Optimum Processing of Unequally Spaced Radar Pulse Trains for Clutter Rejection

A train of radar pulses from one resolution cell can be processed coherently to reject echoes from external clutter and detect targets moving radially with respect to the clutter. Optimum methods of signal processing are defined for systems in which the interpulse spacings are multiply staggered to avoid target blind speeds. Likelihood ratio tests are developed for systems in which the target Doppler frequency is known a priori and for systems employing a bank of filters to cover the target Doppler band. To implement such tests, the N pulses in the train are added with complex weights and the amplitude of the sum compared with a detection threshold. The set of weights which maximizes the average signal-to-clutter ratio is also computed for a single-filter system with unknown target Doppler frequency. When the clutter autocorrelation function is exponential, the clutter covariance matrix can be inverted analytically. This latter result is useful for comparing different interpulse-spacing codes for a particular system application.     

Doppler Processor Rejection of Range Ambiguous Clutter

Doppler processors are used in radar to separate target returns from clutter. When the clutter is at a range farther than the unambiguous range of the radar, the ability to reject the clutter is degraded. In this article the degradation is analyzed for an N-pulse batch processor with Dolph weighting, and the results show how degradation varies with design sidelobe level.     

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.     

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.     

Moving target detection via airborne HRR phased array radar

We study moving target detection in the presence of temporally and spatially correlated ground clutter for airborne high range resolution (HRR) phased array radar. We divide the HRR range profiles into large range segments to avoid the range migration problems that occur in the HRR radar data. Since each range segment contains a sequence of HRR range bins, no information is lost due to the division and hence no loss of resolution occurs. We show how to use a vector autoregressive (VAR) filtering technique to suppress the ground clutter. Then a moving target detector based on a generalized likelihood ratio test (GLRT) detection strategy is derived. The detection threshold is determined according to the desired false alarm rate, which is made possible via an asymptotic statistical analysis. After the target Doppler frequency and spatial signature vectors are estimated from the VAR-filtered data as if a target were present, a simple detection variable is computed and compared with the detection threshold to render a decision on the presence of a target. Numerical results are provided to demonstrate the performance of the proposed moving target detection algorithm     

Adaptive Radar Detection in Doubly Nonstationary Autoregressive Doppler Spread Clutter

The problem of adaptive radar detection in clutter which is nonstationary both in slow and fast time is addressed. Nonstationarity within a coherent processing interval (CPI) often precludes target detection because of the masking induced by Doppler spreading of the clutter. Across range bins (i.e., fast time), nonstationarity severely limits the amount of training data available to estimate the noise covariance matrix required for adaptive detection. Such difficult clutter conditions are not uncommon in complex multipath propagation conditions where path lengths can change abruptly in dynamic scenarios. To mitigate nonstationary Doppler spread clutter, an approximation to the generalized likelihood ratio test (GLRT) detector is presented wherein the CPI from the hypothesized target range is used for both clutter estimation and target detection. To overcome the lack of training data, a modified time-varying autoregressive (TVAR) model is assumed for the clutter return. In particular, maximum likelihood (ML) estimates of the TVAR parameters, computed from a single snapshot of data, are used in a GLRT for detecting stationary targets in possibly abruptly nonstationary clutter. The GLRT is compared with three alternative methods including a conceptually simpler ad hoc approach based on extrapolation of quasi-stationary data segments. Detection performance is assessed using simulated targets in both synthetically-generated and real radar clutter. Results suggest the proposed GLRT with TVAR clutter modeling can provide between 5–8 dB improvement in signal-to-clutter plus noise ratio (SCNR) when compared with the conventional methods.     

Spatially distributed target detection in non-Gaussian clutter

Two detection schemes for the detection of a spatially distributed, Doppler-shifted target in non-Gaussian clutter are developed. The non-Gaussian clutter is modeled as a spherically invariant random vector (SIRV) distribution. For the first detector, called the non-scatterer density dependent generalized likelihood ratio test (NSDD-GLRT), the detector takes the form of a sum of logarithms of identical functions of data from each individual range cell. It is shown under the clutter only hypothesis, that the detection statistic has the chi-square distribution so that the detector threshold is easily calculated for a given probability of false alarm P_F. The detection probability P_D is shown to be only a function of the signal-to-clutter power ratio (S/C)_opt of the matched filter, the number of pulses N, the number of target range resolution cells J, the spikiness of the clutter determined by a parameter of an assumed underlying mixing distribution, and P_F. For representative examples, it is shown that as N, J, or the clutter spikiness increases, detection performance improves. A second detector is developed which incorporates a priori knowledge of the spatial scatterer density. This detector is called the scatterer density dependent GLRT (SDD-GLRT) and is shown for a representative case to improve significantly the detection performance of a sparsely distributed target relative to the performance of the NSDD-GLRT and to be robust for a moderate mismatch of the expected number of scatterers. For both the NSDD-GLRT and SDD-GLRT, the detectors have the constant false-alarm rate (CFAR) property that P_F is independent of the underlying mixing distribution of the clutter, the clutter covariance matrix, and the steering vector of the desired signal     

