme n the HD transmsson mode. In Secton V, we present smulaton results and performance analyses. In Secton VI, we conclude the paper. FIGURE. Full-duplex relay-enhanced cellular network. II. SYSTEM MODEL AND PROBLEM FORMULATION Consder a FD relay-enhanced cellular network consstng of a FD BS, two FD RSs and two HD UEs, as shown n Fg.. We concentrate on the coverage extenson scenaro n whch the drect source-destnaton lnk s weak and the relay s deployed to help forwardng sgnal wthout havng own data to transmt. In specfc, the uplnk transmts sgnal to the RS, and smultaneously the RS forwards the decoded receved sgnal to the BS. Meanwhle, the BS serves the downlnk va another FD RS,.e., the RS. Wthout loss of generalty, a sngle channel s consdered n our work, snce the case of multple channels can be studed n a smlar manner. In ths case, the uplnk and downlnk transmssons take place on the same channel at the same tme. Consequently, there are three types of nterference n the system,.e., the resdual self-nterference at the FD nodes, the uplnk-downlnk nterference among the concurrent uplnk and downlnk transmssons, as well as the relay-access-lnk nterference between the concurrent relaylnk and access-lnk transmssons, as shown by the dashed arrows n Fg.. Let h,j represent the channel gan of the lnk between nodes and j, and g SI represent the resdual self-nterference channel gan n the FD node due to mperfect cancellaton. The wreless channels are modelled to be frequencyflat and quas-statc. And wth the recprocty of wreless lnks, we assume that h,j h j,. Let P denote the transmt power of node, and σ denote the average power of addtve whte Gaussan nose AWGN of each lnk. Accordngly, the nstantaneous sgnal-to-nterference-plusnose ratos SINRs of the access and the relay lnks n the uplnk transmsson can be respectvely expressed as η UL RS η UL RS BS H R, P U + G R P R + H R,BP B + H R,R P R H B,R P R + G B P B + H B,R P R where H,j h,j /σ and G g SI /σ are the normalzed channel gans, representng channel sgnal-to-nose ratos SNRs. In, the term G R P R represents the resdual self-nterference at the RS, whle the terms H R,BP B and H R,R P R represent the nterference from the BS and RS respectvely. Smlarly, accordng to, the recepton at the BS s nterfered by the resdual self-nterference and the smultaneous transmsson at the RS. In the downlnk transmsson, the nstantaneous SINRs of the access and relay lnks can be respectvely expressed as η DL BS RS η DL RS H B,R P B + G R P R + H R, P U + H R, P R 3 H U,R P R + H U, P U + H U, P R 4 Accordng to 3 and 4, the recepton at the downlnk s nterfered by the smultaneous transmssons at the uplnk and RS, whle the recepton at the RS s also nterfered by the resdual self-nterference n addton to the smultaneous transmssons at the uplnk and RS. Wth the decode-and-forward relayng, the achevable endto-end spectral effcences bps/hz of the uplnk and downlnk UEs are respectvely gven by C UL log C DL log + mn + mn ηue UL, ηrs UL BS ηbs RS DL, ηrs DL Clearly, the overall performance of the consdered FD relay-enhanced cellular network largely depends on the management of the resdual self-nterference, the uplnkdownlnk nterference, and the relay-access-lnk nterference. To ths end, the problem of nterest n ths work s to jontly optmze the power control for the uplnk and downlnk transmssons,.e., to optmze the transmt power of the uplnk, RS, BS, and RS, wth the objectve of maxmzng the overall spectral effcency subject to the QoS requrements of the UEs as well as the ndvdual power constrants of the transmttng nodes. Mathematcally, the optmzaton problem s formulated as follows: P: max P C UL + C DL 5 6 s.t. C:CUE UL C: CUE DL C3: 0 P, {,, B, R } 7 where P P U, P R, P B, P R s the optmzed varable; CUE UL and CUE DL are gven by 5 and 6, respectvely; VOLUME 5,

