Adaptive Channel Estimation Techniques for MIMO OFDM Systems

Transcription

1 (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 Korea Md. Kamal osai School of Egieerig Deaki Uiversity Victoria-317, Australia Abstract I this paper, ormalized least mea () square ad recursive least squares () adaptive chael imator are described for multiple iput multiple output (MIMO) orthogoal frequecy divisio multiplexig (OFDM) systems. These CE methods uses adaptive imator which are able to update parameters of the imator cotiuously, so that the kowledge of chael ad oise statistics are ot ecessary. This / CE algorithm requires kowledge of the received sigal oly. Simulatio results demostrated that the 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 CE algorithm provides faster covergece rate compared to CE method. Therefore, i order to combat the more chael dyamics, the CE algorithm is better to use for MIMO OFDM systems. Keywords- MIMO; ; OFDM; I. INTRODUCTION Recetly, multiple iput multiple output (MIMO) chaels have bee itroduced to achieve high data speed requisite by the ext-geeratio commuicatio systems [1]. The use of MIMO chaels provides higher spectral efficiecy versus sigle iput sigle output (SISO), sigle iput multiple output (SIMO), ad multiple iput sigle-output (MISO) chaels, whe the available badwidth is iadequate. Furthermore, the diversity gai of the MIMO chaels is early of secod order whe chael matrix has full rak. Cosequetly, by employig MIMO chaels, ot oly the mobility of the wireless commuicatios ca be icreased but also the algorithm ca be more robust agaist fadig, which makes it efficiet for the requiremets of the ext-geeratio wireless services such as wireless local area etworks (WLANs), worldwide iteroperability for microwave access (WiMAX), wireless fidelity (WiFi), cogitive radio, ad 3rd geeratio partership project (3GPP) log term evolutio (LTE) []. I SISO flat chaels, chael imatio (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 imator ca drastically affect the performace of the receiver [3]. I SISO commuicatios, the chael imators 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 imator is called the blid chael imator. A blid chael imator 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 imator does ot coverge [], [5]. Orthogoal frequecy divisio multiplexig (OFDM) systems have attracted much attetio as a promisig 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) is iserted. So, OFDM systems ca mitigate the effects of multipath ad have high spectrum efficiecy. Therefore, OFDM is the importat techique for ext-geeratio commuicatio. owever, it is strict about CE to exploit the coheret demodulatio, detectio ad decodig [7]. Several CE techiques have bee proposed to mitigate iterchael iterferece (ICI) i OFDM systems. I [8], the least square (LS) CE has bee proposed to miimize the squared differeces betwee the received ad imated sigal. The LS algorithm, which is idepedet of the chael model, is commoly used i equalizatio ad filterig applicatios. But the statistics of chaels i real world chage over time ad iversio of the large dimesioal square matrix turs out to be ill-coditioed. To further improve the accuracy of the imator, Wieer filterig based iterative CE has bee ivigated [9], [1]. owever, this scheme also requires high complexity ad kowledge of chael correlatios. 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 134 P a g e

2 (IJACSA) Iteratioal Joural of Advaced Computer Sciece ad Applicatios, of the mea square error (MSE) betwee the output of the filter ad desired sigal to perform CE [15]. I this paper, ormalized least mea () square ad recursive least squares () adaptive chael imator are described for MIMO OFDM systems. These CE methods uses adaptive imator which are able to update parameters of the imator cotiuously, so that kowledge of chael ad oise statistics are ot required. This / 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 show that the 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 CE algorithm provides faster covergece rate compared to CE method. Therefore, i order to combat the chael dyamics, the 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 / 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 METODS A. LMS CE Method 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 MSE betwee the output of the filter ad desired sigal to perform CE as show i Fig. 1. Trasmitted sequece S(m) Multipath chael model W(m) Mechaism for adaptive update of weight coefficiets W(m) AWGN oise Z(m) R(m) Figure 1. Scheme for adaptive CE. e(m) Filter output Receive sigal - ay kid of CE method. The mai aim of most chael imatio algorithms is to miimize the mea squared error (MMSE) i.e., betwee the received sigal ad its imate [16- ]. I the Fig 1, we have ukow multipath fadig chael, that has to be imated with a adaptive filter whose weight are updated based o some criterio so that coefficiets of adaptive filter should be as close as possible to the ukow chael. The output from the chael ca be expressed as: L 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. The above equatio ca be rewritte as vector otatio [1]: R( m) W( m) S( m) Z( m), () The output of the adaptive filter is Y( m) W ( m) S( m), (3) where W ( m ) is the imated chael coefficiets at time m. The priori imated 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 ( 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 fuctio j( m) E[ e( m) e ( m)] for the adaptive filter structure is j m E R m R m E S R W m R m W m [ ] - [ ] - E[ S] W ( m) W ( m) E[ S( m) S( m)] S C( m) W ( m) - W ( m) C( m) r T D( m) W ( m) W ( m), (5) where r is the variace of the received sigal, C( m) E[ S( m) R( m)] is the cross-correlatio vector betwee the tap iput vector S(m) ad the received sigal r(m), T ad D( m) E[ S( m) S ( m)] is the correlatio matrix of the tap iput sigal S(m). Now takig the gradiet vector with respect to W ( m ): j( m) - C( m) D( m) W ( m) - S( m) R ( m) S( m) S( m) W ( m). (6) (m) Accordig to the method of steep descet, if W is the tap-weight vector at the mth iteratio the the followig recursive equatio may be used to update W : (m) The sigal S(m) is trasmitted via a time-varyig chael W(m), ad corrupted by a additive oise imated by usig 135 P a g e

