Target detection and RCS amplitude estimation in large-scale MIMO radar using free probability theory

In the paper, we consider large-scale multiple-inputmultiple-output (MIMO) radar, in which the numbers of array antennas and snapshots are in the same order of magnitude. Under such a scenario, the conventional MIMO radar signal processing methods using sample covariance matrix as a substitute of statistical covariance matrix will no longer be applicable. We bring the free probability theory (FPT) into the analysis of target detection problem in large-scale MIMO radar systems. The MIMO radar echo signals are represented as a high-dimensional random matrix. On the premise that the random matrix has the asymptotic free behavior, the covariance matrix is estimated by calculating the additive and multiplicative free deconvolution, and their eigenvalues are extracted from the moments based on Newton-Girard formula. Using the proposed method, we can not only make a decision of target existence or not, but also determine the number of the targets, and estimate the amplitude of radar cross section (RCS).