Measurement of Distributed Targets with the Random Signal Radar

A model of a distributed target as a collection of independent, Poisson distributed point scatterers or scattering centers in a range-velocity target space is introduced and is characterized by a deterministic function called the ?scatterer density function.? This function is the density of the point scatterers in the range-velocity space and can be estimated in a relatively straightforward manner by any radar having adequate resolution in both range and velocity and no ambiguities in the region occupied by the distributed target. The use of the random signal radar with a correlator receiver is considered here and the statistical properties of the correlator output, when the return signal is from a distributed target, are derived. It is shown that the spectral density is simply related to the scatterer density function. The technique is illustrated by an example in which the target is a tornado modeled as a cylinder with constant angular velocity. The example suggests that is a possible to remotely estimate the radar cross section per unit volume as a function of distance from the center of the tornado.     

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     

Harmonic Radar Systems for Near-Ground In-Foliage Nonlinear Scatterers

The radar transmission equation for a harmonic radar operating over a planar, finite dielectric Earth through foliage is derived for an interesting class of nonlinear scatterers. The received power can typically depend on range to the (-14) power for small objects near the ground. The maximum detection range of a ground-based system is related to all major system parameters: it is most sensitive to polarization, transmit antenna height, and transmit wavelength; moderately sensitive to transmit power and transmit antenna area; and least sensitive to receive antenna area, harmonic scattering cross section, and mode of data processing. For example, there is seen to be a best apportionment of total available aperture area into disjoint transmit and receive apertures which can be well approximated by the equal gain condition. Also, there is seen to be a critical path distance through foliage; at distances less than this, small wavelengths are desirable and, conversely, the upper transmit frequency limit may be set by nonlinear scatterer response. Airborne synthetic aperture radar systems are discussed and quantification of harmonic noise and effects of scatterer fluctuation are made. A useful phenomenological model of a nonlinear scatterer is given that is consistent with some observations and predicts a frequency dependence. Nonlinear scatterer effects on range resolution are discussed.     

An experiment with an S-band radar using pulse compression andrange sidelobe suppression for meteorological measurements

A major technology barrier to the application of pulse compression for the meteorological functions required by a next generation ATC radar is range/time sidelobes which mask and corrupt observations of weak phenomena occurring near areas of strong extended meteorological scatterers. Techniques for suppressing range sidelobes are well known but without prior knowledge of the scattering medium's velocity distribution their performance degrades rapidly in the presence of Doppler. Recent investigations have presented a “doppler tolerant” range sidelobe suppression technique. The thrust of the work described herein is the extension of previous simulations to actual transmitted dispersed/coded waveforms using the S-band surveillance radar located at Rome Laboratory Surveillance Facility. The objectives of the experiment are: 1) to extend the verification of the simulation of the Doppler tolerant technique; and 2) to demonstrate that the radar transmitter, waveform generator, and receiver imperfections do not significantly degrade resolution, performance or reliability of meteorological spectral moment estimates     

Spatial Correlation of Reverberation Noise in Active Sonar

A linear array of hydrophones is considered for detecting a signal echo from a stationary target in the presence of reverberation. The structure of the optimum (likelihood ratio) detector is compared with that of a beamformer-matched filter detector. The conditions causing an increase in the spatial noise correlation between two hydrophones are the conditions under which the optimum spatial detector performs significantly better than the beamforming detector. A study of the space-time correlation function of reverberation shows that 1) a decrease in scatterer angular spread (or a narrowing of the receiver directivity pattern) tends to increase the spatial correlation, 2) if the scatterer Doppler spread is much less than the signal carrier frequency and if the angular spread is uniform, it is still possible to get a high correlation if the intersensor distance is much smaller than the carrier wavelength. These conditions indicate situations where optimum techniques may be worthwhile.     

Models for Radar Scatterer Density in Terrain Images

Statistical models for the density of strong scatterers detected in high resolution radar images of rural terrain are presented. The probability distribution of the density of these natural terrain detections was found to be negative binomial. The variance of the negative binomial depended strongly on the window size used to measure the density. This dependence indicates that these detections, like those of a Poisson process, are locally uncorrelated, but have a slowly varying mean density whose correlation distance is 1 km or more. Negative binomial parameters were computed using over 200 km2 of terrain image for densities measured using windows sized from 75 m × 75 m to 375 m × 375 m. Average terrain detection densities of 10-3 and 10-4 per resolution cell were evaluated on images with resolutions of 7 and 28 ft.     