4 R req and R req are the mnmum data rate requrements of the and, respectvely; s the maxmum transmt power budget of node. Constrants C and C ensure the qualty of the end-to-end uplnk and downlnk transmssons, respectvely. Constrant C3 guarantees that the transmt power of each transmttng node s wthn the maxmum lmt. III. QoS-AWARE POWER CONTROL DESIGN FOR FD RELAY-ENHANCED CELLULAR NETWORKS P s a non-convex optmzaton problem due to the exstence of nterference terms n the nstantaneous SINRs n -4, especally the mn operaton n the objectve functon. Thus, t s extremely dffcult to obtan the optmal solutons of P drectly. In addton, there also exsts the feasblty ssue n P owng to the exstence of the mnmum spectral effcency demands of the UEs. Throughout ths paper, we assume that the set of per-ue mnmum spectral effcency requrement s feasble under the power constrants of the transmttong nodes, so that we only focus on developng transmt power control scheme. A. OPTIMAL TRANSMIT POWER Proposton : If P s feasble, the optmal transmt power vector P has the followng propertes: P must have at least one component equal to. ηue UL P ηrs UL BS P and ηbs RS DL P ηrs DL P hold. Proof: Defne P PU, P R, P B, P R as a feasble P soluton of P, and R C UL P P + CUE DL as the objectve functon of P. From and, for α >, we have ηue UL αp H R,U PU / α +G > R PR +H R,B PB +H R,R PR P ηue UL and ηrs UL BS αp H B,R PR / α +G > B PB +H B,R PR P ηrs UL BS, hence CUE UL αp P > CUE UL. Smlarly, t can be also proven that CUE DL αp P > CUE DL. In summary, we have R αp P > R. Consequently, the overall spectral effcency R can be contnuously mproved by ncreasng all components of P by a factor α, untl some component P hts ts maxmum transmt power budget. Therefore, the optmal soluton P must have at least one component equal to. Assume that P P, P, P U R B, P s the opt- R mal soluton of P wth ηue UL P ηrs UL BS P. a Case : ηue UL P > ηrs UL BS P. Accordng to and, we can get a feasble soluton P P U, P, R P B, P R such that ηue UL P ηrs UL BS P ηrs UL BS P wth P U < P. Thus, we have CUE UL P CUE UL P accordng to 5. On the other hand, snce the components of P and P are the same except that P U < P, we have η DL BS RS P > η DL BS RS P and ηrs DL P > ηrs DL P accordng to 3 and 4. Then, we have CUE DL P > CUE DL P accordng to 6. As a result, we have R P > R P, whch s contradctory to that P s the optmal soluton of P. b Case : ηue UL P < ηrs UL BS P. Accordng to and, as well as the condton for the exstence of a postve root of quadratc equatons, we can get a feasble soluton P P, P U R, P B, P R such that ηue UL P ηrs UL BS P wth P R < P. Moreover, t s readly proven that ηrs UL BS P < ηue UL P ηrs UL BS P < ηue UL P. Thus, we have CUE UL P > CUE UL P. On the other hand, snce the components of P and P are the same except that P R < P, we have ηbs RS DL P > ηbs RS DL P and ηrs DL P > ηrs DL P accordng to 3 and 4. Then, we have CUE DL P > CUE DL P accordng to 6. As a result, we have R P > R P, whch s contradctory to that P s the optmal soluton of P. In summary, the optmal soluton P must satsfy that ηue UL P ηrs UL BS P. Smlarly, t can be proven that P also must satsfy that ηbs RS DL P ηrs DL P. B. SP-BASED POWER CONTROL ALGORITHM To facltate solvng P, we ntroduce an auxlary varable T T, T, such that mn ηue UL, ηrs UL BS T and mn ηbs RS DL, ηrs DL T. Snce the logarthmc functon s a monotonc and ncreasng concave functon, P can be transformed nto the followng problem wth proper algebrac transformatons. P: mn T,P + T + GR P R + H R,BP B + H R,R P R s.t. C: T H R, P U +GB P B +H B,R P R C: T H B,R P R +GR P R +H R, P U +H R, P R C3: T H B,R P B + HU, P U + H U, P R C4: T C5: T Rreq H U,R P R C6: T Rreq C7: 0 P, {,, R, B} 8 Accordng to 8, the objectve functon of P s a rato of a monomal to a polynomal, and all the constrants are polynomals monomals are also polynomals, such that P s a sgnomal programmng SP problem [0]. Followng the 486 VOLUME 5, 07

5 Algorthm SP-Based Power Control Algorthm Input: the normalzed channel gan vector H, the normalzed resdual self-nterference channel gan vector G, the mnmum data rate requrment vector R req, and the maxmum transmt power budget vector. Output: T and P. 3 Intalze T 0 and P 0 by solvng a feasblty problem subject to the same constrants as n P; 4 Let ε 0 4 be the error tolerance; 5 whle T k T k > ε do { 6 Update the coeffcents β k,n } wth 0; 7 Approxmate the denomnator polynomal of the objectve functon by the monomal f k T wth 9; 8 Solve the resultant GP problem wth the objectve functon defned by to obtan T k and P k ; 9 end successve convex approxmaton approach [] and the arthmetc-geometrc mean nequalty [], P can be solved by solvng a seres of geometrc programmng GP problems subject to the same constrants as n P, where the GP problem n each teraton s constructed by approxmatng the denomnator polynomal of the objectve functon by a monomal based on the value of the optmzed varable from the prevous teraton. To be specfc, the