Parallel Distributed CFAR Detection Optimization Based on Genetic Algorithm with Interval Encoding

Aiming at parallel distributed constant false alarm rate (CFAR) detection employing K/N fusion rule, an optimization algorithm based on the genetic algorithm with interval encoding is proposed. N-1 local probabilities of false alarm are selected as optimization variables. And the encoding intervals for local false alarm probabilities are sequentially designed by the person-by-person optimization technique according to the constraints. By turning constrained optimization to unconstrained optimization, the problem of increasing iteration times due to the punishment technique frequently adopted in the genetic algorithm is thus overcome. Then this optimization scheme is applied to spacebased synthetic aperture radar (SAR) multi-angle collaborative detection, in which the nominal factor for each local detector is determined. The scheme is verified with simulations of cases including two, three and four independent SAR systems. Besides, detection performances with varying K and N are compared and analyzed.     

Fluctuating Target Detection in Clutter Using Sidelobe Blanking Logic

In an earlier paper, Maisel [6] considered two-channel detection systems using a sidelobe blanking logic when a nonfluctuating target was present. This paper is an extension of the earlier work to include fluctuating targets. The Swerling I, II, III, and IV models are considered when single-pulse detection is of interest. An adaptive threshold procedure is also briefly discussed whereby the probability of false alarm at any given resolution cell is maintained constant, even though the input clutter level may vary from cell to cell or from beam position to beam position. Useful data are presented for detection probabilities in the range 0.5 to 0.9, for false alarm probabilities in the range 104 to 10-8, and for a false detection probability of 0.1 for a sidelobe target yielding an apparent signal to total noise power density ratio of 13.0 dB in the main beam receiver.     

A Simple Formula for Radar Detection Probability on Swerling I Targets

A formula is presented for the detection probability on a single scan of a Swerling I target. The formula does not use the Gaussian probability function and is accurate to 1.5 dB for the integration between 10 to 1000 pulses and for false alarm probabilities between 0.693 × 10-3 and 0.693 × 10-6.     

Energy Detection of a Random Process in Colored Gaussian Noise

A likelihood receiver for a Gaussian random signal process in colored Gaussian noise is realized with a quadratic form of a finite-duration sample of the input process. Such a receiver may be called a "filtered energy detector." The output statistic is compared with a threshold and if the threshold is exceeded, a signal is said to be present. False alarm and detection probabilities may be estimated if tabulated distributions can be fitted to the actual distributions of the test statistic which are unknown. Gamma distributions were fitted to the conditional probability densities of the output statistic by equating means and variances, formulas for which are derived assuming a large observation interval. A numerical example is given for the case in which the noise and signal processes have spectral densities of the same shape or are flat. The optimum filter turns out to be a band-limited noise whitener. The factors governing false alarm and detection probabilities are the filter bandwidth, the sample duration, and the signal level compared to the noise. Two sets of receiver operating characteristic curves are presented to complete the example.     

Estimation of radar detection and false alarm probability

The accuracy with which detection and false alarm probabilities can be estimated with a limited amount of measured radar data is addressed. A simple simulation method for estimating the statistical performance of a radar detection system is presented. Confidence limits and a rule of thumb for accuracy for the estimated probabilities are presented along with procedures for calculating them. It is concluded that the minimum value of N used in a detection radar signal simulation should be 10/P_FA when the simple simulation method is used, where P_FA is the probability of false alarm, and that a value closer to 100/P _FA is preferable     

Multistatic-Radar Binomial Detection

The performance of multistatic-radar binomial detectors is investigated. Although conceptually similar to the well-knwn "M-out-of-N" detector frequently considered for monostatic systems, the multistatic detector must cope with false alarms generated by target et ghosting as well as by noise threshold crossings. A procedure for deriving the detection statistics of multistatic binomial detectors ors is presented. The procedure is applied to derive the detection probabilities for a spectrum of false alarm probabilities, target densities, and numbers of radar receivers.     

Clutter Map CFAR Analysis

An analysis of the probability of target detection for a clutter map CFAR using digital exponential filtering has been performed. General performance equations are derived. The probability of detection versus signal-to-noise ratio is plotted for a false alarm probability of 1.E-06 for several weight values. The CFAR loss is plotted for a detection probability of 0.9 and false alarm probabilities of 1.E-06 and 1.E-08.     

Coherent detection in Laplace noise

The discrete-time detection of a time-varying, additive signal in independent Laplace noise is considered. Previous efforts in this area have been restricted to the constant signal, and identically distributed noise case. Theoretical (closed form) expressions for the false alarm and detection probabilities are developed for both the Neyman-Pearson optimal detector and the classical matched filter detector. Comparisons between the two detectors are made which illustrate the effects of signal-to-noise power ratio and sample size for certain false alarm and detection probability constraints. In view of the fact that the optimal Laplace detector is not UMP, we also investigate the effect of signal amplitude mismatch     

A Detection Algorithm for Optical Targets in Clutter

There is active interest in the development of algorithms for detecting weak stationary optical and IR targets in a heavy opticalclutter background. Often only poor detectability of low signal-to-noise ratio (SNR) targets is achieved when the direct correlation method is used. In many cases, this is partly obviated by using detection with correlated reference scenes [1, 2].This paper uses the experimentally justified assumption that most optical clutter can be modeled as a whitened Gaussian randomprocess with a rapidly space-varying mean and a more slowlyvarying covariance [2]. With this assumption, a new constant falsealarm rate (CFAR) detector is developed as an application of the classical generalized maximum likelihood ratio test of Neyman and Pearson. The final CFAR test is a dimensionless ratio. This test exhibits the desirable property that its probability of a false alarm(PFA) is independent of the covariance matrix of the actual noiseencountered. When the underlying noise processes are complex intime, similar considerations can yield a sidelobe canceler CFARdetection criterion for radar and communications. Performance analyses based on the probability of detection (PD)versus signal-to-noise ratio for several given fixed false alarm probabilities are presented. Finally these performance curves are validated by computer simulations of the detection process which use real image data with artificially implanted signals.     

