Multi-coset sampling for power spectrum blind sensing

Power spectrum blind sampling (PSBS) consists of a sampling procedure and a reconstruction method that is able to recover the unknown power spectrum of a random signal from the obtained sub-Nyquist-rate samples. It differs from spectrum blind sampling (SBS) that aims to recover the spectrum instead of the power spectrum of the signal. In this paper, a PSBS solution is first presented based on a periodic sampling procedure. Then, a multi-coset implementation for this sampling procedure is developed by solving the so-called minimal sparse ruler problem, and the coprime sampling technique is tailored to fit into the PSBS framework as well. It is shown that the proposed multi-coset implementation based on minimal sparse rulers offers advantages over coprime sampling in terms of reduced sampling rates, increased flexibility and an extended range of estimated auto-correlation lags. These benefits arise without putting any sparsity constraint on the power spectrum. Application to sparse power spectrum recovery is also illustrated.