Distributed Compressive Sensing: Performance Analysis With Diverse Signal Ensembles

Abstract

Distributed compressive sensing (DCS) is a framework that considers joint sparsity within signal ensembles along with multiple measurement vectors (MMVs). However, current theoretical bounds of the probability of perfect recovery for MMVs are derived to be essentially identical to that of a single MV (SMV); this is because characteristics of the signal ensemble are ignored. In this paper, we introduce two key ingredients, called “Euclidean distances between signals” and “decay rate of signal ensemble,” to conduct a performance analysis of a deterministic signal model under the MMVs framework. We show that, by taking the size of signal ensembles into consideration, MMVs indeed exhibit better performance than SMV. Although our extension can be broadly applied to CS algorithms with MMVs, a case study conducted on a greedy solver, which is commonly known as simultaneous orthogonal matching pursuit (SOMP), will be explored in this paper. When incorporated with our concept by modifying the steps of support detection and signal estimation, we show that the performance of SOMP will be improved to a meaningful extent, especially for short Euclidean distances between signals. Performance of the modified SOMP is verified to meet our theoretical prediction. Moreover, we design a new method based on modified SOMP algorithms for a key application known as cooperative spectrum sensing (CSS). The simulation results demonstrate that our method can benefit from more than one measurement vector, especially when the length of the measurement vectors is smaller than the sparsity of the signals, which is where traditional CS algorithms fail.