International Journal of Scientific & Engineering Research, Volume 4, Issue 8, August ISSN

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1 Intrnational Journal of Scintific & Enginring Rsarch, Volum 4, Issu 8, August Comparison & Prformanc Evaluation of Various Equalization Tchniqus for MIMO ODM Systm *PARUL WADHWA DEPARTMENT O ECE wadhwa2parul@gmail.com ER.GAURAV GUPTA (ASST.PROESSOR) DEPARTMENT O ECE gauravgupta381@gmail.com DOON VALLEY INSTITUTE O ENGINEERING & TECHNOLOGY, KARNAL ABSTRACT- MIMO Systms us multipl inputs and multipl outputs from a singl channl. Thy ar dfind by Spatial Divrsity and Spatial Multiplxing. Th ffct of fading and intrfrnc ffcts can b minimizd with qualizr. Th prformanc of diffrnt qualization tchniqus for MIMO-ODM systm is analyzd. Th BER charactristics for varying numbr of rciving antnna ar dtrmind in mat lab tool box. Th simulation is carrid out & it is obsrvd that th MMSE qualizr basd rcivr is a good choic for rmoving som ISI and rducs th total nois powr. Th rsults show that th BER dcrass as th m x n antnna configuration incrass. Tx2 Gnral Trms-, Bit rror rat, Equalizr, rciving antnna, Signal to nois ratio (Eb/N), transmitting antnna, Kywords- ISI (Intr Symbol Intrfrnc), MIMO (Multipl Input h Multipl output), MMSE (Minimum Man Squar Error), MRC x,r (Maximal Ratio Combining), SNR (Signal to Nois Ratio), Z (Zro. orcing, Txn 1. INTRODUCTION ig. 1 MIMO SYSTEM In th nvr-nding sarch for incrasd capacity in wirlss communication channl it has bn shown that by using MIMO (Multipl Input Multipl Output) systms it is possibl to incras that capacity substantially. Usually fading is considrd as a problm in wirlss communication but MIMO channls uss th fading to incras th capacity. Th systm with multipl antnnas at th transmittr and rcivr is known as multipl input multipl output (MIMO) systms. MIMO systms transmit diffrnt signals from ach transmit lmnt so that th rciving antnna array rcivs a suprposition of all th transmittd signals. All signals ar transmittd from all lmnts onc and th rcivr solvs a linar quation systm to dmodulat th mssag. Th multipl antnnas ar thus usd to incras data rats through multiplxing or to improv prformanc through divrsity. MIMO channl modl is shown in fig.1 with M transmittr and N rcivr antnnas. It is achivd by highr spctral fficincy, link rliability and divrsity (rducd fading). h 1,1 Tx1 Rx1 h 2,2 Rx2 ODM (Orthogonal rquncy Division Multiplxing) ODM is bcoming widly applid in wirlss communications systms du to its high rat transmission capability with high bandwidth fficincy and its robustnss with rgard to multipath fading and dlay. ODM involvs snding svral signals at on givn tim ovr svral diffrnt frquncy channls, or subcarrirs. Th principl of orthogonality hlps to nsur that cross talk dos not occur btwn th carrir frquncis. Dspit th fact that th signals ovrlap in th frquncy domain, it is possibl from a rcivr s point of viw to xtract data from on spcific carrir simply by knowing its frquncy. Rxn

2 Intrnational Journal of Scintific & Enginring Rsarch, Volum 4, Issu 8, August Spac Tim Encod r Spac Tim Encod r ig. 2 MIMO-ODM SYSTEM Th figur shows that th rcivd signal at ach rciv antnna is th suprposition of four distortd transmittd signals. whr 2. MMSE EQUALIZER In MIMO wirlss communication, an qualizr is ndd which is a ntwork that is usd to rcovr a signal that suffrs from Intr symbol Intrfrnc (ISI) and th BER charactristics is improvd and a good SNR is maintaind. A Minimum Man Squar Error (MMSE) stimator is a mthod which rducs th man squar rror (MSE). MMSE qualizr dos not compltly liminat ISI but minimizs th total powr of th nois and ISI componnts in th output Dfinition Man Squar Error IT IT IT IT T T T Sp ac Ti m Pr oc s so r S p a c Ti m D c o d r stimator. In ths cass, on possibility is to sarch th tchniqu that minimizs th MSE within a particular class such as linar stimators. Th linar MMSE stimator is th stimator that achivs minimum MSE from all stimators of th form AY + b. If th masurmnt Y is a random vctor thn A is a matrix and b is a vctor Minimum Man Squar Error (MMSE) qualizr for 2 2 MIMO channl:- Now thr is a mthod to undrstand for xtracting th two symbols which intrfrs with ach othr. In th first tim slot, th rcivd signal on th first rciv antnna is y 1 = h 1,1 x 1 + h 1,2 x 2 + n 1 = h 1,1 h 1,2 x 1 x 2 + n 1. Th rcivd signal on scond rciv antnna is y 2 = h 2,1 x 1 + h 2,2 x 2 + n 2 = h 2,1 h 2,2 x 1 x 2 + n 2 y 1, y 2 - rcivd symbols on th first and scond antnna rspctivly, h 1,1 - channl from 1 st transmit antnna to 1 st rciv antnna, h 1,2 - channl from 2 nd transmit antnna to 1 st rciv antnna, h 2,1 - channl from 1 st transmit antnna to 2 nd rciv antnna, h 2,2 - channl from 2 nd transmit antnna to 2 nd rciv antnna, x 1, x 2 - transmittd symbols and n 1,n 2 - nois on 1 st, 2 nd rciv antnna. Suppos X is an unknown random variabl, and Y is a known random variabl. An stimator X (y) is any function of th masurmnt Y and Man squar rror is mathmatically givn as: MSE = E X X 2 whr th xpctation is takn ovr both X and Y. Th MMSE stimator is dfind as th stimator which achivs minimal MSE. Gnrally, it is vry difficult to dtrmin a closd form for th MMSE Now assuming that th rcivr knows h 1,1, h 1,2, h 2,1, h 2,2, y 1 and y 2. Equivalntly th abov quation is rprsntd as:- Y = hx + n whr, Y= rcivd symbol in channl matrix x= input symbol &

