Coherence, Compressive Sensing, and Random Sensor Arrays

Random sensor arrays are examined from a compressive-sensing (CS) perspective, particularly in terms of the coherence of compressive-sensing matrices. It is demonstrated that the maximum sidelobe level of an array corresponds to the coherence of interest for compressive sensing. This understanding is employed to explicitly quantify the accuracy of array source localization as a function of the number of sources and the noise level. The analysis demonstrates that the compressive-sensing theory is applicable to arrays in vacuum, as well as in the presence of a surrounding linear medium. Furthermore, the presence of a surrounding media with known properties may be used to improve array performance, with this related to phase conjugation and time reversal. Several numerical results are presented to demonstrate the theory.