54 JOUAL OF COMMUICAIOS, VOL 6, O 7, OCOBE 0 Bloc Dagonal recodng Based ower Allocaton for Coordnated Mult-ont ransmsson Jng Han Broadband Wreless Communcatons and Multmeda Laboratory, Key Laboratory of Embedded System and Servce Computng supported by Mnstry of Educaton, ongj Unversty, Shangha, Chna ng Wang,, Fuqang Lu, Yn Zhu Broadband Wreless Communcatons and Multmeda Laboratory, Key Laboratory of Embedded System and Servce Computng supported by Mnstry of Educaton,ongj Unversty, Shangha, Chna Shangha Key Laboratory of Dgtal Meda rocessng and ransmsson, Shangha, Chna Ema: pwang@tongjeducn Abstract hs paper studes power allocaton n coordnated mult-pont (CoM transmsson of 3G LE-Advanced system wth remote rado unts(us power constrants We apply bloc dagonal (BD precodng to downln transmsson, and assume perfect nowledge of downln channels and transmt messages at each transmt pont We propose a modfed water-flng power (MWF allocaton algorthm n order to maxmze the downln sum capacty, at the same tme the low complexty s acheved he nteror-pont method s also used to solve the optmzaton problem Smulatons show that nteror-pont method converges after only a few teratve steps and the system capacty s near-optmal As for complexty and power effcency, MWF acheves a good compromse Index erms CoM, MU-MIMO, power allocaton, optmzaton problem I IODUCIO In conventonal cellular networs, ntra-cell nterference can be elmnated by Orthogonal Frequency Dvson Multple Access (OFDMA However, cochannel nterference of adjacent cells s stl a man factor to mpact the system performance, especally for celledge user throughput In order to meet the requrements of hgher cell-edge throughput and spectrum effcency of next generaton broadband wreless communcaton system, 3G LE-Advanced proposed a mult-cell MIMO technology named coordnated multple pont (CoM transmsson and recepton on August, 008 Accordng to 3G [], CoM s manly characterzed nto two categores: Jont rocessng (J and Coordnated Schedulng/Beamformng (CS/CB In J, data ntended for a partcular UE s jontly processed and transmtted nstantaneously from all the coordnated Manuscrpt receved January 30, 0; revsed Apr 5, 0; accepted June 4, 0 Correspondng author: ng Wang, e-ma: pwang@tongjeducn ponts, whe n CS/CB data s only transmtted from the servng cell Although CoM naturally ncreases system complexty, t yelds great capacty mprovement and coverage benefts [-3] Wth these CoM schemes, especally for CoM J, effcent power allocaton schemes need to be desgned to support jont rado resource management among coordnated cells hs s because the CoM-J transmsson scheme s more lely to be an expanson of the tradtonal sngle cell MIMO transmsson scheme, n whch the system performance s largely nfluenced by power allocaton However, although there are plenty of lteratures that consder power allocaton scheme for cooperatve mult-cell networs, to the author s best nowledge, relatve study on CoM system s few eference [4-6] studed the power allocaton scheme n CoM system eference [4] consdered the power allocaton problem wth carrer aggregaton (CA eference [5] proposed an teratve algorthm of jont antenna selecton and power allocaton wth the purpose of maxmzng the sum rate of coordnated users eference [6] proposed a BS schedulng scheme based on threshold judgment and an teratve power allocaton approach usng E theory However, some system models of the lteratures mentoned above are not practcal eference [7] formulated the cooperatve multcell power allocaton as a networ utty maxmzaton problem and proposed an teratve algorthm that converges to the global optmum eference [8-9] studed the power allocaton scheme based on zero-forcng precodng All these algorthms are based on per-antenna power constrant But, n our paper, we study the power allocaton problem wth per-u power constrant whch fts the stuaton of CoM In LE system, eodeb s composed of a base band unt (BBU and several remote unts (Us, each of whch covers a cell In 3G A #59bs meetng on January, 00, an agreement was reached that CoM technques would only be appled n ntra-eodeb 0 ACADEMY UBLISHE do:04304/jcm6754-58
