IJCSI Internatonal Journal of Computer Scence Issues, Vol. 8, Issue 3, ay 2011 ISSN (Onlne: 1694-0814 A Low-complexty Power and Bt Allocaton Algorthm for ultuser IO-OFD Systems Ayad Habb 1, Khald El Baamran 2 and Abdellah At Ouahman 1 1 Team Telecommuncaton and Computer Networks, FSS, Unversty Cad Ayyad, P.O. Box 2390, arrakech, orocco. 2 Department of Telecommuncatons, ENSA of arrakech, Unversty Cad Ayyad, P. O. Box 575, arrakech, orocco. Abstract In ths paper, we present a low-complexty bt and power allocaton algorthm for multuser IO-OFD downlnk transmsson. In order to mnmze the total transmt power under the condton that users'qos requrements are satsfed, a novel resource allocaton scheme s proposed to explot the multuser dversty gan. The proposed algorthm nvolves adaptve subcarrer allocaton, adaptve modulaton and egen beamformng and acheves sgnfcant mprovement n overall system performance. Smulaton results shows that the proposed algorthm offers a smlar performance and a lower complexty than prevous algorthms. Keywords: ultuser IO OFD, SVD, bt and power allocaton. 1. Introducton Wth the ncreasng requrements for hgh-data-rate multmeda servces, multple-nput multple-output (IO and orthogonal frequency dvson multplexng (OFD technques have receved more and more nterest. IO-OFD s a very promsng technology n future wreless communcaton systems. However, t ntroduces new problems relatng how to utlze systems spatotemporal-spectral and power resources approprately. Wth an effcent dynamc resource allocaton scheme hgh data rate can be provded and dfferent users QoS requrement can be guaranteed [1]. In order to obtan optmal subcarrer power or bt allocatons the greedy algorthm s usually appled. One has to note that ths algorthm s of hgh computatonal complexty and yelds one bt optmal soluton. ost of the exstng algorthms are based on greedy algorthm and requre an teratve procedure for ther mplementaton, whch delays obtanng an optmal soluton and affects the qualty of servce [2]. In IO-OFD systems, the IO channel can be decomposed to a parallel scalar egenmode subchannels by sngular value decomposton (SVD wthout crosstalk from one scalarchannel to the other. The results have shown that the subcarrer andbt allocaton acheved sgnfcant reducton n total transmtpower. ost of the exstng algorthms only use one ortwo of the largest egenmode subchannels to transmt data and neglected the other spatal subchannels. In fact, more egen subchannels can be exploted to transmt data [3,4]. In ths paper, a lowcomplexty adaptve bt and power allocaton algorthm for downlnk IO-OFD systems s nvestgated. We assume that the CSI s perfectly knowen at both the transmtter and recever. A group of parallel sngular value subchannels are frst generated by sngular value decomposton (SVD to the IO-OFD channel. In order to effcently utlze the spatal resources, the proposed algorthm extends the data transmsson to all the non-zero spatal subchannels. The rest of ths paper s organzed as follows. Secton 2 descrbes the system model and defntons. In Secton 3, the proposed algorthm s explaned and n Secton 4 the performance obtaned from
IJCSI Internatonal Journal of Computer Scence Issues, Vol. 8, Issue 3, ay 2011 ISSN (Onlne: 1694-0814 smulatons results s presented. Fnally, some conclusons are drawn. 2. System Descrpton In ths paper, we consder a multusers IO-OFD system wth K users and N subcarrers. The base staton (BS has N t transmt antennas and each user has N r receve antennas. The downlnk system dagram s shown n Fg 1. We assume that the channel state nformaton (CSI s perfectly known to the recever and the transmtter, and the channel changes lttle durng the transmsson [5]. At the transmtter, we assume that user k has a data-rate requrement of R k bts per OFD symbol. In each symbol duraton a data stream composed of R k bts s fed nto a subcarrer and bt allocaton block. The proposed algorthm s appled to assgn dfferent subcarrers to dfferent users. Then the mapped data stream s load to correspondng subcarrers. Transmt precodng matrx V s derved from sngular value decomposton (SVD for every subcarrer, whch changes the spatal channel nto a seres of parallel subchannels wth no crosstalk from each other. After precodng, the data stream s sent to nverse