Coherence Statistics of Structured Random Ensembles and Support Detection Bounds for OMP

TL;DR

This paper analyzes the coherence properties of structured random matrices, specifically RPR matrices, and uses these insights to establish probabilistic support detection guarantees for OMP, demonstrating tight performance bounds especially for sparse signals.

Contribution

The paper introduces a detailed analysis of RPR matrix coherence and derives probabilistic support detection bounds for OMP, enhancing understanding of sparse signal recovery performance.

Findings

Coherence statistics of RPR matrices are characterized.

Support detection guarantees for OMP are established probabilistically.

Performance bounds are tight for sparse signals.

Abstract

A structured random matrix ensemble that maintains constant modulus entries and unit-norm columns, often called a random phase-rotated (RPR) matrix, is considered in this paper. We analyze the coherence statistics of RPR measurement matrices and apply them to acquire probabilistic performance guarantees of orthogonal matching pursuit (OMP) for support detection (SD). It is revealed via numerical simulations that the SD performance guarantee provides a tight characterization, especially when the signal is sparse.