A Novel Approach for Channel Estimation for MIMO-OFDM Systems Using PDP Technique

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1 Communication Technology Vol 2 Issue 8 August-2013 ISSN (Print) A Novel Approach for Channel Estimation for MIMO-OFDM Systems Using PDP Technique 12 Md Tajuddin1 A Mallikarjuna Prasad2 Department Of Electronics and communication Engineering UCEKJNTUK Kakinada A.P. India. 1 taj_niddu@yahoo.co.in 2 a_malli65@yahoo.com Abstract Multiple Input Multiple Output Orthogonal frequency Division Multiplexing (MIMO-OFDM) is considered as eminent technology in the world of wireless communication such as 3rd Generation technology as well as WiMAX. The successful implementation of LMMSE channel estimator in MIMO-OFDM is based on the reduction in the distortions caused by various factors such as by null subcarriers and the residual noise caused by the insufficient number of samples for power delay profile (PDP) estimation. ence we proposed a PDP estimation technique for linear minimum mean square error (LMMSE) channel estimator in MIMO-OFDM system. The proposed technique effectively mitigates the distortions for accurate PDP estimation and the distortion caused by null subcarriers. In addition this technique also reduces the correlation mismatch in the frequency domain. The output of LMMSE channel by using the proposed PDP estimate approaches that of Wiener filtering and Kalman Filtering as results of the mitigation of distortion effects. Keywords wireless communication MIMO OFDMCyclic Prefix Channel Estimation LMMSE. 1. INTRODUCTION In order to satisfy the exponential growing demand of wireless multimedia services a high speed data access is required. Therefore various techniques have been proposed in recent years to achieve high system capacities. Among them is the multiple-input multiple output (MIMO).The MIMO concept has attracted lot of attention in wireless communications due to its potential to increase the system capacity without extra bandwidth [3].Multipath propagation usually causes selective frequency channels. To combat the effect of frequency selective fading MIMO is associated with orthogonal frequency-division multiplexing (OFDM) technique.ofdm is a modulation technique which transforms frequency selective channel into a set of parallel flat fading channels. Recently a worldwide convergence has occurred for the use of Orthogonal Division Frequency Multiplexing as an emerging technology for high data rates. In particular the wireless local network systems such as WiMax WiBro WiFi etc. and the emerging fourth-generation (or the so-called 3.9G) mobile systems are all OFDM based systems [5]. OFDM is a digital multi-carrier modulation scheme which uses a large number of closely-spaced orthogonal sub-carriers that is particularly suitable for frequency-selective channels and high data rates. This technique transforms a frequency selective wide-band channel into a group of non-selective narrow-band channels which makes its robust against large delay spreads by preserving orthogonality in the frequency domain. Multiple Input Multiple Output (MIMO)-Orthogonal Frequency Division Multiplexing (OFDM) provides a considerable performance gain over broadband single antenna systems by obtaining the spatial diversity or multiplexing gain [2]. Considering the availability of channel state information (CSI) most receiver techniques of MIMO-OFDM are designed to achieve the maximum diversity or multiplexing gain. The performance gain depends heavily on accurate channel estimation. The block diagram of MIMO-OFDM system using pilot symbol is shown in figure 1 Fig1. MIMO-OFDM system using pilot symbols The introduction of a so-called cyclic prefix (CP) at the transmitter reduces the complexity at receiver to FFT processing and one tap scalar equalizer at the receiver [5]. A cyclic prefix CP is added at the beginning of each OFDM Page 512

