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 (Grokop, 2004). A different point of view was explored in (Diggavi et al., 2008) where high-rate codes were designed so that they have a high-diversity code embedded within them. It was shown in (Diggavi, 2005) that the diversity-multiplexing (D-M) tradeoff for channels with one degree of freedom (SIMO/MISO) 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 (Dusad, 2006) 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 (Diggavi, 2006). 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.