A CFAR Detector for Mismatched Eigenvalues of Training Sample Covariance Matrix

In this paper, an approach for the adaptive detection of a hypothesized signal in unknown multivariate Gaussian interference-plus-noise is considered under conditions where the set of signal space eigenvalues of the interference-plus-noise covariance matrix of the training samples and the test vector may be mismatched. The detector is required to have the constant false alarm rate (CFAR) property under these conditions. The proposed approach uses two sets of interference-plus-noise data: First, vectors from a reference set, typically from range cells in the vicinity of the test cell that have the same interference-plus-noise covariance matrix C as the test vector, and second, vectors from a training set that are used to compute the weights for interference suppression in the test vector and the reference vectors. Because the matrices C and Σ are unknown, the average power level of the residual interference in the test cell and reference cells after interference suppression is unknown. The adaptive matched filter statistic at the test cell is normalized by the sample mean of similar statistics for the reference cells to evaluate the detection statistic, which is shown to have the CFAR property. The detection performance of the CFAR detector is analyzed and the effect of mismatches in the eigenvalues of the covariance matrices C and Σ is shown to be characterized by a single random variable ρ, defined as the signal-to-interference-plus-noise ratio loss factor. Sample results are provided for purposes of illustration.