Data quantization effects in CFAR signal detection

In this paper, we investigate data quantization effects in constant false alarm rate (CFAR) signal detection. Exponential distribution for the input data and uniform quantization are assumed for the CFAR detector analysis. Such assumptions are valid in the case of radar for a Swerling I target in Gaussian clutter plus noise and a receiver with analog square-law detection followed by analog-to-digital (A/D) conversion. False alarm and detection probabilities of the cell averaging (CA) and order statistic (OS) CFAR detectors operating on quantized observations are analytically determined. In homogeneous backgrounds with 15 dB clutter power fluctuations, we show analytically that a 12-bit uniform quantizer is sufficient to achieve false alarm rate invariance. Detector performance characteristics in nonhomogeneous backgrounds, due to regions of clutter power transitions and multiple interfering targets, are also presented and detailed comparisons are given     

Adaptive array CFAR detection

Presented here is a large class of adaptive array detection algorithms with constant false alarm rate (CFAR), so that the false alarm rate can be set to any preassigned number without knowledge of the noise covariance matrix. This class map incorporate any usual method of cell averaging and any method for array weight vector synthesis. A sufficient condition for CFAR is derived, which is easy to satisfy in practice. Basic system parameters are discussed. An example of detection performance for a simple cell-averaging detector, in which the array weight vector is synthesized by the method of diagonal loading, is provided using Monte Carlo simulations     

Radar CFAR Thresholding in Clutter and Multiple Target Situations

Radar detection procedures involve the comparison of the received signal amplitude to a threshold. In order to obtain a constant false-alarm rate (CFAR), an adaptive threshold must be applied reflecting the local clutter situation. The cell averaging approach, for example, is an adaptive procedure. A CFAR method is discussed using as the CFAR threshold one single value selected from the so-called ordered statistic (this method is fundamentally different from a rank statistic). This procedure has some advantages over cell averaging CFAR, especially in cases where more than one target is present within the reference window on which estimation of the local clutter situation is based, or where this reference window is crossing clutter edges.     

Studies of Logarithmic Radar Receiver Using Pulse-Length Discrimination

Using a logarithmic amplifier giving a detected output followed by a high-pass filter is a technique for reducing adverse effects of distributed clutter in radar receivers. A pulse-length discriminator (PLD) used as the high-pass filter is treated here. Theoretical and experimental results for the loss in detectability introduced by this receiver, as compared with a matched filter or a good approximation thereto, have been obtained. For the case of single-hit detection, losses of 4 to 8 dB are introduced by the logarithmic amplifier/pulse-length discriminator (LOG AMP/PLD) combination; for post-detection integration, the losses are reduced to 2 to 4 dB. The latter values would apply where the LOG AMP/PLD output is presented on a PPI (plan position indicator). Some experimental results of the ability of the LOG AMP/PLD receiver to reject signals of incorrect pulse length show that signals exceeding the design pulse length by more than 25 to 50 percent are effectively suppressed. No significant short-pulse discrimination is obtained from the receiver.     

M-correlated sweeps performance analysis of mean-level CFARprocessors in multiple target environments

This paper is devoted to the detection performance evaluation of the mean-level (ML) constant false-alarm rate (CFAR) detectors processing M-correlated sweeps in the presence of interfering targets. The consecutive pulses are assumed to be fluctuating according to the Swerling I model. Exact expressions are derived for the detection probability of the conventional mean-level detector (MLD) and its modified versions under Rayleigh fluctuating target model. Performance for independent sweeps can be easily obtained by setting the sweep-to-sweep correlation coefficient equal to zero. Results are obtained for both homogeneous and nonhomogeneous background environments. It is shown that for fixed M, the relative improvement over the single sweep case increases as the correlation between sweeps decreases. For the same parameter values, the minimum MLD has the best performance in the presence of extraneous target returns among the reference noise samples     

