Improvmnt Of BER With h Hlp Of MIMO OFDM Uing SBC Cod Structur Atul Kumar Pandy, Santoh Sharma, Ntu Sikarwar Elctronic and Communication Dpartmmt, MPC Gwalior, Elctronic Dpartmnt, JIWAJI Univrity Gwalior Abtract-MIMO OFDM ytm ha bn currntly rcognizd a on of th mot comptitiv tchnology for 4G mobil Communication ytm In thi Papr, a gnral Spac im Block Cod (SBC) tructur i propod for multipl input multipl output-orthogonal Frquncy Diviion Multiplxing (MIMO-OFDM) ytm for x Antnna configuration. h ignal dtction tchnology ud in thi papr for MIMO-OFDM ytm i MMSE Equalization (Linar Dtction chniqu. In thi Papr th Analyi of High lvl of Modulation (i.. QPSK) on MIMO OFDM ytm i prntd. Hr AWGN, Rayligh and Rician channl hav bn ud for analyi purpo and thir ffct on BER for high data rat hav bn prntd. h propod MIMO-OFDM ytm with SBC uing x antnna configuration and 5 FF lngth ha bttr prformanc in trm of BER V SNR thn th othr ytm. Kyword:- MIMO,OFDM, SBC, QPSK tc. I. INRODUCION During th pat dcad, wirl communication ha bnfitd from ubtantial advanc and it i conidrd a th ky nabling tchniqu of innovativ futur conumr product. For th ak of atifying th rquirmnt of variou application, ignificant tchnological achivmnt ar rquird to nur that wirl dvic hav appropriat architctur uitabl for upporting a wid rang of rvic dlivrd to th ur. In th forabl futur, th larg-cal dploymnt of wirl dvic and th rquirmnt of high bandwidth and high data rat application ar xpctd to lad to trmndou nw challng in trm of th fficint xploitation of th achivabl pctral rourc and contitut a ubtantial rarch challng in th contxt of th mrging WLAN and othr indoor multimdia ntwork. Du to th phyical limit impod by th mobil radio channl which cau prformanc dgradation and mak it vry difficult to achiv high bit rat at low rror rat ovr th tim dipriv wirl channl. Othr dtrimntal charactritic ar co-channl intrfrnc (CCI), Dopplr Effct, intntional jamming in military communication and Intrymbol intrfrnc (ISI) inducd by multipath fading; howvr, thr i an irrducibl rror floor that limit on th maximum attainabl tranmiion rat. Spcifically, th mploymnt of multipl antnna at both th tranmittr and th rcivr, which i widly rfrrd to a th MIMO tchniqu, contitut a cotffctiv approach to high throughput wirl communication and rmot ning. h concpt MIMO for both wird and wirl ytm wa firt introducd by Jack Wintr []-[3] in 987 for two baic communication ytm. h firt wa for communication btwn multipl mobil and a ba tation with multipl antnna 34
and th cond for communication btwn two mobil ach with multipl antnna. Whr, h introducd a tchniqu of tranmitting data from multipl ur ovr th am frquncy/tim channl uing multipl antnna at both th tranmittr and rcivr nd. Sparkd off by Wintr pionring work [], Salz [4] invtigatd joint tranmittr/rcivr optimization uing th minimum man quar rror (MMSE) critrion. Sinc thn, Wintr and othr [5] [8] hav mad furthr ignificant advanc in th fild of MIMO. In 996, Rayligh and Cioffi [9] and Fochini [] [] propod nw approach for improving th fficincy of MIMO ytm, which inpird numrou furthr contribution [] [3] for two uitabl architctur for it raliation known a Vrtical Bll-Lab Layrd Spacm(VBLAS), and Diagonal Bll-Lab Layrd Spac-im BLAS (D-BLAS) algorithm ha bn propod by Fochini, which i capabl of achiving a ubtantial part of th MIMO capacity. II. ORHOGONAL FREQUENCY DIVISION MULIPLEXING OFDM i a multicarrir tranmiion tchniqu ud in application catring to both Wird and Wirl Communication. Howvr, in th wird ca, th uag of th trm Dicrt Multi-on i mor appropriat. h OFDM tchniqu divid th frquncy pctrum availabl into many cloly pacd carrir, which ar individually modulatd by low-rat data tram. In thi n, OFDM i imilar to