On Compressive Toeplitz Covariance Sketching

This paper studies the problem of estimating Toeplitz covariance matrices from compressive temporal sketches. In contrast to most existing works on Toeplitz covariance estimation, we simultaneously look at the spatial and temporal sample complexities. To fully exploit the Toeplitz structure, we rely on the sparse-array idea to design the spatial samplers. Then we compare the performances of common unbiased estimators, and derive the conditions in terms of the sampler design under which the estimators yield the same MSE. As for the temporal complexity, for the first time in literature, we provide the non-asymptotic guarantee on entry-wise convergence as a function of the MSE, which reveals the trade-off between spatial and temporal complexities. The theoretical claims are demonstrated by the numerical experiments.