Sparsity-constrained compressed covariance sensing: Enhanced deterministic sampling-based compressed sensing from a mutual coherence perspective

With the ever-increasing scale of sensing problems, simultaneous data acquisition and compression have become crucial in wireless communications, instrumentation, and measurements. In this paper, we propose a sparsity-constrained compressed covariance sensing (SC-CCS) framework for compressed sampling and support recovery of analog signals with sparse spectra. From the sampling perspective, SC-CCS is implemented via periodic non-uniform sampling (PNS). From the recovery perspective, it leverages covariance information for spectrum support estimation. Unlike classical compressed sensing (CS) and compressed covariance sensing, SC-CCS jointly exploits sparsity priors and structural priors. We further analyze the sensing matrix in SC-CCS and prove that, from a mutual coherence perspective, SC-CCS constitutes an enhanced form of deterministic sampling (i.e., PNS)-based CS. Both theoretical analysis and simulation results demonstrate that the mutual coherence of SC-CCS sensing matrices is consistently lower than that of classical CS, particularly when the sampling pattern follows a Golomb ruler. Benefiting from this low coherence, SC-CCS offers a higher potential than CS to achieve exact sparse spectrum support recovery. In addition to theoretical analysis, extensive comparative simulation results support the claimed advantages of SC-CCS. Overall, SC-CCS provides a promising framework for efficient and robust spectrum sensing with sparse features.