denomnator polynomal of the objectve functon n P s denoted as f T + T n u,n T, where u,n T s a monomal. Then, n teraton k, f T can be approxmated by a monomal f k wth T, that s f T f k T n β k,n u,n T/β k,n k β,n 9 u,n T k /f T k 0 and T k denotng the value of T n teraton k. Accordngly, the objectve functon of the GP problem n teraton k s gven by mn T,P n u,n T/β k,n k β,n The teraton s termnated at the loop k f T k T k ε, where ε s the predefned error tolerance. To ths end, we devse an SP-based power control algorthm as presented n Algorthm. As condensng the objectve n the above problem gves us an underestmate of the objectve value, each GP n the condensaton teraton loop tres to mprove the accuracy of the approxmaton to a partcular mnmum n the orgnal feasble regon. Accordng to Lemma and Propostton 3 n [0], the arthmetc-geometrc mean approxmaton 9 satsfes all three condtons for convergence, such that the condensaton method s provably convergent. Moreover, emprcally t almost always obtans the globally optmal power allocaton [0]. FIGURE. Frame structure of the half-duplex relay-enhanced cellular network. IV. OPTIMAL POWER CONTROL IN HD TRANSMISSION MODE In the case of HD transmsson mode, both the BS and RSs work n HD mode, and we consder tme-dvson based transmsson scheme, as shown n Fg.. Specfcally, the uplnk and downlnk transmssons take place n two non-overlappng and equal-length tme frames. Each tme frame conssts of two tme slots, wheren the source node e.g., the uplnk or BS transmts sgnal to the relay e.g., the RS or RS n the frst tme slot, then the relay forwards the decoded receved sgnal to the destnaton node e.g., the BS or downlnk n the second tme slot. In ths scenaro, there s no nterference n the system. Accordngly, the end-to-end spectral effcences bps/hz of the uplnk and downlnk transmssons can be respectvely expressed as C UL_HD 4 log + mn H R, P U, H B,R P R C DL_HD 4 log + mn H B,R P B, H U,R P R 3 Note that for a far comparson, we assume that the duraton of the uplnk and downlnk transmsson n the FD mode s normalzed to, hence that n the HD mode s /. Furthermore, snce there are two tme slots n the the HD two-hop relayng communcatons, there s a factor of /4 n and 3. From and 3, the uplnk and downlnk transmssons are ndependent from each other, therefore the overall spectral effcency maxmzaton problem can be decomposed nto two subproblems as follows: and P3: max P U,P R C UL_HD s.t. C UL_HD P4: max P B,P R C DL_HD s.t. C DL_HD, 0 P, {, } 4, 0 P, {B, R } 5 P3 and P4 are the spectral effcency maxmzaton problems for the uplnk and downlnk transmssons, respectvely. In P3, we notce that the functon mn H R, P U, H B,R P R s a monotonc and ncreasng functon of P U and P R, and logarthm s a monotoncally ncreasng functon. Hence, the objectve functon of P3 s a monotonc and ncreasng functon wth respect to the optmzed varables P U and P R. VOLUME 5,

6 As a result, wthout consderng the mnmum data rate constrant, P3 has a unque global optmum, and the optmal soluton must have at least one component equal to the correspondng maxmum transmt power. Moreover, there exsts multple optmal solutons f H R, H B,R. On the other hand, t s worth mentonng that the achevable end-to-end data rate n two-hop relayng communcatons depends on the smaller one of H R, P and H B,R P. If the two terms are not equal to each other, the surplus part of the bgger one s useless for mprovng the end-to-end data rate, but results n a waste of energy resource. For the sake of the system energy effcency, we can decrease the correspondng transmt power untl the two terms beng equal, so as to reduce the overall power consumpton whle wthout affectng the achevable end-to-end data rate. Based on the analyss above, we have the followng lemma. } Lemma : The transmt power {P, P defned by 6 U R and 7 s an optmal soluton of the optmzaton problem P3 wthout consderng the QoS constrant. P mn H B,R /H R,, P mn H R, /H B,R, 6 7 Proof: Snce the objectve functon of P3 s a monotonc and ncreasng functon wth respect to the optmzed varables P U and P R, P3 wthout the mnmum data rate constrant has a unque global optmum, and the optmal soluton must have at least one component equal to the correspondng maxmum transmt power. Specfcally, f H R, H B,R, then we obtan the unque optmal transmt power of the uplnk,.e., P, whle a range [ of the optmal transmt power of the RS,.e., P H R, /H