FDMA (h bandwidth i dividd into many channl, o that, in a multi-ur nvironmnt, ach channl i allocatd to a ur). Howvr, th diffrnc li in th fact that th carrir chon in OFDM ar much mor cloly pacd than in FDMA (khz in OFDM a oppod to about 3kHz in FDMA), thrby incraing it pctral uag fficincy. h orthogonality btwn th carrir i what facilitat th clo pacing of carrir.. Motivation For Uing OFDM h orthogonality principl ntially impli that ach carrir ha a null at th cntr frquncy of ach of th othr carrir in th ytm whil alo maintaining an intgr numbr of cycl ovr a ymbol priod. h motivation for uing OFDM tchniqu ovr DMA tchniqu i twofold. Firt, DMA limit th total numbr of ur that can b nt fficintly ovr a channl. In addition, inc th ymbol rat of ach channl i high, problm with multipath dlay prad invariably occur. In tark contrat, ach carrir in an OFDM ignal ha a vry narrow bandwidth (i.. khz); thu th rulting ymbol rat i low. hi rult in th ignal having a high dgr of tolranc to multipath dlay prad, a th dlay prad mut b vry long to cau ignificant intr-ymbol intrfrnc (.g. > 5uc). Figur.: Frquncy pctrum howing N channl for an OFDM ytm with N carrirovr bandwidth. OFDM Baic Principl Orthogonality 35
o gnrat OFDM Signal uccfully th rlationhip btwn all carrir mut b carfully controlld in ordr to maintain orthogonality. Shown blow i th frquncy pctrum dpicting th variou carrir/channl (ud intrchangably). Rctangular windowing of tranmittd pul rult in a inc-hapd frquncy rpon for ach channl. A can b n, whnvr any particular carrir frquncy attain pak amplitud,th rmaining carrir hav a null point..3 OFDM Gnration h pctrum rquird i firt chon bad on th input data and th modulation chm ud (typically Diffrntial BPSK, QPSK or QAM). Data to b tranmittd i aignd to ach carrir that i to b producd. Amplitud and pha of th carrir ar calculatd bad on th chon chm of modulation. h rquird pctrum i thn convrtd back to it tim domain ignal by mploying Invr Fourir ranform algorithm lik th Invr Fat Fourir ranform. h nxt tp i that of adding a guard priod to th ymbol to b tranmittd. hi nur robutn againt multipath dlay prad. hi tp can b achivd by having a long ymbol priod, which minimiz intrymbol intrfrnc. h lvl of robutn can b furthr incrad by th addition of a guard priod btwn ucciv ymbol..3. Cyclic Prfix h mot popular and ffctiv mthod of doing thi, i th addition of a cyclic prfix. A cyclic prfix i a copy of th lat part of th OFDM ymbol, which i prpndd to th tranmittd ymbol. hi mak th tranmittd ignal priodic and do not affct th orthogonality of th carrir. Furthr, thi alo play a dciiv rol in avoiding intr-ymbol and intr-carrir intrfrnc. Cyclic Firt Part of Lat Part Prfix ignal of th ignal Figur.3: h Cyclic Prfix i a copy of th lat part of th OFDM ignal A cyclic prfix do howvr introduc a lo in th ignal-to-noi ratio, but thi ffct i uually ngligibl a compard to it ffct on mitigating intrfrnc. A chmatic diagram i hown nxt and a mathmatical modl of a ba band OFDM ytm i now dvlopd. X, X, X N-, c p ranmittr Channl Rcivr (t) (t) (t) g( ;t) Figur.3: Ba band OFDM ytm Modl n(t) (t) (t) N- (t) Sinc th firt OFDM ytm did not u digital modulation and dmodulation chm, th continuou-tim OFDM modl hown abov can b conidrd a th idal OFDM ytm. o build th mathmatical modl, w tart with th wavform ud in th tranmittr and procd all th way to th rcivr..3. ranmittr W aum an OFDM ytm with N carrir, a bandwidth of W Hz and a ymbol (N+) Y, Y, Y N-, 36
