An Alternating Minimization Method for Sparse Channel Estimation

The problem of estimating a sparse channel, i.e. a channel with a few non-zero taps, appears in many fields of communication including acoustic underwater or wireless transmissions. In this paper, we have developed an algorithm based on Iterative Alternating Minimization technique which iteratively detects the location and the value of the channel taps. In fact, at each iteration we use an approximate Maximum A posteriori Probability (MAP) scheme for detection of the taps, while a least square method is used for estimating the values of the taps at each iteration. For approximate MAP detection, we have proposed three different methods leading to three variants for our algorithm. Finally, we experimentally compared the new algorithms to the Cramér-Rao lower bound of the estimation based on knowing the locations of the taps. We experimentally show that by selecting appropriate preliminaries for our algorithm, one of its variants almost reaches the Cramér-Rao bound for high SNR, while the others always achieve good performance.