New clutter suppression approach for multifunction radar-radarresource management for the clutter suppression

The use of constant-false-alarm-rate (CFAR) techniques to keep false alarm rates at a suitable low level is reviewed. Radar resource management for clutter suppression, a novel approach for multifunction phased-array radar that can more effectively suppress clutter, is proposed. The results of a simulation study, which indicate the maximum permissible P_fa and the improvement of detection performance, demonstrate the effectiveness of resource management, especially when an all-neighbor filter is used     

Nonparametric rank detectors on quantized radar video signals

Uniform randomization of ties is required for defining distribution-free ranks of independent and identically distributed quantized samples. Formulas of rank probabilities are given and applied to radar detection under quantized video samples. For some detectors, and assuming Gaussian noise, the asymptotic loss L_∞(q) is calculated versus the normalized quantization step q, and the loss L(q) is estimated by Monte Carlo simulations. Both of these resulted in monotonic functions of q (0<q<1.1) that are independent of the other parameters. Furthermore, L(q)≈L_∞(q )⩽0.45 dB, as q<0.8. The quantization step q is normalized with respect to the noise standard deviation     

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     

Distribution of general noncentral positive definite quadratic formin K-dimensions

The authors present a series solution using Hermite polynomials to the long-standing problem of computing the probability P that positive definite noncentral quadratic form d(x) of a Gaussian random vector x∈R satisfies d( x)⩽r² for any given r∈R. This problem has wide applications in radar, tracking, air traffic control, etc. The fast-converging series solution presented is very accurate and can be performed rapidly using the recursion relations for Hermite polynomials     

Detectability of signals in Laplace noise

Closed-form expressions for the false-alarm and detection probabilities attained by the optimum and the linear detectors of a positive signal in n independent samples of noise having a bilateral exponential or Laplace distribution require lengthy computation when n is large, and those for the optimum detector suffer from round-off error because their terms alternate in sign. It is shown how the method of saddlepoint integration can be conveniently applied to compute these probabilities, and numerical comparisons of the accuracies of the methods are presented. The relative efficiency of the two detectors is calculated as a function of n and found to approach the asymptotic value of 2 very slowly     

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     

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     

Optimal speckle reduction in polarimetric SAR imagery

Speckle is a major cause of degradation in synthetic aperture radar (SAR) imagery. With the availability of fully polarimetric SAR data, it is possible to use the three complex elements (HH, HV, VV) of the polarimetric scattering matrix to reduce speckle. The optimal method for combining the elements of the scattering matrix to minimize image speckle is derived, and the solution is shown to be a polarimetric whitening filter (PWF). A simulation of spatially correlated, K-distributed, fully polarimetric clutter is then used to compare the PWF with other, suboptimal speckle-reduction methods. Target detection performance of the PWF, span, and single-channel |HH|² detectors is compared with that of the optimal polarimetric detector (OPD). A novel, constant-false-alarm-rate (CFAR) detector (the adaptive PWF) is as a simple alternative to the OPD for detecting targets in clutter. This algorithm estimates the polarization covariance of the clutter, uses the covariance to construct the minimum-speckle image, and then tests for the presence of a target. An exact theoretical analysis of the adaptive PWF is presented; the algorithm is shown to have detection performance comparable with that of the OPD     

Finding the best set of K paths through a trellis withapplication to multitarget tracking

A solution is presented to the problem of finding the best set of K completely unmerged paths through a trellis with M _i⩾K states at depth i in the trellis, i=0, 1, 2, . . ., N. Here, `best set' means that the sum of the metrics of all K paths in the set is minimized, and `completely unmerged' means that no two paths pass through a common state. The solution involves using the Viterbi algorithm on an expanded trellis. This result is then used to separate the tracks of K targets optimally in a simplified model of a multitarget radar system. The model includes measurement errors and false alarms, but it does not include the effects of missing detections or merged measurements     

CFAR data fusion center with inhomogeneous receivers

Detection systems with distributed sensors and data fusion are increasingly used by surveillance systems. A system formed by N inhomogeneous constant false alarm rate (CFAR) detectors (cell-averaging (CA) and ordered statistic (OS) CFAR detectors) is studied. A recursive formulation of an algorithm that permits a fixed level of false alarms in the data fusion center is presented, to set the optimum individual threshold levels in the CFAR receivers and the optimum `K out of N' decision rule in order to maximize the total probability of detection. The algorithm also considers receivers of different quality or with different communication channel qualities connecting them with the fusion center. This procedure has been applied to several hypothetical networks with distributed CA-CFAR and OS-CFAR receivers and for Rayleigh targets and interference, and it was seen that in general the fusion decision OR rule is not always the best     

