Diversity Analysis of Symbol-by-Symbol Linear Equalizers

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 $ν$, it achieves the full diversity order of ($ν+1$) while the zero-forcing symbol-by-symbol linear equalizer always achieves a diversity order of one.

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