The Shape of Doppler Spectra from Precipitation

From October 1982 through May 1983 an extensive weather clutter registration program was executed near the Dutch coast. Coherent echo series of 2 s were obtained from a cluster of adjacent antenna pencil beams every 10 or 15 min., mainly between 16:00 and 08:30 h and on the weekends. The beam cluster was pointed toward the intensity maximum of the clutter volume. The radar operated at 5650 MHz. Spectra with 10 Hz Doppler resolution have been computed by averaging over 19 discrete Fourier transforms of overlapping and tapered subseries of 200 echo vectors. To quantify the deviation from a Gaussian shape a spectral variability is defined which is computed for every estimated spectrum. It is found that the deviation from Gaussian is considerable in about one-fourth of the spectra. A selection of "typical worst case" spectra is presented.     

A Comparison of Noncoherent and Coherent MTI Improvement Factors

An analysis based on statistical considerations and Monte Carlo simulations indicates that a noncoherent moving target indicator (MTI) using a linear envelope detector differs from one using a square law envelope detector. The square law envelope detector is usually described in the literature because of ease of analysis, and it is commonly stated or implied that the results are the same for the two cases because of the similar spectral characteristics of the detectors. A comparison is made between the two noncoherent MTIs and the coherent MTI in terms of clutter attenuation and MTI improvement factors.     

Detection Performance in Clutter with Variable Resolution

Experiments were conducted to determine the influence of background clutter on target detection criteria. The experiment consisted of placing observers in front of displayed images on a TV monitor. Observer ability to detect military targets embedded in simulated natural and manmade background clutter was measured when there was unlimited viewing time. Results were described in terms of detection probability versus target resolution for various signal to clutter ratios (SCR). The experiments were preceded by a search for a meaningful clutter definition. The selected definition was a statistical measure computed by averaging the standard deviation of contiguous scene cells over the whole scene. The cell size was comparable to the target size. Observer test results confirmed the expectation that the resolution required for a given detection probability was a continuum function of the clutter level. At the lower SCRs the resolution required for a high probability of detection was near 6 line pairs per target (LP/TGT), while at the higher SCRs it was found that a resolution of less than 0.25 LP/TGT would yield a high probability of detection. These results are expected to aid in target acquisition performance modeling and to lead to improved specifications for imaging automatic target screeners.     

Validation of windblown radar ground clutter spectral shape

We investigate the robustness of the linear matched filter (MF) operating in a Gaussian environment in the presence of a mismatch between the design clutter-power spectral density (PSD) shape and the actual one. The Gaussian, the power-law (PL), and the double-exponential spectral models have been considered with the goal of investigating which one fits best for windblown foliage. We analyze the MF performance in terms of improvement factor, probability of false alarm, and probability of detection by making use of the theoretical models and measured X-band ground clutter data. The numerical results validate the double-exponential spectral model for windblown foliage by showing that the differences in performance prediction between using measured clutter data and modeled clutter data of various spectral shapes (viz., Gaussian, FL, and double-exponential) are minimized when the spectral model employed is of double-exponential shape     

Detection performance in K-distributed and correlatedRayleigh clutters

Performance prediction for a detection system employing noncoherent integration is carried out for a chi-square family of fluctuating targets in K-distributed clutter plus noise. The detection performance for Swerling 11 targets in the K-distributed clutter plus noise is compared with that in exponentially correlated Rayleigh clutter. The results show that the performance prediction based on N pulses integrated in clutter plus noise using the K-distributed clutter model may be approximately equivalent to that using the exponentially correlated Rayleigh-distributed clutter model     

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.     

Spiky sea clutter at high range resolutions and very low grazingangles

X-band (9.5-10.0 GHz) backscatter at near grazing incidence (0.2 deg) from the sea off the coast of Kauai, Hawaii, was measured with a radar characterized by a high spatial resolution in range (0.3 m) and a high temporal resolution (2000 Hz pulse repetition frequency (PRF)). Extensive amounts (over 20 min per measurement) of vertically and horizontally polarized sea clutter data were taken with upwind (UP) and crosswind (CR) transmit geometries during the collection campaign. Specific but representative examples of the clutter were statistically and phenomenologically analyzed over time scales varying from long (200 s), to intermediate (5 s), to short (50 ms), and over range swaths varying from full (160 m), to partial (30 m), to a single range cell (0.3 m). All analyses and results presented here are noncoherent, involving only the clutter amplitudes. Each type of clutter exhibited the characteristic spiky behavior which has come to be expected from microwave sea backscatter observed at low grazing angles and high range resolutions, while showing, between themselves, marked transmit geometry and polarization dependent contrasts, with the horizontally polarized clutter, measured with an UP transmit geometry, being especially notable for its frequently occurring, significant high frequency spectral content. Within the same clutter type, differences were observed in the probability distributions of radar cross sections (RCS) of spatially and temporally extended spiking events     

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     

Improvement Factor of the Phase-Sensitive Noncoherent MTI

The phase-sensitive noncoherent MTI detects targets by relative motion between the target and an extended clutter background. In this type of MTI, the phase of the target is compared with the phase of the clutter in an adjacent range bin. Theoretical analysis of the system's performance is presented. The improvement factors for single- and double-delay periodic filters are derived and computational results are included.     

