On full diversity equalization for precoded block transmission systems

Equalization techniques other than maximum likelihood equalization (MLE) that collect full diversity offered by doubly selective channels are investigated. With appropriate precoding at the transmitter, it is known the both linear equalizers (LE) and MLE collect full multiplicative multipath-Doppler diversity available in the channel. We close the gap between LE and MLE and show that decision feedback equalizers (DFE) also achieve full channel diversity in these channels. For a class of precoders proposed we propose a novel hybrid equalization scheme that also benefits from full channel diversity at a lower complexity compared to full blown MLE. Finally, we show that the amount of redundancy introduced in these precoders is in fact an over-kill for MLE and show that redundancy proportional to channel delay spread is largely enough to allow MLE to collect full channel diversity at a complexity that is exponential in channel delay spread. Simulation results are provided to substantiate all claims made in the paper.