3 Intrnational Journal of Scintific & Enginring Rsarch, Volum 4, Issu 8, August n= nois & in matrix notation it is givn as:- y 1 y 2 = h 1,1 h 1,2 h 2,1 h 2,2 * x 1 x 2 + n 1 n 2 & qualizr impuls rspons to zro at all but on of th NT spacd sampl points in tappd dlay lin filtr. By ltting th numbr of cofficints incrass without bound, infinit lngth qualizr with zro ISI at output can b obtaind. Th Minimum Man Squar Error (MMSE) also tris to find a cofficint W which minimizs E W y x W y x H 2.4. Maximal-ratio combining Equalizr To solv this, a matrix is ndd which satisfis MMSE dtctor for mting this constraint is givn as:- W = [H H H + N I ] 1 H H Whr W - Equalization Matrix, H - Channl Matrix. This matrix is known as th psudo invrs for a gnral m x n matrix & H H H = h 1,1 h 2,1 h1,1 h 1,2 h 2,2 h 1,1 2 + h 2,1 2 h 1,1 h 1,2 + h 2,1 h 2,2 h 1,2 h 1,1 + h 2,2 h 2,1 h 1,2 2 + h 2,2 2 h 1,2 = h 2,1 h 2,2 Whn comparing th quation in Zro orcing qualizr, apart from th N I trm both th quations ar comparabl. In fact, if th nois trm is zro, th MMSE qualizr rducs to Zro orcing qualizr. Th BER for BPSK Modulation in Rayligh fading channl is dfind as:- P b = 1 2 Whr E b NO E b NO +1 P b = E b NO = Signal to Nois Ratio 2.3. Zro orcing Equalizr Zro forcing qualizr rfrs to a form of linar qualization algorithm usd in communication systms which invrts th frquncy rspons of th channl. In this, th qualizr cofficints (C n ) ar chosn to forc th sampls of th combind channl In tlcommunication, maximal-ratio combining is a mthod of divrsity combining in which:- (a) Th signals from M branchs ar wightd according to thir individual signal voltag to nois powr ratios & thn summd. (b) Bfor bing summd, individual signals must b co phasd which gnrally rquirs individual rcivr & phasing circuit for ach antnna lmnt. (c) MRC producs an output with an accptabl SNR qual to sum of individual SNR s. (d) In Maximum Ratio Combining (MRC) amplituds and phass of th data signals rcivd ar adjustd with th hlp of digital signal procssing in such a way that signal addition lads to gains in th S/N ratio and hnc to a bttr bit rror ratio (BER). 3. RESULTS & DISCUSSIONS Equalization Tchniqus ar of normous importanc in th dsign of high data rats wirlss systms. Thy can combat for Intrsymbol Intrfrnc vn in mobil fading channls with high fficincy. Zro forcing Equalizr prforms wll only in thortical assumption that is whn nois is zro. This also hlps to achiv data rat gain, as shown in fig no. 3. Minimum Man Squar Equalizr uss LMS (last man squar) as a critrion to compnsat ISI, as shown in fig.3.

