BER Performance Analysis and Comparison for Large Scale MIMO Receiver

Indian Journal of Science and Technology, Vol 8(35), DOI: 10.17485/ijst/2015/v8i35/81073, December 2015 ISSN (Print) : 0974-6846 ISSN (Online) : 0974-5645 BER Performance Analysis and Comparison for Large Scale MIMO Receiver M. Kasiselvanathan* and N. Sathish Kumar Department of ECE, Sri Ramakrishna Engineering College, Coimbatore - 641022, Tamil Nadu, India; drkasiselvanathanvkm@gmail.com, nsk20022002@gmail.com Abstract: Objective: Multiple Input Multiple Output (MIMO) low complexity CHEMP (Channel Hardening Exploiting Message Passing) receiver which utilizes the channel hardening in the large scale MIMO channel to reduce the complexity. Methods: The Channel Hardening refers that the off diagonal elements of H T H matrix become progressively weaker than the diagonal elements because of the channel gain matrix H size increases. It is used for detection and estimation. The proposed receiver uses Message Passing Detection (MPD) algorithm and the estimation H T H matrix. Findings: Hence, the proposed receiver gives better performance than the Minimum Mean Square Error (MMSE) and Subspace Marginalization with Interference Suppression (SUMIS) detectors since the MPD detection algorithm uses only the matrix multiplication and it does not need the matrix inversion. Improvements: The optimized Low Density Parity Check (LDPC) codes are used to provide the considerable improvement than LDPC cods. Keywords: BER, Channel Hardening, CHEMP Receiver, MIMO, MPD 1. Introduction Multiple Input Multiple Output (MIMO) technology enhances the capacity of wireless networks and/or the reliability of data transmission through wireless media 1,2,3. In Single Input Single Output (SISO) system, the transmitter and also the receiver have one antenna might have limitations to support wireless services of upper information rates. So as to realize high transmission rate, there is a desire to own either high Signal To Noise Ratio (SNR) or wide bandwdth 4. MIMO systems use multiple antennas at both link ends and offers tremendous performance gains without requiring additional bandwidth or traditional power 5. The multiplexing gain (to increase the data rate) and the diversion gain (to increase the transmission reliability) are the two important MIMO gains 6. A scheduling algorithm for MIMO system utilizes the channel effectively without increasing the bandwidth 7. In wireless Communication systems, MIMO configurations with multiple antennas may provide high spectral and power efficiencies 8. MIMO communication in which each Base Station (BS) is given with multiple antennas and conjointly the users are provided with one antenna each. The large scale MIMO systems might accomplish reduced channel estimation, demodulation and decoding complexities at the BS receiver and maintain the great performance 5,9. Linear decoders may reduce the complexity as the number of antennas increases at the antennas 10. In such linear decoders, MMSE algorithm may be used. Several detection algorithms with low complexity can achieve good performance such as that of MMSE detection. Message passing scheme is used for decoding the LDPC codes and turbo codes, and for equalization or detection. It provides low complexity high performance in signal processing and communications 11-13. In this paper, a low complexity receiver for large scale MIMO system is proposed which is based on message *Author for correspondence

BER Performance Analysis and Comparison for Large Scale MIMO Receiver passing and the exploitation of the channel hardening 14. The Channel Hardening refers that the off diagonal elements of H T H matrix become progressively weaker than the diagonal elements because of the channel gain matrix H size increases. The receiver referred to as CHEMP receiver, used for the purpose of detection and the estimation of H T H. The paper is organized in the following sections. The principle of MIMO system model is summarized in section 2. The proposed method is discussed in section 3. The simulation results are discussed in section 4. Finally it is concluded in section 5. 2. System Model Consider a MIMO system with K transmission users and N base station antennas. Every user communicates with a BS having an N number of receiving antennas. The system loading factor is denoted as that is = K/N where 1 (K N). The code rate of LDPC code is r = m/n where m represents the input bits and n represents the coded symbols. Then the n coded bits are modulated and transmitted through the antennas. Let us assume that Q denotes the modulation. The one LDPC code block is transmitted with a n/log 2 ( Q ) channel. Let the channel gain matrix is denoted by H(t) within the i th channel use and also the complex gain from the j th user to the i th BS which is denoted by H ij. Let the modulated symbol vector transmitted within the t th channel is denoted by s(t) Q K, where the j th term in the modulated symbol denoted by s(t) transmitted by the j th user. Consider a perfect synchronization, at the BS the received vector in the t th channel, y (t) is given by y(t) = H(t)s(t) + w(t) (1) Where, w (t) is the noise vector. The equation (1) can be written as Where, R(H) -I(H) H I(H) R(H) R(y) R(s) R(w) y,s =, w = I(y) I(s) I(w) y = Hs + w (2) R(.) denotes the real parts and I(.) denotes the imaginary parts. As the size of antenna will increase the variance of the mutual data in MIMO channel will increase. 3. The Proposed CHEMP Receiver using MPD Algorithm The proposed CHEMP receiver has two parts namely a MPD algorithm and the estimation of H T H matrix. The proposed MPD algorithm deals with the real valued matched filtered receiving vector. Consider the real valued system model in (2) and 4-QAM modulation scheme. H T y = H T Hs + H T w (3) z = Jx + v (4) Where, z = (H T y)/n J = (H T H)/N v = (H T w)/n Figure 1. shows the message passing scheme in MPD algorithm. The large scale MIMO system is modeled as a connected graph 15, where the information symbols in s represent the nodes. Figure 1. Message passing in MPD. Let s define J = H T H. Consider a slow fading channel in which the H remains constant over the frame period. B f represents the length of the frame where each frame is formed from a pilot part and a information part. The pilot part has K channel uses and the information part has B f -K channel uses. Therfore, at the BS the received pilot matrix is given by, Y p = Hs p + W p Y p = ph + W p (5) p = (KE s ) 1/2, E s represents the averearge symbol energy, and W p represents the noise matrix. 2 Indian Journal of Science and Technology