lngth of cond, of which cp cond i th lngth of th cyclic prfix. h tranmittr u th following wavform: k ( t) cp W j k ( t N cp = othrwi ) t [, ].Eqn. of patial multiplxing diffrnt data ymbol ar tranmittd on th radio link by diffrnt antnna on th am frquncy within th am tim intrval. Multipath propogation i aumd in ordr to nur th corrct opration of patial multiplxing,inc MIMO i prforming bttr in trm of channl capacity in a rich cattr multipath nvironmnt than in ca of nvironmnt with lin of ight. whr = (N/W) + cp. A not mut alo b mad of th fact that k (t) = k (t + N/W) whn t i within th cyclic prfix..3.3 Rcivr A filtr bank, matchd to th lat part [ cp,] of th tranmittr wavform Φ k (t), i.., k * t tt, k = othrwi cp...eqn. hi opration ffctivly rmov th cyclic prfix in th rcivr tag of th ytm. All th ISI i containd in th Cyclic Prfix and do not manift itlf in th ampld output obtaind at th rcivr filtr bank. III. MULI INPU MULI OUPU (MIMO) SYSEMS Multi antnna ytm can b claifid into thr main catgori. Multipl antnna at th tranmittr id ar uually applicabl for bam forming purpo. ranmittr or rcivr id multipl antnna for ralizing diffrnt (frquncy, pac) divrity chm.th third cla includ ytm with multipl tranmittr and rcivr antnna ralizing patial multiplxing. In radio communication MIMO man multipl antnna both on tranmittr and rcivr id of a pcific radio link. In ca Figur 3.: Block diagram of a gnric MIMO ytm with tranmittr and rcivr. IV. SPACE IME BLOCK CODE Spac-tim block coding i a tchniqu ud in wirl communication to tranmit multipl copi of a data tram acro a numbr of antnna and to xploit th variou rcivd vrion of th data to improv th rliability of data-tranfr. h fact that th tranmittd ignal mut travr a potntially difficult nvironmnt with cattring, rflction, rfraction and o on and may thn b furthr corruptd by thrmal noi in th rcivr man that om of th rcivd copi of data will b bttr than othr. hi rdundancy rult in a highr chanc of bing abl to u on or mor of th rcivd copi to corrctly dcod th rcivd ignal. 37
An SBC (Spac-tim block cod) i uually rprntd by a matrix. Each row rprnt a tim lot and ach column rprnt on antnna tranmiion ovr tim. tim lot S tranmit antnna S S S S n n n Hr, ij i th modulatd Symbol to b tranmittd in tim lot I from antnna j. hr ar to b tim lot and n tranmit antnna a wll a Nr rciv antnna. hi block i uually conidrd to b lngth. 4. Orthogonality SBC ar originally introducd, and a uually tudid, ar orthogonal. hi man that th SBC i dignd uch that th vctor rprnting any pair of column takn from th coding matrix i orthogonal. h rult of thi i impl, linar, optimal dcoding at th rcivr. 4. Dign of SBCS h dign of SBC i bad on th ocalld divrity critrion drivd by arokh tal.orthogonal SBC can b hown to achiv th maximum divrity allowd by thi critrion. Divrity Critrion Call a codword C = C C C Nt C C.C Nt C C..C Nt And call an rronouly dcodd rcivd codword = Nt. Nt.. Nt hn th matrix c c B(c,) n c n n c c c n n c c c n ha to b full-rank for any pair of ditinct codword c and to giv th maximum poibl ordr of nnr. If intad,b (c,) ha minimum rank b ovr th t of pair of ditinct codword, thn th pac-tim cod offr divrity ordr bnr. An xaminiation of th xampl SBC hown blow rval that thy all atify thi critrion for maximum divrity. 4.3 Encoding 4.3. Alamouti cod Alamouti invntd th implt of all th SBC in 998. It wa dignd for a twotranmit antnna ytm and ha th coding matrix: C c c c * * c whr * dnot complx conjugat It i radily apprnt that thi i a rat- cod. It tak two tim lot to tranmit two ymbol. h ignificanc of Alamouti propoal that it wa th firt dmontration of a mthod of ncoding which nabl full divrity with liar procing at th rcivr. It wa th firt opn-loop tranmit divrity tchniqu. 4.3. Encodr for Alamouti chm h ncodr for Alamouti chm can b n in figur. hi chm with two tranmit antnna and two rciv antnna i intrprtd hr. In Alamouti ncoding chm,during any givn tranmiion priod two ignal ar tranmittd imultanouly from two tranmit antnna. 38
