Abstract
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.
Highlights
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
The considered soft self-iterative equalizer computes the marginal probabilities of information symbol {xt}Tt=0 based on prior probabilities of the receive signals {yt}Tt=0 and {xt}Tt=0, by executing belief propagations in factor graphs. (As a comparison, both Viterbi algorithm and BCJR algorithm execute belief propagation in trellis trees.)
Where the mapping function from log2 |Ω|-tuple to complex symbol xi is usually referred to as modulation format; mi c is the message sent from information node i to channel node c, as explained ; Uc denotes the set of all information nodes incident to channel node c, Uc\{i} denotes Uc excluding information node i; and yc is the received signal at time c
Summary
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. The multipath channels are represented by factor graphs, and soft self-iterative equalizers that execute belief propagation algorithm on factor graphs are studied. 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 factor graph in characterizing multipath channels to per-path level. A reduced-complexity equalizer that avoids or reduces the computations spent on those zero multipath taps is desirable Some efforts along this direction have been made in earlier works, for example, parallel Viterbi and parallel BCJR algorithms in [5, 6], which may require designed control logic for a different multipath scenario.
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