IJSER. S.A.Yuvaraj 1,K.Periyar Selvam 2 K.R.Jayachitra 3

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1 Iteratioal Joural of Scietific & Egieerig Research, Volume 5, Issue 4, April14 18 Adaptive Chael Estimatio Techiques for MIMO OFDM Systems S.A.Yuvaraj 1,K.Periyar Selvam 2 K.R.Jayachitra 3 Abstract I this paper, ormalized least mea () square ad recursive least squares (RLS) adaptive chael estimator are described for multiple iput multiple output (MIMO) orthogoal frequecy divisio multiplexig (OFDM) systems. These CE methods uses adaptive estimator which are able to update parameters of the estimator cotiuously, so that the kowledge of chael ad oise statistics are ot ecessary. This /RLS CE algorithm requires kowledge of the received sigal oly. Simulatio results demostrated that the RLS CE method has better performaces compared CE method for MIMO OFDM systems. I additio, the utilizig of more multiple ateas at the trasmitter ad/or receiver provides a much higher performace compared with fewer ateas. Furthermore, the RLS CE algorithm provides faster covergece rate compared to CE method. Therefore, i order to combat the more chael dyamics, the RLS CE algorithm is better to use for MIMO OFDM systems. Keywords- MIMO; ; OFDM; RLS Orthogoal frequecy divisio multiplexig (OFDM) systems have attracted much attetio as a promisig I. INTRODUCTION techology i wireless commuicatio systems. I OFDM systems, the whole spectrum is divided ito several subcarriers, ad before each OFDM block the cyclic prefix (CP) Recetly, multiple iput multiple output (MIMO) chaels have bee itroduced to achieve high data speed requisite by is iserted. So, OFDM systems ca mitigate the effects of the ext-geeratio commuicatio systems [1]. The use of multipath ad have high spectrum efficiecy. Therefore, MIMO chaels provides higher spectral efficiecy versus OFDM is the importat techique for ext-geeratio sigle iput sigle output (SISO), sigle iput multiple output commuicatio. However, it is strict about CE to exploit the (SIMO), ad multiple iput sigle-output (MISO) chaels, coheret demodulatio, detectio ad decodig [7]. whe the available badwidth is iadequate. Furthermore, the diversity gai of the MIMO chaels is early of secod order Several CE techiques have bee proposed to mitigate whe chael matrix has full rak. Cosequetly, by iterchael iterferece (ICI) i OFDM systems. I [8], the employig MIMO chaels, ot oly the mobility of the least square (LS) CE has bee proposed to miimize the wireless commuicatios ca be icreased but also the squared differeces betwee the received ad estimated sigal. algorithm ca be more robust agaist fadig, which makes it The LS algorithm, which is idepedet of the chael model, efficiet for the requiremets of the ext-geeratio wireless is commoly used i equalizatio ad filterig applicatios. services such as wireless local area etworks (WLANs), But the statistics of chaels i real world chage over time worldwide iteroperability for microwave access (WiMAX), ad iversio of the large dimesioal square matrix turs out wireless fidelity (WiFi), cogitive radio, ad 3rd geeratio to be ill-coditioed. To further improve the accuracy of the parterip project (3GPP) log term evolutio (LTE) [2]. estimator, Wieer filterig based iterative CE has bee ivestigated [9], [1]. However, this scheme also requires high complexity ad kowledge of chael correlatios. 