B,R, ]. On the other hand, when H R, > H B,R, we get the unque optmal tranmt power of the RS,.e., P, whle a range of [ the optmal tranmt power of the uplnk,.e., P H B,R /H R,, ]. Clearly, the transmt power defned by 6 and 7 belongs to the resultant optmal soluton set. Smlarly, we have Lemma for the downlnk transmsson. } Lemma : The transmt power {P B, P defned R by 8 and 9 s an optmal soluton of the optmzaton problem P4 wthout consderng the QoS constrant. P B mn H U,R R /H B,R, B P R mn H B,R B /H U,R, R 8 9 Proof: The proof s smlar to that of Lemma, hence omtted due to the lmted space. Based on Lemma and Lemma, we can derve the followng Proposton to characterze the propertes of the optmal power control scheme for the spectral effcency maxmzaton problem wth QoS guarantees n the HD relayng system. Proposton : In the HD transmsson mode, the overall spectral effcency maxmzaton problem wth QoS requrements s feasble f and only f C UL_HD* P, P and C DL_HD* P B, P R wth 6-9. Moreover, P gven by 6-9 s also the globally optmal soluton. Proof: Accordng to Lemma and Lemma, n absence of the mnmum data rate constrants, C UL_HD* P, P and C DL_HD* P B, P R wth 6-9 are the maxmum achevable end-to-end data rate of the uplnk and downlnk, respectvely. Therefore, t s straghtforward that the overall spectral effcency maxmzaton problem wth QoS constrants s nfeasble f C UL_HD* P, P < R req or C DL_HD* P B, P R < R req. Furthermore, f C UL_HD* P, P and C DL_HD* P B, P R, t s apparent that P gven by 6-9 s also the globally optmal soluton of the overall spectral effcency maxmzaton problem wth QoS constrants. Accordng to Proposton, when the QoS requrements can be guaranteed n the HD transmsson mode, the spectral effcency maxmzaton problem wth QoS requrements has the same optmal soluton as the one wthout the consderaton of the QoS requrements. Ths s due to the fact that there s no any nterference n the system wth the tme-dvson based transmsson scheme, and hence the uplnk and downlnk transmssons are ndependent from each other. However, t s a totally dfferent case for the FD transmsson mode, where the uplnk and downlnk transmssons are tghtly coupled through the self-nterference as well as the nterference among the dfferent lnks due to concurrent transmssons. Ths can be verfed by the numercal results presented n the next secton. V. PERFORMANCE EVALUATION To gan nsght nto the benefts of the FD transmsson on network performance, we consder three power control algorthms amng at maxmzng the overall spectral effcency by jontly optmzng transmt power of the uplnk UE, BS and RSs: FD w. QoS algorthm, wheren FD transmsson at both the BS and RSs s consdered, and the proposed SP-based power control algorthm n Secton III-B s employed to maxmze the overall spectral effcency whle satsfyng dverse QoS requrements of the uplnk and downlnk UEs. FD w.o. QoS algorthm, whch s smlar to the FD w. QoS algorthm but wthout consderng the QoS constrants of the uplnk and downlnk UEs. Conventonal HD algorthm, wheren HD transmsson s consdered, and the optmal transmt power proposed n Lemma and Lemma n Secton IV s adopted VOLUME 5, 07

7 FIGURE 3. a System throughput top-left, b per-user data rate top-rght, c system power consumpton bottom-left, and d system energy effcency bottom-rght versus maxmum transmt power budget of the uplnk P U max for dfferent algorthms. A. EFFECT OF MAXIMUM TRANSMIT POWER CONSTRAINTS In ths secton, we study the effect of the maxmum transmt power budgets of transmttng nodes on network performance, ncludng system throughput, per-user data rate, total power consumpton, and system energy effcency. In ths experment, we assumed the maxmum transmt power budgets of transmttng nodes are : : B : R : 3 : 5 : 3 takng nto account the dfferences n ther processng capablty, and vared from 0.5W to 5W wth the ncrement of 0.5W. In addton, we also made the followng assumptons. The mnmum data rate requrements of the uplnk and downlnk UEs are R req bps/hz and R req bps/hz, respectvely. The normalzed channel gans of the UE-RS.e., access lnk and BS-RS.e., relay lnk lnks are H U, H U,R 8dB and H B,R H B,R 0dB, whle that of the nterference lnks are H R, H U, H R, 3dB and H U, db. The normalzed resdual self-nterference channel gans at the FD nodes are G R G R G B 3dB. As shown n Fg. 3 a, the achevable system throughput of each algorthm mproves wth the ncrease of the maxmum transmt