A localized adaptive MTD processor

The problem of achieving the optimum moving target indicator (MTI) detection performance in strong clutter of unknown spectrum when the set of data available to the estimation of clutter statistics is small due to a severely nonhomogeneous environment is studied. A new adaptive implementation, called the Doppler domain localized generalized likelihood ratio processor (DDL-GLR), is proposed, and its detection performance is studied in detail. It is shown that the DDL-GLR is a data-efficient implementation of the high-order optimum detector and has several advantages of practical importance over the adaptive processors     

Clutter Performance of Coherent Pulse Trains for Targets with Range Acceleration

The clutter performance of coherent pulse trains is examined when the duration of the pulse train is increased to values for which range acceleration effects must be taken into account. The problem of target detection against a clutter background with differential Doppler is studied in terms of the range acceleration effects on the conventional Doppler response. Specifically considered are the consequences on the sidelobe level and width of the main Doppler lobe. The analysis shows that the sidelobe level remains essentially unchanged when the range acceleration mismatch becomes significant. However, the main Doppler response broadens in proportion to the magnitude of the acceleration mismatch. Thus, an increase of the signal duration for better Doppler resolution is useful only until acceleration effects spread the Doppler spectrum of the clutter and eliminate the differential Doppler between targets and clutter.     

Further results on adaptive filtering with embedded CFAR

Among the few known adaptive filtering algorithms which have an embedded (integrated) constant false alarm rate (CFAR) performance feature, the generalized likelihood ratio (GLR) test algorithm has been found to be robust in non-Gaussian clutter. This paper examines the detection performance of the GLR algorithm in nonhomogeneous/nonstationary clutter environments which lead to nonidentical distribution of secondary (training) data. For two common types of nonhomogeneity, i.e., the so-called “signal contamination” and “clutter edge”, the asymptotic detection performance is derived and compared with simulations. These asymptotic results are relatively simple to use and they predict the GLR performance in nonhomogeneous environments quite well. The GLR performance loss due to the nonhomogeneity is also evaluated. It is found that the “generalized angle” between the desired and contaminating signal plays an important role in the study of the effects of signal contamination. It is also found that the performance degradation due to the clutter edge depends largely on the width of the clutter spectrum and target-clutter Doppler separation     

海杂波谱的机理及时变特性分析

针对海杂波背景下目标检测问题的实际需求,在机理分析的基础上,利用实测数据对海杂波谱的时变特性进行了分析。首先,分析了波束照射区域内由海表面波浪运动引起的多普勒频移和展宽现象,以及随雷达工作参数之间的依赖关系;然后,对已有海杂波谱机理研究结果进行了分析和总结。在此基础上,利用加窗的周期图法估计得到海杂波的时间-多普勒谱,进而从相关时间的统计特性、谱宽与时域海杂波拖尾程度的依赖关系两个层面对海杂波谱的时变特性进行了分析。分析结果可为海杂波谱建模、海杂波抑制及目标检测方法设计提供理论指导。     

Radar Target Detection and Map-Matching Algorithm Studies

Results of a study of adaptive threshold target detection and map-matching algorithms are presented. Log threshold processing is shown to be preferred over linear threshold processing when the clutter data surrounding the target cell is contaminated by other targets, decoy corner reflectors, or bright clutter cells. Whereas previous studies have resorted to extensive Monte-Carlo simulations of log threshold algorithms, the results were obtained using a novel analytical approach based upon Parseval's theorem.     

Structures for radar detection in compound Gaussian clutter

The problem of coherent radar target detection in a background of non-Gaussian clutter modeled by a compound Gaussian distribution is studied here. We show how the likelihood ratio may be recast into an estimator-correlator form that shows that an essential feature of the optimal detector is to compute an optimum estimate of the reciprocal of the unknown random local power level. We then proceed to show that the optimal detector may be recast into yet another form, namely a matched filter compared with a data-dependent threshold. With these reformulations of the optimal detector, the problem of obtaining suboptimal detectors may be systematically studied by either approximating the likelihood ratio directly, utilizing a suboptimal estimate in the estimator-correlator structure or utilizing a suboptimal function to model the data-dependent threshold in the matched filter interpretation. Each of these approaches is studied to obtain suboptimal detectors. The results indicate that for processing small numbers of pulses, a suboptimal detector that utilizes information about the nature of the non-Gaussian clutter can be implemented to obtain quasi-optimal performance. As the number of pulses to be processed increases, a suboptimal detector that does not require information about the specific nature of the non-Gaussian clutter may be implemented to obtain quasi-optimal performance     