Optimal serial distributed decision fusion

The problem of distributed detection involving N sensors is considered. The configuration of sensors is serial in the sense that the Jth sensor decides using the decision it receives along with its own observation. When each sensor uses the Neyman-Pearson test, the probability of detection is maximized for a given probability of false alarm, at the Nth stage. With two sensors, the serial scheme has a performance better than or equal to the parallel fusion scheme analyzed in the literature. Numerical examples illustrate the global optimization by the selection of operating thresholds at the sensors     

Improved multilevel quantization for detection of narrowbandsignals

Nearly optimum quantization levels for multileveled quantizers in radar receivers and distributed-detection are calculated for preassigned false-alarm probability Q₀ by maximizing the detection probability Q_d after replacing both Q ₀ and (1-Q_d) by the saddlepoint approximations. Narrowband signals of random phase and with both fixed and Rayleigh-fading amplitudes in Gaussian noise are treated, and the loss in signal detectability incurred by quantization is estimated     

Performance of receivers with linear detectors

The false-alarm and detection probabilities of a receiver summing M independent outputs of a linear detector are calculated by numerical saddlepoint integration. The saddlepoint approximation is also considered. Both constant-amplitude and Rayleigh-fading signals are treated, and the relative efficiency of the quadratic and the linear detectors for these is calculated for a broad range of values of M . The numerical integration method is the more efficient, the smaller the false-alarm probability or the false-dismissal probability, that is, under just those conditions for which the terms in the Gram-Charlier series oscillate most violently and the series becomes least reliable. The simpler saddlepoint approximation yields values that in those same regions have been found close enough to the exact probabilities to be adequate for most engineering purposes. The larger the number M of samples, the more efficient methods are     

False alarm control using Doppler estimation

A technique which uses maximum-likelihood estimates (MLEs) of target Doppler and target amplitude is developed for rejecting clutter residues. Multiple estimates are made and consistency checks are applied to the estimates. Simulation results indicate that for large clutter-to-noise ratios (C/N⩾55 dB) the probability of false alarm from clutter residues is reduced from 1.0 to below 0.01     

CCRS C/X-airborne synthetic aperture radar: An Rand D tool for the ERS-1 time frame

The airborne synthetic-aperture radar (SAR) system developed for the Canada Centre for Remote Sensing (CCRS) is described. It consists of two radars, at C-band and X-band. Each radar incorporates the following features: dual-channel receivers and dual-polarized antennas; a high quality, 7-look, real-time processor; a sensitivity time control for range-dependent gain control; a motion-compensation system for antenna steering in azimuth and elevation; and baseband I and Q signal phase rotation. The system also uses a high-power transmitter with a low-power back-up. The SAR maps to either side of the aircraft, at high or low resolution, at incidence angles which in high resolution span 0° to 80°. Radar operating parameters, data products, key specifications and the motion compensation scheme used are presented. Properties of the real-time imagery are discussed and examples of C-band SAR data in the three operating modes 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     

Fractal interpolation of radar signatures for detecting stationarytargets in ground clutter

The fundamentals of fractal geometry are reviewed, and its application to the millimeter-wave radar detection of stationary targets in a clutter background is described. First, high-range-resolution (HRR) profiles are used to determine the fractal interpolation functions needed to create fractal signatures. The fractal dimension is then determined for these signatures. On the basis of the value of the fractal dimension, the signature is declared to represent either a target of interest or clutter. The results of a CFAR (constant false alarm rate) simulation are presented to illustrate the performance of the method. They indicate that the fractal dimension feature used seems to be independent of amplitude. Thus, the fractal dimension information combined with traditional amplitude processing techniques will improve probabilities of detection     

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.     

Identification of rational transfer function from frequencyresponse sample

A method for identifying a transfer function, H(z)=A(z)/B(z), from its frequency response values is presented. Identifying the transfer function involves determining the unknown degrees and coefficients of the polynomials A(z) and B( z), given the frequency response samples. The method for finding the parameters of the transfer function involves solving linear simultaneous equations only. An important aspect of the method is the decoupled manner in which the polynomials A(z) and B(z) are determined. The author presents two slightly different derivations of the linear equations involved, one based on the properties of divided differences and the other using Vandermonde matrices or, equivalently, Lagrange interpolation. A matrix synthesized from the given frequency response samples is shown to have a rank equal to the number of poles in the system