4 Intrnational Journal of Scintific & Enginring Rsarch, Volum 4, Issu 8, August BER for BPSK modulation with 2x5 MIMO and MMSE,Z and MRC qualizr (Rayligh cha (BER for BPSK modulation with 2xN MIMO ) 1-1 sim (ntx=2, nrx=5, MMSE) thory (ntx=2,nrx=2, Z) thory (ntx=2,nrx=2, MRC) 1-1 sim (ntx=2, nrx=2, MMSE) thory (ntx=2,nrx=2, Z) thory (ntx=2,nrx=n, MRC) Avrag Eb/No,dB ig.3 Plot for BER for BPSK modulation for MMSE, MRC and Z Equalizr in Rayligh Channl for (2 5) MIMO systm. BER and SNR valus for MMSE, MRC and Z Equalizr in 2 2 MIMO systm. Minimum Man Squar Equalizr not only liminats ISI componnts but also minimizs th total powr of nois as shown in fig no.4 as compard to Zro orcing Equalizr th rsults in lowring th chancs of incorrct dcisions rsulting in normous intrfrnc cancllation as shown in fig no 4 and thr is a lss improvmnt in th Avrag Eb/No,dB ig.4 Plot for BER and SNR for MMSE for diffrnt numbr of rcivrs. rom th simulation, rsults in th form of bar chart ar shown in th fig.6 shows that th of MMSE qualizr basd rcivr is lss as compard to Zro orcing Equalizr. As shown in Tabl1.1 th BER for Thortical MRC is.581, Simulatd MMSE is.925 and for Thortical Z is This shows that MRC has lowr BER as compard to MMSE in vry cas.

5 Intrnational Journal of Scintific & Enginring Rsarch, Volum 4, Issu 8, August BER for BPSK modulation with 2x2 MIMO.6 9 x 1-3 and MMSE,Z and MRC BER Valus for MMSE,MRC and Z Eb/No Equalizr in (2 2)MIMO systm No of MRC Z MMSE Rcivrs Column Column Z Eb/No MRC Eb/No,dB MMSE Eb/No Column ig.5 Plot for BER and SNR for MMSE, MRC and Z Equalizr in Rayligh Channl for (2 2) MIMO systm. Column Th simulations wr carrid out at MATLAB which mans kping th transmittr antnna as two and Column vary th numbr of antnnas in th rcivr sid as shown in figur blow. Column BER for BPSK modulation with 2xN MIMO for MMSE.12 Column Column Column Column Column Column Column Column numbr of rcivrs ig.6 Bar graph plot for BER with varying numbr of rcivrs. rom th MATLAB figur window shown in fig.5 shows th consolidatd rsult in th form of chart comparison. rom fig.6, it is vidnt that BER dcrass as th rcivr antnna incrass for Minimum Man Squar Equalizr. or a bttr clarity

6 Intrnational Journal of Scintific & Enginring Rsarch, Volum 4, Issu 8, August th data from th fig.3 is takn and plottd in th form of bar chart as shown in fig.6. Similarly now th antnna configuration is varid namly 2 n as shown in fig.6, as th numbr of rcivrs (n) is incrasd kping th numbr of transmittrs (m=2) as constant, Th Bit Error rat dcrass in MMSE qualizr with incras in rcivrs. Th following obsrvations ar mad. Z has low computational complxity. It minimizs th probability of a squnc rror. Hnc from th abov graphs it is vidnt that th BER dcrass as th numbr of rciving antnna incrass with rspct to numbr of transmitting antnna in Z qualizr basd MIMO rcivr. This qualizr is usd for mobil communication link. ig.3 and 5 and tabl 1.1 shows that as th no. of rcivrs (n) is incrasd kping th no. of transmittr (m=2) as constant it is vidnt that th Bit Error Rat (BER) dcrass in MMSE qualizr and also whn th numbr of transmittrs is lss than th numbr of rcivrs. In this analysis w considr a fixd antnna MIMO antnna configuration and compard th prformanc with th thr typs of qualizr basd rcivr namly MRC, MMSE and Z. Comparativ valus of BER for fixd MIMO configuration and how th two diffrnt qualizrs xhibit th BER charactristics for a particular Eb/No valu using BPSK modulation mthod. As th no of rcivrs (n) is incrasd kping th no of transmittrs (m) constant it is vidnt that th (BER) dcrass. 4. CONCLUSION To conclud this papr provids th dtaild knowldg of th ky issus in th fild of mobil communication. Th data transmission at high bit rat is ssntial for many srvics such as vido, high quality audio and mobil intgratd srvic digital ntwork. Whn data is transmittd at high bit rats ovr mobil radio channls, th channl impuls rspons can xtnd ovr many symbol priods which lads to Intrsymbol Intrfrnc. Th ultimat goal is to provid univrsal prsonal and multimdia communication without rgard to mobility or location with a high data rats. To achiv such an objctiv a strong qualization tchniqu i.. MMSE is takn. Th rcivr schm is basd on MMSE. prformanc for MIMO-MMSE in corrlatd Rayligh flat fading channl is bttr than Zro orcing Equalizr. Two typs of simulation analysis ar carrid out at MATLAB. Th Simulation analysis that by varying th rcivr antnna kping transmittr antnna constant for a particular typ of qualizr basd rcivr at a particular Eb/No valu using BPSK modulation mthod. Simulation analysis 2 prsnts about th fixd MIMO antnna configuration and compar th prformanc with th thr typs of qualizr basd rcivr namly MRC, MMSE and Z. Th Zro orcing Equalizr rmovs all ISI and is idal only whn th channl is noislss. Whn th channl is noisy, th Zro orcing Equalizr has a tndncy to amplify th nois and is much suitd for static channls with high SNR. Though MMSE is a balancd linar qualizr it dos not liminat ISI compltly but instad minimizs th total powr of th nois and ISI componnts in th output. Th MMSE qualizr givs minimum BER valus for corrsponding Eb/No valus. As th numbr of transmittrs is lss and mor in numbr, BER dcrass for a particular valu of Eb/No valu. BER prformanc of MRC Equalizr is suprior to MMSE Equalizr. Th BER valus from fig.3 ar.581 for MRC and.925 for MMSE. Basd on th mathmatical modling and th simulation rsult it is infrrd that th MRC qualizr is th bst of th thr qualizrs. 5. REERENCES [1] Rick S. Blum, Y (Goffry) Li, Jack H. Wintrs, and Qing Yan, Improvd Spac Tim Coding for MIMO-ODM Wirlss Communications, IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 49, NO. 11, NOVEMBER 21. [2] Kai-Kit Wong, Mmbr, IEEE, Ross D. Murch, Snior Mmbr, IEEE, and Khald Bn Ltaif, llow, IEEE, Prformanc Enhancmnt of Multiusr MIMO Wirlss Communication Systms, IEEE TRANSACTIONS ON

