Optimum Active Array Processing Structure and Space-Time Factorability

An active array processor is concerned with the problem of detecting a signal echo, reflected from a target, in the presence of reverberation (clutter). The processor can also be used to estimate target range and bearing. It is a priori not evident whether the optimum (likelihood ratio) detector can be factored into spatial and temporal operations, thus resulting in a simpler processor implementation. This paper studies this problem for a linear continuous array in a reverberation-limited environment. Conditions on signal, reverberation, and array parameters are derived under which the optimum detector is factorable. The validity of using factorability as a criterion of signal design is briefly examined. Finally, the relationship between space-time factorability and range-bearing estimates is pointed out.     

Optimum Signal and Filter Design in Underwater Acoustic Echo Ranging Systems

Optimization of the filter, the signal, and the signal and filter jointly are studied in the sonar environment under noise and reverberation limited conditions. The maximization of the receiver output signal-to-interference ratio is used as a performance criterion with unit energy constraint on both signal and filter. In the filter design problem, the optimum filter function is the solution of a linear integral equation. The kernel of the integral equation is a function of the target and medium scattering functions and the reverberation distribution. In the signal design problem, a similar type of integral equation is obtained as in the filter optimization problem. In the joint signal and filter design problem, it is shown that the optimum signal and filter functions are the solutions to a pair of linear integral equations with the largest (SIR)O. Several examples are investigated for different mediums and reverberation distributions with the finite matrix approximation method. An interative technique is used to compute the joint optimization of signal and filter.     

Mismatched Filtering of Sonar Signals

A replica correlator (matched filter) is an optimum processor for a receiver employing a pulse of continuous wave (CW) signal in a white Gaussian noise background. In an active sonar, however, when the target of interest has low Doppler shift and is embedded in a high reverberation background, this is not so. High sidelobes of the correlator frequency response pass a significant portion of the signal contained in the mainlobe of the reverberation spectrum. In order to reduce the sidelobes of the correlator output spectrum and at the same time keep the increase in its 3 dB bandwidth to a small amount, we propose lengthening of the replica of the transmitted signal and weighting it by a Kaiser window. It is demonstrated that by extending the weighted replica by 50 percent compared with the transmitted signal, it is possible to reduce the sidelobe levels to at least 40 dB below the mainlobe peak, with the concomitant increase of the 3 dB band-width by less than 5 percent. The degradation in signal-to-noise ratio (SNR) performance for such a ?mismatched? filter receiver with respect to the matched filter is less than 1.5 dB.     

High-Resolution Imaging of Tropospheric Radio Scatterers

A two-dimensional matched filter technique is described for processing ing the signal from a pulsed coherent troposcatter link to obtain high crosspath resolution "maps" showing the relative positions of individual scatterers. For a typical tropolink (station displacement 200 km; midpath beam halfwidth 2 km; wavelength 0.3 meters) crosspath resolution is about 4.5 meters under perfect conditions. Vertical resolution is inversely proportional to scatterer height, but even for wide bandwidth signals is never better than hundreds of meters. Slight velocity mismatches between the signal and filter degrade crosspath resolution considerably so that the scatterers' velocity must be known accurately a priori. Crosspath resolution is relatively insensitive to mismatch in signal and filter record lengths. Random fluctuations of the velocity of a scatterer seriously degrade crosspath resolution. For the typical tropolink parameters and with a 10 m/s scatterer crosspath velocity and a 0.2 m/s standard deviation ion fluctuation the crosspath resolution degrades by an order of magnitude. It is concluded that the matched filter imaging scheme will produce images of individual scatterers if specific atmospheric conditions ions exist. The best results are obtained if the received signal comes from a single scattering layer at a known height, with scatterers moving at a known constant horizontal velocity, with no along-path or vertical components. Such a layer would be observed during night time or early morning when convective and mixing processes are at a minimum.     

Optimum Spatial Processing of Passive Sonar Signals

The spatial structure of the likelihood ratio array processor for detecting a monochromatic plane wave signal in Gaussian noise is compared with a conventional beam-forming detector. Conditions are determined under which the optimum detector performs significantly better than the conventional detector. Conditions are also found under which the beamformer is itself near optimal.     