1. S.A. Yuvaraj, Ph D Research Scholar St. Peters Uiversity 2. K. Periyar Selvam, Ph D Research Scholar St. Peters Uiversity 3. K.R. Jayachitra, Ph D. Research Scholar St. Peters Uiversity 214 I SISO flat chaels, chael estimatio (CE) ad its precisio do ot have a drastic impact o the performace of the receiver. Whereas i outdoor MIMO chaels, the precisio ad speed of covergece of the chael estimator ca drastically affect the performace of the receiver [3]. I SISO commuicatios, the chael estimators may or may ot use the traiig sequece or ot. Although the distributio of the traiig symbols i a block of data affects the performace of systems [4], but due to simplicity, it is covetioal to use the traiig symbols i the first part of each block. If the traiig sequece is ot used, the estimator is called the blid chael estimator. A blid chael estimator uses iformatio latet i statistical properties of the trasmittig data [5]. I full-rak MIMO chaels, the use of a iitial traiig data is madatory, ad without it, the chael estimator does ot coverge [2], [5]. The most importat research topic i the wireless commuicatios is the adaptive CE where the chael is rapidly time-varyig. The time-varyig multipath chael ca be represeted by a tap-delayed lie with time varyig coefficiets ad fixed tap spacig. A adaptive algorithm is a process that chages its parameters as it gai more iformatio of its possibly chagig eviromet. Amog umerous iterative techiques that exist i the ope literature, the popular category of approaches which are obtai from the miimizatio of the mea square error (MSE) betwee the output of the filter ad desired sigal to perform CE [1-15]. I this paper, ormalized least mea () square ad recursive least squares (RLS) adaptive chael estimator are described for MIMO OFDM systems. These CE methods uses

2 Iteratioal Joural of Scietific & Egieerig Research, Volume 5, Issue 4, April14 19 adaptive estimator which are able to update parameters of the estimator cotiuously, so that kowledge of chael ad oise statistics are ot required. This /RLS CE algorithm requires kowledge of the received sigal oly. This ca be doe i a digital commuicatio system by periodically trasmittig a traiig sequece that is kow to the receiver. Simulatio results ow that the RLS CE method has better performaces compared CE method for MIMO OFDM systems. I additio, the utilizig of more multiple ateas at the trasmitter ad/or receiver provides a much higher performace compared with fewer ateas. Furthermore, the RLS CE algorithm provides faster covergece rate compared to CE method. Therefore, i order to combat the chael dyamics, the RLS CE algorithm is better to use for MIMO OFDM systems. We use the followig otatios throughout this paper: bold face ad upper lower letter are used to represet matrix ad vector. Superscripts x * ad x T deote the cojugate ad cojugate traspose of the complex vector x respectively, ad the symbol E(.) deotes expectatio. The remaider of the paper is orgaized as follows. The /RLS CE scheme is preseted i sectio II, ad its performace is aalyzed i sectio III. Fially, some cocludig remarks are give i sectio IV. II. CE METHODS fuctio j (m) E[e( m)e * (m)] forthe adaptive filter A. LMS CE Method structure is A adaptive algorithm is a process that chages its parameters as it gai more iformatio of its possibly j (m ) E[R (m )R (m )] - E[S ]R * W (m ) - R (m )W (m) chagig eviromet. Amog umerous iterative techiques est est that exist i the ope literature, the popular category of E[S ] W est (m )W est (m )E [S (m )S (m )]S approaches which are obtai from the miimizatio of