Robust recovery of wideband block-sparse spectrum based on MAP and MMSE estimator

Indirect spectrum sensing mainly concerns the measurement and analysis of primary wideband analog signal. This paper proposes two robust algorithms based on maximum a-posteriori probability (MAP) and minimum mean-squared error (MMSE) estimators to recover wideband block-sparse spectrum and then detect the spectrum holes in compressive spectrum sensing (CSS). In each iteration of the referred Block-sparse Orthogonal Matching Pursuit based on iterative MAP (BOMP-IMAP) algorithm, one index of block is firstly identified to expand the estimated support. And then, wideband block-sparse spectrum can be recovered through approximating the MAP estimator. Finally, the residual is updated and put into next iteration. In order to approximate the MMSE estimator, the Random BOMP-IMAP (RandBOMP-IMAP) algorithm utilizes a randomized block identification of BOMP-IMAP algorithm to generate multiple solutions, which is followed by the fusion of them to obtain the final approximation. Numerical simulation results concerning probability of detection and detection time under certain noise level or measurement number validate the superiority of the proposed algorithms.