power budgets of the transmttng nodes, owng to the ncreasng avalable energy at each transmttng node. Moreover, the FD w.o. QoS algorthm acheves the hghest system throughput among the three algorthms. Compared wth the conventonal HD mode, the FD mode s able to mprove the spectral effcency sgnfcantly by transmttng and recevng sgnals at the same tme. It leads to the remarkable superorty of the FD w.o. QoS algorthm over the Conventonal HD algorthm. On the other hand, n the FD mode, the uplnk and downlnk transmssons nterfere wth each other, n addton to the resdual self-nterference at the FD nodes. It makes the achevable data rate n two drectons tghtly coupled. In ths case, n order to fulfll the QoS requrements of the uplnk and downlnk UEs, the FD w. QoS sacrfces a certan amount of system throughput. On the contrary, wthout the consderaton of the QoS constrants of the uplnk and downlnk transmssons, the FD w.o. QoS algorthm acheves the maxmum system throughput at the cost of unfarness between the uplnk and downlnk transmssons. Accordng to the per-user data rate llustrated n Fg. 3 b, we observe that the uplnk n the FD w.o. QoS algorthm doesn t obtan any servce at all, VOLUME 5,

8 although the downlnk s allocated wth a very hgh data rate. From Fg. 3 a, we also observe that there s an ntersecton of the two curves of the FD w. QoS and Conventonal HD algorthms. When there s less avalable transmt power, the FD w. QoS algorthm outperforms the Conventonal HD algorthm on system throughput owng to the mproved spectral effcency acheved by the FD mode. It s worth mentonng that even when the avalable transmt power s very lmted, the FD w. QoS algorthm stll satsfes the QoS demands of the uplnk and downlnk UEs, whereas the Conventonal HD algorthm fals as shown n Fg. 3 b. When the avalable transmt power s ncreased to a certan extent, the Conventonal HD algorthm begns to overtake the FD w. QoS algorthm. Ths stems from the fact that the suffcent transmt power compensates for the loss of spectral effcency n the HD mode, whereas the FD w. QoS algorthm s restrcted by the QoS constrants as well as the uplnk-downlnk nterference and self-nterference. As descrbed n Secton IV, there s no nterference n the tme-dvson based HD system, and hence the uplnk and downlnk transmssons are ndependent of each other. In ths case, gven the channel gans of the access and relay lnks, the achevable system throughput merely depends on the avalable transmt power. Consequently, the more the transmt power, the hgher the system throughput. Furthermore, we observe from Fg. 3 c that the system power consumpton of the FD w. QoS algorthm s the lowest, and the growth rate s also the slowest among these three algorthms. In contrast, both the FD w.o. QoS and Conventonal HD algorthms consume power n a relatvely aggressve manner. As expected, the system energy effcency of the FD w. QoS algorthm s superor to that of the other two algorthms as llustrated n Fg. 3 d. B. EFFECT OF SELF-INTERFERENCE In ths secton, we study the effect of the resdual selfnterference at the FD nodes on system throughput and system power consumpton. In ths experment, we assumed the normalzed resdual self-nterference channel gans are G R G R G B γ SI, and vared γ SI from 0.5dB to 8dB wth the ncrement of 0.5dB. Besdes, we also made the followng assumptons. The mnmum data rate requrements of the uplnk and downlnk UEs are R req bps/hz and R req bps/hz, respectvely. The maxmum transmt power budgets are,, B, Pmax R, 6, 0, 6 W. The normalzed channel gans of the UE-RS and the BS-RS lnks are H U, H U,R 8dB and H B,R H B,R 0dB, whle that of the nterference lnks are H R, H U, H R, 3dB and H U, db. From Fg. 4 a and b, we observe that both the system throughput and system power consumpton of the FD w. QoS and FD w.o. QoS algorthms declne wth the ncrease of the normalzed resdual self-nterference FIGURE 4. a System throughput top and b system power consumpton bottom versus the normalzed resdual self-nterference channel gan γ SI for dfferent algorthms. channel gan γ SI. In contrast, snce the Conventonal HD algorthm s rrelevant to the self-nterference, ts system throughput and system power consumpton reman at a fxed value when varyng γ SI. In the FD mode, apparently the larger the γ SI, the hgher the self-nterference level. In order to mtgate the self-nterference and hence mprove the qualty of sgnal recepton, the FD nodes