A new CFAR sidelobe canceler algorithm for radar

Signal or target detection is sometimes complicated by the presence of strong interference. When this interference occurs mainly in the sidelobes of the antenna pattern, a solution to this problem is realized through a sidelobe canceler (SLC) implementation. Since the false-alarm probability is a system parameter of special importance in radar, an interference-canceling technique for radar application should maintain the false-alarm probability constant over a wide range of incident interference power. With the requirements of sidelobe interference cancellation and constant false alarm rate (CFAR), a new algorithm for radar detection in the presence of sidelobe interference is developed from the generalized likelihood ratio test of Neyman-Pearson. In this development, the received interference is modeled as a nonstationary but slowly varying Gaussian random process. Cancellation of the sidelobe interference is based upon a `synchronous' estimate of the spatial covariance of the interference for the range gate being tested. This algorithm provides a fixed false-alarm rate and a fixed threshold which depend only upon the parameters of the algorithm     

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.     

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 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.     

Performance Data for a Double-Threshold Detection Radar

A problem f requently encountered by radar systems analysts is the evaluation of the "double-threshold" or M out of N detection process. Detection probabilities of this process are binomially distributed, making it difficult to obtain exact results for large values of the number of samples and for low probabilities of false alarm. In this paper, the M out of N detection algorithm is defined and detection performance is calculated for the special cases of the nonfluctuating target and Swerling cases I and 11 for false alarm probabilities of 106, 10-8 and 10-10.     

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     

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     

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.     

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.     

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     

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 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     

Detection of a Distributed Target

The influence of increasing range resolution on the detectability of targets with dimensions greater than the resolution cell is studied. An N-cell target model is assumed, which contains k reflecting cells, each reflecting independently according to the same Rayleigh amplitude distribution. It will be referred to as the (N,k) target. Detection based on one transmitted pulse is performed against a background of white normal noise. Detection in stationary clutter is also considered. The optimum detector is obtained but, in view of its complexity, the performance of a simpler detector, the square-law envelope detector with linear integrator (SLEDLI), is analyzed, and a formula for the probability of detection is obtained. Graphs are presented which show the probability of detection as a function of signal-to-noise ratio (SNR) for various values of N k, and false alarm probability. For N/k not too large it is shown that the SLEDLI is near optimum.     

Radar detection in clutter

Clutter is defined as any unwanted radar return. The presence of clutter in a range/Doppler cell complicates the detection of a target return signal in that cell. In order to quantify the effect of clutter on the probability of detection, we must first specify sets of models suitable for representing the clutter and target. The simplest and most common model for clutter is based on the gamma density. We include two additional models, the NCG and NCGG clutter models for low grazing angles. They are motivated by physical arguments, the latter of which can accommodate the well-known phenomenon of speckle. Using one of these models for clutter together with one of several models for targets, we determine, in a range/Doppler cell, expressions for probabilities of detection of a target in the presence of clutter. It is important to control the probability of false alarms. The presence of clutter in a cell necessitates an increase in the detection threshold setting in order to control false alarms, thus lowering the probability of detection. If the clutter level is unknown, then we need to take measurements of the clutter and use it to adjust the threshold. The more clutter samples we take, the better the estimate of the clutter level and the less is the resulting detection loss. Using the expressions for the probability of detection in clutter, we can quantify the detection loss for a pair of commonly used constant false-alarm rate (CFAR) techniques and investigate how the loss varies with different parameter values, especially with regard to the number of clutter samples taken to estimate the clutter level.     