the 2 MSE betwee the output of the filter ad desired sigal to perform CE as ow i Fig. 1. r C (m )W est (m ) - W est (m )C (m) D (m )W T Es (m )W (m), (5) AWGN t Est oise 2 Z(m) where is the variace of the received sigal, Trasmitte R d sequece Receive sigal S(m) Multipath chael model W(m) Mechaism for adaptive of weight update coefficiets West(m) + R(m) e(m) Filter output ]. I the Fig 1, we have ukow multipath fadig chael, that has to be estimated with a adaptive filter whose weight are updated based o some criterio so that coefficiets of adaptive filter ould be as close as possible to the ukow chael. The output from the chael ca be expressed as: L-1 R (m) W (m, l ) S (m - l ) Z (m), (1) l where S(m-l) is the complex symbol draw from a costellatio s of the lth paths at time m-l, L is the chael legth, Z(m) is the AWGN with zero mea ad variace ζ 2. The above equatio ca be rewritte as vector otatio [1]: R( m) W (m) S (m) Z (m), (2) The output of the adaptive filter is Y (m) W est (m) S (m), (3) where W est ( m) is the estimated chael coefficiets at time m. The priori estimated error sigal eeded to update the weights of the adaptive filter is e( m) R (m) - Y (m) W (m)s (m ) Z (m) W est (m )S (m) (4) This error sigal is used by the CE to adaptively adjust the weight vector so that the MSE is miimized. Now the cost C (m) E[ S (m) R( m)]is the cross-correlatio vectorbetwee the tap iput vector S(m) ad the received sigal r(m), ad D( m) E[ S (m) S T (m)] is the correlatio matrix of the tap iput sigal S(m). Now takig the gradiet vector with respect to W est (m) : j (m)- 2C (m) 2D(m) W est (m) 2S (m)r * (m) 2S (m)s (m)w est (m). (6) Accordig to the method of steepest descet, if W est (m) is the tap-weight vector at the mth iteratio the the followig recursive equatio may be used to update W est (m) : Figure 1. Scheme for adaptive CE. The sigal S(m) is trasmitted via a time-varyig chael W(m), ad corrupted by a additive oise estimated by usig ay kid of CE method. The mai aim of most chael estimatio algorithms is to miimize the mea squared error (MMSE) i.e., betwee the received sigal ad its estimate [16-214

3 Iteratioal Joural of Scietific & Egieerig Research, Volume 5, Issue 4, April14 2 W est () W est (m ) - 1/ 2j (m) W est (m )S (m )[R * (m ) - W est (m )S (m)] W est (m ) S (m )e * (m), (7) where W est (m+1) deotes the weight vector to be computed at iteratio (m + 1) ad η is the LMS step size which is related to the rate of covergece. The smaller step size meas that a loger referece or traiig sequece is eeded, which would reduce the payload ad hece, the badwidth available for trasmittig data. The term [ S ( m)e * ( m) ] represets the correctio factor or adjustmet that is applied to the curret estimate of the tap-weight vector. I order to improved system performace, takig ito accout the variatio i the sigal level at the filter iput ad selects a ormalized step size parameter i.e., S ( m) W () W (m) e * (m), (8) coveiece of computig, let D(m) = R (m) ad est est S (m)s (m) D (m -1)S (m) K (m) (13) The iterative procedure is started with a iitial guess W est (). K (m) D( m) S (m) R -1 (m) S (m) (15) Therefore, the based CE is least sesitive to the scalig 1-1 S H (m)d (m -1)S (m) of its iput sigal variatio. Therefore, this algorithm is able to sese the best possible chael coefficiets are chagig. The K(m) is referred as a gai matrix. We may rewrite (9) as: B. RLS CE Method D( m) -1 D( m -1) - -1 K (m) s H (m) D( m -1) (14) The RLS CE requires