JOUAL OF COMMUICAIOS, VOL 6, O 7, OCOBE 0 55 scenaro for el-0 [0] A bloc dagram of the system s shown n Fg In the paper, we wl focus on power allocaton n MU- CoM-J system wth per-u power constrant We adopt BD precodng transmsson scheme, because we thn t s a scheme wth the greatest potental due to the fact that t has been used n most CoM-related proposals Fg etwor opology of CoM J submtted to 3G A In the paper, we frst propose a MWF algorthm he core s to fnd the range of heght of the water surface by usng a smple and effcent teratve algorthm n order to satsfy the U power constrant We then study the power allocaton problem from the mathematcal aspect of vew, and use the barrer method to fnd a near-optmal soluton he rest of the paper s organzed as follows In secton II, the system model of coordnated mult-pont transmsson wth BD precodng and problem formulaton wl be descrbed n deta In secton III, we propose the modfed water-flng power allocaton algorthm, and then present optmzaton soluton algorthm by usng nteror-pont methods Smulaton results are shown n Secton IV he concluson follows n secton V II SYSEM MODEL AD OBLEM FOMULAIO A etwor Archtecture We consder an ntra-eodeb CoM system consstng of M Us wth users (UE served Each U and UE are equpped wth n and n antennas, respectvely Snce the system s usng BD precodng, the number of antennas should meet the condtons M n n n ( M n We use H to represent the downln channel from all the M cooperatve Us to the th user Let H= H, H,, H denote the channel of all users he elements of H are assumed to be ndependent zero mean complex Gaussan random varables wth unt varance hus, matrx H s full ran, whch means each user has n ndependent spatal substreams of data he receved sgnal of the th user can be denoted as where y = HUs+ HUs+ n ( =, ( Mn s ndcates the transmtted n s addtve whte symbols for the th user complex Gaussan nose vector, normalzed so that ts covarance matrx s the dentty matrx - + represents all the H = H,,H,H, H users channel expect the th user U s BD precodng matrx, whch should satsfy HU = 0 Snce H s assumed to be a full ran matrx, we have ran( mn( n ( -, n M n ( - We H = = perform sngular value decomposton (SVD on ( (0 H * H = U V,V ( (0 where V holds the last ( nm - n( - rght sngular vectors, whch forms an orthogonal bass for the null space of H (0 hus, we have HV = 0, whch means nter-user nterference has been elmnated We (0 then perform SVD on HV n order to decompose the channel nto ndependent parallel sub-channels (0 ( (0 HV = U V, V (3 where s a n n dagonal matrx, whose element λ / ( j =, n s the sngular values of ( parallel sub-channels V holds the n sngular vectors / wth non-zero sngular values hus, U = WΛ (0 ( / = V V Λ, where Λ = dag(,,,, ndcates the power allocated on the th user s n j th substream he equvalent channel of user now (0 ( can be wrtten as HV V consstng of n ndependent sub-channels, each of whch has a gan of λ / ( j =,, n Fg System Structure of Downln CoM-J 0 ACADEMY UBLISHE
56 JOUAL OF COMMUICAIOS, VOL 6, O 7, OCOBE 0 B roblem Formulaton BD precodng enables the system to transmt multple data streams to each user whe removng the nter-user nterference he whole system channel can now be seen as ndependent parallel sub-channels he rate of n the j th sub-channel of the th user s gven by = log ( + λ (4 Defne w as an element of W representng a mappng relaton between and the transmt power of the th U s l th antenna he total transmttng power of the th U can be wrtten as n n U = j= l= (5 = w ( =, M Let MAX _ E _ U be the power constrant of each U herefore, our optmzaton problem to maxmze the sum rate wth per-u power constrant can be formulated as st n (O max log ( + λ = j= c: 0 ( =,, j =,, n c : ( =, M U MAX _ E _ U It s easy to notce that the objectve functon and constrants are all convex over the soluton set hus, t s a convex optmzaton problem [] III OWE ALLOCAIO ALGOIHMS A Modfed Water-flng ower Allocaton Algorthm (MWF Snce the entre system has been decomposed nto ndependent sub-channels, one way of solvng n the optmal power allocaton problem s usng the conventonal water-flng strategy If s the total volume of water fled nto a vessel, the depth of water at each sub-channel s the power allocated to t, and / λ traces out the bottom of the vessel [] S 5 S 4 S 3 S S λ λ λ 3 λ4 λ5 Fg3 Intervals Dvded by the Bottom of the Vessel Here, we can not use the water-flng strategy drectly because of the per-u power constrant Let s defne µ [0, + as the heght of the water surface he bottom of the vessel naturally dvdes [0, + nto n left-closed