Signal Resolution via Digital Inverse Filtering

Research in numerous areas is directed toward the resolution of multiple overlapping signals in a noisy environment. These areas include radar, sonar, speech, seismology, and electrophysiology. Sometimes matched filters are used; other times inverse filters are employed. This paper discusses one approach to the analysis of the resolution of inverse filters. Our method is to compromise the trade-off between signal resolution and the output signal-to-noise ratio (SNR). A performance measure for the inverse or deconvolution filter is defined as a quantity proportional to the harmonic mean of the resolution and the SNR. An optimum output pulse duration is obtained using this criterion, where the pulse shape has been previously selected and the input signal waveform is known. In addition, upper and lower bounds for the output pulse duration are presented. Graphs are given which allow the designer to select the optimum inverse filter output pulse duration for a desired signal resolution and an estimated SNR.     

A Nonadaptive Processing of Radar Pulse Trains for Clutter Rejection

The problem of detecting coherent pulse trains with uniform amplitude in a clutter-plus-noise environment is considered. A radar processor for detecting targets moving radially with respect to the clutter is proposed. The minimum interpulse spacing of the transmitted signal is assumed long enough that returns are not received simultaneously from different ranges within a region of extended clutter, and the central frequency of the clutter power spectrum is postulated to be known. The processor is singled out as the linear filter, orthogonal to the clutter central frequency component, which yields the maximum ratio of peak signal power to average noise power. The filter can be implemented by slightly modifying the structure of the conventional matched filter. The performance of such a filter is compared with that achievable if full a priori knowledge of the input interference were available and with that of the conventional matched filter. This comparison is made on a signal-to-interference power ratio basis after assuming a transmitted signal consisting of equally spaced pulses and an interference characterized by an exponential covariance matrix.     

Post Mixer Spectra of Periodic FM Altimeters with Area Target Returns

A periodic FM altimeter is postulated and its illuminated area target modeled as an array of elemental scatterers. A computational form is then developed expressing the desired post mixer spectrum as a sum of spectral components corresponding to the individual scatterer returns. Application of the model is made to the case of a triangular linear sweep FM altimeter and samples of the calculated post mixer spectrum presented, illustrating the effects of antenna beam geometry, target surface properties, and modulation parameters.     

On suboptimal detection of 3-dimensional moving targets

The author designates matched filters that are completely characterized by the velocity of the target as assumed velocity filters (AVFs). Like most matched filtering techniques where the signal parameters range in a continuum, the AVF must be implemented suboptimally by partitioning the velocity space. The author investigates the possibility of using a signal-to-noise ratio (SNR) loss factor as the criterion for the partition. The loss factor is a measurement of the loss of SNR at the output of the matched filter due to mismatch of filter parameters. In the scenario of detecting a moving satellite from a ground-based sensor, because of the vast sky the sensor has to search, it is important to keep the number of filters minimal. The author shows that, with a fixed loss factor, the number of filters required for coverage increases linearly as the span of the two-dimensional velocity space increases quadratically. The rate of increase is further reduced when the loss factor is made proportional to expected target angular speed     

Intrusion location capability added to synergistic radar technology

There is a new trend in the outdoor security market that demands more precision in identifying the crossing area of an intruder. Often called intrusion location capability, this capability also presents inherent features such as more accuracy in camera pre-set positioning and temporary disabling of sub-zone and individual sensitivity level per sub-zone. However even though market trend demands them, such features must have minimum impact to overall system cost. How the synergistic radar technology can be modified to offer intruder location capability to a sub-zone area as precise as 10% of the total zone length is presented. For a typical zone length of 100 meters, the zone is sub-divided into up to ten equally spaced sub-zones of 10 meters each, giving an intrusion crossing point resolution of 10 meters. Synergistic radar technology can be applied to buried, surface, wall and roof applications. This intrusion location capability also applies to each of these applications     

Estimating Target Lengths Shorter Than the Radar Pulse Width

This paper discusses the performance and sensitivity of a maximum-likelihood length estimation algorithm which was originally developed to estimate the separation between unresolved point scatterers. It shows that when the two-scatterer target model is valid, the algorithm reliably estimates lengths shorter than the Rayleigh limit provided that the strength of no third interior scatterer (or its equivalent created by a few very closely spaced scatterers) is greater than the geometric mean of the strengths of the fore and aft scatterers.     

Controlled Alteration of Wideband Radar Oata

A procedure is described for obtaining weights for a transversal filter which will degrade the range resolution and alter the sidelobe levels of the sampled version of a time envelope whose spectrum is band. limited and known. The two general cases of super-and sub-Nyquist rate sampling are discussed.     

