Automatic censored mean level detector using a variability-based censoring with non-coherent integration
Introduction
The immunity of a constant false alarm rate (CFAR) processor to the presence of spurious targets and clutter edges among the reference window is one of the main concerns of radar systems. The category of order statistics (OS)-based CFAR [1], [2], [3] have been proposed to improve the robustness of the mean level detectors against nonhomogeneous environments. Rickard and Dillard [2] proposed a class of CFAR, known as CMLD(k), in which the k largest range cells are censored from the reference window. It is well known that the fixed censoring points detectors [1], [2], [3], [4] yield good performances as long as the cells from outlying returns are properly discarded. However, in these CFAR processors, the censoring points are preset and invariant for all further processing. If insufficient a priori knowledge about the environment is available, the censored cells may be poorly selected, causing poor detection or excessive false alarm rate. To circumvent this problem, Himonas and Barkat [5] proposed the ACMLD and GTL–CMLD in which the censoring points are dynamically determined. Both the ACMLD and the GTL–CMLD are based on the same cell-by-cell censoring procedure, and their performance was studied for a single pulse processing. In [6], Smith and Varshney introduced the concept of the variability index (VI) CFAR detection. In [7], we proposed the automatic censored cell-averaging detector based on ordered data variability (ACCA–ODV). This processor uses iterative data variability, as shape parameters, to reject or accept the ordered cells under investigation. It was shown that the ACCA–ODV detector exhibits a small detection loss in a homogeneous environment and performs robustly in non-uniform clutter. The study was done for single pulse processing. In this paper, we consider an extension and a generalization of the work in [7] to the case of M-pulse non-coherent integration. The proposed detector is based on the selection of the optimal CMLD(k) according to the current environment, where k is the estimated number of censored cells, and thus we call it Opt-CMLD. In order to obtain the most representative ranked sample for the noise level estimation, we use the iterative variability-based censoring algorithm [7], which performs on a cell-by-cell to discard the unwanted samples.
The paper is organized as follows. After a discussion of the statistical assumptions and models made here, we briefly describe the proposed detector (Opt-CMLD) in Section 2. In Section 3, we recall the basic principles of the ODV-based censoring algorithm. We also show how we compute the ODV thresholds, according to the prescribed probability of false censoring (Pfc), in a homogeneous Gamma-distributed clutter. An exact expression for the probability of false alarm of the Opt-CMLD when processing M non-coherent pulses is derived in Section 4. Section 5 is devoted to the performance analysis of the detector under consideration, while in Section 6 we present our conclusions along with a discussion of our results.
Section snippets
Basic assumptions and problem formulation
In a CFAR processor with an M-pulse non-coherent integration, the square law detected range samples, reflected from the mth emitted pulse, are sent serially into a shift register of length N+1 as shown in Fig. 1. The N+1 samples correspond to the even number N of reference cells Xk,m, k=1,2 ,…, N, surrounding the test cell X0,m. The samples Xk,m refer to the received echo at kth range bin for the mth transmitted pulse. We assume an independent Gaussian clutter-plus-noise at different range bins,
Automatic censoring
In this section, we recall the basic concept of the ODV algorithm [7] by introducing the necessary adjustments for the case of M pulses. The main idea is to consider that there are, at least, p (p<N) samples among the N reference cells, which are drawn from a homogeneous population. Consequently, the p lowest cells are assumed to be the initial estimation of the background. In order to update iteratively this initial estimation, we form the sequence of rank ordered subsets Ek(x) of length (p+1)
Analysis of Opt-CMLD with non-coherent integration
In this section, we derive an exact expression for the Pfa of the Opt-CMLD when processing M non-coherently reflected pulses. For the proposed detection scheme, the total noise level estimate Z is obtained by adding the M individual noise levels Zm, where Zm is a local estimator for each reflected pulse. Because of the pulse-to-pulse non-correlation, the moment generating function (MGF) ΦZ(ω) of the total noise power is the product of the individual MGFs of Zms. Thus, , where ΦZm
Results and discussions
In this section, we present several simulation results, and analyze the censoring efficiency as well as the detection performances of the Opt-CMLD. For the ODV-based censoring technique, we used the optimum parameters found in [7], namely Pfc=10−2 and p>N/2 representing the length of the initial population. In all our numerical results we have taken p=12 and N=16 reference cells. The choice of the parameter p has been motivated by the two following conditions: first, the statistic VI offers
Conclusion
In this paper, a censoring technique using variability statistics to enhance the robustness of the CMLD in multiple pulse non-coherent processing, has been addressed. Through the performance analysis, it was shown that the association of the ODV-based algorithm with fixed censoring point CFAR detectors provides attractive properties against non-homogeneous environments. For the non-coherent integration, we proposed a detection scheme, which is different from the conventional one. This approach,
Acknowledgment
The authors are grateful to the reviewers for their constructive comments.
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