7 Intrnational Journal of Scintific & Enginring Rsarch, Volum 4, Issu 8, August COMMUNICATIONS, VOL. 5, NO. 12, DECEMBER 22. [3] Jiang Yu, Kyong Jin Kim, Jrry D. Gibson, Ronald A. Iltis, Channl Estimation and Data Dtction for MIMO-ODM Systms, GLOBECOM 23. [4] Quntin H. Spncr, Studnt Mmbr, IEEE, A. L Swindlhurst, Snior Mmbr, IEEE, and Martin Haardt, Snior Mmbr, IEEE, Zro-orcing Mthods for Downlink Spatial Multiplxing in Multiusr MIMO Channls, IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 52, NO. 2, EBRUARY 24. [5] Gordon L. Stubr, llow, IEEE, John R. Barry, Mmbr, IEEE, Stv W. Mclaughlin, Snior Mmbr, IEEE, YE (Goffry) LI, Snior Mmbr, IEEE, Mary Ann Ingram, Snior Mmbr, IEEE, and Thomas G. Pratt, Mmbr, IEEE, Broadband MIMO-ODM Wirlss Communications, PROCEEDINGS O THE IEEE, VOL. 92, NO. 2, EBRUARY 24. [6] Ttsushi Ab, Takahiro Asai and Hirohito Suda, A Practical Throughput Comparison of MIMO- CDMA and MIMO-ODM, IEEE 24. [7] Bartosz Milczark and Witold Krzymin, Throughput of Ralistic Multi-Usr MIMO-ODM Systms, ISSSTA 24, Sydny, Australia, 3 Aug. - 2 Sp. 24. [8] Tasang Yoo and Andra Goldsmith, Optimality of Zro-orcing Bam forming with Multiusr Divrsity, IEEE 25. [9] N.Sathish Kumar, Dr. K.R.Shankar Kumar, Prformanc Analysis of M*N Equalizr basd Minimum Man Squar Error (MMSE) Rcivr for MIMO Wirlss Channl, Intrnational Journal of Computr Applications ( ) Volum 16 No.7, bruary 211. [1] Wirlss Communications (Principls & Practic), scond dition by Thodor S. Rappaport. affiliatd from Kurukshtra Univrsity, Kurukshtra in yar 211. Sh is currntly doing rsarch on various qualization tchniqus for MIMO Systms. Gaurav Gupta rcivd his M.Tch dgr from UIET, Kurukshtra in 212. H rcivd his B.Tch dgr from SKIET, Kurukshtra affiliatd from Kurukshtra Univrsity, Kurukshtra in 27. Prsntly h is working as an Assistant Profssor in Doon Vally Institut of Enginring & Tchnology, Karnal affiliatd from Kurukshtra Univrsity. Parul Wadhwa is pursuing hr M.Tch from Doon Vally Institut of Enginring & Tchnology, Karnal affiliatd from Kurukshtra Univrsity, Kurukshtra. Sh rcivd hr B.Tch dgr in Elctronics and Communication Enginring from Doon Vally Institut of Enginring & Tchnology, Karnal