Delay diversity codes for frequency selective channels

Space-time coding for the flat fading, quasi-static MIMO wireless channel has received widespread attention. This paper treats space-time code design for frequency selective channels from a single carrier modulation perspective. We present a general framework for analyzing space-time codes for delay spread channels based on PEP analysis. It is shown that as in the flat fading case, diversity gain is driven by the minimum rank of the pairwise codeword difference matrices. Delay spread, however, imposes a block Hankel structure on the codewords which may prevent certain codes designed for the flat fading case from exploiting full spatio-temporal diversity when used over frequency selective channels. We explicitly show this diversity loss for the delay diversity code. We show that a properly generalized delay diversity (GDD) code achieves full diversity over frequency selective channels. Finally we propose an extension to the GDD which fits naturally in a multi-carrier setting.