all the past samples of the iput ad W (m -1) K (m) H(m), (16) the desired output is available at each iteratio. The objective fuctio of a RLS CE algorithm is defied as a expoetial weighted sum of errors squares: K (m) D( m) S (m) R -1 (m ) H (m) - WH (m -1)S (m) (17) c(m) = λ -m e H (m)e(m) + δλ W H (m)w(m), (9) Therefore, equatio (17) is the recursive RLS CE m = 1 algorithm where δ is a positive real umber called regularizatio parameter, e(m) is the prior estimatio error, ad λ is the expoetial forgettig factor with < λ < 1. The prior estimatio error is the differece betwee the desired respose ad estimatio sigal: to update chael coefficiet. III. ANALYTICAL RESULTS The error performace of the aforemetioed iterative e(m) = H(m) - WH (m) S(m) (1) The objective fuctio is miimized by takig the partial derivatives with respect to W() ad settig the results equal to zero. δc ( m) - 2 λ -m S (m)e H (m) + 2δλW (m) δw (m) - 2 λ -m S (m )[H (m ) - W H (m )S (m )] H +2δλ W (m) W (m )[ λ -m S (m )S H (m ) +δλ I ] λ -m S (m)h H (m) R s (m )W (m ) R (m) W (m) R 1 (m ) R (m) (11) where R s (m) s is the Trasmitted auto-correlatio matrix R s (m) -m S (m)s H (m) I R s (m -1) S (m)s H (m) m1 ad R (m) is The cross correlatio matrix i.e., R (m) -m S (m)h H (m)r (m -1) S (m)h H (m). Accordig to the Woodbury idetity, the above R (m) ca be writte as -2 R -1 (m -1)S (m)s H (m)r -1 (m -1) R - Sh 1 (m) -1 R -1 (m -1) - s h 1-1 S H (m)r -1 (m -1)S (m) For estimatio algorithm is explored by performig extesive computer simulatios. I these simulatios, we cosider 2 by 2, 4 by 4, 6 by 6, ad 8 by 8 MIMO OFDM systems. The data symbol is based o Q-PSK modulatio. The forgettig factor is.9 ad learig rate is.4, ad sigal to oise ratio is 15 db. From the simulatio results, oe ca observed that the RLS CE (12) (m) S (m) (15) 214

4 Iteratioal Joural of Scietific & Egieerig Research, Volume 5, Issue 4, April14 21 method has better performaces compared CE method. I additio, the utilizig of more multiple ateas at the trasmitter ad/or receiver provides a much higher BER x6 MIMO-OFDM chael estimatio RLS Furthermore, the RLS CE algorithm provides faster covergece rate compared to NLS CE method. Therefore, i order to combat the chael dyamics, the RLS CE algorithm is better to use for OFDM systems. But the RLS CE algorithm is suffered from a computatioal complexity poit of view. I additio, the RLS algorithm has the recursive iversio of a estimate of the autocorrelatio matrix of the iput sigal as its corerstoe; problems arise, if the autocorrelatio matrix is rak deficiet. 2x2 MIMO-OFDM chael estimatio Iteratio umber Figure 4. 6 by 6 MIMO systems 8x8 MIMO-OFDM chael estimatio RLS -1 RLS Iteratio umber Figure 2. 2 by 2 MIMO systems x4 MIMO-OFDM chael estimatio Figure 3. 4 by 4 MIMO systems Iteratio umber Figure 5. 8 by 8 MIMO systems IV. CONCLUSION Recetly, multiple iput multiple output (MIMO) trasmissio has bee well kow as oe of the most importat practical techique to combat fadig as well as icrease the chael capacity of wireless commuicatio systems. I this paper, ad RLS adaptive chael estimator are described for MIMO OFDM systems. Simulatio results demostrated that the RLS CE method has better performaces compared CE method for MIMO OFDM systems. I additio, the utilizig of more multiple ateas at the trasmitter ad/or receiver provides a much higher performace compared with fewer ateas. Therefore, i order to combat the chael dyamics, the RLS CE algorithm is better to used for MIMO OFDM systems. 214

