Near-Optimum Sparse Channel Estimation Based on Least Squares and Approximate Message Passing

Accurately estimating the sparse channel with sequential under-sampled received signal is a challenging problem in broadband wireless communication systems, especially when prior knowledge of the sparsity level and the probability distribution of the sparse channel is unavailable. A joint least-squares (LS) and approximate-message-passing (AMP) algorithm based on sparse Bayesian learning (SBL) model, named LS-AMP-SBL, is proposed to approach the optimal performance given by Oracle-LS, where Oracle-LS requires exact knowledge of the support of the sparse channel. The proposed algorithm has three steps. First, AMP-SBL estimates the sparse channel iteratively until convergence. Then, based on the coarse estimated channel of the first step and an adaptable threshold derived from the effective noise level, the support of the sparse channel can be detected with a high probability. The third step is to estimate the sparse channel using LS with the estimated support from the second step. By introducing a proper and adaptable threshold based on AMP-SBL operation, the proposed scheme is capable of accurately detecting the support of the spare channel, and thus achieves a near-optimal performance but with a much lower complexity than both simultaneous orthogonal matching pursuit and basic pursuit. Simulation results demonstrate that the proposed LS-AMP-SBL can approach the performance bound given by Oracle-LS.