fast-fourer-transformaton (IFFT module to do OFD modulaton for every transmt antenna, the cyclc prefx (CP s added to every OFD symbol and then transmtted. At the recever, the smlar adverse process s taken. Fgure 1: The system model of downlnk multuser IO- OFD. Let H k, n denotes the N r N t channel matrx of user k on subcarrer n. By SVD, the channel matrx can be decomposed nto H k, n =U k,n Λ k, n V k, n H = =1 u k, n λ k, n (v k, n H (1 where (. H represents the complex conugate transpose 1 2 N of a matrx. U k,n =[u k, n, u k,n u r k, n ] and 1 2 N V k, n =[v k,n, v k, n v t k, n ] are the sngular vectors, Λ k, n s the dagonal matrx wth sngular value of H k, n, and =rank( H k,n s the rank of H k, n The stream data over subcarrer n s demultplexed nto substream. Let S=[s 1, s 2 s ] T denotes the transmtted symbol of substream. The correspondng transmt power dagonal matrx s P=dag( p 1, p 2 p. By precodng the transmtted symbol vector S wth 1 1 2 V k, n =[v k,n, v k, n v k, n ], the transmtted sgnal vector can be wrtten as: 1 X =V k, n 1 P 2 S= =1 v k, n p s (2 r k,n =[r 1, r 2 r N r ] T =H k,n X +n (3 Where n s the complex whte Gaussan nose vector wth every dmenson a varance of σ 2. At the recever, by decodng the receve symbol vector r k,n by (u k, n H, we get the receved data symbol on spatal subchannel. y =(u k,n H r k, n =(u k,n H (H k, n X +n y =(u k,n y =λ k, n H ( =1 (v k,n u k, n H ( =1 λ k,n v k, n (v k,n H ( =1 v k, n p s +(u k,n H n p s +(u k, n H n y =λ k, n p s +(u k, n H n (4 Wth precodng and decodng the transmt symbol vector respectvely by V k, n and U k,n, we can notce from equaton (4 that the IO channel s transformed nto parallel sngle-nput sngle-output (SISO subchannels wthout crosstalk when the CSI s perfectly known at the transmtter and the recever. 3. Resource allocaton algorthm In ths secton a resource allocaton algorthm s presented for downlnk multuser IO-OFD system. To avod severe co-channel nterference (CCI, we do not allow
IJCSI Internatonal Journal of Computer Scence Issues, Vol. 8, Issue 3, ay 2011 ISSN (Onlne: 1694-0814 more than one user to share the same subcarrer, we assume that p k, n s the requred power to transmt b k,n bts on th spatal subchannel over nth subcarrer of user k. S k {1,2,..., N } denote the set of subcarrers of user k, and BER target s the obectve bt error rate, the optmzaton problem can be formulated as: nmze P T = Subect to K n=1 k=1 =1 BER k,n N =1 p k, n =R k,n p k,n =BER Target S S = S 1 S 2 S K ={1,2,..., N } =rank( H k,n When S 1... S K are dsont, the system can be vewed as a sngle user system on each subcarrer. So, we can transform the problem of mnmzng the total transmt power to a problem of mnmzng the power requred on each subcarrer [6], then the optmzaton problem n (5 can be rewrtten as: nmze Subect to p k, n =1 p k, n =R k,n =1 BER k,n =BER Target (6 S S = S 1 S 2 S K ={1,2,..., N } =rank( H k,n Denote f k (c be the requred transmt power to transmt c bts satsfyng target bt error rate ( BER k when channel gan s unty. In the case of -ary Quadrature Ampltude odulaton (QA, f k (c can be represented as [7] f k (c= N [ Q 1( 0 BER k (2 3 4 ]2 c 1 (7 (5 Q( x= 1 t 2 e 2 dt 2π x In order to guarantee users QoS requrements, the requred power, to transmt b k,n bt on the th spatal subchannel over nth subcarrer for user k, s gven by [9] p k, n = f k(b k,n (λ k, n 2 (8 Let Δ P k,n denote the addtonal power needed for transmttng one addtonal bt on the th spatal subchannel over nth subcarrer for user k. It s gven by Δ P k,n = f (b k k, n +1 f k (b k,n We defne the term G k as follows N G k = n =1 =1 (λ k,n 2 (9 (λ k,n 2 N 0 (10 To solve the problem of mnmzaton the total transmt power, we present our approach n two steps: the frst step s to allocate the subcarrers to the user that has the largest G k. In the second step we assgn the bts and power to user k over all subcarrer n S k on the subchannel that requres the least addtonal power. Let Ne (k be the number of subcarrers for user k Ne (k= floor (N / K (11 We assume that the data rate R k, n for user k on subcarrer n s constant, so R k, n can be expressed as R R k, n =round ( k Ne(k (12 Our algorthm s descrbed as follows: N 0 where denotes the varance of the Addtve Whte 2 Gaussan Nose (AWGN and Q( x s the Q-functon [8].
