BER ANALYSIS OF V-BLAST MIMO SYSTEMS UNDER VARIOUS CHANNEL MODULATION TECHNIQUES IN MOBILE RADIO CHANNELS

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1 202 Iteratoal Coferece o Computer Techology ad Scece (ICCTS 202) IPCSIT vol. 47 (202) (202) IACSIT Press, Sgapore DOI: /IPCSIT.202.V47.24 BER ANALYSIS OF V-BLAST MIMO SYSTEMS UNDER VARIOUS CANNEL MODULATION TECNIQUES IN MOBILE RADIO CANNELS Gurpreet Sgh, Pryaka Mshra 2 ad Rahul Vj 3 Departmet of Electrocs ad Commucato, Jaypee Uversty of Iformato Techology, Wakaghat, Sola,.P., INDIA 7325 Abstract. Multple Iput Multple Output (MIMO) systems have bee extesvely studed cotext of wreless commucato system, whch promsg the both creased capacty ad lk level relablty. I ths paper we wll preset a aalyss of the Vertcal Bell Laboratores Layered Space-Tme (V-BLAST) system at hgh sgal-to ose rato (SNR) rego usg BPSK, QPSK ad 6-QAM modulato techque by usg varous decodg techques. We wll cosder a pot-to-pot MIMO commucatos over a depedet, detcally dstrbuted (..d) Raylegh flat fadg chael wth N trasmttg ateas ad M (M N) recevg ateas. We wll aalyze the zero-forcg V-BLAST (ZF-V-BLAST), mmum measquared-error (MMSE-V-BLAST), zero-forcg Ordered Seral Iterferece Cacellato V-BLAST (ZFOSIC V-BLAST), mmum mea-squared-error Ordered Seral Iterferece Cacellato V-BLAST (MMSEOSIC V-BLAST) ad Maxmum Lkelhood V-BLAST (ML-V-BLAST) decodg techques wth respect to ther BER performaces. V-BLAST system s compared wth dfferet modulato techque ad system gets better result BPSK modulato. Fally we wll coclude that ML- VBLAST decodg techque gves the better performace tha other decodg techques usg BPSK modulato. Further smulato results for BPSK modulato wth oly ML decodg techque usg varous ateas at put ad output. I ths we got optmal result for 4 x 4 ateas for V-BLAST system. Keywords: Multple put multple output (MIMO), Vertcal Bell Laboratores Layered Space-Tme (V- BLAST), zero-forcg V-BLAST (ZF--BLAST), mmum mea-squared-error (MMSE-V-BLAST), Maxmum Lkelhood (ML) Ordered Seral Iterferece Cacellato (OSIC).. Itroducto Wreless commucato system wth mult-atea arrays has bee a feld of tesve research o the last years. The use of multple ateas at both the trasmtter ad the recever sdes ca drastcally mprove the chael capacty ad data rate. The study of the performace lmts of MIMO system becomes very mportat sce t wll gve lot deas uderstadg ad desgg the practcal MIMO systems. There are may schemes that ca be appled to MIMO systems such as space tme block codes, space tme trells codes ad the Vertcal Bell Labs Space-Tme system (V-BLAST). I ths paper, we study the geeral V-BLAST system wth Maxmum Lkelhood (ML), Zero Forcg (ZF) ad Mmum Mea Squared Error (MMSE) detectors fadg chaels by usg varous modulato techques such as BPSK, QPSK ad 6-QAM. Space Tme Layered Archtecture offers a bg crease capacty ad data rate, promsg a lear growth wth the sze of atea array uder some crcumstaces []. Frst Bell Laboratores Layered Space- Tme Archtecture ow wdely kow as D-BLAST [2] s oe of the approaches to crease the data rate ad capacty of the system. D-BLAST has a computatoal complexty. Gurpreet Sgh. Tel.: ( ). E-mal address:(gurpreet_2828@hotmal.com). 23

