Joint estimation and decoding for sparse channels via relaxed belief propagation

We consider the problem of communicating efficiently over an N-block Rayleigh-fading channel with a K-sparse L-length discrete-time impulse response (with 0 <; K <; L <; N), where both the channel´s coefficients and support are unknown to both the transmitter and receiver. For this, we propose to use bit-interleaved coded orthogonal frequency division multiplexing (OFDM) in conjunction with a novel belief-propagation (BP) based demodulation scheme. Unlike the conventional “decoupled” approach, where pilots are used to estimate the sparse channel, and the resulting channel estimate is used for data decoding, we perform joint sparse-channel estimation and data decoding. Simulations suggest that the proposed scheme performs remarkably well at both low and high-SNR-achieving, e.g., the channel capacity prelog factor-with reasonable complexity: O(NL).