Distributed Compressive Sensing: Performance analysis with diverse signal ensembles

Distributed compressive sensing is a framework considering jointly sparsity within signal ensembles along with multiple measurement vectors (MMVs). The current theoretical bound of performance for MMVs, however, is derived to be the same with that for single MV (SMV) because the characteristics of signal ensembles are ignored. In this work, we introduce a new factor called "Euclidean distances between signals" for the performance analysis of a deterministic signal model under MMVs framework. We show that, by taking the size of signal ensembles into consideration, MMVs indeed exhibit better performance than SMV. Although our concept can be broadly applied to CS algorithms with MMVs, the case study conducted on a well-known greedy solver, called simultaneous orthogonal matching pursuit (SOMP), will be explored in this paper. We show that the performance of SOMP, when incorporated with our concept by modifying the steps of support detection and signal estimations, will be improved remarkably, especially when the Euclidean distances between signals are short. The performance of modified SOMP is verified to meet our theoretical prediction.