3 (IJACSA) Iteratioal Joural of Advaced Computer Sciece ad Applicatios, W ( m 1) W ( m) - 1/ j( m) W m S m R m W m S m [ - ] W m S m e m, (7) where W (m1) 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 imate 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., Sm W m W m e m S( m) S( m) ( 1), (8) W (). The iterative procedure is started with a iitial guess Therefore, the based CE is least sesitive to the scalig of its iput sigal variatio. Therefore, this algorithm is able to sese the b possible chael coefficiets are chagig. B. CE Method The CE requires all the past samples of the iput ad the desired output is available at each iteratio. The objective fuctio of a CE algorithm is defied as a expoetial weighted sum of errors squares: -m c(m) = λ (m) (m) δλ W (m)w(m), (9) e e m = 1 where δ is a positive real umber called regularizatio parameter, e(m) is the prior imatio error, ad λ is the expoetial forgettig factor with < λ < 1. The prior imatio error is the differece betwee the desired respose ad imatio sigal: e(m) = (m) - W (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. Cm W( m) -m - S( m) e ( m) W ( m) m 1 -m - S( m)[ ( m) - W ( m) S( m)] W ( m) m 1 -m -m [ ] W m S m S m I S m m m 1 m 1 R ( m) W ( m) R ( m) s W( m) sh R 1 ( m) R ( m) (11) s sh where R (m) s is the trasmitted auto-correlatio matrix -m s s( ) m1 R m S m S m I R m S m S m ad i.e., R is the cross correlatio matrix sh (m) -m sh sh( ). m 1 R m S m m R m S m m Accordig to the Woodbury idetity, the above be writte as R (m) sh ca - Rsh ( m ) S( m) S ( m) Rsh ( m ) Rsh ( m) Rsh ( m ) - (1) 1 S ( m) Rsh( m ) S( m) For coveiece of computig, let D(m) = R sh (m) ad D( m ) S( m) Km (13) 1 S ( m) D( m ) S( m) The K(m) is referred as a gai matrix. We may rewrite (9) as: D m D m K m s m D m ( ) - ( ) (14) So simply (13) to K m D m S m R m S m sh (15) Substitutig (14), (15) ito (11), we obtai the followig CE formula W ( m) W ( m ) K( m)[ ( m) - W ( m ) s( m)] W ( m ) K( m) ( m), (16) where ε(m) is a prior imatio error as ( m) ( m) - W ( m) S( m) (17) Therefore, equatio (17) is the recursive CE algorithm to update chael coefficiet. III. ANALYTICAL RESULTS The error performace of the aforemetioed iterative imatio algorithm is explored by performig extesive computer simulatios. I these simulatios, we cosider by, 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 CE 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 136 P a g e

4 (IJACSA) Iteratioal Joural of Advaced Computer Sciece ad Applicatios, performace compared with fewer ateas. Furthermore, the CE algorithm provides faster covergece rate compared to NLS CE method. Therefore, i order to combat the chael dyamics, the CE algorithm is better to use for OFDM systems. But the CE algorithm is suffered from a computatioal complexity poit of view. I additio, the algorithm has the recursive iversio of a imate of the autocorrelatio matrix of the iput sigal as its corerstoe; problems arise, if the autocorrelatio matrix is rak deficiet x6 MIMO-OFDM chael imatio x MIMO-OFDM chael imatio Iteratio umber - Figure 4. 6 by 6 MIMO systems 8x8 MIMO-OFDM chael imatio Iteratio umber Figure. by MIMO systems 4x4 MIMO-OFDM chael imatio Iteratio umber Figure 5. 8 by 8 MIMO systems Iteratio umber Figure 3. 4 by 4 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 adaptive chael imator are described for MIMO OFDM systems. Simulatio results demostrated that the 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 137 P a g e

