International Journal Of Comutational Engineering Research (ijceronline.com) Vol. 2 Issue. Investigation on Channel Estimation techniques for MIMO- OFDM System for QAM/QPSK Modulation Rajbir Kaur 1, Charanjit Kaur 2 1 Assistant Prof., ECE, University College of Engineering, Punjabi University, Patiala, India, 2 Student, ECE, University College of Engineering, Punjabi University, Patiala, India Abstract: Multile Inut Multile Outut (MIMO) systems has rovide high transmission data rate without increasing transmitting ower for wireless communication systems. The erformance can be further imroved by roerly estimating the channel at the receiver side. In this aer, investigation on various channel estimation techniques for MIMO-OFDM has been done and a new aroach based on time-domain interolation (TDI) has been resented. TDI is obtained by transforming outut of estimator to time domain through Inverse Discrete Fourier Transform (IDFT), zero adding and going back to frequency domain through Discrete Fourier Transform (DFT). The comarison has been carried out between ower of true channel and estimated ower for the given channel using LS, LS-Sline and MMSE for QPSK/QAM modulation at SNR 3dB. It is investigated that by alying the DFT over the estimated ower of channel for QPSK, the erformance of the channel estimators becomes better. Keywords: Channel estimation, Discrete Fourier transform (DFT), Least square error (LS), Minimum mean square error (MMSE), MIMO-OFDM, QAM, QPSK. 1. Introduction MIMO-OFDM is an imortant art of modern wireless communication standards such as IEEE 82.11n, 4G, 3GPP LTE and WiMAX [1]. It can eliminate the effect of frequency selective fading and significantly increase both the system s caacity and sectral efficiency. The data rate can be increased by satial multilexing without consuming more frequency resources and without increasing the total transmit ower. The erformance of the system deends generally on modulation schemes, channel estimation techniques used to estimate channel. The caacity of communication system increases linearly with the number of antennas, when erfect knowledge about the channel is available at the receiver. In ractice, the channel estimation rocedure is done by transmitting ilot (training) symbols that are known at the receiver. Further, channel estimation deends on the attern of transmitting ilots. Block tye and comb tye atterns have been considered in this aer. LSE, MMSE algorithms have been used to estimate the channel. Simulations and comarisons are carried out for QPSK and QAM data using LSE, MMSE algorithms with and without DFT. In this aer channel imulse resonse has been estimated and comared using LS, MMSE and DFT based estimation techniques. The aer is organized as follows. In Section 2, MIMO system is described. Section 3 discusses Channel Estimation in MIMO-OFDM System. Section 4 describes channel estimation based on DFT. Simulation and results for the erformance of LS, MMSE and DFT based techniques are given in section. Section 6 concludes the aer. 2. MIMO System MIMO communication uses multile antennas at both the transmitter and receiver to exloit the satial domain for satial multilexing and/or satial diversity. Satial multilexing [2]-[3] has been generally used to increase the caacity of a MIMO link by transmitting indeendent data streams in the same time slot and frequency band simultaneously from each transmit antenna, and differentiating multile data streams at the receiver using channel information about each roagation ath. In contrast to satial multilexing, the urose of satial diversity is to increase the diversity order of a MIMO link to mitigate fading by coding a signal across sace and time so that a receiver could receive the relicas of the signal and combine those received signals constructively to achieve a diversity gain. Issn 22-3(online) Setember 212 Page 1419
International Journal Of Comutational Engineering Research (ijceronline.com) Vol. 2 Issue. Figure 1. (a) Satial Multilexing (b) Satial Diversity Fig. 1.1 deicts a MIMO-OFDM [4] system consists of N T transmitter antennas, N receiver antennas and K number of sub-carriers. Each transmitter (or receiver) antenna uses an ordinary OFDM modulator (or demodulator). OFDM symbol generated in r th transmitted antenna for R ( r a ) ( ) n denotes th n time index, before transmitting the vector is rocessed by an A 1 IFFT P/S 1 1 FFT B 1 K-oint B k P/S B 1 A N T IFFT FFT N T N R K-oint B k Figure 2. MIMO-OFDM Inverse Fast Fourier Transform (IFFT) block with K oints and a CP of length is added to its beginning. The lengths of CP have to fulfill the inequality of L L 1 in which L is the maximum length of channel imulse resonse (CIR) among all g sub-channels. At the receiver, after discarding the CP, OFDM symbol is received after rocessing Fast Fourier Transform (FFT) []. 3. Channel Estimation in MIMO-OFDM System An accurate estimate of the imulse resonse of the channel can be obtained, if the receiver has a rior knowledge of the information being sent over the channel. The ilots are transmitted on all subcarriers in eriodic intervals of OFDM blocks for a slow fading channel, where the channel is constant over a few OFDM symbols and this tye of ilot arrangement is known as block tye ilot arrangement. The ilots are transmitted at all times but with an even sacing on the subcarriers, reresenting a comb tye ilot lacement as shown in Fig. 3 for a fast fading channel, where the channel changes between adjacent OFDM symbols. With interolation techniques the estimation of channel at data subcarrier can be obtained using channel estimation at ilot subcarriers [6]. Issn 22-3(online) Setember 212 Page 142
