Successive Refinement of Diversity for Fading ISI MISO Channels

Multiplexing rate and diversity impose a fundamental trade-off in wireless communications. This tradeoff was investigated for Inter-symbol Interference (ISI) channels in [8]. A different point of view was explored in [2], [5], [6] where high rate codes were designed so that they have a high-diversity code embedded within them. It was shown in [6] that the diversity multiplexing (D-M) tradeoff is successively refinable i.e., one can perfectly embed a high diversity code within a high rate code. The performance of such diversity embedded codes were investigated for ISI channels in [3] where it was shown that for SISO/SIMO ISI fading channels the D-M tradeoff is still successively refinable, in contrast to parallel flat fading channels [7]. The main result of this paper is that the diversity multiplexing tradeoff for fading MISO ISI channels is indeed successively refinable. This is related to a deterministic structural observation about the asymptotic behavior of frequency response of channel with respect to fading strength of time domain taps as well as a coding scheme to take advantage of this observation.