Factor-Graph-Based Soft Self-Iterative Equalizer for Multipath Channels
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Factor-Graph-Based Soft Self-Iterative Equalizer for Multipath Channels Ben Lu Silicon Laboratories, Inc., Austin, TX 78735, USA Email: [email protected]
Guosen Yue NEC Laboratories America, Inc., Princeton, NJ 08540, USA Email: yueg@nec labs.com
Xiaodong Wang Department of Electrical Engineering, Columbia University, New York, NY 10027, USA Email: [email protected]
Mohammad Madihian NEC Laboratories America, Inc., Princeton, NJ 08540, USA Email: [email protected] Received 30 April 2004; Revised 23 August 2004 We consider factor-graph-based soft self-iterative equalization in wireless multipath channels. Since factor graphs are able to characterize multipath channels to per-path level, the corresponding soft self-iterative equalizer possesses reduced computational complexity in sparse multipath channels. The performance of the considered self-iterative equalizer is analyzed in both single-antenna and multiple-antenna multipath channels. When factor graphs of multipath channels have no cycles or mild cycle conditions, the considered self-iterative equalizer can converge to optimum performance after a few iterations; but it may suffer local convergence in channels with severe cycle conditions. Keywords and phrases: factor graph, equalizer, iterative processing, multipath fading, MIMO.
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INTRODUCTION
A multipath fading channel, which can be mathematically described by a convolution of transmitted signals and linear channel response, is one of many typical channel models occurring in digital communications. In general, an equalizer that makes detection based on a number of adjacent received symbols is necessary to achieve optimal or near-optimal performance in multipath channels. In classical communication theory, different representations of multipath channels have led to equalizers with different designs. By representing multipath channels as trellis structures, the optimum sequence detector can be computed by the Viterbi algorithm [1], and the optimum symbol detector can be computed by BCJR algorithm [2]. Starting from the transfer function This is an open-access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
representation of linear multipath systems, people proposed various low-complexity designs such as linear zero-forcing (ZF) equalizer, linear minimum mean-square-error (MMSE) equalizer, nonlinear zero-forcing decision feedback equalizer (ZF-DFE), non-linear MMSE-DFE, and so forth. [3]. In this work, the multipath channels are represented by factor graphs, and soft self-iterative equalizers that execute belief propagation algorithm on factor graphs are studied. (Please refer to [4] for an excellent tutorial on factor graph and its applications.) One question might rise regarding the motivation of this work, since we have already had both Viterbi algorithm and BCJR algorithm as exact optimum equalizers. The answer to this question lies in the flexibility of fa
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