Diversity Order of Infinite-length Symbol-by-symbol Linear Equalization

The processing complexity of optimal receivers in frequency selective channels grows exponentially with the channel memory length. Linear receivers, alternatively, offer significantly less complexity with the cost of performance degradation. Such degradation can be due to not fully capturing the inherent frequency diversity or degraded coding gain. In this paper we investigate how effectively the receivers with linear equalization can capture the frequency diversity gain. The analyses reveal that minimum mean-square error (MMSE) linear equalizers incur no diversity loss compared to maximum-likelihood sequence detection (MLSD). Specifically, we show that for a channel with memory length ν, MMSE linear equalizers achieve full diversity gain of (ν +1). On the other hand, zero-forcing (ZF) linear equalizers always achieve the diversity gain 1, irrespective of channel memory length.