Ll-CFAR: a flexible and robust alternative

A new family of constant false alarm rate (CFAR) processors is introduced. An Ll-CFAR forms its noise power estimate by linearly filtering ranked samples from the reference set; the weights of this combination, however, depend not only on the rank, but also on the relative proximity of the sample to the cell under test. From the class of Ll-CFARs may be chosen members which effectively censor spurious targets; members which exhibit impressive control of false alarm in the presence of a clutter edge; and members which are robust against both such inhomogeneities. While the design of such schemes is involved, their implementation is not significantly more burdensome than that of plain ordered statistic CFAR (OS-CFAR). After a discussion of the stochastic training of Ll-CFAR, the performance is thoroughly assessed under the most commonly encountered instances of environmental conditions, and compared with those of classical CFAR techniques     

A variably trimmed mean CFAR radar detector

A variably trimmed mean (VTM) constant false alarm rate (CFAR) detector in which the threshold is determined by processing a linear combination of a group of ordered samples in each window is introduced. Unlike the trimmed mean detector, the number of ordered samples that require further processing is allowed to vary according to a data-dependent rule. It is demonstrated that the VTM detector exhibits performance characteristics that are independent of the total (stationary) noise power. Simulated performance results are presented for regions of clutter power transitions and for multiple target environments to illustrate the possible improvement over the order-statistic detector that can be obtained by using a VTM detector     

A new and robust CFAR detection algorithm

A constant false alarm rate (CFAR) detection method which is based on a combination of median and morphological filters (MEMO) is proposed. The MEMO algorithm has robust performance with small CFAR loss, very good behavior at clutter edges and high detection performance in the case of closely spaced narrowband signals (targets). The proposed MEMO method is favourably compared with cell averaging (CA) and ordered statistics (OS) CFAR detectors. The Monte Carlo method is employed to analyze the MEMO-CFAR detector     

Radar modelling to improve CFAR performance in the littoral

Littoral operation of radars poses severe signal processing difficulties due to the highly stressing, inhomogeneous clutter. This report describes an initial investigation into the feasibility of utilising site specific radar modelling to provide a localized estimate of the clutter statistics which can then be used to predict the required threshold to maintain a given false alarm rate. The technique has been applied to littoral clutter recordings obtained from the experimental S-band phase array radar, MESAR2. Results are presented for the technique in comparison with a conventional, non-adaptive, cell averaging CFAR. The paper concludes that significant performance enhancements are possible through the use of this new technique.     

Improved CFAR performance in the littoral

Littoral operation of radars poses severe signal processing difficulties due to the highly stressing, inhomogeneous clutter. This report describes an initial investigation into the feasibility of utilising site-specific radar modelling to provide a localised estimate of the clutter statistics which can then be used to predict the required threshold to maintain a given false alarm rate. The technique has been applied to littoral clutter recordings obtained from the experimental S-band phased array radar, MESAR2. Results are presented for the technique in comparison with a conventional, non-adaptive, cell averaging CFAR. This paper concludes that significant performance enhancements are possible through the use of this new technique.     

A new distributed constant false alarm rate detector

A new constant false alarm rate (CFAR) test termed signal-plus-order statistic CFAR (S+OS) using distributed sensors is developed. The sensor modeling assumes that the returns of the test cells of different sensors are all independent and identically distributed In the S+OS scheme, each sensor transmits its test sample and a designated order statistic of its surrounding observations to the fusion center. At the fusion center, the sum of the samples of the test cells is compared with a constant multiplied by a function of the order statistics. For a two-sensor network, the functions considered are the minimum of the order statistics (mOS) and the maximum of the order statistics (MOS). For detecting a Rayleigh fluctuating target in Gaussian noise, closed-form expressions for the false alarm and detection probabilities are obtained. The numerical results indicate that the performance of the MOS detector is very close to that of a centralized OS-CFAR and it performs considerably better than the OS-CFAR detector with the AND or the OR fusion rule. Extension to an N-sensor network is also considered, and general equations for the false alarm probabilities under homogeneous and nonhomogeneous background noise are presented.     

