In the context of compressed sensing (CS), simultaneous orthogonal matching pursuit (SOMP) algorithm is an important iterative greedy algorithm for multiple measurement matrix vectors sharing the same non-zero locations. Restricted isometry property (RIP) of measurement matrix is an effective tool for analyzing the convergence of CS algorithms. Based on the RIP of measurement matrix, this paper shows that for the K-row sparse recovery, the restricted isometry constant (RIC) is improved to $delta_{K+1}<rac{sqrt{4K+1}-1}{2K}$ for SOMP algorithm. In addition, based on this RIC, this paper obtains sufficient conditions that ensure the convergence of SOMP algorithm in noisy case.

We propose a cooperative compressed spectrum sensing scheme for correlated signals in wideband cognitive radio networks. In order to design a reconstruction algorithm which accurately recover the wideband signals from the compressed samples in low SNR (Signal-to-Noise Ratio) environments, we consider the multiple measurement vector model exploiting a sequence of input signals and propose a cooperative sparse Bayesian learning algorithm which models the temporal correlation of the input signals. Simulation results show that the proposed scheme outperforms existing compressed sensing algorithms for low SNRs.