IJCSI Internatonal Journal of Computer Scence Issues, Vol. 8, Issue 3, ay 2011 ISSN (Onlne: 1694-0814 4. Performance analyss The performance of the proposed algorthm s nvestgated n ths secton. In our smulaton system, the channel s modeled as Ralegh fadng channel. The bandwdth of the system s 2.5Hz and the number of transmt data for each user s R k =192bts. The proposed algorthm (PA s compared wth a novel resource allocaton algorthm presented n [9] and dynamc subcarrer allocaton wth only the best egen subchannel (DSA-BES [10]. Fgure 2 shows the total transmt power versus the number of users for BER=10 3, number of subcarrers N =256 and N t =N r =4. It can be seen that the proposed algorthm gves almost the same results as Algorthm n [9] and gves better results compared to the DSA-BES especally when the number of users s large. Fgure 2: Total transmt power versus the number of users fork = 20,N = 256 N r =4 and BER=10 3. Fgure 3 shows the same smulaton as Fgure 2 except n ths case the number of subcarrers s N =128. When we compare the result n the Fgure 2 wth the result n the Fgure 3, we can see that the total transmt power ncreases when the number of subcarrers n the system decreases. It can also see that proposed algorthm (PA keeps the same performances that n Fgure 2.
IJCSI Internatonal Journal of Computer Scence Issues, Vol. 8, Issue 3, ay 2011 ISSN (Onlne: 1694-0814 the number of users for dfferent values of BER. Smulaton results shows that the total transmt power s decreasng wth the ncrease n the BER value. Fgure 3: Total transmt power versus the number of users for K = 20, N = 128, N r =4 and BER=10 3 In order to nvestgates the mpact of the number of antenna, Fgure 4 shows the total transmt power versus the number of users for BER=10 3, number of subcarrers N = 128, the number of receve antenna N r =2 and the number of transmt antenna N t =4. the smulaton results demonstrate that the requred transmt power for proposed algorthm (PA and the algorthm n [9] s ncreased when the number of receve antennas s decreased. the reason s that the number of exploted spatal subchannels decreases. Fgure 5: Total transmt power versus the number of users for K = 20,N = 128, N r =4 for dfferent values of BER. In order to compare the computatonal complexty between the proposed algorthm and the algorthm n [9], we compare the needed CPU tmes for runnng each algorthm. Fgure 6 shows the CPU tmes needed for runnng each algorthm versus the number of users for K =20, N =128, N t =N r =4 and BER=10 3 It can be seen that our algorthm converge rapdly than the algorthm n [9] especally when the number of users s large. Fgure 4: Total transmt power versus the number of users for K=20,N=128, N r =2 N t =4 and BER=10 3 Fgure 5 shows the total transmt power of the PA versus Fgure 6: Total transmt power versus the number of users for K = 20,N = 128, N r =4 and BER=10 3.