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     

宽带信号角跟踪和四通道单脉冲方案

分析了宽带信号角跟踪的特殊问题及其实现方案。基于互相关函数的角误差检测方法,推导出了在非相关噪声及相关噪声背景下差路信号的输出信噪比及其角度随机误差的数学表达式,进而给出了带宽增益和最佳带宽的概念,以及提高输出信噪比的方法。为了在低载噪比（C/N）时获得角捕获所需要的和路信号以及差路的归一化信号,提出了四通道单脉冲方案。最后归纳出了低C/N时宽带信号角捕获和角跟踪的几种方法并提出了建议。     

Specification and Performance of Passive Sonar Spectral Estimators

The application of existing estimation theory to the problem of specification and performance of passive sonar spectral estimators is considered. The classification function is addressed, so that the signal is assumed to be present, and so that the energy arrival angle is known. The spatial filter considered is a line array of M equally spaced omnidirectional hydrophones. Signal and ambient noise are both zero-mean, wide-sense, stationary Gaussian random processes that differ in their spatial correlation across the face of the array. The signal is a plane wave that can be made totally spacially corrected between array elements by inserting delays between sensors to invert the signal propagation delay. The noise correlation is a function of frequency, bandwidth, element separation, and the relative time delay between sensors. Under these assumptions, the Cramer-Rao lower bound is derived for the class of unbiased estimates of signal power in a narrow frequency band at the hydrophone in the presence of correlated ambient noise of known power. The bound is examined numerically, resulting in a threshold phenomenon with M that constitutes a new design consideration. In addition, there is a striking insensitivity to realistic values of ambient noise correlation, and there are ranges in signal-to-noise ratio for which one gains more by increasing M than by increasing the bandwidth-time product. Specific processors, including a new unbiased estimator when noise power is unknown, are developed.     

A Suboptimum Rank Test for Nonparametric Radar Detection

The optimum rank detector structure, in the Neyman-Pearson sense and under Gaussian noise conditions, is approximated by a suboptimum structure that depends on an adjustable parameter. This new rank detector, which operates on radar video signal, includes other well-known detectors as particular cases. The asymptotic relative efficiency (ARE) of the proposed rank detector is computed, with its maximum value the ARE of the locally optimum rank detector (LORD). The detection probability versus signal-to-noise ratio, and the effects of interfering targets are also calculated by Monte-Carlo simulations for different parameter values.     

Measuring the Masses of Supermassive Black Holes

Supermassive black holes reside at the centers of most, if not all, massive galaxies: the difference between active and quiescent galaxies is due to differences in mass accretion rate and radiative efficiency rather than whether or not they have nuclear black holes. In this contribution, methods for measuring the masses of supermassive black holes are discussed, with emphasis on reverberation mapping which is most generally applicable to accreting supermassive black holes and, in particular, to distant quasars where time resolution can be used as a surrogate for angular resolution. Indirect methods based on scaling relationships from reverberation mapping studies are also discussed, along with their current limitations.     

Detection of stochastic signals in the frequency domain

The optimum detector for a random signal, the estimator-correlator, is difficult to implement. If the power spectral density (PSD) of a continuous time signal is known, a locally optimum detector is available. It maximizes the deflection ratio (DR), a measure of the detector output signal-to-noise ratio (SNR). A discrete version of this detector is developed here, called the discrete-MDRD, which takes a weighted sum of the spectral components of the signal data as the detection statistic. Its derivation is applicable to nonwhite noise samples as well. A comparison of this new detector against three other common types, through their DR values and simulation results, reveals that the discrete-MDRD is near optimal at low SNRs. When the PSD of a signal is not known, a common test statistic is the peak of the PSD of the data. To reduce spectral variations, the PSD estimator first divides the data sequence into several segments and then forms the averaged PSD estimate. The segment length affects the DR values; the length that maximizes the DR is approximately the reciprocal of the signal bandwidth. Thus for unknown signal PSD, a detector that approaches the maximum DR is realizable from just the knowledge of the signal bandwidth, which is normally available. Examples and simulation results are provided to illustrate the properties and performance of the new detector     

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.     

电离层色散对DS/FH-BPSK信号解调性能影响

相位连续的DS/FH(Direct Sequence/Frequency Hopping,直接序列/跳频)扩频信号的扩频带宽比直扩信号更宽,在电离层的非线性相位以及跳频频点变化这两者的共同作用下,该信号的BPSK(Binary Phase Shift Keying,二相相移键控)解调性能明显恶化。依据随机变量概率分布的数学规律,推导得到了在背景电离层色散条件和跳频频点均匀分布前提下,某种DS/FH卫星测控信号的引导信号和长周期信号BPSK误码率的变化规律,并在特定信号参数条件下进行了误码率仿真。     

基于共轭循环平稳特性的二维波达方向估计方法

 提出了一种具有阵列孔径扩展能力的共轭循环平稳二维波达方向（DOA）估计方法。该方法通过引入伪采样,充分利用了阵元输出之间共轭循环互相关函数的时间维信息,扩展了阵列有效孔径,提高了算法DOA估计精度,具有较好的低信噪比适应能力。该方法避免了最优时延选择问题,无需谱峰搜索,且其二维角度参数能够自动配对,具有较低的计算量。计算机仿真结果验证了该方法的有效性。     

