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 (Pfa) 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 (Pd) 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.