A Method for Setting a Test Signal Level Relative to Noise

A method is described for adjusting the leval of an RF test signal generator relative to the noise level at the receiver output. The method compares a detected output to a threshold and counts the number of times noise and signal plus noise cross the threshold in a given number of tries. By setting the threshold at a given false alarm probability for noise alone and then adding the test signal and adjusting its level to give a specified detection probability, the signal-to-noise ratio can be calibrated to an accuracy that depends on the number of samples used to measure the probabilities. The false alarm and detection probabilities are given for best accuracy as well as the rms error in signal-to-noise ratio as a function of the number of samples used.     

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     

Optimal radar threshold determination in Weibull clutter andGaussian noise

A technique is presented for determining the ideal detection threshold when Gaussian noise and Weibull distributed clutter returns are present on a radar receiver and neither is dominant. Quantitative data is presented for several clutter types and false alarm probabilities     

Cascaded detector for multiple high-PRF pulse Doppler radars

A postdetection design methodology for a multiple high-pulse-repetition frequency (PRF) pulse Doppler radar has been developed. The postdetection processor consists of an M out of N detector where range and target ambiguities are resolved, followed by a square-law detector which enhances the minimum signal-to-noise (S/N) power-ratio per pulse burst performance. For given probabilities of false alarm and detection, formulas are derived from which the three thresholds associated with the cascaded detector can be found. Fundamental tradeoffs between the minimum S/N required, number of ghosts, and the number of operations (NOPs) that the cascaded detector must perform are identified. It is shown that the NOPs and the number of ghosts increase and the minimum S/N required decreases as the binary M out of N detector passes more detections to the square-law detector     

Matched subspace CFAR detection of hovering helicopters

A constant false alarm rate (CFAR) strategy for detecting a Gaussian distributed random signal against correlated non-Gaussian clutter is developed. The proposed algorithm is based on Scharf's matched subspace detector (MSD) and has the CFAR property with respect to the clutter amplitude probability density function (apdf), provided that the clutter distribution belongs to the compound-Gaussian family and the clutter covariance matrix is known to within a scale factor. Analytical expressions of false alarm and detection probabilities are derived. An application to the problem of detecting hovering helicopters against vegetated ground clutter is reported     

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.     

A persymmetric multiband GLR algorithm

By exploring the covariance structure information to reduce the uncertainty in adaptive processing, a persymmetric generalized likelihood ratio algorithm (PGLR) is developed together with the closed-form expressions of probabilities of detection and false alarm. This multiband algorithm, which requires less computation, can significantly outperform the corresponding unstructured multiband GLR algorithm, especially in a severely nonstationary and/or nonhomogeneous interference environment. Simulation shows that the constant false alarm rate (CFAR) performance of the new algorithm is as insensitive as that of the unstructured multiband GLR to the departure of interference distribution from Gaussian     

A Boolean algebra approach to multiple sensor voting fusion

A technique for integrating multiple-sensor data using a voting fusion process that combines the individual sensor outputs is described. An important attribute of the method is the automatic confirmation of the target by the fusion processor without the need to explicitly determine which sensors and what level of sensor participation are involved. A three-sensor system, with multiple confidence levels in each sensor, is discussed to illustrate the approach. Boolean algebra is used to derive closed-form expressions for the multiple sensor-system detection probability and false-alarm probability. Procedures for relating confidence levels to detection and false alarm probabilities are described through an example. The hardware implementation for the sensor system fusion algorithm is discussed     

Comments on, `Improved multilevel quantization for detection ofnarrowband signals' by C.W. Helstrom

It is shown that optimum quantization levels may be obtained by using C.W. Helstrom's approach of the above named work (see ibid., vol.AES-24, p.141-147, Mar. 1988) but maximizing exact detection probabilities instead of approximations to it if the moment generating function of the test statistic can be expressed in rational form. Adaptive levels may be obtained for the quantizers by cell averaging, leading to constant false alarm rate (CFAR) detectors     

Importance sampling for characterizing STAP detectors

This paper describes the development of adaptive importance sampling (IS) techniques for estimating false alarm probabilities of detectors that use space-time adaptive processing (STAP) algorithms. Fast simulation using IS methods has been notably successful in the study of conventional constant false alarm rate (CFAR) radar detectors, and in several other applications. The principal objectives here are to examine the viability of using these methods for STAP detectors, develop them into powerful analysis and design algorithms and, in the long term, use them for synthesizing novel detection structures. The adaptive matched filter (AMF) detector has been analyzed successfully using fast simulation. Of two biasing methods considered, one is implemented and shown to yield good results. The important problem of detector threshold determination is also addressed, with matching outcome. As an illustration of the power of these methods, two variants of the square-law AMF detector that are thought to be robust under heterogeneous clutter conditions have also been successfully investigated. These are the envelope-law and geometric-mean STAP detectors. Their CFAR property is established and performance evaluated. It turns out the variants have detection performances better than those of the AMF detector for training data contaminated by interferers. In summary, the work reported here paves the way for development of advanced estimation techniques that can facilitate design of powerful and robust detection algorithms