e.g., BS or RSs may reduce ther transmt power, resultng n a decrease n data rate of the correspondng lnks. Accordng to 5 and 6, the achevable end-to-end data rate of the two-hop decode-and-forward relayng communcatons s lmted by the weaker one of the two hops. Moreover, the stronger one of the two hops s useless for mprovng the end-toend data rate, but aggravates the nterference to the other concurrent transmssons. Thus, the transmttng node of the stronger hop wll reduce the transmt power accordngly. Ultmately, t leads to the decrease n the end-to-end data rate and hence the system throughput and system power consumpton. As shown n Fg. 4 a, wth the growng selfnterference channel gan, the achevable system throughput n the FD mode wll eventually fall below that n the HD mode VOLUME 5, 07

9 wth each other. In ths case, ncreasng one could lead to a decrease n another one. As shown n Fg. 5 b, the FD w. QoS algorthm fulflls the ncreasng data rate requrement of the uplnk at the expense of a decrese n data rate of the downlnk. Specfcally, when the mnmum data rate requrement of the uplnk s not greater than that of the downlnk,.e., when R req QoS algorthm merely satsfes the mnmum demand of the uplnk, whereas provdes the downlnk wth a data rate as hgh as possble, so as to maxmze the system throughput whle fulfllng the QoS requrements of the UEs. R req U, the FD w. When R req ncreases to.5bps/hz, there s an evdent leap n the date rate of the uplnk, but on the contrary the data rate of the downlnk steeps down to the mnmum threshold. In our experment, the FD w. QoS algorthm fals to satsfy the QoS demands of the UEs when R req s equal to 5bps/Hz, but n contrast the outage happens n the Conventonal HD algorthm snce R req s equal to.5bps/hz. It reveals that the FD mode s more advantageous n provdng users wth dverse QoS guarantees, thereby mprovng the qualty of experence of users. FIGURE 5. a System throughput top and b per-user data rate bottom versus the mnmum data rate requrement of uplnk R req for dfferent algorthms. C. EFFECT OF MINIMUM QoS CONSTRAINTS In ths secton, we study the effect of the mnmum data rate requrement of uplnk on system throughput and the peruser data rate. In ths experment, we fxed the mnmum data rate requrement of the downlnk to R req bps/hz, and vared that of the uplnk.e., R req from 0.5bps/Hz to 4.5bps/Hz wth the ncrement of 0.5bps/Hz. In addton, we also made the followng assumptons. The maxmum transmt power budgets are,, B, 6, 0, 6 W. The normalzed channel gans of the UE- RS and BS-RS lnks are H U, H U,R 5dB and H B,R H B,R 8dB, whle that of the nterference lnks are H R, H U, H R, 3dB and H U, db. The normalzed resdual self-nterference channel gans at the FD nodes are G R G R G B 3dB. From Fg. 5 a, we observe that gven the mnmum data rate of the downlnk, the system throughput of the FD w. QoS algorthm declnes wth the ncrease of the mnmum data rate requrement of the uplnk, due to the ncreasng uplnk-downlnk nterference. In the FD mode, the smultaneous uplnk and downlnk transmssons nterfer wth each other, and hence ther attanable data rate nteracts, Pmax R D. EFFECT OF UE-RS LINK QUALITY In ths secton, we study the effect of the normalzed channel gan of the UE-RS lnks on system throughput and per-user data rate. In ths experment, we assumed the normalzed channel gans of the UE-RS lnks are H U, H U,R γ UE - RS, and vared γ UE - RS from 5dB to 75dB wth the ncrement of 5dB. Besdes, we also made the followng assumptons. The normalzed channel gans of the BS-RS lnks are H B,R H B,R 5dB. The mnmum data rate requrements of the uplnk and downlnk UEs are R req bps/hz and R req bps/hz, respectvely. The maxmum transmt power budgets are,, B, Pmax R, 6, 0, 6 W. The normalzed channel gans of the nterference lnks are H R, H U, H R, db and H U, db. The normalzed resdual self-nterference channel gans at the FD nodes are G R G R G B db. As shown n Fg. 6 a, the system throughput of each algorthm mproves frstly and then tends to be stable wth the ncrease of γ UE - RS, gven the normalzed channel gans of the BS-RS lnks. It s straghtforward that the enhanced lnk qualty s conducve to mprove the achevable endto-end data rate and hence the system throughput. On the other hand, snce the weaker hop s the bottleneck for the achevable end-to-end data rate of the two-hop decode-andforward relay communcatons, the end-to-end data rate of the uplnk and downlnk transmssons and hence the system throughput becomes saturated when γ UE - RS s ncreased to a certan value. More mportantly, we observe from Fg. 6 a that the algorthms wth FD mode are evdently superor to the one wth HD mode, owng to the enhanced spectral effcency acheved by FD mode. Furthermore, the gap between the FD w. QoS and FD w.o. QoS algorthms s shrnkng and becomes zero eventually as γ UE - RS ncreases. VOLUME 5,