Pade approximations for detectability in K-clutter and noise

The Pade approximation (PA) method is used to analyze the detection performance of single and multiple pulse radar systems operating in K-distributed clutter and thermal noise. Simple approximations for false-alarm and detection probabilities are obtained, using lower order moments for the detection decision statistic. Both envelope and squaring detector laws are considered, with noncoherent integration, for independent and correlated K clutter. The target is assumed to be pulse-to-pulse Rayleigh fading. The methods are a substantial application of the PA methods we have previously published     

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.     

The Effect of MTI Filter and Number of Unique Staggers on First-Null Depth and Clutter Attenuation

A recent series of papers have provided a model for a staggered-PRF radar which can be used to estimate both the depth of the first null (which is dependent upon the ratio of some function fM(?) of the set of M sampling deviations {?m} to the average sampling interval) and the clutter attenuation (as a function of the product of fM(?) and clutter standard deviation ?c). Some inconsistencies in the aforementioned papers are discussed and it is shown that realistic filters and typical stagger-ratio sets produce results which differ significantly from the idealized-filter predictions. Furthermore, even after filtering the residual clutter power at dc is shown to be more significant than the power in all the displaced clutter spectra postulated by the aforementioned model.     

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.     

基于常规多普勒滤波器组结构的合成宽带距离像性能分析

为了消除散布效应对宽带信号的不利影响,可以利用多个窄带信号合成宽带信号;同时,通过在子带内处理相干脉冲串,可进行杂波抑制、目标速度估计和区分不同速度的目标。然而,在子带内分别使用常规多普勒滤波器组,会引进多普勒散布效应所造成的输出失配误差,从而造成合成距离像的失真。分析了多普勒散布效应与子带常规多普勒滤波器组输出失配之间的关系,推导了运动目标通过滤波器组后所成高分辨距离像的距离走动公式,给出了适合子带常规多普勒滤波器组的目标速度临界值。仿真实验验证了以上结论。     

Ionospheric scintillation-induced integration losses forspace-based radar

An estimate of the impact of very severe ionospheric conditions on the coherent and noncoherent integration process from a two-way, transionospheric, propagation path is obtained for a specific type of frequency-diverse waveform. A bound on the total integration loss that would result from using this waveform during such ionospheric conditions is obtained through the analysis of data from the wideband satellite experiment     

Clutter Spectra of Low PRF AMTI Pulse-Doppler Radar

Approximate expressions are derived for the video clutter spectra in the receiver of a low pulse repetition frequency (PRF), airborne moving target indicator (AMTI), pulse-Doppler radar for both step-scanning and continuous-scanning antennas. The receiver is assumed to process the received waveform with a clutter-tracking oscillator and a window function is employed to obtain short-term spectra. Except for the broadening effects of the window function, it is shown that the clutter spectrum can be simply related to the antenna voltage-gain pattern. It is further shown, in the scanning antenna case, that the combined spectral broadening due to platform motion and antenna scanning cannot be assumed to be the result of the convolution of the separate effects unless the antenna gain pattern has a Gaussian shape. The approximate clutter expressions are illustrated by examples and are shown to agree well with the results of computer calculations.     

On Clutter Modeling and the Spectra of Two-Dimensional Gauss-Markov Random Signals

The spectral properties of two-dimensional isotropic clutter signals are examined for the cases in which 1) the clutter has an exponential spatial autocorrelation function, and 2) the clutter is a two-dimensional Gauss-Markov random signal. The one- and twodimensional power spectral densities before and after antenna filtering are obtained, and some of the differences and similarities between these two models are discussed in the context of spectral analysis.     

On Increasing Usable MTI Filter Bandwidth by Removing Linear-Phase Constraint

It has been shown in the literature that the linear-phase constraint of finite-duration impulse-response (FIR) digital filters can, under certain circumstances, be effectively traded either for a better filter amplitude response or a reduction in the number of filter coeficients. It is shown that such a tradeoff can be exploited for moving target indicator (MTI) radar signal processors to increase the usable bandwidth for target detection. Although it is demonstrated that the increase is significant for narrowband (ground) clutter, it is negligible for wideband (weather) clutter.     

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