Detection capabilities evaluation of a constrained structured covariance matrix estimator for radar applications

In this paper we deal with the problem of estimating the disturbance covariance matrix for radar signal processing applications, when a limited number of training data is present. We determine the Maximum Likelihood (ML) estimator of the covariance matrix starting from a set of secondary data, assuming a special covariance structure (i.e. the sum of a positive semidefinite matrix plus a term proportional to the identity), and a condition number upper-bound constraint. We show that the formulated constrained optimization problem falls within the class of MAXDET problems and develop an efficient procedure for its solution in closed form. Remarkably, the computational complexity of the algorithm is of the same order as the eigenvalue decomposition of the sample covariance matrix. At the analysis stage, we assess the performance of the proposed algorithm in terms of detection capability of an Adaptive Matched Filter (AMF) receiver with the proposed estimator in place of the sample covariance matrix, for a spatial processing. The results show that the AMF with the structured constrained covariance matrix estimator can achieve higher Detection Probabilities (PD), than some counterparts available in open literature.