Asymptotically Optimal Estimation Algorithm for the Sparse Signal with Arbitrary Distributions

In this paper, we propose a sparse signal estimation algorithm that is suitable for many wireless communication systems, especially for the future millimeter wave and underwater communication systems. This algorithm is not only asymptotically optimal, but also robust to the distribution of nonzero entries of the sparse signal. Then, we derive its upper bound and lower bound, and show that the mean square error of the proposed algorithm can approach the minimum mean square error bound when the signal noise ratio goes to infinite or zero. Numerical simulations verify our theoretical analysis and also show that the proposed algorithm converges faster than existing algorithms, e.g., turbo-type signal recovery-discrete fourier transform, approximate message passing, etc.