A PERFORMANCE COMPARISON OF TWO TIME DIVERSITY SYSTEMS USING CMLD-CFAR DETECTION FOR PARTIALLY CORRELATED CHI-SQUARE TARGETS AND MULTIPLE TARGET SITUATIONS * Toufik Laroussi and ** Mourad Barkat * Département d'Electronique; Université de Constantine; Constantine 25000; Algeria. Phone/Fax: 213-31-81-90-10. E-mail: toufik_laroussi@yahoo.fr ** Department of Electrical Engineering, American University of Sharjah, P. O. Box 26666, Sharjah, United Arab Emirates. Phone: 971-6-515-2932, Fax: 971-6-515-2979. E-mail: mbarkat@aus.edu ABSTRACT In radar systems, detection performance is always related to target models and background environments. In time diversity systems, the probability of detection is shown to be sensitive to the degree of correlation among the target echoes. In this paper, we derive exact expressions for the probabilities of false alarm and detection of a pulse-to-pulse partially correlated target with 2K degrees of freedom for the Censored Mean Level Detector Constant False Alarm Rate (CMLD-CFAR). The analysis is carried out for the "non conventional time diversity system" (NCTDS). The obtained results are compared with the "conventional time diversity system" (CTDS) in both single and multiple target situations. 1. INTRODUCTION According to Swerling’s models, if only one pulse per scan hits a target, we cannot distinguish between cases I and II and cases III and IV. However, if multiple pulses are transmitted per antenna scan, the problem of detecting slow fluctuating targets and fast fluctuating targets can be easily overcome. Nevertheless, we should take into consideration the partial correlation of the target signal, otherwise the processor fails to predict the actual system performance. In other words, the more we know about the statistics of the target signal, the better the detection is. In the literature of CFAR detection, the echoed signals of the transmitted pulses are processed non coherently within the same receiver. Dealing with either uncorrelated or partially correlated data samples, we often seek to improve detection while maintaining a constant false alarm rate. Several authors have considered different applications of the non coherent integration. Here, we only list very few of them [1-3]. In [1], Kanter has studied the detection performance of a noncoherent integration detector accumulating M-correlated pulses from a Rayleigh target with two degrees of freedom. The noise was assumed to be uncorrelated. Wiener [2] extended the work in [1] by deriving exact expressions for the probabilities of detection for partially correlated chi-square targets with four degrees of freedom. The work done in [1, 2] used a fixed threshold detection. It is known that radar detectors with fixed threshold can not maintain a CFAR, and thus adaptive threshold detection is considered. Hou [3] used the method of residues to evaluate exact formulas for the detection performance for the chi-square family with 2K degrees of freedom. The idea of processing independently the received target pulses to yield preliminary decisions in distributed CFAR detection, was first suggested by Himonas and Barkat [4, 5]. They studied the case of partially correlated target returns with different architectures of time diversity and distributed CFAR detectors to minimize the effect of the correlation factor among the received target pulses. They called it "time diversity systems" referring to multiple-pulse systems. El Mashade [6, 7] has thoroughly developed this idea by considering the integration of all the individual noise level estimates. More precisely, as shown in figure 1, the reference samples of the individual pulse returns are ranked in an ascending order. Then, each ordered window is processed by the suited one-pulse order-statistic algorithm. Finally, the obtained noise level estimates are added to get the overall background level. Consequently, for the sake of comparison, we shall adopt in this paper the terminology "conventional time diversity system" (CTDS) to refer to the non coherent integration accumulating many pulses and processing them as an entity to form the noise level estimate [1-3]. and "non conventional time diversity system" (NCTDS) to refer to the technique used in [6, 7]. In summary, we observe that the work using the NCTDS did not show a comparison of the CMLD-CFAR detector with its corresponding detector for the CTDS in neither single nor multiple target situations. Moreover, the two systems did not consider the general case of a pulse-to- pulse partially correlated chi-square target with 2K degrees of freedom. To complete the study, we introduce a detailed detection analysis for a mathematical model representing the case of detecting a pulse-to-pulse chi-square partially correlated target with 2K degrees of freedom embedded in a pulse-to-pulse Rayleigh and uncorrelated thermal noise. The paper is organized as follows. In Section 2, we formulate the statistical model. In Section 3, we derive the exact false alarm probability (P fa ). Then, in Section 4, we give the moment generating function (mgf) of the test cell under hypothesis H 1 in terms of K and use it to derive the 14th European Signal Processing Conference (EUSIPCO 2006), Florence, Italy, September 4-8, 2006, copyright by EURASIP