False Alarm Analysis of the AMF Algorithm for Mismatched Training

Adaptive signal detection algorithms in unknown interference are generally formulated under the assumption that training sets are available for the estimation of the test cell interference characteristics. A significant problem occurs in applications such as radar surveillance when the interference covariance matrices of vectors from the training cells and that of the test cell vector are mismatched. False alarm rates may increase beyond acceptable levels and thus overwhelm a receiver if the interference in the test cell is not adequately cancelled. A number of adaptive detection algorithms with the constant false alarm rate (CFAR) property have been designed assuming the availability of training data that have the same covariance matrix as the interference in the test cell (although the adaptive coherence estimator algorithm requires the two covariance matrices to be related by a positive multiplicative constant that is not required to be known). The detection threshold in these CFAR detectors can be selected without knowledge of the interference-plus-noise covariance matrix. To the best of our knowledge, an analytical characterization of the performance effects of a receiver using a mismatched training set (perhaps inadvertently) in adaptive detection is currently not available. This paper addresses the problem analytically. An exact analysis of the effects of interference covariance matrix mismatch on the performance of the adaptive matched filter test is carried out. Results provide insights to the specific aspects of covariance matrix mismatch that cause the increase in false alarms when compared to the matched training set case. Analytical results are illustrated with an example and verified independently with simulations. These results are useful in developing CFAR algorithms under conditions of mismatched training.