Multiple-target analysis of adaptive detection of partially correlated χ² targets

Abstract

Target radar characteristics are the driving force in the design and performance analysis of all radar systems. The fluctuation rate of a radar target may vary from essentially independent return amplitudes from pulse-to-pulse to significant variation only on a scan-to-scan basis. An important class of targets is represented by the so-called moderately fluctuating Rayleigh and χ2 targets, which, when illuminated by a coherent pulse train, return a train of correlated pulses with a correlation coefficient in the range 0 < ρ < 1 (intermediate between SWII and SWI models in the case of Rayleigh targets) and (intermediate between SWIV and SWIII models in the case of χ2 targets). The detection of partially correlated χ2 targets with two and four degrees of freedom is therefore of great importance. This paper describes the detection performance analysis of the ordered-statistics (OS) based constant false alarm rate (CFAR) detectors for the case where the radar receiver postdetection integrates M pulses of an exponentially correlated signal from targets which exhibit χ2 statistics with two and four degrees of freedom. Exact formulas for the detection probabilities are derived, in the absence as well as in the presence of spurious targets, which are assumed to be fluctuating in accordance with the χ2 fluctuation model with the same degrees of freedom.