International Journal Of Comutational Engineering Research (ijceronline.com) Vol. 2 Issue. Figure 3. Block Tye Pilot Arrangement and Comb Tye Pilot Arrangement [6] In this aer, whereas LS- Sline, iece-wise, second order, time domain interolation technique has been emloyed for estimating channel at data subcarriers. 3.1. Channel estimation at ilot subcarriers Various algorithms such as Least Square (LS), Minimum MMSE have been emloyed for estimating channel at ilot subcarriers. 3.1.1. Least Square (LS) Algorithm Let A is the diagonal matrix of ilots as A diag A, A1,, AN 1, N is the number of ilots in one OFDM symbol, ĥ is the imulse resonse of the ilots of one OFDM symbol, and Z is the AWGN channel noise. If there is no ISI, the signal received is written as [1] B AFh Z (1) where B the vector of outut signal is after OFDM demodulation as B B, B1,, BN 1, 1 LS A B Because of no consideration of noise and ICI, LS algorithm is simle, but obviously it suffers from a high MSE. 3.1.2. Minimum Mean Square Error If the channel and AWGN are not correlated, MMSE estimate of is given by [11] 1 S S B where SB EB SBB EBB S A 2 AS A Z IN MMSE B BB are the cross covariance matrix between and B, and auto-covariance matrix of B resectively. 2 matrix of. Z is the noise-variance. If estimator as below 1 MMSE B BB S S B S T S (2) (3) is auto-covariance 2 and Z are known to the receiver, CIR could be calculated by MMSE 1 1 2 1 S A AS A Z IN A LS E b 2 S S A A (4) Z LS At lower value of the erformance of MMSE estimator is much better than LS estimator. MMSE estimator could gain N 1-1 db more of erformance than LS. 3.2. Channel estimation at data subcarriers In order to estimate channel at data sub-carriers by using the channel information at ilot sub-carriers, an efficient interolation technique is necessary in comb-tye ilot based channel estimation. 3.2.1. Piecewise Constant Interolation Channel is estimated by revious ilot in Piecewise constant interolation. And the channel estimation is given by, k lm m l, m M, l,1,, N 1 () where M = No. of subcarriers (N)/ No. of ilot (N) l = ilot carrier index. Issn 22-3(online) Setember 212 Page 1421
International Journal Of Comutational Engineering Research (ijceronline.com) Vol. 2 Issue. 3.2.2. Cubic Sline Interolation The cubic sline interolation is given by [2], k lm m c l 1 c l Mc l 1 Mc l where M = No. of subcarriers (N)/ No. of ilot (N ) l = ilot carrier index. l is the first order derivative of 1 1 M m M m l,1,, N 1 m M, (6) l, and 3 2 c1 M M 3m 2m c M M Cubic sline interolation with higher order interolation can be used for better interolation accuracy. 4. Channel Estimation Based On DFT Alication of DFT on LS, MMSE channel estimation can imrove the erformance of estimators by eliminating the effect of noise. Let Ĥk denote the estimate of channel gain at the k th subcarrier, obtained by either LS or MMSE channel estimation method. Taking the IDFT of the channel estimate N k [ ] 1, k IDFT [ k ] h [ n ] z [ n ] h [ n ], n,1,..., N 1 (8) where z[n] denotes the noise comonent in the time domain. Eliminate the imact of noise in time domain, and thus achieve higher estimation accuracy. h[ n] z[ n], n,1,2,..., L 1 hdft [ n] (9), otherwise Taking the DFT remaining L elements to transform in frequency domain [12-14] [ k] DFT h ( n) (1) DFT DFT Simulations are carried out for channel estimation using LS-Linear, LS-sline, MMSE methods for QPSK and QAM modulation schemes. The Simulation results show that the erformance of DFT based channel estimator is much better over the LS, MMSE estimator in case of QPSK, but the symbol rate decreases. Fig. 2, 3 and 4 reresents the erformance of above mentioned channel estimator with and without DFT.. Simulations and Results In this simulation work, first the random ilot sequence of length 8, where X { 1,1} and data sequence of length 24, a {,1} are generated. Sequence a is modulated using 16-QAM at SNR = 2dB, 3dB, 4dB. The ilot symbols are inserted in the modulated data sequence using ilot duration of 4 symbols and forms a new data sequence A. After ilot insertion data sequence A is converted into time domain sequence using 32-oint IFFT and 4 symbol CP is added, the resultant sequence is denoted as a t. The guard interval or the length of the CP is longer than the maximum delay sread of the channel. The sequence a t is then transmitted over a randomly generated 3-ta channel. AWGN is added to the received signal. The CP is removed from the noise corruted received signal which is then subject to FFT. Now, since the transmitted ilots and received ilots are known, the CSI is estimated using LS Linear, LS-Sline Interolation and MMSE. (7) Issn 22-3(online) Setember 212 Page 1422
