COMPRESSED SENSING BLOCK MAP-LMS ADAPTIVE FILTER FOR SPARSE CHANNEL ESTIMATION AND A BAYESIAN CRAMER-RAO BOUND

This paper suggests to use a Block MAP-LMS (BMAP-LMS) adaptive filter instead of an Adaptive Filter called MAP-LMS for estimating the sparse channels. Moreover to faster convergence than MAP-LMS, this block-based adaptive filter enables us to use a compressed sensing version of it which exploits the sparsity of the channel outputs to reduce the sampling rate of the received signal and to alleviate the complexity of the BMAP-LMS. Our simulations show that our proposed algorithm has faster convergence and less final MSE than MAP-LMS, while it is more complex than MAP-LMS. Moreover, some lower bounds for sparse channel estimation is discussed. Specially, a Cramer-Rao bound and a Bayesian Cramer-Rao bound is also calculated.