Bit Rat Information Sourc MPSK- Mappr [, ] SBC MIMO * * X X Figur 4.:Encodr for Alamouti cod * [, ] * [, ] h two-by-two pac-tim block cod i formally writtn in matrix form a IME * * Whr, th xplanation i: At tim t, antnna tranmit i, and imultanouly, antnna tranmit. At tim t+, whr i th ymbol duration, ignal tranmiion i witchd,with o * tranmittd by antnna and i * im ultanouly tranmittd by antnna. V. SIMULAION RESULS Lt u firt th rpon of MIMO without OFDM thn w will tart with th MIMO with OFDM. It i clarly n from th imulation rult of MIMO with MMSE without OFDM that, in incra SNR thn Probability of rror will gt dcra.now w want to find practically th rult of MIMO with MMSE uing OFDM how thi will chang th obtainabl rror. BER for BPSK modulation with x MIMO and MMSE qualizr (Rayligh channl) - - -3-4 im (nx=, nrx=, MMSE) -5 5 5 5 3 Avrag Eb/No,dB Figur 5.: BER with MIMO and MMSE without OFDM Diffrnt ca of tting imulation paramtr:- Ca I: Numbr of ranmitting Antnna = Numbr of Rciving Antnna = FF Lngth = 64 Fram Lngth = 5 Channl Ordr L = 5 Cyclic Prfix Lngth = 6 Hr aftr tting imulation paramtr w find that th Minimum Man Squar i hown by.5 with SNR and aftr varying SNR w gt trmndou dcra in BER.S th following graph of MIMO with MMSE with OFDM: Figur 5.: MIMO OFDM SBC with MMSE and 64 point FF Ca II.6.5.. MIMO OFDM SBC with MMSE and 64 point FF 5 5 5 3 Numbr of ranmitting Antnna = Numbr of Rciving Antnna = FF Lngth = 56 Fram Lngth = 5 Channl Ordr L = 5 Cyclic Prfix Lngth = 6 Hr aftr tting imulation paramtr a hown abov, w find that th Minimum Man Squar i hown by with SNR and aftr varying SNR w gt trmndou dcra in BER. S th 39
following graph of MIMO with MMSE with OFDM: Figur 5.4: MIMO OFDM with MMSE and 5 point FF Figur 5.3 : MIMO OFDM SBC with MMSE Ca III and 56 point FF Numbr of ranmitting Antnna = Numbr of Rciving Antnna = FF Lngth = 5 Fram Lngth = 5 Channl Ordr L = 5 Cyclic Prfix Lngth = 6 Hr aftr tting imulation paramtr a hown abov, w find that th Minimum Man Squar i hown by with SNR and aftr varying SNR w gt trmndou dcra in BER. S th following graph of MIMO with MMSE with OFDM: 5.5..5..5 5 5.5..5..5 MIMO OFDM SBC with MMSE and 56 point FF 5 5 5 3 MIMO OFDM SBC with MMSE and 5 point FF 5 5 5 3 Ca IV Numbr of ranmitting Antnna = Numbr of Rciving Antnna = FF Lngth = 56 Fram Lngth = 5 Channl Ordr L = Cyclic Prfix Lngth = 6 Hr aftr tting imulation paramtr a hown abov, w find that th Minimum Man Squar i hown by 5 with SNR and aftr varying SNR w gt trmndou dcra in BER.. S th following graph of MIMO with MMSE with OFDM:.5 5 5.5..5..5 Figur 5.5 :MIMO OFDM SBC with MMSE and 56 point FF with channl ordr= Ca V MIMO OFDM SBC with MMSE and 56 point FF channl ordr= 5 5 5 3 Numbr of ranmitting Antnna = Numbr of Rciving Antnna = FF Lngth = 5 Fram Lngth = 5 Channl Ordr L = Cyclic Prfix Lngth = 6 Hr aftr tting imulation paramtr a hown abov, w find that th Minimum Man Squar i hown by 4 with SNR and aftr varying SNR w gt 4
trmndou dcra in BER.. S th following graph of MIMO with MMSE with OFDM: 5 5.5..5..5 Figur 5.6: MIMO OFDM SBC with MMSE and 5 point FF with channl ordr= Ca VI 5 5 5 3 Numbr of ranmitting Antnna = Numbr of Rciving Antnna = FF Lngth = 64 Fram Lngth = 5 Channl Ordr L = 5 Cyclic Prfix Lngth = 3 Hr aftr tting imulation paramtr a hown abov, w find that th Minimum Man Squar i hown by.7 with SNR and aftr varying SNR w gt trmndou dcra in BER. S th following graph of MIMO with MMSE with OFDM:.8.7.6.5.. MIMO OFDM SBC with MMSE and 5 point FF with Channl ordr= MIMO OFDM SBC with MMSE and 64 point FF with L=5 and CPLn=3 5 5 5 3 Figur 5.7 : MIMO OFDM SBC with MMSE and 64 point FF with L=5 and CPLn=3 Ca VII Numbr of ranmitting Antnna = Numbr of Rciving Antnna = FF Lngth = 64 Fram Lngth = 5 Channl Ordr L = 5 Cyclic Prfix Lngth = 64 Hr aftr tting imulation paramtr a hown abov, w find that th Minimum Man Squar i hown by.9 with SNR and aftr varying SNR w gt trmndou dcra in BER. Simulation of th cript took minut. S th following graph of MIMO with MMSE with OFDM:..9.8.7.6.5.. 