Diversity Analysis of Symbol-by-Symbol Linear Equalizers

TL;DR

This paper shows that MMSE symbol-by-symbol linear equalizers in frequency-selective channels can achieve full diversity order, unlike zero-forcing equalizers, thus balancing complexity and performance effectively.

Contribution

It demonstrates that MMSE linear equalizers do not suffer diversity loss and achieve full diversity order, a significant improvement over zero-forcing equalizers.

Findings

MMSE equalizers achieve full diversity order of (ν+1).

Zero-forcing equalizers have a diversity order of one.

Full diversity is maintained with MMSE equalizers in frequency-selective channels.

Abstract

In frequency-selective channels linear receivers enjoy significantly-reduced complexity compared with maximum likelihood receivers at the cost of performance degradation which can be in the form of a loss of the inherent frequency diversity order or reduced coding gain. This paper demonstrates that the minimum mean-square error symbol-by-symbol linear equalizer incurs no diversity loss compared to the maximum likelihood receivers. In particular, for a channel with memory $\nu$, it achieves the full diversity order of ($\nu+1$) while the zero-forcing symbol-by-symbol linear equalizer always achieves a diversity order of one.