2 Communication Technology Vol 2 Issue 8 August-2013 ISSN (Print) symbol to eliminate Inter Carrier Interference (ICI) and Inter Symbol Interference (ISI). The inserted cyclic prefix (CP) is equal to or longer than to the channel [4]. The pilot-aided channel estimation based on the linear minimum mean square error (LMMSE) technique is optimum in the sense of minimizing mean square error (MSE) when the receiver knows the channel statistics [6][11]. To obtain the frequency domain channel statistics at the receiver power delay profile (PDP) estimation schemes have been proposed [7][8]. These schemes are based on the maximum likelihood (ML) estimation by taking advantage of the cyclic prefix (CP) segment of OFDM symbols. owever the ML PDP estimators require very high computational complexity for obtaining an accurate PDP. Another approach for improving the performance of LMMSE channel estimation employs an approximated PDP (i.e. uniform or exponential model) with the estimation of second-order channel statistics which are mean delay and root-mean-square (RMS) delay spread [9]. The channel delay parameters are estimated using pilots with low computational complexity. Therefore the LMMSE channel estimator with the approximated PDP is appropriate for practical applications such as a WiMAX system. owever the performance degradation is caused by both the correlation mismatch and the estimation error of delay parameters. To reduce the correlation mismatch in the frequency domain and to mitigate the various distortions we propose a PDP estimation technique for the LMMSE channel estimator of MIMO-OFDM systems. 2. EXISTING SYSTEM The system here is a MIMO-OFDM system with T transmit and U receive antennas and k total subcarriers. Suppose that the MIMO-OFDM system transmits kd subcarriers at the central spectrum assigned for data and pilots with k kd virtual subcarriers in order to control interferences with other systems. The CIRs corresponding to different transmit and receive antennas in MIMO systems usually have the same PDP[10]. Let Ct[ktnt] be the pilot subcarrier for the tth transmit antenna at the ntth OFDM symbol The pilot inserted OFDM symbol is transmitted over the wireless channel after performing an inverse fast Fourier transform (IFFT) and adding a CP. It is assumed that the length of CP cp is longer than the channel maximum delay ch pilot symbol for the uth receive antenna can be represented Bu[ t] (At)Fthtu + nu (1) Channel impulse response vector at the tth transmit antenna and uth receive antenna is tu [tu[ t 0] tu [ t 1]... tu [ t Pilot vector at the tth OFDM symbol ch] ]T (2) At [Ct [ 1 nt] Ct [ 2 t]... Ct [ kt t]]t (3) denotes a pilot vector at the tth OFDM symbol for ℱt and t nu is a complex additive white Gaussian noise (AWGN) vector at the uth receiver antenna with each entry having a zero-mean and variance of σ. We assume that the pilot subcarriers are distributed over a time and frequency grid as in Fig. 2 to preserve the orthogonality of pilots among different transmit antennas. Kt ℱt and t t represent the index sets for the pilot subcarriers of the tth antenna port in the frequency and time domains. Fig.2.Pilot symbol arrangement in a physical resource block of the LTE OFDM system. 3. POWER DELAY PROFILE ESTIMATION Channel impulse response can be estimated approximately using the regularized least squares (RLS) channel estimation with a fixed length of Lcp at the (T U)th antenna port[4] tu (F F + ILCP )-1 D (At)Bu[ t] tbu[ t] (4) where is a small regularization parameter and I cp is the cp cp identity matrix. To get the PDP from the estimated CIR we need to consider the above equation and the ensemble average of E{ hrtuhrtu } DR D +σ D Where R t D (5) t { htu htu } and D (F F + ILCP )-1F F Page 513

3 Communication Technology Vol 2 Issue 8 August-2013 ISSN (Print) ere the diagonal elements of the channel covariance matrix R represent the PDP of multipath channel within the length of cp and all off-diagonal elements are zeros. ence the covariance matrix can be expressed as Rhh (Th) where Th[t0 t1... tlch ]T.Unfortunately Rhh is distorted by D which is an ill-conditioned matrix due to the presence of F F. Thus instead of calculating D-1 we investigate the method for eliminating the spectral leakage of D. The covariance matrix of the estimated CIR is defined as R DRhhD which can be expressed as R Ddiag(tlvl) D (6) where vl is a unit vector with the lth entry being one and otherwise zeros. Let T and Xl be the cp 1 vectors defined asall the column vector containing all the diagonal elements of R and (v ) D Then T x0 t0 + x1 t1 + + x cp-1t cp 1 Xth (7) where X[x0 x1 x cp 1] is defined as a distortion matrix by D.since the non-diagonal elements of X are composed of the leakage powers of V for all. From the Gershgorin circle theorem a strictly diagonally dominant matrix is non-singular It is noted that the distortion matrix is a strictly diagonally