CFAR Detection in Clutter With a Kronecker Covariance Structure

Abstract

In this paper, an approach for the design and analysis of coherent constant false alarm rate (CFAR) detectors in clutter and interference with a Kronecker covariance structure is described. In a two-dimensional example considered, the interference-plus-noise matrix ${\mathbf X} \in {\mathbb{C}}^{N \times L}$ is modeled by a doubly correlated, zero-mean multivariate complex Gaussian distribution described by two covariance matrices ${\mathbf C}$ and ${\mathbf R}$ that are unknown to the receiver. The concatenated columns of ${\mathbf X}$ has a structured covariance matrix $\mathbf \Sigma$ given by ${\mathbf \Sigma } = {\mathbf R}^{*} \otimes {\mathbf C}$ . In the approach described, an estimate of ${\mathbf R}$ is used to “prewhiten” and match filter all the rows of both the training data matrices and the test data matrix. The processing enables one to reduce the detection problem to a one-dimensional case that can be handled by any one of the several adaptive detection algorithms. The proposed algorithm for the doubly correlated clutter is analyzed to show that the detection performance is determined by two statistically independent signal-to-interference-plus-noise loss factors both of which have complex beta distributions. Sample results show that the proposed approach requires training samples that is a multiple of $N+L$ , while an adaptive detection algorithm that do not explicitly use the Kronecker constraint on the covariance structure requires training samples that is a multiple of $N \times L$ for comparable detection performance.