Nonparametric Radar Extraction Using a Generalized Sign Test

A nonparametric procedure used in a constant false alarm rate (CFAR) radar extractor for detecting targets in a background of noise with unknown statistical properties is described. The detector is based on a generalization of the well-known two-sample sign test and thus requires a set of reference noise observations in addition to the set of observations being tested for signal presence. The detection performance against Gaussian noise is determined for a finite number of observations and asymptotically, for both nonfluctuating and pulse-to-pulse Rayleigh fluctuating target statistics. It is noted that the performance loss, as compared to the optimum parametric detector, depends critically on the number of reference noise observations available when the number of hits per target is not large. In the same case a much larger loss is also found for a pulse-to-pulse fluctuating target even though the asymptotic loss is the same as for a nonfluctuating target. A comparison is finally made with a detector based on the Mann-Whitney test, which usually is considered to be one of the better nonparametric procedures for the two-sample case.     

单载波干扰对星载扩频应答机码跟踪回路影响研究

扩频码同步是基于扩频体制卫星测控通信中的一项关键技术。研究单载波对星载扩频应答机中全时间超前-滞后非相干跟踪回路的影响,分析单载波干扰存在时跟踪抖动的恶化程度,给出相应的数学表达式,并进行了Matlab仿真。仿真结果表明：在一定的跟踪回路带宽下,恶化程度随着系统的扩频增益或频偏的增加而减小,并随着干信比的增加而增加。单载波干扰不变的前提下,恶化程度随着回路带宽的增加而增加。     

Optimum detection and location estimation of target lines in the range-time space of a search radar

The average likelihood ratio detector is derived as the optimum detector for detecting a target line with unknown normal parameters in the range-time data space of a search radar, which is corrupted by Gaussian noise. The receiver operation characteristics of this optimum detector is derived to evaluate its performance improvement in comparison with the Hough detector, which uses the return signal of several successive scans to achieve a non-coherent integration improvement and get a better performance than the conventional detector. This comparison, which is done through analytic derivations and also through simulation results, shows that the average likelihood ratio detector has a better performance for different SNR values. This result is justified by showing the disadvantages of the Hough method, which are eliminated by the optimum detector. To have an estimate for the location of the detected target line in the optimum detection method as the Hough method, which detects and localizes the target lines simultaneously, we present the maximum a posteriori probability estimator. The estimation performance of the two methods is then compared and it is shown that the maximum a posteriori probability estimator localizes the detected target lines with a better performance in comparison with the Hough method.     

Variance Analysis of the Angle Output Voltage for an Amplitude Monopulse Receiver

The amplitude-comparison monopulse receiver utilizes two overlapping antenna patterns to determine the angle of arrival of an incoming RF signal for use in a direction-finding application. The thermal noise introduced by the receiver distorts the signal, causing an error in determining the exact angle of arrival of the signal. The analysis derives an expression for the deviation of the angle output voltage, or the angular error, due to receiver noise as a function of 1) the angle of arrival and 2) the signal-to-noise ratios of the two channels of the receiver. A receiver using a square-law detector and one using a linear detector are analyzed.     

Sample Size Considerations for Adaptive Arrays

Digital control of adaptive arrays has been shown to be a feasible alternative to analog feedback-loop control. As the eigenvalue spread of the correlation matrix no longer controls the speed of adaption, one merely has to ensure that enough samples have been taken so that the matrix estimate is close to the true matrix. While previous studies have assumed ideal conditions, it is shown here that if the true signal direction is not known exactly or if the data containing the interference are corrupted by a desired signal, then more samples are required to ensure that the estimated weighting vector gives a near optimal performance.     

Energy Detection of a Random Process in Colored Gaussian Noise

A likelihood receiver for a Gaussian random signal process in colored Gaussian noise is realized with a quadratic form of a finite-duration sample of the input process. Such a receiver may be called a "filtered energy detector." The output statistic is compared with a threshold and if the threshold is exceeded, a signal is said to be present. False alarm and detection probabilities may be estimated if tabulated distributions can be fitted to the actual distributions of the test statistic which are unknown. Gamma distributions were fitted to the conditional probability densities of the output statistic by equating means and variances, formulas for which are derived assuming a large observation interval. A numerical example is given for the case in which the noise and signal processes have spectral densities of the same shape or are flat. The optimum filter turns out to be a band-limited noise whitener. The factors governing false alarm and detection probabilities are the filter bandwidth, the sample duration, and the signal level compared to the noise. Two sets of receiver operating characteristic curves are presented to complete the example.