Trellis-Based Equalization for Sparse ISI Channels Revisited

TL;DR

This paper revisits trellis-based equalization for sparse ISI channels, proposing a unified framework for complexity reduction and demonstrating that linear filtering enables efficient, near-optimal equalization for general sparse channels.

Contribution

It introduces a unified factor graph-based framework for complexity reduction in trellis equalization and shows linear filtering can enable efficient equalization for general sparse channels.

Findings

P-VA achieves significant complexity reduction for certain sparse channels.

Linear filtering enables standard trellis algorithms to work efficiently on general sparse channels.

Numerical results confirm the effectiveness of the proposed receiver structure.

Abstract

Sparse intersymbol-interference (ISI) channels are encountered in a variety of high-data-rate communication systems. Such channels have a large channel memory length, but only a small number of significant channel coefficients. In this paper, trellis-based equalization of sparse ISI channels is revisited. Due to the large channel memory length, the complexity of maximum-likelihood detection, e.g., by means of the Viterbi algorithm (VA), is normally prohibitive. In the first part of the paper, a unified framework based on factor graphs is presented for complexity reduction without loss of optimality. In this new context, two known reduced-complexity algorithms for sparse ISI channels are recapitulated: The multi-trellis VA (M-VA) and the parallel-trellis VA (P-VA). It is shown that the M-VA, although claimed, does not lead to a reduced computational complexity. The P-VA, on the other hand, leads to a significant complexity reduction, but can only be applied for a certain class of sparse channels. In the second part of the paper, a unified approach is investigated to tackle general sparse channels: It is shown that the use of a linear filter at the receiver renders the application of standard reduced-state trellis-based equalizer algorithms feasible, without significant loss of optimality. Numerical results verify the efficiency of the proposed receiver structure.