dominant matrix satisfying [X] >Σ [X] for all distortion of D can be eliminated as T X-1Th E{gt.u [nt]}-σ D the (8) gt.u [nt] is defined as the received sample vector for estimating PDP at the (T U)th antenna port on the ntth OFDM symbol D X-1 Dg(D t D t ). A.PDP Estimation in Practical MIMO-OFDM Systems The received sample vector can be expressed as gt.u [nt] Dg( htu htu ) + ntu + etu we assume tu is an effective noise by AWGN and etu 2 { X-1Dg(D htu n {a} denotes the )} real part of a. The sample average is given by g t u [ n t ] N tu[nt] <D (htu h tu)>n +< tu >N +<etu>n (9) (10) (11) When is sufficiently large the PDP can be perfectly estimated since <Dg (htu h tu)>n Th < nt u > σ D and <etu>n 0 To improve the accuracy of PDP estimation with insufficient samples we mitigate the effective noise as follows <gt.u [nt]>n <Dg (htu h tu)>n + ZN (12) ZN <etu>n + < tu >N σ D is defined as a residual noise vector in which each entry has a zero-mean. Then the error of PDP estimation with samples can be calculated as en(<dg (htu htu)>n th) + ZN (13) Since [Th] 0 for all the PDP can initially be estimated as init tu[nt] (14) where stu[ t] is the sample vector of proposed PDP estimator with the th entry stlu[ t] g [n ] σ D 0 l if g [n ] > Otherwise l D (15) To mitigate the detrimental effect of residual noise ZN the proposed scheme estimates the average of residual noise at the zero-taps of th. At the th entry of init the zero-tap can be detected as < 1 (16) 0 Where is defined as a threshold value for the zero-tap detection so the average of residual noise at the zero-taps can be estimated as Ravg (17) Nz represents the total number of detected zero-taps. With the mitigation of residual noise the th tap of the PDP estimate can be expressed as 0 uavg if > Ravg otherwise (18) Then the estimated PDP can be used to obtain the frequencydomain channel correlation in the LMMSE channel estimator. The LMMSE technique using the estimated PDP outperforms the conventional methods since the correlation mismatch is reduced by the proposed PDP. 4. PERFORMANCE AND COMPLEXITY ANALYSIS The impulse channel estimator with the imperfect pdp is given by D F Dg T F F Dg T F + σ I (19) Where F is the d cp matrix.t T + e is expressed as the estimated PDP where the th element of e is defined as Page 514

4 Communication Technology Vol 2 Issue 8 August-2013 ISSN (Print) [ ] { [ ] (20) From the matrix inversion lemma we can convert F Dg T F + σ I F NF where M (F Dg(T )F + σ I ) N (I + F F Dg(e (21) the approximated PDP which is uniform or exponential model with the channel delay parameter estimation is plotted. It is required to note that the LMMSE techniques using the estimated PDP shows better performance than the conventional methods as this technique reduces the correlation mismatch. )) the coefficient matrix for LMMSE channel estimation with can be rewritten as (22) + ( )F (F Dg (T )F + σ I ) coefficient matrix for Wiener filtering and D is is the given by ( )F F NF +F Dg(e )F (F Dg T F + σ I) (23) The matrix error covariance of LMMSE channel estimation with the imperfect PDP can be obtained as ( ( + σ )( F ) Dg( )( F Ft D F) ) { }. Where Using the error covariance matrix the frequency-domain MSE of the proposed scheme is given by ( ( ) ) Fig 3: MSE Performance of LMMSE technique using the estimated PDP over ETU channel. (24) Fig 4 shows the MSE performance of the LMMSE technique over the exponentially power decaying six path Rayleigh fading channel model The performance of the proposed scheme is better than that of the existing methods. (25) Where ( ) denotes the trace operation of Et. With a sufficiently large amount of samples 0 thus the MSE of the projected theme achieves that of Wiener filtering and kalman filtering. The complexness by the PDP estimation technique is O( + kt + ).Once the pilot spacing is mounted within the frequency domain all entries of and X are constant so ( + ЄI ) and will be computed one time and their values will be kept. The extra complexness is then reduced to O ( + ). 5. SIMULATION RESULTS Total number of sub channels here are 301 and total number of Pilots used are 12 and guard interval length (Cp) is 40.The Mean Square error (MSE) performance of LMMSE technique using the estimated PDP is as shown in fig 3 where all underlying links are modeled as extended typical urban (ETU) channel. The performance of LMMSE technique using Fig 4: Performance of LMMSE technique using the estimated PDP over 6 Ray exponential channel with variable channel maximum delays. In fig 5 the MSE performance of LMMSE technique using the estimated PDP for different mobile equipment speeds ranging from 0 to 100 kmph at 30db SNR and Doppler Page 515