M. Kasiselvanathan and N. Sathish Kumar 4. Simulation Results In order to assess the performance of MIMO receiver algorithms, the simulation results are obtained by using MATLAB communication toolbox. The simulated results show that the performance of coded and uncoded BER performance which is discussed as follows. The uncoded BER performance of MPD algorithm is obtained for N = 128 and K = 16, K = 32, K = 64, K = 128 with the loading factor = 1. The uncoded BER of MPD is plotted at an average of SNR in db. Figure 2. shows the performance of the uncoded BER of MPD algorithm and SUMIS detector for N = 128 and K = 16, K = 32, K = 64, K = 128. It is seen that BER performance of MPD improves significantly that the SUMIS detector. Figure 3. shows the performance of the uncoded BER of CHEMP receiver and SUMIS for N = 128 and K = 16, K = 32, K = 64, K = 128. For large value of N, The uncoded BER performance of CHEMP receiver shows the significant improvement compared to SUMIS detector. Figure 4. shows the performance of the uncoded BER of MPD algorithm and MMSE for N = 128 and K = 16, K = 32, K = 64, K = 128. It is observed that BER performance of MPD is better than the MMSE detection. Figure 5. shows the performance of the uncoded BER of CHEMP receiver and MMSE for N = 128 and K = 16, K = 32, K = 64, K = 128. It is observed that BER performance of CHEMP receiver is better than the MMSE detection. From the Figures BER performance is significantly enhanced because the loading factor ( ) is reduced. The performance of the coded BER of CHEMP receiver and LDPC decoder for N = 128 and K = 16, K = 32, K = 64, K = 128 is obtained. The rate of the LDPC encoder is 1/2. The receivers processes the detection and decoding operation jointly after receiving n coded bits. Figure 6. shows the performance of coded BER of CHEMP receiver and SUMIS detector for N = 128 and K = 16, K = 32, K = 64, K = 128. It is seen that the CHEMP receiver provides less complexity since it does not need matrix inversion. For large value of N, the coded BER performance of CHEMP receiver is improved than the SUMIS detector. From the Figure 7., the coded BER performance of CHEMP receiver is better than SUMIS and MMSE detectors. Table 1 shows the performance comparison of the complexity between MPD, MMSE and SUMIS detectors for N = 128 and K = 16, K = 32, K = 64, K = 128. From the Table 1, it is noted that for large value of N, the complexity of MPD is less than the MMSE and SUMIS detectors. Figure 2. Uncoded BER performance of MPD and SUMIS For N = 128 and K = 16, K = 32, K = 64, K = 128. Figure 3. Uncoded BER performance of CHEMP receiver and SUMIS for N = 128 and K = 16, K = 32, K = 64, K = 128. Figure 4. Uncoded BER performance of MPD and MMSE for N = 128 and K = 16, K = 32, K = 64, K = 128. Indian Journal of Science and Technology 3

BER Performance Analysis and Comparison for Large Scale MIMO Receiver Table 1. Performance comparison of the complexity between MPD, MMSE and SUMIS detectors for N = 128 and K = 16, K = 32, K = 64, K = 128 Complexity (No of real operations x10 2 ) K N = 128 MMSE SUMIS MPD 16 0.7760 0.7320 0.7261 32 1.0160 0.9760 0.9310 Figure 5. Uncoded BER performance of CHEMP receiver and MMSE for N = 128 and K = 16, K = 32, K = 64, K = 128. 64 1.4260 1.2260 1.2060 128 1.6260 1.3260 1.2260 5. Conclusion Figure 6. Coded BER performance of CHEMP receiver and SUMIS for N = 128 and K = 16, K = 32, K = 64, K = 128. Figure 7. Coded BER performance of CHEMP receiver, SUMIS and MMSE for N = 128 and K = 16, K = 32, K = 64, K = 128. The low complexity CHEMP receiver is proposed that achieves better performance in large scale MIMO system. The CHEMP receiver is exploiting the channel hardening. The simulated results obtained provides the better BER perfromacne than conventional detectors since MPD algorithm does not need matrix inversion. The proposed receiver provides less complexity than the SUMIS and MMSE detectors. 6. References 1. Lakshmi Narasimhan T, Chockalingam A. Channel Hardening-Exploiting Message Passing (CHEMP) receiver in large scale MIMO systems. IEEE Transactions on Information Theory. 2014; 8(5):847-60. 2. Vardhan KV, Rajan BS, Mohammed SK, Chocklingam A. A low-complexity detector for large MIMO systems and multicarrier CDMA systems. IEEE Journal Selected Areas in Communications. 2008; 26(3):473-85. 3. Mohammed SK, Zaki A, Chocklingam A, Rajan BS. High rate space time coded large-mimo systems: low-complexity detection and channel estimation. IEEE Journal Selected Topics in Signal Processing. 2009; 3(6):958-74. 4. Raut PW, Badjate SL. MIMO-Future Wireless Communication. International Journal of Innovative Technology and Exploring Engineering. 2013; 2(5):102 6. 5. Cerato B, Viterbo E. Hardware implementation of a low complexity detector for large MIMO. Proceedings of 4 Indian Journal of Science and Technology

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