Optimized Signal Mappings for BICM-ID Systems Over Fast Fading MIMO Channels Muammar A. Alfasi, Yousef R. Shayan Department of Electrical and Computer Engineering , Concordia University Montreal, Canada Email:{m_alfasi, yshayan}@encs.concordia.ca Abstract— As shown in the literature, the performance of bit- interleaved coded modulation systems (BICM-ID) depends on the binary sequences mapping to constellation symbols. In this pa- per, we present a new multidimensional mapping for multi-input multi-output communication systems employing BICM-ID over fast fading channel. To introduce the optimized mapping, cost function is derived based on upper bound on the pairwise error probability over fast fading. Analytical and simulation results show that the optimized mapping outperforms the conventional mapping, and other proposed mappings. I. INTRODUCTION Until the introduction of BICM by Zehavi [1], Coded modulation (TCM) technique proposed by Ungerboeck [2], where coding and modulation are optimized together is be- lieved to provide better performance in digital communica- tions especially in AWGN channels. In BICM, coding and modulation are optimized separately. Through the use of ran- dom bit-interleaver, the diversity of code is increased at the cost of decreasing free Euclidean distance. Therefore, the sys- tem performance improves over fading channels and degrades over AWGN channels. To improve the system over AWGN and further over fading channels, BICM with iteration be- tween demapper and decoder was developed [3]. In [3], it was shown that a good design of mapper can increase the harmonic mean of the squared Euclidean distance after ideal feedback ( 2 h d ). Higher harmonic mean of the squared Euclidean dis- tance after ideal feedback gives a better asymptotic perfor- mance in BICM-ID systems. Further, in [4] based on 2 h d and using binary switching algorithm (BSA), optimum mappings were found for BICM-ID. In [5], it was shown that MIMO provides a significant in- crease in data rate, bandwidth efficiency and system capacity. The increasing demand for wireless multimedia, which re- quires higher data rate and better power efficiency compared to current wireless communication systems, motivates the use of BICM-ID with multiple antennas at the transmitter and re- ceiver side. In [6] the bit error rate performance of BICM-ID with MIMO was studied. Recently, the use of multidimen- sional mapping to further improve MIMO with BICM-ID has been investigated in [7]. In [7] locally optimized multidimen- sional mappings were found for MIMO-BICM-ID systems. In this paper, we propose an optimized multidimensional mapping for MIMO-BICM-ID over fast Rayleigh fading channel. Our mappings are optimized based on 2 h d which yields in the asymptotic optimum performance of the system. Analysis and simulation results show the advantage of the optimized mapping over conventional mapping, and locally optimized mapping in [7]. This paper is organized as follows: In section II, the system model is introduced. In section III, an upper bound on the pairwise error probability over Rayleigh fast fading is derived and cost function is proposed. In section IV, proposed map- ping is introduced. In section V, simulation results are pro- vided. The conclusion is given in section VI. II. SYSTEM MODEL Figure (1) shows the structure of transmitter and receiver of the system considered in this paper. The communication system consists of convolutional encoder concatenated in pa- rallel with pseudorandom bit-interleaver and multidimensional mapper. Since the design of encoder is independent from the mapper and the focus of this paper is on the optimization of mapper, we use rate ½, 8- state simple channel encoder (g1= 15, g2= 17, octal). Bit-interleaver was designed according to the approach given in [3]. Let’s define m M 2 = , where m is the number of bits in the conventional constellation symbol, and M is the number of symbols in conventional constella- tion. The multidimensional mapper takes simultaneously mn bits and map them to one n 2 -dimensional signal x , where n is the number of conventional constellation points s in one multidimensional signal x . This creates a bigger constellation ψ consisting of n M multidimensional signals. The bandwidth efficiency does not change as a result of the introduction of this multidimensional mapping. Because of its high data rate, V-Blast is used as space-time transmission technique and the multidimensional signal x , is sent through the multiple trans- mit antennas. Let’s consider a system with t M transmit antennas, and r N receive antennas. The received signal at the j-th receive anten- na, and time l is given by: 978-1-4244-3584-5/09/$25.00  2009 IEEE ISWCS 2009 502 Authorized licensed use limited to: CONCORDIA UNIVERSITY LIBRARIES. Downloaded on February 16,2010 at 16:36:23 EST from IEEE Xplore. Restrictions apply.