Distributed Compressive Sensing: Performance Analysis with Diverse Signal Ensembles

TL;DR

This paper introduces a new performance analysis framework for distributed compressive sensing that considers Euclidean distances between signals, demonstrating improved performance of MMVs over SMVs, especially with closely spaced signals.

Contribution

It proposes a novel concept of Euclidean distances for analyzing MMV performance, showing that MMVs outperform SMVs when signals are closely spaced, and modifies SOMP to leverage this insight.

Findings

MMVs outperform SMVs when signals are close.

Modified SOMP shows significant performance improvements.

Theoretical predictions are validated by experiments.

Abstract

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 no assumption about signal ensembles is made. In this work, we propose a new concept of inducing the factor called "Euclidean distances between signals" for the performance analysis of MMVs. The novelty is that the size of signal ensembles will be taken into consideration in our analysis to theoretically show that 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.