A General Framework for the Design and Analysis of Sparse FIR Linear Equalizers

TL;DR

This paper introduces a versatile framework for designing sparse FIR linear equalizers by transforming the problem into a sparsest-approximation task, analyzing dictionary coherence, and validating through numerical experiments.

Contribution

It presents a general approach to sparse equalizer design using dictionary-based sparsest-approximation, including analysis of dictionary coherence and practical validation.

Findings

The framework effectively designs sparse FIR equalizers.

Dictionary coherence impacts sparsification strength.

Numerical experiments confirm the framework's utility.

Abstract

Complexity of linear finite-impulse-response (FIR) equalizers is proportional to the square of the number of nonzero taps in the filter. This makes equalization of channels with long impulse responses using either zero-forcing or minimum mean square error (MMSE) filters computationally expensive. Sparse equalization is a widely-used technique to solve this problem. In this paper, a general framework is provided that transforms the problem of sparse linear equalizers (LEs) design into the problem of sparsest-approximation of a vector in different dictionaries. In addition, some possible choices of sparsifying dictionaries in this framework are discussed. Furthermore, the worst-case coherence of some of these dictionaries, which determines their sparsifying strength, are analytically and/or numerically evaluated. Finally, the usefulness of the proposed framework for the design of sparse FIR LEs is validated through numerical experiments.