Detectability Loss Due to "Greatest Of" Selection in a Cell-Averaging CFAR

Curves are presented showing the additional constant false-alarm rate (CFAR) loss which results when a "greatest of" logic is imple mented between the leading and lagging sets of reference cells. Thee analytical results for a square law detector and a Swerling case 1 fluctuating target are supplemented by simulation results for a nonfluctuating target, and envelope and logarithmic detector laws.     

Limiting Performance of Generalized Sign Test Detector

The limiting performance of the generalized sign test detector as the number M of target returns becomes infinite has been derived by Hansen and Olsen [1]. Simple expressions are derived herein for the limiting performance for finite M as K, the number of noise samples in the reference set, becomes infinite. Curves are presented which indicate how this limiting performance is approached as K is increased for both constant target returns and fluctuating target returns.     

Analysis of CA-CFAR processors for linear-law detection

A method for evaluating the performance of cell-averaging constant false alarm rate (CA-CFAR) processors which use the amplitude of echo signals rather than their squared amplitude is presented. Results for the case of Rayleigh clutter/noise statistics are given. Detection probabilities are evaluated for the case of a Rayleigh fluctuating target embedded in Rayleigh clutter/noise for linear-law CA-CFAR processors. These results are observed to be practically identical to those of square-law CA-CFAR processors for which analytical expressions are readily available. These observations are verified using Monte Carlo simulations. The same conclusion is reached in the case of a nonfluctuating target embedded in Rayleigh clutter/noise for which only simulation results are presented     

Trimmed Generalized Sign and Modified Median Detectors for Multiple Target Situations

The trimmed generalized sign (TGS) nonparametric detector is introduced. The TGS and the modified median detector (MMD) are considered in situations when more than one target is present. Their performance is obtained through Monte Carlo simulations and compared with that of the generalized sign (GS) detector when detecting nonfluctuating signal in Gaussian noise.     

Binary integration of fluctuating targets

The detection performance of a binary integrator (M-out-of-N detector) against nonfluctuating, slowly fluctuating, and quickly fluctuating targets is given. Since the solution for the slowly fluctuating target is numerically intensive, a simpler approximate solution is developed. This approximation is very accurate and is valid even when the noise power varies from pulse to pulse within a single antenna scan     

Modified Generalized Sign Test Processor for 2-D Radar

The modified generalized sign test processor is a nonparametric, adaptive detector for 2-D search radars. The detector ranks a sample under test with its neighboring samples and integrates (on a pulse-to-pulse basis) the ranks with a two-pole filter. A target is declared when the integrated output exceeds two thresholds. The first threshold is fixed and yields a 10-6 probability of false alarm when the neighboring samples are independent and identically distributed. The second threshold is adaptive and maintains a low false-alarm rate when the integrated neighboring samples are correlated and when there are nonhomogeneities, such as extraneous targets, in the neighboring cells. Using Monte Carlo techniques, probability of false-alarm results, probability of detection curves, and angular accuracy curves have been generated for this detector. The detector was built and PPI photographs are used to indicate the detector's performance when the radar is operated over land clutter.     

Detection analysis of the MX-MLD with noncoherent integration

The detection performance of the maximum mean level detection (MX-MLD) when noncoherent integration is used under both nonfluctuating and chi-square fluctuating target models is analyzed. Finite series are obtained in all cases. Required thresholds and constant false-alarm rate loss curves are presented, with emphasis on the important Swerling case II model     

Performance of a Two-Sample Mann-Whitney Nonparametric Detector in a Radar Application

The detection of signals in an unknown, typically non-Gaussian noise environment, while attempting to maintain a constant false-alarm rate, is a common problem in radar and sonar. The raw receiver data is commonly processed initially by a bank of frequency filters. The further processing of the outputs from the filter bank by a two-sample Mann-Whitney detector is considered. When the noise statistics in all filters are identical, the Mann-Whitney detector is distribution free, i. e., the false-alarm probability may be prescribed in advance regardless of the precise form of the noise statistics. The primary purpose of this paper is to demonstrate the potential advantage of nonparametric detectors over conventional detectors. The signal detection performance of the Mann-Whitney detector is compared to that of an ordinary linear envelope detector plus integrator in the presence of Gaussian and several hypothetical forms of non-Gaussian noise. This comparison is made for both uniform and nonuniform distributions of noise power across the filter bank. Besides providing a much more constant false-alarm rate than the conventional detector, the Mann-Whitney detector's signal detection performance is found also to be much less sensitive to the form of the noise statistics. In one case, its detection sensitivity is found to be 11 dB better than that of the conventional detector. Even when the noise power density is made moderately nonuniform across the filter bank, the detection performance of the Mann-Whitney detector is found not to be significantly affected.     

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     

Search radar detection and track with the Hough transform. III.Detection performance with binary integration

For pt.II see ibid., vol. 30, no 1, (Jan. 1994). This paper considers how well a Hough transform detector with binary integration improves the performance of a typical surveillance radar. For Hough transform detection, binary integration offers some advantages over noncoherent integration when multiple targets appear in range-time space or when the detector receives signals with a wide range of power. We derive expressions for P_F and P_D for a Hough transform binary integrator and apply the expressions to a typical surveillance radar. The results show that for the case considered, the binary Hough integrator improves the power budget of the radar by about 3 dB for a nonfluctuating target and 1 dB for a highly fluctuating target     

三种两样本非参量CFAR检测算法分析

介绍了3种两样本非参量CFAR检测算法的基本工作原理,利用实测未知统计概率分布海杂波数据对它们的检测性能进行了研究,并与参量CA-CFAR检测器进行了对比.研究表明:在强海杂波条件下,GS-CFAR检测器的检测性能最优;在弱海杂波条件下,Savage-CFAR检测器的检测性能最优;相比于CA-CFAR检测器,3种两样本...     