10 resdual self-nterference, the uplnk-downlnk nterference, and the relay-access-lnk nterference. Specfcally, we formulated the power control desgn as a non-convex optmzaton problem, wth the objectve of maxmzng the system spectral effcency subject to the QoS requrements of the uplnk and downlnk UEs as well as the ndvdual power constrants of the uplnk UE, BS, and RSs. We characterzed the propertes of the optmal transmt power allocaton, and developed a SP-based power control algorthm to obtan the globally or at least locally optmal power allocaton. In addton, we also derved the closed-form optmal transmt power allocaton for the spectral effcency maxmzaton problem n the HD transmsson mode. We conducted extensve smulaton experments to study the effects of the dfferent factors on system performance. Smulaton results demonstrate that FD relayng can acheve hgher the spectral and energy effcency than HD relayng, and also has better QoS provsonng ablty. Our results provde mportant gudelnes for desgnng full-duplex networks. FIGURE 6. a System throughput top and b per-user data rate bottom versus the normalzed channel gan of the UE-RS lnks γ UE - RS for dfferent algorthms. It mples that when the lnk qualty s mproved to a certan extend, the QoS constrants are met nherently even n the FD w.o. QoS algorthm, and moreover the FD w. QoS and FD w.o. QoS algorthms have the same optmal solutons, thereby achevng the same system throughput. Although the system throughput mproves wth the ncrease of γ UE - RS as llustrated n Fg. 6 a, we observe from Fg. 6 b that the data rate of the uplnk and downlnk UEs n the algorthms wth FD mode experences the dfferent trends due to the changng lnk qualty and nterference envronment. At the begnnng, the uplnk s only allocated wth a data rate of the mnmum demand n the FD w. QoS algorthm and zero n the FD w.o. QoS algorthm. On the contrary, the data rate of the downlnk mproves sgnfcantly wth the ncrease of γ UE - RS n both algorthms. When γ UE - RS s ncreased to 40dB, there s an evdent mprovement on the data rate of the uplnk, and a certan amount of decrease n that of the downlnk. Ultmately, the data rate of both the uplnk and downlnk UEs becomes stable. VI. CONCLUSION In ths paper, we studed QoS-aware nterference mtgaton for the FD relay-enhanced cellular networks to address the REFERENCES [] J. Ba and A. Sabharwal. 0. Dstrbuted full-duplex va wreless sde channels: Bounds and protocols. [Onlne]. Avalable: arxv.org/abs/.5300 [] J. I. Cho, M. Jan, K. Srnvasan, P. Levs, and S. Katt, Achevng sngle channel, full duplex wreless communcaton, n Proc. ACM MobCom, Sep. 00, pp.. [3] M. Jan et al., Practcal, real-tme, full duplex wreless, n Proc. ACM MobCom, Sep. 0, pp.. [4] M. Duarte, C. Dck, and A. Sabharwal, Experment-drven characterzaton of full-duplex wreless systems, IEEE Trans. Wreless Commun., vol., no., pp , Dec. 0. [5] Z. Tong and M. Haengg, Throughput analyss for full-duplex wreless networks wth mperfect self-nterference cancellaton, IEEE Trans. Commun., vol. 63, no., pp , Nov. 05. [6] S. Wang, V. Venkateswaran, and X. Zhang, Explorng full-duplex gans n mult-cell wreless networks: A spatal stochastc framework, n Proc. IEEE INFOCOM, Apr. 05, pp [7] X. Xe and X. Zhang, Does full-duplex double the capacty of wreless networks? n Proc. IEEE INFOCOM, Apr./May 04, pp [8] M. Duarte et al., Desgn and characterzaton of a full-duplex multantenna system for WF networks, IEEE Trans. Veh. Technol., vol. 63, no. 3, pp , Mar. 04. [9] M. A. Amr Khojastepour, K. Sundaresan, S. Rangarajan, and M. Farajzadeh-Tehran, Scalng wreless full-duplex n mult-cell networks, n Proc. IEEE INFOCOM, Apr./May 05, pp [0] Y. Yang and N. B. Shroff, Schedulng n wreless networks wth fullduplex cut-through transmsson, n Proc. IEEE INFOCOM, Apr. 05, pp [] T. Rhonen, S. Werner, R. Wchman, and E. Z. B, On the feasblty of full-duplex relayng n the presence of loop nterference, n Proc. IEEE SPAWC, Jun. 009, pp [] T. K. Baranwal, D. S. Mchalopoulos, and R. Schober, Outage analyss of multhop full duplex relayng, IEEE Commun. Lett., vol. 7, no., pp , Jan. 03. [3] R. Hu, C. Hu, J. Jang, X. Xe, and L. Song, Full-duplex mode n amplfyand-forward relay channels: Outage probablty and ergodc capacty, Int. J. Antennas Propag., vol. 04, Feb. 04, Art. no [4] T. Rhonen, S. Werner, and R. Wchman, Hybrd full-duplex/half-duplex relayng wth transmt power adaptaton, IEEE Trans. Wreless Commun., vol. 0, no. 9, pp , Sep. 0. [5] I. Krkds, H. A. Suraweera, and C. Yuen, Amplfy-and-forward wth full-duplex relay selecton, n Proc. IEEE ICC, Jun. 0, pp [6] N. Nomkos, T. Charalambous, I. Krkds, D. Vouyoukas, and M. Johansson, Hybrd cooperaton through full-duplex opportunstc relayng and max-lnk relay selecton wth transmt power adaptaton, n Proc. IEEE ICC, Jun. 04, pp VOLUME 5, 07

11 X. Huang et al.: Power Control for FD Relay-Enhanced Cellular Networks Wth QoS Guarantees [7] K. Yang, H. Cu, L. Song, and Y. L, Effcent full-duplex relayng wth jont antenna-relay selecton and self-nterference suppresson, IEEE Trans. Wreless Commun., vol. 4, no. 7, pp , Jul. 05. [8] H. Cu, M. Ma, L. Song, and B. Jao, Relay selecton for two-way full duplex relay networks wth amplfy-and-forward protocol, IEEE Trans. Wreless Commun., vol. 3, no. 7, pp , Jul. 04. [9] B. P. Day, A. R. Margetts, D. W. Blss, and P. Schnter, Full-duplex MIMO relayng: Achevable rates under lmted dynamc range, IEEE J. Sel. Areas Commun., vol. 30, no. 8, pp , Sep. 0. [0] M. Chang, C. W. Tan, D. P. Palomar, D. O Nell, and D. Julan, Power control by geometrc programmng, IEEE Trans. Wreless Commun., vol. 6, no. 7, pp , Jul [] B. R. Marks and G. P. Wrght, A general nner approxmaton algorthm for nonconvex mathematcal programs, Oper. Res., vol. 6, no. 4, pp , 978. [] D. T. Ngo, S. Khakurel, and T. Le-Ngoc, Jont subchannel assgnment and power allocaton for OFDMA femtocell networks, IEEE Trans. Wreless Commun., vol. 3, no., pp , Jan. 04. FAN WU receved the Ph.D. degree from the Unversty of Electronc Scence and Technology of Chna, Chna, n 05. He s currently an Assocate Professor wth the School of Communcaton and Informaton Engneerng, Unversty of Electronc Scence and Technology of Chna. Hs research nterests nclude broadband wreless access networks, vehcular networks, and wreless sensor networks. XIAOYAN HUANG receved the Ph.D. degree from the Unversty of Electronc Scence and Technology of Chna, Chna, n 0. She s currently an Assocate Professor wth the School of Communcaton and Informaton Engneerng, Unversty of Electronc Scence and Technology of Chna. Her research nterests are generally n wreless communcatons and networkng, wth a focus on cross-layer desgn and optmzaton for broadband wreless networks. KUN YANG SM 08 receved the B.Sc. and M.Sc. degrees from the Computer Scence Department, Jln Unversty, Chna, n 99 and 994, respectvely, and the Ph.D. degree from the Department of Electronc and Electrcal Engneerng, Unversty College London UCL, U.K, n 007. He s currently a Char Professor wth the School of Computer Scence and Electronc Engneerng, Unversty of Essex, where he s leadng the Network Convergence Laboratory, U.K. He s also a Professor wth UESTC, Chna. He joned the Unversty of Essex n 003. He was wth UCL on several European Unon EU research projects for several years. He manages research projects funded by varous sources, such as UK EPSRC, EU FP7/H00, and ndustres. He has publshed over 00 journal papers. Hs man research nterests nclude wreless networks, future Internet technology and network vrtualzaton, moble cloud computng, and networkng. He serves on the edtoral boards of both IEEE and non-ieee journals. He has been a Fellow of the IET snce 009. VOLUME 5, 07 SUPENG LENG M 05 receved the Ph.D. degree from Nanyang Technologcal Unversty, Sngapore, n 005. He s currently a Professor wth the School of Communcaton and Informaton Engneerng, Unversty of Electronc Scence and Technology of Chna. Hs research focuses on resource, spectrum, energy, routng and networkng n wreless sensor networks, broadband wreless access networks, smart grd, and vehcular networks. He has authored over 00 research papers n recent years. He serves as an Organzng Commttee Char and a TPC member for many nternatonal conferences, as well as a revewer for over ten nternatonal research journals. 4869

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