Performance analysis of ML-CFAR detection for partially correlated chi-square targets in Rayleigh correlated clutter and multiple-target situations

The problem of adaptive constant false alarm rate detection of a pulse-to-pulse partially correlated target with 2K degrees of freedom in pulse-to-pulse partially Rayleigh correlated clutter and multiple-target situations is addressed. Both the target and the clutter covariance matrices are assumed to be known and are modelled as first-order Markov Gaussian processes. An exact expression for the probability of false alarm (P_fa) for the mean level detector is derived. It is shown that it depends on the degree of pulse-to-pulse correlation of the clutter samples. The probability of detection (P_d) is shown to be sensitive to the degree of correlation of the target returns and the degree of correlation of the clutter returns as well. Swerling´s well-known cases I, II, III and IV are handled as extreme limits of the proposed model.