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     

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.     

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     

Improved algorithm for estimating pulse repetition intervals

This paper presents an improved algorithm for estimating pulse repetition intervals (PRIs) of an interleaved pulse train which consists of several independent radar signals with different PRIs. The original version of this algorithm is a complex-valued autocorrelation-like integral, which leads to a kind of PRI spectrum wherein the locations of the spectral peaks indicate the PRI values. The original algorithm, however, has a serious drawback in that it is vulnerable to timing jitter (PRI jitter). We analyze the cause of this vulnerability and propose an improved algorithm using overlapped PRI bins which have shifting time origins. The improved algorithm has proven to be quite effective in obtaining the PRI spectrum for jittered pulse trains, which enables detection of mean PRIs by thresholding     

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.     

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     

Hansen's Method Applied to the Inversion of the Incomplete Gamma Function, with Applications

Hansen's method for obtaining the threshold for a speciried false alarm probability following noncoherent integration after square law detection is applied to finding the inverse of the incomplete gamma function. The method is algebraic and direct, circumventing the necessity for repeated evaluation of an integral or of a finite series. The method is applied to finding any specified percentile of the chi-square distribution and to finding the required signal-to-noise ratio for a specified detection probability of a Swerling II target.     

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.     

The Detection Performance of the Siebert and Dicke-Fix CFAR Radar Detectors

The Siebert and the Dicke-fix CFAR radar detectors, used to maintain a constant false alarm rate (CFAR) in radar receivers under very similar circumstances, are considered. The Siebert detector represents the maximum-likelihood detection procedure for a signal in Gaussian noise of unknown power level, whereas the Dicke-fix makes use of a bandpass limiter to normalize the input and thus ensure a constant false alarm rate. The detection performance of the two detectors is determined and a comparison shows that over a wide range of parameters, the Dicke-fix introduces a loss which is approximately 1 B larger than for the Siebert detector.     

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     

CFAR detection of distributed targets in non-Gaussian disturbance

The subject of detection of spatially distributed targets in non-Gaussian noise with unknown statistics is addressed. At the design stage, in order to cope with the a priori uncertainty, we model noise returns as Gaussian vectors with the same structure of the covariance matrix, but possibly different power levels (heterogeneous environment). We also assume that a set of secondary data, free of signal components, is available to estimate the correlation properties of the disturbance The proposed detector assumes no a priori knowledge about the spatial distribution of the target scatterers and ensures the constant false alarm rate (CFAR) property with respect to both the structure of the covariance matrix and the power levels. Finally, the performance assessment, conducted modeling the disturbance as a spherically invariant random process (SIRP), confirms its validity to operate in real radar scenarios     

Distributed target detection in compound-Gaussian noise with Rao and Wald tests

The problem of detecting distributed targets in compound-Gaussian noise with unknown statistics is considered. At the design stage, in order to cope with the a priori uncertainty, we model noise returns as Gaussian vectors with the same structure of the covariance matrix, but possibly different power levels. We also assume that a set of secondary data, free of signal components, is available to estimate the covariance matrix of the disturbance. Since no uniformly most powerful test exists for the problem at hand we devise and assess two detection strategies based on the Rao test, and the Wald test respectively. Remarkably these detectors ensure the constant false alarm rate property with respect to both the structure of the covariance matrix as well as the power levels. Moreover, the performance assessment, conducted also in comparison with the generalized likelihood ratio test based receiver, shows that the Wald test outperforms the others and is very effective in scenarios of practical interest for radar systems.     

Signal-to-Noise Ratio Calculations in Pulse and Pulse Doppler Radars

In low pulse-repetition frequency (PRF) pulse radars, signal-to-noise ratio (SNR) is usually calculated on a per pulse basis and this value is then multiplied by the number of pulses integrated to obtain the SNR for a given duration of target illumination. In high PRF pulse Doppler radars, SNR is usually calculated by using the centerline power of the transmitted signal spectrum as the target return power because the centerline is kept in the receiver and returns of the PRF lines are notched out [1]. We show here that both methods of SNR calculations are entirely equivalent for matched transmit-receive radar systems.     

Maximizing the Usable Bandwidth of MTI Signal Processors

A technique is presented for maximizing the percentage of usable Doppler bandwidth throughout which a radar return can be detected while maintaining an acceptable clutter suppression. The technique employs the weighted Chebyshev approximation to the design of a transversal high-pass digital filter which has an optimal passband ripple for a given number of filter weights and associated integration gain consistent with the required increase in signal-to-noise ratio needed for acceptable probabilities of detection and false alarm. Conventional approaches to the design of a movingtarget arget indictor (MTI) filter which maximizes the improvement factor by clutter suppression typically improve the signal-to-background noise ratio over less than 50 percent of the range between dc and the pulse-repetition frequency fT. This technique can increase the usable bandwidth to 80 percent or more of fT. Two examples are included which utilize parameter values from the Army Missile Command's experimental radar and demonstrate the interactive influence of such filter parameters as the number of weights, passband ripple and bandedge, and stopband attenuation and cutoff.     

Detection of Slow Fluctuating Targets with Frequency Diversity Channels

In this paper an exact closed-form expression for the radar detection probability is derived and results are plotted for a frequency diversity radar receiver. The receiver model performs post-detection integration on all received pulses in all diversity channels. The target model assumed is the slow fluctuating Rayleigh-distributed (Swerling case I target) scatterer. Each of the M frequency diverse channels receives N amplitude-correlated returns to give a total of NM post square-law detection integrations. The tabulated data falls between the two extreme cases, that for which all the returns are amplitude-correlated and that for which each return is independent. The plotted results fall close to the figures obtained through simple empirical relationships.     

Decentralized CFAR signal detection

The authors develop the theory of CA-CFAR (cell-averaging constant false-alarm rate) detection using multiple sensors and data fusion, where detection decisions are transmitted from each CA-CFAR detector to the data fusion center. The overall decision is obtained at the data fusion center based on some k out of n fusion rule. For a Swerling target model I embedded in white Gaussian noise of unknown level, the authors obtain the optimum threshold multipliers of the individual detectors. At the data fusion center, they derive an expression for the overall probability of detection while the overall probability of false alarm is maintained at the desired value for the given fusion rules. An example is presented showing numerical results     

Low-altitude target detection by coastline operated marine radar

Relevant to a Richian family of fluctuating targets with a composite background of sea-plus-land clutter, the performance prediction of a radar operating in near-coastal regions is elucidated by assuming noncoherent integration of the pulses. Considering the dominance of land clutter, a modified K-distributed statistic is indicated for the overall clutter envelope; and the corresponding probability of false alarm and probability of detection are deduced for fixed threshold detection (s) based on N pulses integrated in the presence of the sea-plus-land clutter and the noise. Even when the target offers a dominant scattered echo, the worst situations of the land clutter affecting the detection performance are indicated     

Distributed binary integration

A distributed radar detection system that employs binary integration at each local detector is studied. Local decisions are transmitted to the fusion center where they are combined to yield a global decision. The optimum values of the two thresholds at each local processor are determined so as to maximize the detection probability under a given probability of false alarm constraint. Using an important channel model, performance comparisons are made to determine the integration loss     

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.