5 performace compared with fewer ateas. Therefore, i order to combat the chael dyamics, the CE algorithm is better to used for MIMO OFDM systems. REFERENCES [1] G. J. Foschii ad M. J. Gas, O limits of wireless commuicatios i a fadig eviromet whe usig multiple ateas, Wireless Pers. Commu., vol. 6, o. 3, pp , Mar [] E. Karami, Trackig performace of least squares MIMO chael imatio algorithm, IEEE Tras. O Wireless Comm. vol. 55, o.11, pp. 1-9, Nov. 7. [3] V. Pohl, P.. Nguye, V. Jugickel, ad C. Vo elmolt, ow ofte chael imatio is eeded i MIMO systems, i Proc. IEEE Global Telecommu. Cof., o. 1, pp Dec. 3, [4] S. Addireddy, L. Tog, ad. Viswaatha, Optimal placemet of traiig for frequecy-selective block-fadig chaels, IEEE Tras. If. Theory, vol. 48, o. 8, pp , Aug.. [5] L. Tog, Blid sequece imatio, IEEE Tras. O Commu., vol. 43, o. 1, pp , Dec [6] A. Vosoughi ad A. Scaglioe, Chael imatio for precoded MIMO systems, i Proc. IEEE Workshop Statist. Sigal Process., pp , Sep. 8 Oct. 1, 3. [7] J. Li, J. Ma, S. Liu chael imatio with superimposed traiig, i Proc. It. Co. o Comm. Techology, 8. [8] A. Acora, C. B. Meili, ad D. T. Slock, Dow-sampled impulse respose least-squares chael imatio for LTE OFDMA, i Proc. It. Co. o Acoustics, Speech, ad Sigal Processig, pp. III 93 III 96, Apr. 7. [9] L. A. M. R. D. Temio, C. N. I Macho, C. Rom, T. B. Sorese, ad P. Mogese, Iterative chael imatio with robust wieer filterig i LTE dowlik, i Proc. It. Co. o VTC, pp. 1-5, Sept. 8. [1] J. J. V. D. Beek, O. E. M. Sadell, S. K. Wilsoy, ad P. O. Baorjesso, O chael imatio i OFDM systems, i Proc. It. Co. o VTC, vol., pp , July [11] S. ayki, Adaptive Filter Theory, Pretice-all Iteratioal Ic, [1] F. Adachi,. Tomeba, ad K. Takeda, Frequecy-domai equalizatio for broadbad sigle-carrier multiple access, IEICE Tras. o Commu., vol. E9-B, o. 5, pp , May 9. [13] S. Yameogo, J. Palicot, ad L. Cariou, Blid time domai equalizatio of SC-FDMA sigal, i Proc. Vehicular Techology Coferece, Sept. 9, pp. 14. [14] S. Y. Park, Y. G. Kim, ad C. G. Kag, Iterative receiver for joit detectio ad chael imatio i OFDM systems uder mobile radio chaels, IEEE Tras. o Vehicular Techology, vol. 53, o., pp , Mar. 4. [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. 8, pp [16] W. C. Jakes, Ed., Microwave mobile commuicatios. New York: Wiley-IEEE Press, Ja [17] B. Karakaya,. Arsla, ad. A. Curpa, Chael imatio for LTE uplik i high Doppler spread, i Proc. Wireless Commu. Ad Networkig Coferece, Apr. 8, pp [18] R. C. Alvarez, R. Parra-Michel, A. G. O. Lugo, ad J. K. Tugait, Ehaced chael imatio usig superimposed traiig based o uiversal basis expasio, IEEE Tras. o Sigal Process., vol. 57, o. 3, pp , Mar. 9. [19] A. Kalayciogle ad. G. Ilk, A robust threshold for iterative chael imatio i OFDM systems, Radio Egieerig joural, vol. 19, o. 1, pp. 3 38, Apr [] Q. Li, G. Li, W. Lee, M. il Lee, D. Mazzarese, B. Clerckx, ad Z. Li, MIMO techiques i WiMAX ad LTE: a feature overview, IEEE Commu. Magazie, vol. 48, o. 5, pp. 86 9, May. 1. (IJACSA) Iteratioal Joural of Advaced Computer Sciece ad Applicatios, 138 P a g e