# Design and Analysis of Sparsifying Dictionaries for FIR MIMO Equalizers

## TL;DR

This paper introduces a unified framework for designing sparse FIR MIMO equalizers by transforming the problem into sparse approximation tasks, analyzing dictionary choices, and reducing computational complexity, with demonstrated superior performance.

## Contribution

It presents a novel framework that converts equalizer design into sparse approximation problems and evaluates dictionary effectiveness, improving computational efficiency and performance.

## Key findings

- Proposed a general sparse equalizer design framework.
- Analyzed dictionary coherence for sparsifying effectiveness.
- Demonstrated improved performance over conventional methods.

## Abstract

In this paper, we propose a general framework that transforms the problems of designing sparse finite-impulseresponse linear equalizers and non-linear decision-feedback equalizers, for multiple antenna systems, into the problem of sparsestapproximation of a vector in different dictionaries. In addition, we investigate several choices of the sparsifying dictionaries under this framework. Furthermore, the worst-case coherences of these dictionaries, which determine their sparsifying effectiveness, are analytically and/or numerically evaluated. Moreover, we show how to reduce the computational complexity of the designed sparse equalizer filters by exploiting the asymptotic equivalence of Toeplitz and circulant matrices. Finally, the superiority of our proposed framework over conventional methods is demonstrated through numerical experiments.