基于小生境遗传算法的分布式OS-CFAR检测系统优化与性能分析

 利用小生境遗传算法,对不同检测窗长度和检测信噪比的三传感器分布式 OS-CFAR检测系统进行了优化设计,给出了一组针对不同检测环境与融合方式的搜索结果。分析表明,对于非一致环境下分布式 OS-CFAR检测系统,小生境遗传算法是一种良好的优化算法。利用搜索结果,研究了不同融合方式下环境变化对分布式 OS-CFAR检测系统的性能影响,结果表明,“或”融合对检测环境的非一致变化具有较强的鲁棒性,而“3选2”融合和“与”融合对检测环境的变化比较敏感。     

OS-CFAR theory for multiple targets and nonuniform clutter

The performance of a cell averaging constant false-alarm rate (CA-CFAR) detector degrades rapidly in nonideal conditions caused by multiple targets and nonuniform clutter. The ordered-statistic CFAR (OS-CFAR) is an alternative to the CA-CFAR. The OS-CFAR trades a small loss in detection performance relative to the CA-CFAR in ideal conditions for much less performance degradation in nonideal conditions. A formula is given for the detection probability of the OS-CFAR when there are multiple Swerling I targets in the CFAR window, and a formula is given for the probability of false alarm in nonuniform Raleigh clutter     

Nonparametric Radar Extraction Using a Generalized Sign Test

A nonparametric procedure used in a constant false alarm rate (CFAR) radar extractor for detecting targets in a background of noise with unknown statistical properties is described. The detector is based on a generalization of the well-known two-sample sign test and thus requires a set of reference noise observations in addition to the set of observations being tested for signal presence. The detection performance against Gaussian noise is determined for a finite number of observations and asymptotically, for both nonfluctuating and pulse-to-pulse Rayleigh fluctuating target statistics. It is noted that the performance loss, as compared to the optimum parametric detector, depends critically on the number of reference noise observations available when the number of hits per target is not large. In the same case a much larger loss is also found for a pulse-to-pulse fluctuating target even though the asymptotic loss is the same as for a nonfluctuating target. A comparison is finally made with a detector based on the Mann-Whitney test, which usually is considered to be one of the better nonparametric procedures for the two-sample case.     

Radar Detection of Correlated Targets in Clutter

This paper provides general models of radar echoes from a target. The rationale of the approach is to consider the echoes as the output of a linear dynamic system driven by white Gaussian noise (WGN). Two models can be conceived to generate N target returns: samples generated as a batch, or sequentially generated one by one. The models allow the accommodation of any correlation between pulses and nonstationary behavior of the target. The problem of deriving the optimum receiver structure is next considered. The theory of "estimator-correlator" receiver is applied to the case of a Gaussian-distributed time-correlated target embedded in clutter and thermal noise. Two equivalent detection schemes are obtained (i. e., the batch detector and the recursive detector) which are related to the above mentioned procedures of generating radar echoes. A combined analytic-numeric method has been conceived to obtain a set of original detection curves related to operational cases of interest. Finally, an adaptive implementation of the proposed processor is suggested, especially with reference to the problem of on-line estimation of the clutter covariance matrix and of the CFAR threshold. In both cases detection loss due to adaptation has been evaluated by means of a Monte Carlo simulation approach. In summary, the original contributions of the paper lie in the mathematical formulation of a powerful model for radar echoes and in the derivation of a large set of detection curves.     

CFAR detection and estimation for STAP radar

The algorithm presented here provides both a constant false-alarm rate (CFAR) detection and a maximum likelihood (ML) Doppler-bearing estimator of a target in a background of unknown Gaussian noise. A target is detected, and its parameters estimated within each range gate by evaluating a statistical test for each Doppler-angle cell and by selecting the cell with maximum output and finally comparing it with a threshold. Its CFAR performance is analyzed by the use of the sample matrix inversion (SMI) method and is evaluated in the cases of a fully adaptive space-time adaptive processing (STAP) and two partially adaptive STAPs. The performances of these criteria show that the probability of detection is a function only of the sample size K used to estimate the covariance matrix and a generalized signal-to-noise ratio. The choice of the number K is a tradeoff between performance and computational complexity. The performance curves demonstrate that the finer the resolution is, the poorer the detection capability. That means that one can trade off the accuracy of ML estimation with the performance of the CFAR detection criterion     

