Design and Analysis Framework for Sparse FIR Channel Shortening

TL;DR

This paper introduces a comprehensive framework for designing sparse channel shortening equalizers and target impulse response filters by transforming the problem into sparsest-approximation tasks, evaluating dictionary choices, and validating through experiments.

Contribution

It presents a novel general framework for sparse FIR filter design in broadband channels, including analysis of dictionary effectiveness and practical validation.

Findings

The framework effectively designs sparse CSE and TIR filters.

Different dictionaries' sparsifying effectiveness is analytically and numerically evaluated.

Numerical experiments confirm the framework's practical usefulness.

Abstract

A major performance and complexity limitation in broadband communications is the long channel delay spread which results in a highly-frequency-selective channel frequency response. Channel shortening equalizers (CSEs) are used to ensure that the cascade of a long channel impulse response (CIR) and the CSE is approximately equivalent to a target impulse response (TIR) with much shorter delay spread. In this paper, we propose a general framework that transforms the problems of design of sparse CSE and TIR finite impulse response (FIR) filters into the problem of sparsest-approximation of a vector in different dictionaries. In addition, we compare several choices of sparsifying dictionaries under this framework. Furthermore, the worst-case coherence of these dictionaries, which determines their sparsifying effectiveness, are analytically and/or numerically evaluated. Finally, the usefulness of the proposed framework for the design of sparse CSE and TIR filters is validated through numerical experiments.