Expectation Propagation as Turbo Equalizer in ISI Channels

Abstract

In probabilistic equalization of channels with inter-symbol interference, the BCJR algorithm and its approximations become intractable for high-order modulations, even for moderate channel dispersions. In this paper, we introduce a novel soft equalizer to approximate the symbol a posteriori probabilities (APP), where the expectation propagation (EP) algorithm is used to provide an accurate estimation. This new soft equalizer is presented as a block solution, denoted as block-EP (BEP), where the structure of the matrices involved is exploited to reduce the complexity order to O(L N2), i.e., linear in the length of the channel, L, and quadratic in the frame length, N. The solution is presented in complex-valued formulation within a turbo equalization scheme. This algorithm can be cast as a linear minimum-mean-squared-error (LMMSE) turbo equalization with double feedback architecture, where constellations being discrete is a restriction exploited by the EP that provides a first refinement of the APP. In the experiments included, the BEP exhibits a robust performance, regardless of the channel response, with gains in the range 1.5-5 dB compared with the LMMSE equalization. © 2016 IEEE.