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

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 letter. 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.