Radiometric detection of spread-spectrum signals in noise ofuncertain power

The standard analysis of the radiometric detectability of a spread-spectrum signal assumes a background of stationary, white Gaussian noise whose power spectral density can be measured very accurately. This assumption yields a fairly high probability of interception, even for signals of short duration. By explicitly considering the effect of uncertain knowledge of the noise power density, it is demonstrated that detection of these signals by a wideband radiometer can be considerably more difficult in practice than is indicated by the standard result. Worst-case performance bounds are provided as a function of input signal-to-noise ratio (SNR), time-bandwidth (TW) product and peak-to-peak noise uncertainty. The results are illustrated graphically for a number of situations of interest. It is also shown that asymptotically, as the TW product becomes large, the SNR required for detection becomes a function of noise uncertainty only and is independent of the detection parameters and the observation interval     

Calculating Detection Probabilities for Adaptive Thresholds

In calculating detection probabiities for radar and sonar systems it is usually assumed that the threshold required to yield a certain probability of false alarm is known. This is often not the case for real systems and therefore the threshold must be estimated using some measure related to the test statistic. This paper presents a calculation technique that handles estimated (adaptive) thresholds in a general framework that can be applied easily to many detection problems. False alarm and detection probabilities are calculated from the characteristic function of the noise or signal plus noise variate and the characteristic function of the threshold estimate. To illustrate the method the detection performance of overlapped discrete Fourier transforms (DFTs) is calculated for a narrowband Gaussian target signal.     

Evaluating the Detectability of Gaussian Stochastic Signals by Steepest Descent Integration

It is shown how to compute the detection probability of certain signals by numerical integration of the Laplace inversion integral involving the characteristic function or the moment-generating function of the detection statistic. The contour of integration is taken as the path of steepest descent of the integrand and is determined numerically as the integration proceeds. The method is applied to calculating the performance of the optimum detector of a Gaussian stochastic signal in white noise when the signals actually present have a different average s.n.r. from that assumed in the design. Results are presented for narrowband signals with Lorentz and rectangular spectral densities. The detectability of the former is shown to be more sensitive than that of the latter to the value of the design s.n.r. The relative disadvantage of the threshold detector, also assessed by this method, is smaller for signals with a rectangular than for those with a Lorentz spectral density.     

Performance of a Two-Sample Mann-Whitney Nonparametric Detector in a Radar Application

The detection of signals in an unknown, typically non-Gaussian noise environment, while attempting to maintain a constant false-alarm rate, is a common problem in radar and sonar. The raw receiver data is commonly processed initially by a bank of frequency filters. The further processing of the outputs from the filter bank by a two-sample Mann-Whitney detector is considered. When the noise statistics in all filters are identical, the Mann-Whitney detector is distribution free, i. e., the false-alarm probability may be prescribed in advance regardless of the precise form of the noise statistics. The primary purpose of this paper is to demonstrate the potential advantage of nonparametric detectors over conventional detectors. The signal detection performance of the Mann-Whitney detector is compared to that of an ordinary linear envelope detector plus integrator in the presence of Gaussian and several hypothetical forms of non-Gaussian noise. This comparison is made for both uniform and nonuniform distributions of noise power across the filter bank. Besides providing a much more constant false-alarm rate than the conventional detector, the Mann-Whitney detector's signal detection performance is found also to be much less sensitive to the form of the noise statistics. In one case, its detection sensitivity is found to be 11 dB better than that of the conventional detector. Even when the noise power density is made moderately nonuniform across the filter bank, the detection performance of the Mann-Whitney detector is found not to be significantly affected.     

Bayesian Detection of Targets of Unknown Location

In this paper the array detection problem for certain deterministic signals in spatially uncorrelated Gaussian noise is formulated in Bayesian terms and the required likelihood ratios and resulting performance characteristics are obtained. Primary emphasis is on detection of targets of unknown spatial location using a likelihood ratio approach, with the target location treated as a random parameter, rather than an estimator-correlator approach. The tradeoff among array parameters and signal parameters is demonstrated. It is shown that the dominant uncertainty affecting detection performance seems to be that of location when compared with uncertainty on energy and/or phase.     

