Sparsity order estimation for sub-Nyquist sampling and recovery of sparse multiband signals

The application of the Compressed Sensing (CS) paradigm to the sampling of sparse wireless signals allows a significant reduction of the sampling rate compared to the one dictated by the Nyquist sampling theorem. The majority of the theoretical results derived within CS are expressed in terms of the known sparsity order of the signal. In this work we address the problem of sparsity order estimation of multiband signals with unknown sparse spectral supports. We show that it can be estimated directly in the compressed domain as the dimension of the signal subspace of the observations' covariance matrix. We analyze how the results of the sparsity estimation can be utilized during the reconstruction step and which requirements it imposes on the performance of the subspace estimation algorithms. The results of the numerical study demonstrate that the reconstruction step is particularly sensitive to type II errors. This in turn indicates that the classical non-parametric model order selection algorithms might be unfavorable for this application since they tend to underestimate model order in the low SNR regime. As a remedy we propose to apply parametric approaches that allow to compromise resulting probabilities of over- and underestimation.