5 Communication Technology Vol 2 Issue 8 August-2013 ISSN (Print) frequency z is shown. All underlying links are modeled as ETU channels. Fig 5 shows the MSE of LMMMSE technique using the estimated PDP achieves better results than the conventional methods even at high Doppler frequencies. 6.CONCLUSIONS We proposed a Power delay profile estimation technique for the LMMSE channel estimator in MIMO-OFDM systems. The CIR estimates at each path of the MIMO channels were used to obtain the PDP. For accurate PDP estimation we considered the spectral leakage effect from virtual subcarriers and the residual noise caused by the insufficient number of estimated CIR samples. The simulation results shows that the performance of LMMSE channel estimation using the proposed PDP estimates is much better than the existing methods proposed PDP estimate approaches that of Wiener filtering and kalman filtering due to the mitigation of distortion effects. REFERENCES [1] Young-Jin Kin and Gi-ong Im Pilot symbol Assisted power delay profile estimation for MIMO-OFDM systems IEEE communications letters Vol.16 No.1 Jan Fig 5: Performance of LMMSE technique using the estimated PDP over ETU channels with different mobile equipment speeds. Fig 6 shows simulation and analysis results of the frequency domain LMMSE channel estimation with various no. of samples for obtaining the PDP at 20db SNR ( N TU). The simulation results correspond to the channel estimation performance at the first OFDM symbol of antenna port 1 is as shown in fig 2. We obtain the analytic results by using the coefficient matrix for LMMSE channel estimation with the perfect or imperfect PDP at the antenna port. In Fig 6 it is observed that the MSE of proposed technique improves the MSE performance with an increase in the no. of samples for PDP estimation. [2]. C. Won and G.. Im Iterative cyclic prefix reconstruction and channel estimation for a STBC OFDM system IEEE Commun. Lett. vol. 9 pp Apr [3] A.J.Paulraj D.A.Gore R.U.Nabar and.bolcskei An overview of MIMO communications A key to gigabit wireless Proc. IEEE vol. 92no. 2 pp Feb [4] B.Muquet Z.Wang G. B.Giannakis M.de Courville and P. Duhamel Cyclic prefixing or zero padding for wireless multicarrier transmissions? IEEE Trans. Commun. vol. 50 no. 12 pp Dec [5] 3GPP Web-site Long Term Evolution of the 3GPP radio technology [6] S. Omar A. Ancora and D. T. M. Slock Performance analysis of general pilot-aided linear channel estimation in LTE OFDMA systems with application to simplified MMSE schemes in Proc. IEEE PIMRC [7] T. Cui and C. Tellambura Power delay profile and noise variance estimation for OFDM IEEE Commun. Lett. vol. 10 pp Jan [8] X. Gong C. Zhao W. Xu and M. Jiang Power delay profile estimation for MIMO-OFDM systems over time-varying multipath channels in Proc. IEEE ICCT [9] K. C. ung and D. W. Lin Pilot-based LMMSE channel estimation for OFDM systems with power-delay profile approximation IEEE Trans. Veh. Technol. vol. 59 pp Jan Fig 6: Simulation and analysis results of LMMSE channel estimation over ETU channel with various samples for PDP estimation. [10] Y. Li J..Winters and N. R. Sollenberger MIMO-OFDM for wireless communications: signal detection with enhanced channel estimation IEEE Trans. Commun. vol. 50 pp Sep Page 516

6 Communication Technology Vol 2 Issue 8 August-2013 ISSN (Print) [11] Abdelhakim Khlifi and Ridha Bouallegue Performance Analysis of LS and LMMSE Channel Estimation Techniques for LTE Downlink Systems International Journal of Wireless & Mobile Networks (IJWMN) Vol. 3 No. 5 October 2011 AUTOR S PROFILE MD Tajuddin received B.Tech degree in Electronics and Communication Engineering in 2011 from an affiliated college of JNTUK Andhra Pradesh. e is currently doing his M.Tech in Computer and Communication from Jawaharlal Nehru Technological University Kakinada India. Dr. A. Mallikarjuna Prasad professor in E.C.E is working in JNTU Kakinada for past 10 years and did his B.Tech in ECE from Nagarjuna University during e did his M.Tech in Electronics & Instrumentation from Andhra University in 1992 and completed his PhD in 2009 from JNTU in the field of Antennas. Page 517