Space-Time Codes for Frequency Selective Channels

Space-time coding for the flat fading, quasistatic MIMO wireless channel has received wide spread attention. While there has been some effort on code design for the frequency selective environments, the work has mostly been confined to multi-carrier modulation. This paper treats code design for a delay spread channel from a single carrier modulation perspective. We assume a coherent receiver and no channel knowledge at the transmitter. We present a framework for analyzing space-time codes for a delay spread channel. We show that as in the flat fading case, the diversity gain is driven by the minimum rank of the matrices obtained by subtracting any two codewords. However, the frequency selective environment imposes a block Hankel structure on the codewords due to which codes designed for the flat fading case when used over frequency selective channels may actually lose diversity order. We show this explicitly for the delay diversity code, a popular spacetime code for flat fading channels. We propose a generalized delay diversity code which has full diversity in a frequency selective environment. Keywords— MIMO systems, fading channels, diversity methods