IJCSI Internatonal Journal of Computer Scence Issues, Vol. 8, Issue 3, ay 2011 ISSN (Onlne: 1694-0814 4. Concluson In ths paper, a low complexty algorthm for bt, subcarrer and power allocaton for IO-OFD downlnk system has been presented. The proposed algorthm mnmzes the total transmt power under the condton that users QoS requrements are satsfed. The smulaton results demonstrate that the proposed algorthm offers almost the same requred transmt power than the algorthm n [9]. oreover, the proposed algorthm converge rapdly than the prevous algorthms especally when the number of users s large. References [1] YJ Zhang and KB Letaef. (2006 Dynamc multuser resource allocaton and adaptaton for wreless ystems, IEEE Wreless Commun, pp.38-47. [2] Pan YH, Letaef KB, Cao ZG. (2004 Dynamc resource allocaton wth adaptve beamformng for IO/OFD systems under perfect and mperfect CSI, Proceedngs of IEEE WCNC, Atlanta, GA,USA,pp.93-97.. [3] Z. Hu and G. Zhu and Y. Xa and et al. (2004 ultuser subcarrer and bt allocaton for IO-OFD systems wth perfect and partal channel nformaton., Proceedngs of IEEE WCNC, Atlanta, USA, pp.1188 1193. Ayad Habb was born n Benellal, orocco n 1979. He receved hs Lcense degree (equv. B.A. n computer scence from the Unversty of Cad Ayyad, arrakesh, orocco, n 2002, hs dplomat n Computer Engneerng from Ecole Normale suppereure, arrakesh, n 2003 and hs D.E.S.A. (equv..a. n Electrcal Engneerng from the Unversty of Cad Ayyad, arrakech, orocco, n 2007, He s currently a Ph.D. Student at the same unversty. Hs research nterests nclude multuser IO-OFD systems, communcaton theory and computer networks. Khald El Baamran was born n Ouarzazate, orocco n 1976. He receved the PhD degrees n telecommuncaton Engneerng from the Unversty of Cad Ayyad, arrakesh, orocco n 2005. He s presently workng as an Assstant Professor n the ENSA of arrakesh, Unversty of Cad Ayyad, arrakesh, orocco. Hs research nterests nclude communcaton theory, multuser nformaton theory, OFD systems, and IO-OFD systems. Abdellah At Ouahman receved the doctorate thess n Sgnal Processng from the Unversty of Grenoble, France, n November 1981. Hs research was n Sgnal Processng and Telecommuncatons. Then he receved the PhD degree n Physcs Scence from the Unversty of Scences n arrakesh, orocco, n 1992. He s now Professor and responsble of the Telecommuncatons and Computer Scence and Networkng laboratory n the Faculty of Scences Semlala n arrakesh, orocco. Hs research nterests nclude the sgnal and mage processng and codng, telecommuncatons and networkng. Actually he s a drector of Natonal School of Appled Scences, arrakesh. He has publshed several research papers n Journals and Proceedngs. [4] Nana Leng, Shouy Yang, Yanhu Lu and Ln Q (2007 Dynamc Spatal Subcarrer and Power Allocaton for ultuser IO- OFD System., IEEE Wreless Communcatons, Networkng and oble Computng, 2007.WCom 2007, Shangha, Vol. 34, No. 4, pp.46 58. [5] Leung, R. and Taubman, D. (2005 Dynamc Spatal Subcarrer and Power Allocaton for ultuser IO-OFD System., IEEE Transactons on Image Processng, pp.180 183. [6] T. Cover and J. Thomas. (2006 Elements of nformaton theory,2 nd ed.,wley. [7] J. Proaks. (2008 Dgtal communcatons, 5th ed., cgraw-hll. [8] Y. W. Cheong and R.S Cheng and K.B. Latef and R.D. urch (1999 ultuser OFD wth adaptve subcarrer, bt and power allocaton, PIEEE J. Select.Areas Commun,Vol. 17, pp.1747-1758. [9] Qaoyun Sun and Hu Tan and Shuang Wang and Kun Dong and Png Zhang. (2009 Novel resource allocaton algorthms for multuser downlnk IOOFDA of FuTURE B3G systems, Progress n Natural Scence, Vol. 19, pp.1141-1146. [10] C. Y. Wong, C. Y. Tsu and R. S. Cheng, and K. B. Letaef. (1999 A real-tme sub-carrer allocaton scheme for multple access downlnk OFD transmsson, IEEE VTC, Vol. 2, pp.1124 1128.