5 5 5 3 Figur 5.8: MIMO OFDM SBC with MMSE and 64 point FF with L=5 and CPLn=64 Ca VIII MIMO OFDM SBC with MMSE and 64 point FF with L=5 and CP LEN=64 Numbr of ranmitting Antnna = Numbr of Rciving Antnna = FF Lngth = 64 Fram Lngth = Channl Ordr L = 5 Cyclic Prfix Lngth = 6 Hr aftr tting imulation paramtr a hown abov, w find that th Minimum Man Squar i hown by.58 with SNR and aftr varying SNR w gt trmndou dcra in BER. If w compar prformanc of Fram Lngth 5 and w find that th rror obtainabl ar.9 4
and.58. S th following graph of MIMO with MMSE with OFDM: Figur 5.9: Simulation of Br of Bpk with MIMO and MMSE without OFDM VI..6.5.. MIMO OFDM SBC with MMSE and 64 point FF with L=5,CpLEn=6 and Fram Lnth= 5 5 5 3 CONCLUSION W ralizd that th MIMO play vry important rol in wirl communication now a day With combination of OFDM and MMSE w achivd bttr rpon of our conidrd qualizr. MIMO ytm ar ud for nhancmnt of capacity improvmnt in SNR at th rcivr and to tranmit data at highr rat. hi papr mainly dicu th ffct on th rduction in bit rror rat by changing OFDM paramtr. W may improv bit rror rat prformanc by incraing no.of tranmit antnna( X ) and no.of rciving antnna(r X ). Improvmnt in OFDM paramtr lik fram lngth and FF lngth giv a larg amont of rduction in BER.fram lngth and FF lngth giv a larg amont of rduction in BER. REFERENCES [] G. J. Fochini, Layrd pac-tim architctur for wirl communication in a fading nvironmnt whn uing multilmnt antnna, Bll Lab. chnology. Journal, Vol., No., PP. 4-59(996). [] J. Salz, Digital tranmiion ovr crocoupld linar channl, A& ch. J., vol.64, pp. 47 59,(Jul. Aug. 985). [3] S. Chng and S. Vrdu, Gauian multi-acc channl with ISI: Capacity rgion and multiur watrfilling, IEEE ran. Inf. hory, vol. 39, no. 3, pp. 773 785,(May 993). [4] J. H. Wintr, J. Salz, and R. D. Gitlin, h impact of antnna divrity on th capacity of wirl communication ytm, IEEE ran. commun., vol. 5, no. 34, pp. 74 75, (Fb./Mar./Apr. 994). [5] J. Yang and S. Roy, On joint tranmittr and rcivr optimization for multipl-input multipl-output (MIMO) tranmiion ytm, IEEE ran. Commun., vol. 4,no., pp. 3 33, (Dc. 994). [6] J. H. Wintr, h divrity gain of tranmit divrity in wirl ytm with Rayligh fading, IEEE ran. Vh. chnol., vol. 47, no., pp. 9 3, (Fb. 998). [7] G. G. Raligh and J. M. Cioffi, Spatiotmporal coding for wirl communication, in Proc. 996 IEEE Global lcommunication Conf. (GLOBECOM 96), Nov. 8, vol. 3, pp. 89 84, (996). [8] G. J. Fochini, Layrd pac-tim architctur for wirl communication, Bll Lab. chnology. Journal, Vol. 6, No.3, PP. 3-335(998). [9] B. Lu and X. Wang, Itrativ rcivr for multiur pac-tim coding ytm, IEEE J. Sl. Ara Commun., vol. 8, no., pp. 3 335, (Nov. ). 4
[] X. Zhu and R. D. Murch, Layrd pacfrquncy qualization in a ingl-carrir MIMO ytm for frquncy-lctiv channl, IEEE ran. Wirl Commun., vol. 3, no. 3, pp. 7 78, (May 4). [] M. R. McKay and I. B. Colling, Capacity and prformanc of MIMO-BICM with zroforcing rcivr, IEEE ran. Commun., vol. 53, no., pp. 74 83, (Jan. 5). [] J.H.Kotcha and A.M.Sayd, ranmit ignal dign for optimal timation of Corrlatd Journal of hortical and Applid Information chnology 5 - JAI. All right rrvd. www.jatit.org MIMO channl Kotcha, IEEE tranaction on ignal procing, Vol.5, PP.546-577(Fb 4). [3] A. J. Paulraj, D. A. Gor, R. U. Nabar, and H. Bölcki An ovrviw of MIMO communication-a Ky to Gigabit Wirl, Procding of th IEEE, Vol. 9, No., PP. 98-8(Fb. 4). 43