2 To mtgate the computatoal complexty of D-BLAST [2], we wll use a smplfed verso of BLAST kow as Vertcal-Bell Laboratores Layered Space-Tme (V-BLAST) [3]. I V-BLAST at the trasmtter de-multplexes the put data streams to depedet sub-streams, whch are trasmtted parallel over the trasmttg ateas. At the recever ed, ateas receve the sub-streams, whch are mxed ad supermposed by ose. Detecto of sub-streams at recever of V-BLAST s doe by applyg Order determato, Sequetal terferece ullg ad Sgal Cacellato [3]. Although V-BLAST s kow equvalet to a Decso Feedback Equalzer (DFE) ad s optmal terms of achevg the chael capacty [4]. I a..d Raylegh Flat fadg chael wth N trasmttg ateas ad M recevg ateas (M N), the frst detected sub-stream has a dversty ga of oly M-N.The frst sub stream s the bottleeck whch lmts the overall performace of the scheme. Oe ca apply the optmal orderg techque to mtgate ths bottleeck effect [3]. At each detecto step the recever should detect the data substream wth the larg post processg Sgal to Nose Rato (SNR). owever, t s show [5] optmal orderg does ot mprove the dversty ga whe there are two trasmttg ateas (N=2) but dversty ga remas ukow f we applyg optmal orderg ad help to mprove geeral cases [6]. 2. System Model of V-BLAST The V-BLAST system [3] s smplfed verso of D-BLAST [2] that tres to reduce ts computatoal complexty. But dog so trasmt dversty s loss. A hgh-level block dagram of a V-BLAST system s show Fg. 2.. Ecoder A sgle data stream s de-multplexed to m sub-streams, ad each sub-stream s the ecoded to symbols ad fed to ts respectve trasmtter. Trasmtters -m operate co-chael at symbol rate /T symbols/sec, wth sychrozed symbol tmg Decoder The decoder eeds to demodulate the symbols o the receved vector. If chael ecodg s used, the the demodulated symbols eed to be buffered utl the whole block ca be decoded. Otherwse, the demodulato ca be doe mmedately. Several decoders are possble for ths archtecture ad these decoders are explaed bellow oe by oe. Data VECTOR ENCODER..d Raylegh Flat Fadg Chael VBLAST sgal processg ad Decoder Data Maxmum Lkelhood Decoder The ML recever performs optmum vector decodg ad s optmal the sese of mmzg the error probablty. ML recever s a method that compares the receved sgals wth all possble trasmtted sgal vectors whch s modfed by chael matrx ad mates trasmt symbol vector C accordg to the Maxmum Lkelhood prcple, whch s show as: C argm r C F Where, F s the Frobeus orm V-BLAST Zero Forcg (ZF) Fg. VBLAST Trascever system C 24

3 Zero Forcg s the lear MIMO techque. The processg takes place at the recever where, uder the assumpto that the chael matrx s vertble, s verted ad the trasmtted MIMO vector s s mated by The soluto of ZF s gve by: s = Wx = s = x x = ( ) Where () represets the pseudo-verse V-BLAST Mmum Mea Square Error (MMSE) The MMSE recever suppresses both the terferece ad ose compoets, whereas ZF recever removes oly the terferece compoets. Ths mples that the mea square error betwee the trasmtted symbols ad the mate of the recever s mmzed. ece MMSE s superor to ZF the presece of ose. At low SNR, MMSE becomes matched flter ad at hgh SNR, MMSE becomes Zero Forcg (ZF). For MMSE-V-BLAST, the ullg vector for the th layer s w * = I h, =, 2... N sr M Where = C cossts of the frst I colums of Zero Forcg wth Ordered Seral Iterferece Cacellato (OSIC) OSIC s bascally based o subtracto of terferece of already detected elemets of s from the recever vector x. Ths results a modfed recever vector whch effectvely fewer terferers are preset. Decodg algorthm cossts of bascally three steps whch are summarzg ) Compute, fd the mmum squared legth row of, say t s the p-th ad permute t to be last row. Permute colums of accordgly. 2) From the mate of the correspodg elemets of s. I case of ZF: ( s ) W x = p Where the weght vector W equals row N t of the permuted 3) Whle M->0 go back to step, but ow wth: ( M ) = ( h h )... M So we ca see here wth respect to ZF, the ZF wth OSIC algorthm troduces extra complexty MMSE wth Ordered Seral Iterferece Cacellato (OSIC) I order to do OSIC wth MMSE, the the algorthm resultg as follows Covarace matrx ca be wrtte as 2 2 [( s s )( s s ) ] = σ ( αi ) σ P Covarace matrx of the mato error ( ) detecto. s x s wll be used to determe good orderg for ) Compute W (P s obtaed whle determg W). Fd the small dagoal etry of P ad suppose ths s the p th etry. Permute the p th colum of to be last colum ad permute the rows of W accordgly. 2) From the mate of the correspodg elemets of s. I case of MMSE: M ( s ) W x = p 25

4: BER for VBLAST usg 6QAM modulato Fg.5: BER usg VBLAST usg BPSK modulato usg ML decodg Fg.2.

