Decision-feedback maximum-likelihood decoder for fading channels

We propose a novel decision-feedback maximum-likelihood decoder for fading channels. These channels have memory due to fading correlation, and the complexity of maximum-likelihood decoding for such channels grows exponentially with memory length. Therefore, in practice, the encoded bit stream is typically interleaved prior to transmission and the deinterleaved bit stream is decoded as for an additive white Gaussian noise (AWGN) channel, independent of the fading statistics. Our decision-feedback decoding algorithm uses a sufficient statistic for past outputs which is computed recursively based on past channel outputs and feedback decisions. Using this statistic, the maximum-likelihood input sequence is determined with a complexity independent of the channel memory. In Rayleigh fading our decoding algorithm decreases the bit-error-rate (BER) by up to three orders of magnitude compared to the conventional technique. We also study another similar decoding algorithm which recursively computes the sufficient statistic based only on past outputs. The decoder performance using either statistic is roughly equivalent, although the decision-feedback decoder performs slightly worse on poor channels due to error propagation. BER simulation results for our decoding techniques are presented for several different fading models and modulation types. Based on the extremely poor performance of the conventional decoder, we propose a simple improvement to conventional decoding which uses channel weighting. The channel weighting reduces the BER of the conventional decoder significantly in all cases.