5 Iteratioal Joural of Scietific & Egieerig Research, Volume 5, Issue 4, April14 22 chael estimatio i OFDM systems, Radio Egieerig REFERENCES joural, vol. 19, o. 1, pp , Apr [2] Q. Li, G. Li, W. Lee, M. il Lee, D. Mazzarese, B. Clerckx, ad Z. [1] G. J. Foschii ad M. J. Gas, O limits of wireless commuicatios i a fadig eviromet whe usig multiple Li, MIMO techiques i WiMAX ad LTE: a feature ateas, Wireless Pers.Commu., vol. 6, o. 3, pp , overview, Mar IEEE Commu. Magazie, vol. 48, o. 5, pp , May. [2] E. Karami, Trackig performace of least squares MIMO chael estimatio algorithm, IEEE Tras. O Wireless Comm. vol. 55, o.11, pp , Nov. 27. [3] V. Pohl, P. H. Nguye, V. Jugickel, ad C. Vo Helmolt, How ofte chael estimatio is eeded i MIMO systems, i Proc. IEEE GlobalTelecommu. Cof., o. 1, pp Dec. 23, [4] S. Addireddy, L. Tog, ad H. Viswaatha, Optimal placemet of traiig for frequecy-selective block-fadig chaels, IEEE Tras. If.Theory, vol. 48, o. 8, pp , Aug. 22. [5] L. Tog, Blid sequece estimatio, IEEE Tras. O Commu., vol. 43, o. 12, pp , Dec [6] A. Vosoughi ad A. Scaglioe, Chael estimatio for precoded MIMO systems, i Proc. IEEE Workop Statist. Sigal Process., pp , Sep. 28 Oct. 1, 23. [7] J. Li, J. Ma, S. Liu RLS chael estimatio with superimposed traiig, i Proc. It. Co. o Comm. Techology, 28. [8] A. Acora, C. B. Meili, ad D. T. Slock, Dow-sampled impulse respose least-squares chael estimatio for LTE OFDMA, i Proc.It. Co. o Acoustics, Speech, ad Sigal Processig, pp. III 293 III 296, Apr. 27. [9] L. A. M. R. D. Temio, C. N. I Macho, C. Rom, T. B. Sorese, ad P. Mogese, Iterative chael estimatio with robust wieer filterig i LTE dowlik, i Proc. It. Co. o VTC, pp. 1-5, Sept. 28. [1]J. J. V. D. Beek, O. E. M. Sadell, S. K. Wilsoy, ad P. O. Baorjesso, O chael estimatio i OFDM systems, i Proc. It. Co. o VTC, vol. 2, pp , July [11] S. Hayki, Adaptive Filter Theory, Pretice-Hall Iteratioal Ic, [12] F. Adachi, H. Tomeba, ad K. Takeda, Frequecy-domai equalizatio for broadbad sigle-carrier multiple access, IEICE Tras. o Commu., vol. E92-B, o. 5, pp , May 29. [13] S. Yameogo, J. Palicot, ad L. Cariou, Blid time domai equalizatio of SC-FDMA sigal, i Proc. Vehicular Techology Coferece, Sept. 29, pp. 14. [14] S. Y. Park, Y. G. Kim, ad C. G. Kag, Iterative receiver for joit detectio ad chael estimatio i OFDM systems uder mobile radio chaels, IEEE Tras. o Vehicular Techology, vol. 53, o. 2, pp , Mar. 24. [15] J. Berkma, C. Carboelli, F. Dietrich, C. Drewes, ad W. Xu, O 3G LTE termial implemetatio-stadard, algorithms, complexities ad challeges, i Proc. Wireless Commu. ad Mobile Computig Coferece, Aug. 28, pp [16] W. C. Jakes, Ed., Microwave mobile commuicatios. New York: Wiley-IEEE Press, Ja [17] B. Karakaya, H. Arsla, ad H. A. Curpa, Chael estimatio for LTE uplik i high Doppler spread, i Proc. Wireless Commu. Ad Networkig Coferece, Apr. 28, pp [18] R. C. Alvarez, R. Parra-Michel, A. G. O. Lugo, ad J. K. Tugait, Ehaced chael estimatio usig superimposed traiig based o uiversal basis expasio, IEEE Tras. o Sigal Process., vol. 57, o. 3, pp , Mar. 29. [19] A. Kalayciogle ad H. G. Ilk, A robust threold for iterative 214

Adaptive Channel Estimation Techniques for MIMO OFDM Systems

Adaptive Channel Estimation Techniques for MIMO OFDM Systems (IJACSA) Iteratioal Joural of Advaced Computer Sciece ad Applicatios, Adaptive Chael Estimatio Techiques for MIMO OFDM Systems Md. Masud Raa Dept. of Electroics ad Radio Egieerig Kyug ee Uiversity South