improvement of greedy algorithms with prior information for sparse signal recovery

Abstract

The state-of-the-art technology of compressed sensing (CS) has received great attention for sparse signal processing. Allowing accurate recovery of sparse signals, CS can be applied wireless communication, internet of things (IoT), machine type communications (MTC). In particular, by modeling the channel profiles as a sparse signals with complex Gaussian distributed nonzero elements in MTC, the performance of channel estimation and device detection can be improved by exploiting CS technique.

In this study, I improve greedy algorithms to recover sparse signals with complex Gaussian distributed nonzero elements, when the probability of sparsity pattern is known a priori. By exploiting this prior probability, I derive a correction function that minimizes the probability of incorrect selection of a support index at each iteration of the orthogonal matching pursuit (OMP). In particular, I employ the order statistics of exponential distribution to create the correction function. Simulation results demonstrate that the correction function significantly improves the recovery performance of OMP and subspace pursuit (SP) for random Gaussian and Bernoulli measurement matrices.