False alarm analysis of the envelope detection GO-CFAR processor

The greatest of constant false alarm rate processor (GO CFAR) is a useful architecture for adaptively setting a radar detection threshold in the presence of clutter edges. The GO CFAR input is often the envelope detected in-phase (I) and quadrature (Q) channels of the baseband signal (x_e=√(I²+Q²)). This envelope detection can also be approximated using x=a max{|I|,|Q|}+b min{|I|,|Q|} which requires less complex hardware (a and b are simple multiplying coefficients). The envelope GO CFAR processor and several envelope approximation GO CFAR processors are compared in terms of the probability of false alarm (PFA) performance. Closed-form expressions which describe the PFA performance are given and their accuracy evaluated. It is shown that for all cases, the PFA is proportional to the number of reference cells n for small threshold multiplier T and inversely proportional to n for large T. A region of intersection occurs where the PFA is the same for two different values of n. For example, at T'=1.68 in the |I|+|Q| GO CFAR (a=1, b=1) the PFA for n=1 is equal to the optimal n=∞ fixed-threshold PFA (PFA=0.112)     

Adaptive Radar Detection with Asymptotically Regulated False-Alarm Rate

An adaptive detection procedure is described by which the detection threshold is so adjusted as to provide an asymptotic false-alarm probability PFA that is approximately invariant with changes in radar clutter return amplitude probability density functions (pdf's) in a broad class. The class includes Rayleigh, chi, Weibull, and lognormal pdf's. The receiver noise is also taken into account. The clutter-plus-noise pdf is approximated by a truncated generalized Laguerre series, the coefficients of which are estimated from the radar returns using "cell averaging" techniques. This estimation is assumed to be perfect. The results obtained indicate that the "bias" error, defined as the normalized difference between the design PFA and the asymptotic PFA corresponding to the computed threshold, lies within a fraction of an order of magnitude for 10-3?PFA ? 10-6. For PFA ?10-6 the bias error is more than an order of magnitude. These results are for the case when a single independent radar return is processed at a time. The bias error decreases as the number of postdetection integrations of independent returns increases.     

Modified Savage and Modified Rank Squared Nonparametric Detectors

A modified form of the basic Savage statistic is considered and the performance of a modified Savage (MS) nonparametric detector using this modified statistic is derived. Also, a detector using a modified rank squared statistic (MRS) is introduced. The asymptotic relative efficiency (ARE) of the detectors is determined for chisquare, Rician, and log-normal signal fluctuations when the background noise is assumed Gaussian. The ARE performance of the generalized sign (GS) and Mann-Whitney (MW) detectors is also determined for these families of fluctuations. The ARE performance of the various detectors is then compared, and the results of a computer simulation are presented in which, for a finite number of samples, the performance of the modified detectors is compared with the performance of the GS and MW detectors. It is shown that when using a large number of reference noise samples, the ARE of the GS and MW detectors, the MRS and RS detectors, and the MS and Savage detectors are 0.75, 0.868, and 1, respectively. It is also shown that when using a finite number of reference noise samples the MS and MRS detectors can give a superior performance to that obtained with the MW detector, and that this is particularly true in the cases in which the degree of signal fluctuation is high.     

Analysis of an adaptive CFAR detector in non-Gaussian interference

Coherent signal detection in non-Gaussian interference is presently of interest in adaptive array applications. Conventional array detection algorithms inherently model the interference with a multivariate Gaussian random vector. However, non-Gaussian interference models are also under investigation for applications where the Gaussian assumption may not be appropriate. We analyze the performance of an adaptive array receiver for signal detection in interference modeled with a non-Gaussian distribution referred to as a spherically invariant random vector (SIRV). We first motivate this interference model with results from radar clutter measurements collected in the Mountain Top Program. Then we develop analytical expressions for the probability of false alarm and the probability of detection for the adaptive array receiver. Our analysis shows that the receiver has constant false alarm rate (CFAR) performance with respect to all the interference parameters. Some illustrative examples are included that compare the detection performance of this CFAR receiver with a receiver that has prior knowledge of the interference parameters