Our scope in this paper is to provide a complete analysis of CFARdetection of fluctuating targets when the radar receiver incoherently integrates M returned pulses from a chi-squared fluctuating targets with two and four degrees of freedom and operates in a multitarget environment. Since the Swerling models of fluctuating targets represent a large number of such type of radar targets, we restrict our attention here to this interesting class of fluctuation models. There are four categories of such representation; namely SWI, SWII, SWIII, and SWIV. SWI and SWIII represent scan-to- scan fluctuating targets, while SWII and SWIV represent fast pulse-to-pulse fluctuation. Exact expressions are derived for the probability of detection of all of these models. A simple and an effective procedure for calculating the detection performance of both fixed-threshold and adaptive-threshold algorithms is obtained. The backbone of this procedure is the ω-domain representation of the cumulative distribution function of the test statistic of the processor under consideration. In the CFARcase, the estimation of the noise power levels from the leading and the trailing reference windows is based on the OS technique. The performance of this detector is analyzed in the case where the operating environment is ideal and where it includes some of extraneous targets along with the target under test. The primary and the secondary outlying targets are assumed to be fluctuating in accordance with the four Swerling's models cited above. The numerical results show that, for large SNR, the processor detection performance is highest in the case of SWIV model while it attains its minimum level of detection in the case of SWI model. Moreover, SWII model has higher performance than the SWIII representation of fluctuating targets. For low SNR, on the other hand, the reverse of this behavior is occurred. This observation is common either for fixed-threshold or for adaptive-threshold algorithm.
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