4 Where the weght vector W ateas 3) Whle M->0 go back to step, but ow wth: M equals row M of the permuted W ad M s the umber of trasmttg ( M ) = ( h h )... M So here we ca see that we get optmal orderg by usg MMSE wth OSIC 3. Smulatos ad Result Fg.2: BER for VBLAST usg BPSK modulato Fg.3: BER for VBLAST usg QPSK modulato Fg.4: BER for VBLAST usg 6QAM modulato Fg.5: BER usg VBLAST usg BPSK modulato usg ML decodg Fg.2. shows all the smulato results for BPSK modulato wth ML, MMSE, ZF, ZF-OSIC ad MMSE-OSIC detectors for 2x2 (Raylegh Chael). At a certa Bt Error Rate Pot, BER=0.00, there s approxmately.6 db SNR dfferece betwee MMSE ad MMSEOSIC detector. The dfferece s smaller tha that we expected ad SNR dfferece betwee ZF ad ZFOSIC s approx 4db. We ca see here that performace curve of these two systems are close to each other whe SNR s low, but gap gets larger whe SNR gets hgher. Whe the SNR s large, the post detecto of SNR may effected by chael matrx. Whe BER=0.00, we eed SNR=3db VBLAST system ad we eed SNR=4.6 Db orderg system. There s dfferece of oly.6db, thus we ca use OSIC orderg system stead of smple VBLAST system sce these two schemes perform smlarly. 26

5 Fg.3. shows all the smulato results for QPSK modulato wth ML, MMSE, ZF, ZF-OSIC ad MMSE-OSIC detectors for 2x2 (Raylegh Chael). At a certa Bt Error Rate Pot, BER=0.00, there s approxmately 4 db SNR dfferece betwee MMSE ad MMSEOSIC detector ad SNR dfferece betwee ZF ad ZFOSIC s approx 3db. The dfferece betwee ML ad MMSEOSIC s about 2db ad dfferece s smaller tha as we expected. We ca see here that performace curve of these two systems are close to each other whe SNR s low, but gap gets larger whe SNR gets hgher. Whe SNR s less that meas ose s large, post detecto SNR s affected by ose. Whe the SNR s large, the post detecto of SNR may effected by chael matrx. Whe BER=0.00, we eed SNR=3db VBLAST system ad we eed SNR=4.6 Db orderg system. Fg.4. shows all the smulato results for QAM-6 modulato wth MMSE, ZF, ZF-OSIC ad MMSE- OSIC detectors for 2x2 (Raylegh C hael). For 6QAM ML decodg techque s too complex so we do ot do ML decodg for hgher modulato. At a certa Bt Error Rate Pot, BER=0.00, there s approxmately 3 db SNR dfferece betwee MMSE ad MMSEOSIC detector ad SNR dfferece betwee ZF ad ZFOSIC s approx 3db.. We ca see here that performace curve of these two systems are close to each other whe SNR s low, but gap does ot gets larger whe SNR gets hgher as we expected. 4. Cocluso I ths paper, we studed MIMO V-BLAST system performace uder..d Raylegh chael. Further ths system s compared wth dfferet modulato techque ad system gets better result BPSK modulato.fg.5 shows the smulato results for BPSK modulato wth oly ML decodg techque usg varous ateas at put ad output. I ths we wll more optmal result for 4 x 4 ateas for V- BLAST system. 5. Refereces []. I.E. Telatar, Capacty of mult-atea Gaussa chaels, Europea Trasactos o Telecommucatos, vol. 0, o.6, pp , November/December 999. [2]. G.Fosch, Layered space-tme archtecture for wreless commucato a fadg evromet whe usg multple ateas, Bell Labs, Techcal Joural 2, 996, appeared Volume, umber 2, pp [3]. G.D.Golde, G.J.Fosch, R.A. Valezuela, ad P.W.Wolasky, Detecto algorthm ad tal laboratory results usg the V-BLAST space-tme commucato archtecture, Electro Lett.vol.35, o., pp.45, 999. [4]. G.Gs ad J.M.Coff, O the relatoshp betwee V-BLAST ad GDFE, IEEE Commucatos letters, vol. 5, pp , September 200. [5]. S.Loyka ad F. Gago, Performace aalyss of the V-BLAST algorthm: a aalytcal approach, IEEE Trasactos o Wreless Commucatos. Vol. 3, pp , July [6]. L.Zheg ad D.Tse, Dversty ad multplexg: A fudametal trade-off multple-atea chaels, IEEE Trasactos o Iformato Theory, vol. 49, pp , May [7]. K.I.Pederse, J.B.Aderso, J.P.Kermoal ad P.E.Mogese, A stochastc multple-put multple-output rado chael model for evaluato of space-tme codg algorthms, Proc. VTC 200 Fall, Bosto, vol. 2, pp , Sep [8]. M.Varaas ad T.Guess, Optmum decso feedback multuser equalzato wth successve decodg acheves the total capacty of the Gaussa multple-access chael, Coferece Record of the Thrty-Frst Aslomar Coferece o sgals, Systems ad computers, vol. 2, pp , Nov [9]. A.M.Tulo ad S.Verdu, Radom Matrx Theory ad Wreless Commucatos. aover, MA 02339, USA: ow publshers Ic., [0]. E.Bgler, J.Proakes ad S.Shama, Fadg Chael: Iformato Theoretc ad Commucato Aspects, IEEE Tras. O formato Theory, Vol. 44, pp , oct

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