rght-open ntervals denoted by S, S,, S n as shown n Fg3 In MWF, we frstly determne whch nterval µ s n by usng a smple teratve algorthm hen we obtan µ by analyzng a set of lnear functons Our teratve algorthm wors as follows Intalzeα = n + epeat α = α, = mn( S α Use water-flng algorthm to allocate power among sub-channels, and update Calculate U accordng to (5 Unt ( =, M U MAX E U S α hus, we now value of accordng to (6 µ And we can determne the µ / λ when µ / λ = 0 when µ < / λ From (5 and (6, U (6 can be wrtten as a functon of µ hat s to say, we now have M lnear functons of one varable, each of whch can be expressed as BS = a µ + b ( a and b are coeffcents For each = ( =, M, we can get a U MAX E U correspondng Fnally, we calculate µ he water surface µ equals mn( accordng to (6 µ B Interor-pont Methods Consderng (O s a convex optmzaton problem, we solve the problem by a partcular nteror-pont algorthm, the barrer method he man dea of the method s to approxmately formulate the nequalty constraned problem as an unconstraned problem by an ndcator functon We construct the ndcator functon as n B ( = ln( = j= M n n + MAX _ E _ U w = = j= l= ln( Hence, the barrer functon s defned as: G (, r = log ( + λ rb ( (7 n (8 = j= σ 0 ACADEMY UBLISHE
JOUAL OF COMMUICAIOS, VOL 6, O 7, OCOBE 0 57 + Snce r s very small, G (, r s an approxmaton of the orgnal objectve functon As r decreases, the approxmaton becomes more accurate Also, when tends to the boundary of the feasble set S, G (, r ncreases to hus, B( buds a barrer at the boundary of S (O can now be smplfed to the followng equvalent problem (O whch can be easy solved (O mn G (, r st nt S Let ndcate the optmal soluton he barrer method can be descrbed as follows Intalze, r, coeffcent β (0, ε > 0 epeat Calculate by mnmzng (9, startng at f rb( < ε Brea; We fnd the optmal soluton else Update = and r = βr ; end, tolerance IV SIMULAIO ESULS In ths secton, we perform computer smulatons to evaluate the performance of the proposed ntra-eodeb power allocaton algorthms and to compare t wth other tradtonal method We consder one sngle eodeb wth 3 Us here are users served at the same tme Each U has 4 antennas, and each user s equpped wth antennas he channel H s assumed to be quas-statc flat aylegh fadng and ce fadng wth ce factor equal to 0 Also, deal channel estmaton s used In the smulaton, we compare MWF and nteror-pont methods wth equal power allocaton strategy he ntal values of parameters of nteror-pont algorthm are set as 3 γ =, β = /3 and ε = 0 We mplement the algorthms under dfferent power constrants of U It s shown n Fg4 and Fg 5 that CoM has a gan over the tradtonal sngle cell MU-MIMO transmsson scheme hs s because n CoM-J strategy there are more transmt antennas and the nter-cell nterference s elmnated he sum rate of users of barrer method outperforms those of the other two algorthms under varous U power constrants, snce the barrer method approaches to the optmal soluton on every teratve step Besdes, MWF has more obvous rate gan than equal power allocaton when the power constrant of U s small, whch s consstent wth the property of tradtonal water-flng algorthm As for power effcency, Fg6 plots the data rate per watt We can see that MWF has the hghest power effcency whe the performance of the barrer method s relatvely poor hat means n order to obtan the same data rate, the barrer method may requre more transmt power Besdes, the teratve number of MWF s related to the number of sub-channels, whch s very small n practcal system However, the teratve number of barrer method s always ept n about tmes n our smulaton hus, we can see that MWF has much lower complexty and hgher effcency Sum ate, bt/s/hz 0 9 8 7 6 5 4 3 Equal ower Allocaton Optmal ower Allocaton Waterfl n Sngle Cell 8 9 0 3 4 5 6 7 8 ower Constrants of Each U, dbm Fg4 Sum ate of the users under Dfferent ower Constrants, aylegh Fadng Sum ate, bt/s/hz 5 5 05 Equal ower Allocaton Optmal ower Allocaton Waterfl n Sngle Cell 0 8 9 0 3 4 5 6 7 8 ower Constrants of Each U, dbm Fg 5 Sum ate of the users under Dfferent ower Constrants, ce Fadng Data ate, bt/s/hz/w 4 3 0 9 8 7 6 Equal ower Allocaton Optmal ower Allocaton 5 8 9 0 3 4 5 6 7 8 ower Constrans of Each U, dbm Fg6 Bt ate per Watt 0 ACADEMY UBLISHE