Passive ranging of a low observable ballistic missile in agravitational field

In this paper we present an estimation algorithm for tracking the motion of a low-observable target in a gravitational field, for example, an incoming ballistic missile (BM), using angle-only measurements. The measurements, which are obtained from a single stationary sensor, are available only for a short time. Also, the low target detection probability and high false alarm density present a difficult low-observable environment. The algorithm uses the probabilistic data association (PDA) algorithm in conjunction with maximum likelihood (ML) estimation to handle the false alarms and the less-than-unity target detection probability. The Cramer-Rao lower bound (CRLB) in clutter, which quantifies the best achievable estimator accuracy for this problem in the presence of false alarms and nonunity detection probability, is also presented. The proposed estimator is shown to be efficient, that is, it meets the CRLB, even for low-observable fluctuating targets with 6 dB average signal-to-noise ratio (SNR). For a BM in free flight with 0.6 single-scan detection probability, one can achieve a track detection probability of 0.99 with a negligible probability of false track acceptance     

Threshold Control for Automatic Detection in Radar Systems

In automatic detection in radar systems an estimate of background clutter power is used to set the detection threshold. Usually detection cells surrounding the cell under test for the presence of a target are used to estimate the clutter power. In the research reported herein, the target location is taken to be uncertain and thus returns from a target could corrupt this clutter power estimate. It is shown how the threshold should be varied to compensate for the resulting degradation in detection performance. The threshold control procedure is based on a priori information about target location that could be supplied by the radar's tracking system. In addition, a simple procedure for calculating detection and false alarm probabilities for Swerling II target models is presented.     

CFAR integration processors in randomly arriving impulseinterference

Time diversity transmission is often used to circumvent the high probability of a deep fade on a single transmission which may result in loss of the signal. One way to combat deep fades is to postdetection integrate the received observations from each range resolution cell. The false alarm rate of the postdetection integrator (PI) is extremely sensitive to randomly arriving impulse interference. Such interfering pulses may be unintentionally generated by nearby radars or intentionally generated by pulse jammers seeking to destroy the visibility of the radar. The binary integrator (PI) which uses an M-out-of-L decision rule is insensitive to at most M-1 interfering pulses. We consider the adaptive implementation of the PI and BI detectors for constant false alarm rate (CFAR) operation. We show that the CFAR BI detector when the “AND” (L-out-of-L) decision rule is used exhibits more robust false alarm control properties in the presence of impulse interference at the expense of severe detection loss when no interference is present. The CFAR adaptive PI (API) detector is proposed to alleviate this problem. The CFAR API detector implements an adaptive censoring algorithm which determines and censors with high probability the interference samples thereby achieving robust false alarm control in the presence of interference and optimum detection performance in the absence of interference     

Probability of Detecting a Swerling I Targetet on Two Correlated Observations

Modern radars characterized by electronically steered beams, frequency agility, and range-ambiguous waveforms can use a processing technique whereby each new detection is followed by a second dwell to verify the initial detection. The second dwell is used to minimize false alarms and to resolve range and/or Doppler ambiguities. Under the assumption of a Swerling I target model, the target cross section remains constant when both dwells occur on the same scan and the same transmission frequency is used. Analytic expressions have been developed for the probability of detecting a Swerling I target on both of the correlated dwells (same target cross section). These expressions are used to calculate the probability of a second dwell detection given a first dwell detection and the probability of at least one detection on two dwells. These probabilities are compared with those of independent dwells (independent target cross sections) which result when two transmission frequencies of sufficient separation are utilized.     

Optimal polarimetric detection of radar target in a slowlyfluctuating environment of clutter

It is shown that in a situation where a radar target is distant enough from the radar and is included in a natural or artificial clutter environment in such a manner that the conventional detection methods fail, it is possible to improve the radar detection performance by using appropriate signal processing on two orthogonal polarization states. A CFAR (constant false alarm rate) polarimetric detection system based on the study of the polarization difference between clutter and target is proposed. Since the polarization state of the clutter echoes fluctuates slowly from cell to cell, an autoregressive model can be applied to the components of the polarization vector to predict the detection thresholds needed to follow the polarization state variation. The detection thresholds are determined to maintain a false alarm probability equal to 10^-6. The presence of a target registers as a significant variation of the estimation error of the polarization vector. Results obtained from measurements of simple and canonical targets with artificial clutter are presented, and these results validate the principle of polarimetric detection