The Nonparametric Detection of Signals Embedded in Log-Normal Noise

The nonparametric detection of signals embedded in log-normal noise is discussed. The generalized sign (GS), Mann-Whitney (MW), modified Savage (MS), and modified rank squared (MRS) non-parametic detectors are considered and are compared with the mean and trimmed mean (TM) detectors when envelope detection is used. The detection of both nonfluctuating and Rayleigh fluctuating signals is considered.     

Performance of a Mean Level Detector Processing M-Correlated Sweeps

The performance of a mean level detector processing M-correlated consecutive sweeps is derived. Performance when sweeps are independent can be obtained simply as a special case. The background noise is assumed stationary Gaussian and pulses are fluctuating according to the Swerling I model. Results are obtained for both finite and infinite reference noise samples. It is shown that for fixed M the relative improvement over the single hit case increases when the correlation between sweeps decreases and as the probability of false alarm is kept at lower rates.     

非参量量化秩检测器的性能研究

 许多作者讨论过非参量秩检测器在雷达信号处理中的应用。秩检测器首先把接收波形样本转换为秩。如果检验单元和参考单元的噪声样本独立和分布,则无信号时检验单元的秩具有离散均匀分布,与输入噪声的分布无关。所以秩检测器可能提供分布自由的恒虚警率性能。量化秩检测器（QRD）只对二进量化秩进行积累,所以它实现起来很经济。本文分析QRD的检测性能。证明QRD有一最佳秩量化门限（ORQT）。确定高斯和韦伯噪声中的ORQT。另外,把QRD同高斯噪声中的局部最佳秩检测器和最佳参量检测器进行比较。     

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.     

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.     

Pade approximations for detectability in K-clutter and noise

The Pade approximation (PA) method is used to analyze the detection performance of single and multiple pulse radar systems operating in K-distributed clutter and thermal noise. Simple approximations for false-alarm and detection probabilities are obtained, using lower order moments for the detection decision statistic. Both envelope and squaring detector laws are considered, with noncoherent integration, for independent and correlated K clutter. The target is assumed to be pulse-to-pulse Rayleigh fading. The methods are a substantial application of the PA methods we have previously published     

Nonparametric rank detectors under K-distributed clutter in radar applications

This correspondence deals with a comparative analysis of parametric detectors versus rank ones for radar applications, under K-distributed clutter and nonfluctuating and Swerling II target models. We show that the locally optimum detectors (LODs) (optimum for very low signal-to-clutter ratio (SCR)) under K-distributed clutter are not practical detectors; on the contrary, asymptotically optimum detectors (optimum for high SCR) are the practical ones. The performance analysis of the parametric log-detector and the nonparametric (linear rank) detector is carried out for independent and identically distributed (IID) clutter samples, correlated clutter samples, and nonhomogeneous clutter samples. Some results of Monte Carlo simulations for detection probability (P/sub d/) versus SCR are presented in curves for different detector parameter values.     

Optimum and mismatched detection against K-distributed plusGaussian clutter

We derive the optimum radar receiver to detect fluctuating and non-fluctuating targets against a disturbance which is modeled as a mixture of coherent K-distributed and Gaussian-distributed clutter. In addition, thermal noise, which is always present in the radar receiver, is considered. We discuss the implementation of the optimum coherent detector, which derives from the likelihood ratio test under the assumption of perfectly known disturbance statistics, and evaluate its performance via a numerical procedure, when possible, and via Monte Carlo simulation otherwise. Moreover, we compare the performance of the optimum detector with those of two detectors which are optimum for totally Gaussian and totally K-distributed clutter respectively, when they are fed with such a mixed disturbance. We conclude that, though the optimum detector has a larger computational cost, it provides sensibly better detection performance than the mismatched detectors in a number of operational situations. Thus, there is a need to derive suboptimum target detectors against the mixture of disturbances which trade-off the detection performance and the implementation complexity     

Detection Performance of the Cell Averaging LOG/CFAR Receiver

The cell averaging LOG/CFAR receiver is a special implementation of a constant-false-alarm-rate (CFAR) receiver in which the noise level estimate is derived from a set of contiguous time samples of the output of a logarithmic (LOG) detector as obtained from a tapped delay line. This CFAR receiver is capable of operating over a larger dynamic range of noise levels than a conventional cell averaging CFAR receiver, but with somewhat poorer detectability. The performance in stationary Gaussian noise of the cell averaging LOG/CFAR receiver with no post-detection integration is determined in this paper. For a small number of reference noise samples, results were obtained by a Monte Carlo simulation using the technique of importance sampling. For a large number of reference noise samples, a second moment analysis gave the desired results. Both these results can be summarized in the following simple formula, NLOG = 1.65NLIN - 0.65, which relates the number of reference samples required by each of the two receivers for equivalent performance. Thus, for the cell averaging LOG/CFAR receiver to give the same detection performance as the conventional cell averaging CFAR receiver, the number of reference noise samples has to be increased by up to 65 percent.