Diversity and Coding Gain of Linear and Decision-Feedback Equalizers for Frequency-Selective SIMO Channels

Since the introduction of the diversity-rate tradeoff by Zheng and Tse for ML reception in frequency-flat MIMO channels, some results have been obtained also for the diversity behavior of suboptimal receivers such as linear and decision-feedback equalizers for frequency-selective SIMO channels. However, these results are limited to infinite length equalizers. Furthermore, so far attention has focused mostly on just diversity order aspects of diversity. In this paper we analyze the diversity of more practical FIR equalizers. We show in particular that in the case of multiple subchannels, the diversity of infinite length filters can also be attained by FIR equalizers of sufficient length. Increasing the filter lengths improves the coding gain though. Whereas the diversity order determines the slope of the asymptote at high SNR, the coding gain determines its position