On communication over unknown sparse frequency-selective block-fading channels

The problem of reliable communication over unknown frequency-selective block-fading channels with sparse impulse responses is considered. In particular, discrete-time impulse responses with block-fading interval N, length L <; N, and exactly S ≤ L non-zero coefficients are considered, where both the locations and values of non-zero coefficients change independently across blocks and are apriori unknown. Assuming that the non-zero coefficients and noise are both Gaussian, it is first shown that the ergodic noncoherent channel capacity has pre-log factor 1 - S over N for any L. Then, a pilot-aided transmission (PAT) scheme and noncoherent decoder are proposed which are capable of communicating with arbitrarily small error probability using only S pilots per fading block. Furthermore, the achievable rate of this scheme is shown to have the optimal pre-log factor, i.e., 1 - S/N. Finally, a lower complexity PAT scheme is proposed, whose ε-achievable rate has the pre-log factor 1 - S+1/N for any ε >; 0.¹