Parallel and Cloud Computing Research (PCCR) Volume 1 Issue 2, July 2013 www.seipub.org/pccr 17 Analysis of Adaptive Detection of Partially- Correlated χ 2 Targets in Multitarget Environments Mohamed B. El Mashade Electrical Engineering Dept., Faculty of Engineering, Al Azhar University, Nasr City, Cairo, Egypt ElMashade@yahoo.com Abstract The target's characteristics play an important role in the design and performance analysis of all radar systems. The fluctuation rate of such a target may vary from essentially independent return amplitudes from pulse-to-pulse to significant variation only on a scan-to-scan basis. The correlation coefficient between the two consecutive echoes in the dwell-time is equal to unity for the SWI and SWIII cases while it is zero for the SWII and SWIV models. An important class of targets is that represented by the so-called moderately fluctuating Rayleigh and  2 targets. The detection of partially correlated  2 targets with two and four degrees of freedom is therefore of great importance. Our goal in this paper is to analyze the detection performance of the most familiar candidates of CFAR techniques for the case where the radar receiver post- detection integrates M pulses of an exponentially correlated signal from targets which exhibit  2 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. As predicted, the CA detector has the best homogeneous performance while the OS scheme gives the best target multiplicity performance when the number of outlying targets is within its allowable values. Keywords Post-detection Integration; Partially Correlated  2 Targets; Swerling Fluctuation Models; CFAR Detection Techniques; Target Multiplicity Environments I. Introduction The complete radar signal over a multiple observation interval is called a pulse train. Fluctuating pulse trains occur often in practice. When a radar target consists of several relatively strong reflecting surfaces displaced from one another by the order of a wavelength, the amplitude and phase of the composite radar echo are sensitive to the spatial orientation of the target. Moreover, if the target has relative motion with respect to the radar, it presents a time varying radar cross section. This change may be a slow variation and occur on a scan-to-scan basis (on successive antenna scans across a target) or on a pulse-to-pulse basis (on successive sweeps). Because it is difficult to predict the exact nature of the change, a statistical description is often adopted to characterize the target radar cross section [Meyer, 1973]. Target fluctuation is defined as variation in the amplitude of a target signal, caused by changes in target aspect angle, rotation, vibration of target scattering sources, or changes in radar wavelength. 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. Three families of radar cross-section fluctuation models have been used to characterize most target populations of interest: the  2 family, the Rice family, and the log-normal family [Aloisio, 1994]. The  2 family includes the Rayleigh (SWI & SWII) model with two degree of freedom (=1), the four degree of freedom (=2) model (SWIII & SWIV), the Weinstock model (<1), and the generalized model ( a positive real number). The  2 models are used to represent complex targets such as aircraft and have the characteristic that the distribution is more concentrated about the mean as the value of the parameter  is increased [Swerling, 1997]. The advantages of the Swerling target models are that they bracket a large number of real target classes [Di Vito, 1999]. It is often assumed that the Swerling cases bracket the behavior of fluctuating targets of practical interest. However, recent investigations of target cross section fluctuation statistics indicate that some targets may have probability of detection curves which lie considerably outside the range of cases which are satisfactorily bracketed by the Swerling cases. An important class of targets is represented by the so-