Zero-Forcing Precoding for Frequency Selective MIMO Channels with $H^\infty$ Criterion and Causality Constraint

TL;DR

This paper develops a method for designing optimal causal zero-forcing precoders for frequency selective MIMO channels, addressing worst-case performance and providing a novel numerical approach for performance evaluation.

Contribution

It introduces a construction of optimal causal precoders not limited to finite or rational responses and presents a new numerical method to compute their performance limits.

Findings

Optimal causal precoders can be constructed without finite or rational impulse response limitations.

A novel numerical approach enables the computation of the best achievable performance index.

The method improves understanding of worst-case performance in frequency selective MIMO channels.

Abstract

We consider zero-forcing equalization of frequency selective MIMO channels by causal and linear time-invariant precoders in the presence of intersymbol interference. Our motivation is twofold. First, we are concerned with the optimal performance of causal precoders from a worst case point of view. Therefore we construct an optimal causal precoder, whereas contrary to other works our construction is not limited to finite or rational impulse responses. Moreover we derive a novel numerical approach to computation of the optimal perfomance index achievable by causal precoders for given channels. This quantity is important in the numerical determination of optimal precoders.