Measurements of L-band inland-water surface-clutter Doppler spectra

Although radar surface-clutter reflectivities from terrain are generally much greater than those from water, strong Bragg resonances at low but non-zero Doppler frequencies in backscatter from small inland bodies of water might potentially cause false alarms for moving target indicator (MTI) or other Doppler signal-processing techniques designed for target detection in ground clutter. To provide data for investigating this concern, measurements of L-band radar backscatter were recorded from the surface of a small inland freshwater reservoir in central Massachusetts. These measurements were of unusually high system stability and spectral purity so as to provide up to 80 dB of available spectral dynamic range. Strong Bragg spikes occurred in the clutter Doppler spectra from the reservoir at low (3 to 4 Hz) but non-zero Doppler frequencies. This strong Bragg resonance was persistent in time and space throughout the measurements. Spectral results are presented for all four combinations of linear polarization. Comparison with tree clutter spectral results indicates that, when an occasional water body comes under surveillance at vertical polarization in otherwise generally forested terrain, water clutter spectral density is expected to exceed surrounding-terrain tree clutter spectral densities in the Bragg-offset Doppler vicinity by large amounts     

Probability of Detecting a Fluctuating Target Immersed in Both Noise and Clutter

The probability of detecting either a Swerling 1 or Swerling 2 target immersed in both Rayleigh-distributed noise and log-normally distributed clutter is calculated. Results are presented which demonstrate the effect of noise-to-clutter ratio, signal-to-noise ratio, and number of pulses integrated on the detection statistics.     

Correspondence - Optimum Radar Signal for Detection in Clutter

It is shown that in order to maximize the detectability of a radar target in clutter whose Doppler is unknown and is uniformly distributed over the Doppler bandwidth a simple CW or narrowband signal is optimal. The optimality criterion is the average deflection coefficient, with the averaging being over target Doppler frequency. Most remarkably the result does not depend on the clutter spectrum but holds for any distribution of clutter energy with frequency.     

GLRT subspace detection for range and Doppler distributed targets

A generalized likelihood ratio test (GLRT) is derived for adaptive detection of range and Doppler-distributed targets. The clutter is modeled as a spherically invariant random process (SIRP) and its texture component is range dependent (heterogeneous clutter). We suppose here that the speckle component covariance matrix is known or estimated thanks to a secondary data set. Thus, unknown parameters to be estimated are local texture values, the complex amplitudes and Doppler frequencies of all scattering centers. To do so, we use superresolution methods. The proposed detector assumes a priori knowledge on the spatial distribution of the target and has the precious property of having a constant false alarm rate (CFAR) with the assumption of a known speckle covariance matrix or by the use of frequency agility.     

Radar CFAR Thresholding in Clutter and Multiple Target Situations

Radar detection procedures involve the comparison of the received signal amplitude to a threshold. In order to obtain a constant false-alarm rate (CFAR), an adaptive threshold must be applied reflecting the local clutter situation. The cell averaging approach, for example, is an adaptive procedure. A CFAR method is discussed using as the CFAR threshold one single value selected from the so-called ordered statistic (this method is fundamentally different from a rank statistic). This procedure has some advantages over cell averaging CFAR, especially in cases where more than one target is present within the reference window on which estimation of the local clutter situation is based, or where this reference window is crossing clutter edges.     

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     

Radar/Sonar Signal Design for Bounded Doppler Shifts

In many detection and estimation problems, Doppler frequency shifts are bounded. For clutter or multipath that is uniformly distributed in range and symmetrically distributed in Doppler shift relative to the signal, detectability of a point target or a communication signal is improved by minimizing the weighted volume of the magnitude-squared autoambiguity function. When clutter Doppler shifts are bounded, this volume is in a strip containing the range axis on the range-Doppler plane. For scattering function estimation, e.g., for weather radar, Doppler flow meters, and distributed target classifiers, it is again relevant to minimize ambiguity volume in a strip. Strip volume is minimized by using a pulse train, but such a signal has unacceptably large range sidelobes for most applications. Other waveforms that have relatively small sidelobe level within a strip on the range-Doppler plane, as well as small ambiguity volume in the strip, are obtained. The waveforms are composed of pulse pairs that are phase modulated with Golay complementary codes.