International Journal Of Comutational Engineering Research (ijceronline.com) Vol. 2 Issue. 1 LS with and without DFT 1 LS with and without DFT - LS without DFT LS with DFT 1 1 2 LS -SPLINE with and without DFT 1 - LS without DFT LS with DFT 1 1 2 LS -SPLINE with and without DFT 1 - LS-SPLINE without DFT LS-SPLINE with DFT 1 1 2 MMSE with and without DFT 1 - LS-SPLINE without DFT LS-SPLINE with DFT 1 1 2 MMSE with and without DFT 1 - MMSE without DFT MMSE with DFT 1 1 2 QPSK - MMSE without DFT MMSE with DFT 1 1 2 Figure 4. Performance of MIMO-OFDM System using various Channel Estimations with and without DFT for QPSK and QAM at SNR 3 db In the simulations, the ower of true channel and ower obtained by using this estimation have been considered. The detectors at the receiver utilize this estimated channel to obtain the information out of the received signal which is then demodulated to get random bits. It is observed that simulation results become better if the estimated outut from various estimators is subject to DFT. For subcarrier index 1, true channel ower comes out to be 7.294dB. The simulations have been also calculated using LS linear for 1 th subcarrier index for QPSK at SNR=3dB and the estimated ower is calculated as 6.879dB and result imroved by.7 db with alication of DFT technique. For LS-sline without DFT, the estimated ower is calculated to be 7.22dB, whereas on alying DFT erformance of this estimation technique is imroved by.3 db. For MMSE the estimated ower is calculated as 7.2 db and erformance imroved by..21 db on alying MMSE with DFT. For LSsline without DFT for 1th subcarrier index at SNR=3dB for QAM the estimated ower is calculated to be 7.27dB. Whereas on alying DFT over this estimation technique gives 7.24 db of ower. For MMSE the estimated ower for 1th subcarrier index at SNR=2dB for QAM is calculated as 7.173 db and erformance imroved by.29 db on alying MMSE with DFT. At higher SNR=4dB, Estimated ower using LS linear, for 1th subcarrier index for QAM is calculated as 6.92dB whereas on alying DFT over this estimation technique, the simulation results imroved by.6 db. Simulation results show that MMSE with DFT erforms better than other estimations at the cost of comutational comlexity. The number of symbol errors in case of QPSK is 2 whereas in case of QAM value become 22. 6. Conclusion MIMO-OFDM has the caability of transmitting information at high data rate without increasing the transmitting ower. The erformance of the system can be imroved by estimating the channel arameters effectively. From the simulations it is concluded MMSE algorithm estimates the channel much better than LS at the cost of increasing comlexity. The results imrove when the outut of estimator is subject to DFT. Moreover it is observed the QPSK data symbols results in less number of errors as comared to QAM at cost of decrease in symbol rate. A trade off has made for the erformance of MIMO- OFDM system among comlexity, symbol rate and symbol errors. QAM Issn 22-3(online) Setember 212 Page 1423
International Journal Of Comutational Engineering Research (ijceronline.com) Vol. 2 Issue. References [1] Andrea Goldsmith,Wireless Communication, Cambridge University Press, 2. [2]. Jiang and P. A. Wilford, A hierarchical modulation for ugrading digital broadcasting systems, IEEE Transaction on Broadcasting, vol. 1, 222-229, June 2. [3] Siavash M. Alamouti, A Simle Transmit diversity Technique for Wireless Communications, IEEE Journal on Select Areas in Communications, Vol. 16, No. 8, October 1998. [4] PAN Pei-sheng, ZENG Bao-yu, Channel estimation in sace and frequency domain for MIMO-OFDM systems, ELSEVIER journal of China Universities of Posts and Telecommunications, Vol. 16, No. 3, Pages 4-44, June 29. [] Mohammad Torabi, Antenna selection for MIMO-OFDM Systems, ELSEVIER journal on Signal Processing, Vol. 88, Pages 2431-2441, 28. [6] Meng-an sieh, Channel Estimation for OFDM Systems based on Comb-Tye Pilot arrangement in frequency selective fading channels, IEEE Transaction on Wireless Communication,vol.2, no. 1, 217-22, May 29.. [7] M. R. McKay and I. B. Collings, Caacity and erformance of MIMO-BICM with zero-forcing receivers, IEEE Trans. Commun., vol. 3, no. 1,. 74 83, Jan. 2. [8] Minn,. and Bhargava, V.K., An investigation into time-domain aroach for OFDM channel estimation, IEEE Trans. on Broadcasting, 4(4), 4 49, 1999. [9] Van de Beek, J.J., Edfors, O., Sandell, M. et al. Analysis of DFT-based channel estimators for OFDM, Personal Wireless Commun., 12(1), 7, 2. [1] Fernandez-Getino Garcia, M.J., Paez-Borrallo, J.M., and Zazo, S. DFT-based channel estimation in 2D-ilot-symbolaided OFDM wireless systems, IEEE VTC 1, vol. 2,. 81 814, May 21. Issn 22-3(online) Setember 212 Page 1424