Estimation of covariance matrices satisfying sparsity priors

点击翻译按钮获取中文摘要

The success of Compressive Sensing (CS) is based on the observation that high-dimensional signals can often be described by a very small number of signal dependent active parameters.This project proposes a CS based approach to the estimation of second order statistics of stochastic vectors and sequences. These processes are assumed to satisfy a sparsity prior on the second order statistics, for example, small support area or low rank of the covariance matrix.Although the problem of estimating covariance matrices can be translated into a seemingly standard CS problem, the Kronecker product structure of the underlying measurement matrix prevents the application of standard results from the literature, for example, those based on coherence and the restricted isometry property. Alternative arguments and algorithms have to be developed, keeping in mind that sparsity conditions on the covariance matrix may become involved. Motivated by applications in communications, we study time-frequency structured measurement matrices in detail. On the stochastic side, this leads to questions on the the covariance estimation problem for WSSUS channels. With respect to communications, we consider Single-Input-Single-Output and Multiple-Input-Multiple-Output stochastic operators, with and without correlated subchannels. We will use CS techniques to estimate stationary stochastic processes based on a limited number of measurements and then turn to the identification problem for the covariance of non-stationary so-called underspread processes.