Power spectrum blind sampling using minimum mean square error and weighted least squares

We present a new power spectrum recovery method in the context of power spectrum blind sampling. As sampling device we propose a multicoset sampler, which provides sub-Nyquist rate samples. A weighted least squares (WLS) criterion is adopted with the aim to define a power spectrum recovery algorithm that minimizes the mean square error (MSE) of the correlation estimate of the input signal. It is analytically shown that the optimal weighting matrix is equal to the inverse of the covariance matrix of the correlation estimate of the sub-Nyquist rate samples. The derived weight can also be shown to be optimal in MSE sense for power spectrum estimation. We also provide an optimization framework for the design of multicoset sampling patterns that minimize the MSE of the compressive WLS power spectrum estimator. The resulting integer nonlinear programming problem is solved by using exhaustive search.