Clutter Suppression by Complex Weighting of Coherent Pulse Trains

Uniform coherent pulse trains offer a practical solution to the problem of designing a radar signal possessing both high range and range-rate resolution. The Doppler sensitivity provides some rejection of off-Doppler (clutter) returns in the matched filter receiver. This paper considers the use of a processor in which members of the received pulse train are selectively weighted in amplitude and phase to improve clutter suppression. The techniques described are particularly suitable for rejecting interference entering the processor through ambiguous responses (range sidelobes) of the signal. The complex weights which are derived are optimum in the sense that they produce the maximum clutter suppression for a given detection efficiency. In determining these weights, it is assumed that the distribution of clutter in range and range rate relative to targets of interest is known. Thus, clutter suppression is achieved by reducing the sidelobe levels in specified regions of the receiver response. These techniques are directly applicable to array antennas; the analogous antenna problem would be to reduce sidelobe levels in a particular sector while preserving gain. Complex weighting is most successful when the clutter is limited in both range and velocity.     

Maximum Likelihood Energy Detection of Mary Orthogonal Signals

The literature on energy detection is extended by applying it to the processing of M'ary orthogonal communication signals of arbitrary time-bandwidth product. Guassian noise channel transition probabilities are derived for maximum likelihood energy detection, modified to the extent of including an erasure threshold. Relations and computational techniques are described for determining the symbol erasure and error probabilities for general signal alphabet sizes (M) and time-bandwidth products. When time of arrival is known exactly and Doppler is negligible, gible, it is determined that energy detection is inferior to noncoherent matched filter detection. For time-bandwidth products of the order of 100 and error probabilities around 10 3, a loss of about 5 dB occurs which is attributable to a lack of knowledge of the detail signal structure. However, for problems where time of arrival and/ or Doppler are unknown, energy detection will perform nearly as well as matched filter detection of, for example, spread spectrum signals, and is also simpler to implement. General energy detection performance curves are given in terms of required signal energy for specific error and erasure probabilities, as a function of M'ary and time-bandwidth product.     

Matched Filter Criteria and Range Weighting for Weather Radar

The effective weighting function for weather radar is defined. This weighting function considers the effects of both the transmitted signal and the receiver filter. It is used to assign effective ranges to samples taken at prescribed times. For uniformly distributed targets it is shown that "signal"-to-noise ratio depends on the receiver filter, transmitted signal envelope, and receiver noise spectral density. Maximization of this signal-to-noise ratio when range resolution constraints are imposed is discussed, and a receiver design approach specifically adapted for Doppler weather radars is developed.     

空中发射初始状态对运载火箭有效载荷的影响

空中发射可以明显提高火箭有效载荷,减少火箭发射场地的数量和高额的维护经费,缩短发射周期。本文研究了空中发射初始状态对运载火箭有效载荷的影响,通过飞行轨道的模型简化,首先建立了火箭飞行的数学模型,然后定量地分析了发射高度和发射速度对火箭入轨后有效载荷的影响。研究结果表明：若提高发射高度和发射速度,可以明显增加有效载荷,且基本发射高度、发射速度分别与有效载荷表现为线性关系。相对地面发射来说,如果初始高度达到30千米,有效载荷提升到1.63倍;如果初始高度达到30千米,初始速度达到1000米每秒（约3马赫）,有效载荷将是传统地面发射的5.43倍。单纯从初始高度和速度的因素看,初始发射速度对有效载荷提升的影响更显著,故在考虑经济性情况下设计发射平台时应更加注重发射速度的提高。     

HPM对伪码脉冲无线电引信的压制干扰效应仿真

为了对高功率微波作用于伪码脉冲无线电引信的干扰效果进行分析,建立了引信信号处理模型并进行了计算机仿真。仿真结果表明,在频率对准的情况下,当 HPM进入引信距离门对回波信号造成压制时,由于 HPM的信号频带较宽,覆盖了多普勒滤波器带宽,多普勒滤波器的输出信号幅度仍可达到启动门限电平,压制干扰无效。     

Detection of Known Signals in Nonstationary Noise

The basic design of a nonlinear, time-invariant filter is postulated for detecting signal pulses of known shape imbedded in nonstationary noise. The noise is a sample function of a Gaussian random process whose statistics are approximately constant during the length of a signal pulse. The parameters of the filter are optimized to maximize the output signal-to-noise ratio (SNR). The resulting nonlinear filter has the interesting property of approximating the performance of an adaptive filter in that it weights each frequency band of each input pulse by a factor that depends on the instantaneous noise power spectrum present at that time. The SNR at the output of the nonlinear filter is compared to that at the output of a matched filter. The relative performance of the nonlinear system is good when the signal pulses have large time-bandwidth products and the instantaneous noise power spectrum is colored in the signal pass band.     

Probability Densities and Characteristic Functions for Fluctuating Targets

Probability density functions and characteristic functions for the projected area of a tumbling target object are derived together with the densities and characteristic functions for the corresponding signal-plus-noise voltage output of an infrared sensor. Several cases are considered in which the signal pulse arrival time is either known or unknown, a matched filter or a suboptimum filter is used; the signal pulse shape is either Gaussian or is unspecified; and the target orientation angles are either uniformly or nonuniformly distributed.