297 Iterative Multi-User Detection for OFDM Using Biased Mutation Assisted Genetic Algorithms M. Jiang and L. Hanzo1 School of ECS, Univ. of Southampton, S017 1BJ, UK. Tel: +44-703-593 125, Fax: +44-703-593 045 Email: 11h@ecs.soton.ac.uk, http://www-mobile.ecs.soton.ac.uk Abstract - Space Division Multiple Access (SDMA) aided Or- also been employed in OFDM systems [7, 8] for achieving a near- thogonal Frequency Division Multiplexing (OFDM) systems assisted optimum performance. Against this background, the novel contri- by efficient Multi-User Detection (MUD) techniques have recently bution of this paper is that we propose a MMSE-assisted Itera- attracted intensive research interests. As expected, Maximum Like- tive GA (IGA) MUD invoking a technique referred to here as the lihood (ML) detection was found to attain the best performance, Biased Q-function Based Mutation (BQM) designed for improv- although this was achieved at the cost of a high computational com- ing the performance of a TTCM-aided multi-user SDMA-OFDM plexity. Forward Error Correction (FEC) schemes such as Turbo system. Our simulation results show that the proposed MMSE- Trellis Coded Modulation (TTCM) can be efficiently amalgamated IGA assisted TTCM-SDMA-OFDM system is capable of achiev- with SDMA-OFDM systems for the sake of improving the achiev- ing an Eb/No gain of about 6dB in comparison to the TTCM- able performance without bandwidth expansion. In this contri- assisted MMSE-SDMA-OFDM benchmarker system both in low- bution, a MMSE-aided Iterative GA (IGA) MUD is proposed for and high-throughput modem scenarios, such as 4QAM and 16QAM, employment in a TTCM-assisted SDMA-OFDM system, which is respectively, while maintaining a substantially lower complexity capable of achieving a similar performance to that attained by its than that imposed by the optimum ML MUD. optimum ML-aided counterpart at a significantly lower complex- The structure of this paper is as follows. The SDMA MIMO chan- ity, especially at high user loads. Moreover, when the proposed nel model is described in Section 2.1, while the overview of the pro- novel Biased Q-function Based Mutation (BQM) scheme is em- posed TTCM-aided SDMA-OFDM system using the MMSE-IGA MUD ployed, the IGA-aided system's performance can be further im- is given in Section 2.2, followed by the introduction of the novel BQM proved by achieving an Eb/No gain of about 6dB in comparison scheme of Section 3. Our simulation results are provided in Section 4, to the TTCM-aided MMSE-SDMA-OFDM benchmarker system while Section 5 concludes our findings. both in low- and high-throughput modem scenarios, respectively, while still maintaining a modest complexity. 2. SYSTEM MODEL 1. INTRODUCTION 2.1. SDMA MIMO Channel Model Space Division Multiple Access (SDMA) based Orthogonal Frequency In SDMA uplink systems, each of the L simultaneous mobile users Division Multiplexing (OFDM) [1] communication invoking Multi- employs a single transmit antenna, while the BS's receiver exploits P User Detection (MUD) techniques has recently attracted intensive re- antennas. At the kth subcarrier of the nfth OFDM symbol received search interests. In SDMA Multi-Input-Multi-Output (MIMO) systems by the P-element receiver antenna array we have the received com- the transmitted signals of L simultaneous uplink mobile users - each plex signal vector x[n, k], which is constituted by the superposition equipped with a single transmit antenna - are received by the P differ- of the independently faded signals associated with the L mobile users ent receiver antennas of the Base Station (BS). At the BS the individual and contaminated by the Additive White Gaussian Noise (AWGN), ex- users' signals are separated by Multi-User Detectors (MUDs) with the pressed as: aid of the user-specific spatial signature constituted by their channel transfer functions or, equivalently, Channel Impulse Responses (CIRs). x Hs + n, (1) In the literature, Maximum Likelihood (ML) detection [1, 2] was found to give the best performance, although this was achieved at the cost where the (P x 1)-dimensional vector x, the (L x 1)-dimensional vec- of a dramatically increased computational complexity, especially in tor s and the (P x 1)-dimensional vector n are the received, transmitted the context of a high number of users and higher-order modulation and noise signals, respectively. Here we have omitted the indices [n, k] schemes. By contrast, Minimum Mean-Square Error (MMSE) [1, 2] for each vector for the sake of notational convenience. Specifically, the detection exhibits a low complexity, while suffering from a perfor- vectors x, s and n are given by: mance loss. Furthermore, the achievable performance can be significantly im- X (XI, X2, . XP) , (2) proved, if Forward Error Correction (FEC) schemes are incorporated s = ( 8(2) (L))T into the SDMA system. Various Coded Modulation (CM) [3] schemes ' ' 4 have attracted intensive research interests, since they are capable of (ni, ?2, **P) (4) achieving a substantial coding gain without bandwidth expansion. It was shown in [4] that Turbo Trellis Coded Modulation (TTCM) [3] T generally provides the best performance in the family of CM schemes channel transfer functions (FD-CCHTF) of the L users and is given by: in the specific context of the SDMA-OFDM system investigated. HH1 () HL Genetic Algorithms (GAs) [5] have been applied to a number of H = (H : H :,. H()), (5) problems, such as machine learning and modelling adaptive processes. Furthermore, GA-based multiuser detection has been proposed for Code where H(1) (1 - 1, ... ., L) is the vector of the FD-CHTFs associated Division Multiple Access (CDMA) systems [6]. Recently, GAs have with the transmission paths from the 1th user's transmit antenna to each __________________________ ~~~~~of the P-element receiver antenna array, which is expressed: Acknowledgements: The work reported in this paper has formed part of the Wireless Enabling Techniques work area of the Core 3 Research Programme H(1) - (H(1l, H( ,H(l))T, 1 {1, L},... (6) of the Virtual Centre of Excellence in Mobile and Personal Communications,' ' ' ' ' ' Mobile VCE, www.mobilevce.com, whose funding support, including that of EPSRC, is gratefully acknowledged. Fully detailed technical reports on this where H( ) (I - 1, .. ., L; p =1, ... ., F) associated with different research are available to Industrial Members of Mobile VCE. user/receiver pairs are assumed to be independent.