On Communication Over Unknown Sparse Frequency-Selective Block-Fading Channels

This paper considers the problem of reliable communication over discrete-time channels whose impulse responses have length L and exactly S ≤ L non-zero coefficients, and whose support and coefficients remain fixed over blocks of N >; L channel uses but change independently from block to block. Here, it is assumed that the channel´s support and coefficient realizations are both unknown, although their statistics are known. Assuming Gaussian non-zero-coefficients and noise, and focusing on the high-SNR regime, it is first shown that the ergodic noncoherent channel capacity has pre-log factor 1-(S)/(N) for any L. It is then shown that, to communicate with arbitrarily small error probability at rates in accordance with the capacity pre-log factor, it suffices to use pilot-aided orthogonal frequency-division multiplexing (OFDM) with S pilots per fading block, in conjunction with an appropriate noncoherent decoder. Since the achievability result is proven using a noncoherent decoder whose complexity grows exponentially in the number of fading blocks K, a simpler decoder, based on S+1 pilots, is also proposed. Its ε-achievable rate is shown to have pre-log factor equal to 1-(S+1)/(N) with the previously considered channel, while its achievable rate is shown to have pre-log factor 1-(S+1)/(N) when the support of the block-fading channel remains fixed over time.