58 JOUAL OF COMMUICAIOS, VOL 6, O 7, OCOBE 0 V COCLUIO In ths paper, we formulate the optmal power allocaton problem wth per-u power constrant n mult-user CoM-J networ to acheve the maxmal sum rate of the system We frst propose a MWF algorthm he algorthm roughly determnes the range of µ, before obtanng the sub-optmal soluton through solvng a set of equatons Snce the power allocaton problem s convex optmzaton, we then use barrer method to obtan the optmal soluton We construct the barrer functon to transform the orgnal equalty constraned problem to an unconstraned problem whch can be easy solved Smulaton results show that the barrer method can get the near-optmal sum data rate, whe usng relatvely more transmt power Consderng the algorthm complexty and power effcency, MWF s a good compromse alternatve ACKOWLEDGEME hs wor was supported by the atonal Scence and echnology Major roject of Chna under Grant 0ZX03003-00, Sno-Fnland Internatonal Cooperaton roject under Grant 00DFB040, atonal atural Scence Foundaton of Chna under Grant 60379 and the Openng roject of Shangha Key Laboratory of Dgtal Meda rocessng and ransmsson under grant 00KF04 EFEECES [] -0999, Fnal eport of 3G SG A WG #56bs v00, March, 009 [] -00936, CoM J n FDD downln, Alcatel-Lucent Shangha Bell, Alcatel-Lucent, A#60, February, 00 [3] -0069, Evaluaton of DL CoM for Hgh Load and Low Load Scenaros, Huawe, A#60, February, 00 [4] Wang Xaoyong, Xao Dengun, Jng Xaojun, A orvel ower Allocaton Algorthm under CoM wth CA, nd IEEE Internatonal Conference on Broadband etwor & Multmeda echnology (IC-BM, 009, pp66-70 [5] J Qng, Xaohu L, a'an Lu, Yongqang He and Guanghu Yu, A Jont Antenna Selecton and ower Allocaton Algorthm for CoM Systems, IEEE 4th Internatonal Conference on Advanced Informaton etworng and Applcatons Worshops, 00, pp 69-7 [6] Yadong Lu, Gang Wu, Shu Fang, Xanxue Fan, BS Schedulng and Iteratve ower Allocaton for the Mult- Cell Downln MIMO Systems, 7th Internatonal Conference on Informaton, Communcatons and Sgnal rocessng (ICICS, 009 [7] Yosa Hadsusanto, Lars hele, Voler Jungncel, Dstrbuted Base Staton Cooperaton va Bloc- Dagonalzaton and Dual-Decomposton, IEEE Global elecommuncatons Conference (GLOBECOM, 008, pp-5 [8] Yachen Wang, Jngsa Jang, Yanhong Fan, Ye L, Coordnated ransmsson wth Bloc Dagonalzaton n MIMO Broadcast, 6th Internatonal Conference on Wreless Communcatons etworng and Mobe Computng (WCOM, 00 [9] u Yanpng, ang Hong, ang Lun, Zero-forcng based coordnated mult-pont transmsson system and power allocaton, Applcaton esearch of Computers, 7(5, 00, pp98-90 [0] Draft eport of 3G SG A WG #59bs v00, January, 00 [] Stephen Boyd and Leven Vandenberghe, Convex Optmzaton, Cambrdge Unversty ress, 004 [] Davd se and ramod Vswanath, Fundamentals of Wreless Communcaton, Cambrdge Unversty ress, 005 [3] Quentn H Spencer, A Lee Swndlehurst, Martn Haardt, Zero-Forcng Mehtods for Downln Spatal Multplexng n Mult-User MIMO Channels, IEEE ransactons on Sgnal rocessng, 5(, 004, pp 46-47 Jng Han was born n Shangha, Chna 987 She receved the BS Degree n communcaton engneerng (009 from ongj Unversty Currently, she s a graduate student at Broadband Wreless Communcatons and Multmeda Laboratory n ongj Unversty She has publshed 3 papers Her research nterest s resource allocaton n wreless communcaton systems ng Wang was born n Chna, 978--8 He graduated from the department of computer scence and engneerng at Shangha Jaotong Unversty, Chna and receved h D degree n 007 Hs major feld of study s wreless communcaton He joned the college of electronc and nformaton engneerng at ongj Unversty n 007 and now s a lecturer Hs current and prevous nterests nclude routng algorthms and resource management n wreless networs, vehcular ad hoc networ and vdeo transcodng Fuqang Lu was born n Chna, 963-3-7 He graduated from the department of automaton at Chna Unversty of Mnng and receved h D degree n 996 Hs major feld of study s sgnal processng ow he s a professor n the department of nformaton and communcaton engneerng at ongj Unversty Hs man research nterests are n routng algorthms n wreless broadband access and mage manpulaton Yn Zhu was born n Chna, 974 She receved MS degree n Communcaton and Informaton system from Soochow Unversty n 003 and s a lecturer of Unversty of Scence and echnology of Suzhou ow she s a hd canddate of ongj Unversty wth research area n next generaton broadcast wreless communcaton 0 ACADEMY UBLISHE