噪声调制连续波雷达信号波形射频隐身特性

雷达信号波形的射频(RF)隐身性能是雷达系统能否适应现代战场环境的重要因素,雷达射频隐身信号波形设计是现代雷达系统设计中的重要课题.首先,在介绍随机噪声信号雷达原理的基础上,基于Schleher截获因子阐述了噪声调制连续波雷达信号波形的射频隐身特性.然后,分析了高斯噪声相位和频率调制连续波雷达输出自相关函数和高斯噪声相...     

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.     

Background noise suppression for signal enhancement by noveltyfiltering

The enhancement of weak signals in the presence of background and channel noise is necessary to design a robust automatic signal detection and recognition system. The autoassociative property of neural networks can be used to map the identifying characteristics of input source waveforms or their spectra. This paper is directed at the exploitation of such neural network properties for novelty filtering that improves the detection probability of weak signals by learning and subsequent subtraction of noise background from the input waveform. A neural-network-based preprocessor that learns to selectively filter out the background noise without significantly affecting the signal will be highly useful in solving practical signal enhancement problems. An analytical basis is established for the operation of neural-network-based novelty filters that enhance the signal detectability in the presence of noise background and channel noise     

Calculating Detection Probabilities for Systems Employing Noncoherent Integration

Cumulative probability distributions that occur in radar and sonar detection problems are calculated directly from the characteristic function by using a Fourier series. The error in the result is controlled by two parameters which can be adjusted to suit the application. The technique is applied to the problem of determining the detection performance of consecutive discrete Fourier transforms (DFTs) for a narrowband Gaussian signal with a rectangular spectrum. Since the characteristic function is used directly in its product form this technique does not suffer from the numerical problems associated with the partial fraction approach. The technique can handle many different problems in a single computational structure making it a valuable tool in system performance studies.     

An adaptive array detector with mismatched signal rejection

An adaptive detection algorithm with a sensibility parameter for rejecting unwanted signals is presented. This algorithm is a simple modification of the generalized likelihood ratio (GLR) detector (or test) for detecting a signal in zero mean Gaussian noise with unknown correlation matrix. Specifically, the adaptive detection algorithm is obtained by introducing an arbitrary positive scalar, which is called the sensitivity parameter, into the GLR detector as a multiplier of an already existing quadratic term. The GLR detector then becomes a special case of this detector for the unity sensitivity parameter. It is shown that the sensitivity parameter controls the degree to which unwanted signals are rejected. From numerical examples, it is demonstrated how the sensitivity parameter can be chosen such that unwanted signals, can be rejected while maintaining acceptable detection loss for slightly mismatched signals. Further insight into previous work on adaptive detection is also given     

Detection Probabilities for Log-Normally Distributed Signals

The amplitude and power of a large family of radio signals are observed to have log-normal probability density functions. Among these are signals propagated through random inhomogeneous media, a notable example being low frequency atmospheric radio noise. Of greater importance are certain radar targets that have been observed to have essentially log-normal density functions. Both ships and space vehicles may fall into this category. Curves of probability of detection vs. signal-to-noise ratio for the case of log-normal signals in Gaussian noise have been computed and are presented in this paper. The curves apply for square-law detection with varying degrees of postdetection linear integration. Both fully correlated and completely uncorrelated fluctuating signals are considered. It is shown that for log-normal signal distributions having large variances, the probability of detection differs significantly from that obtained using curves based on an assumed Rayleigh signal distribution.     

Decision-Directed Detector for Overlapping PCM/NRZ Signals

A decision-directed (DD) technique for the detection of overlapping PCM/NRZ signals in the presence of white Gaussian noise is investigated. The performance of the DD detector is represented by probability of error PE versus input signal-to-noise ratio (SNR). To examine how much improvement in performance can beachieved with this technique, PE's with and without DD feedback are evaluated in parallel. Further, analytical results are compared with those found by Monte Carlo simulations. The results are shown in good agreement.     

Output Signal-to-Noise Ratio for Amplitude and Intensity Modulated Laser

General expressions are obtained for output SNR for both amplitude- and intensity-modulated lasers, where bandlimited Gaussian noise has been chosen as a modulating signal, and in the presence of background light. Two types of modulating signals are considered: the baseband and bandpass modulating signals. Detailed calculations are made for output SNR when an ideal narrowband optical filter is used. The dependence of output SNR on several parameters, such as the center frequency of the modulating signal, the effective average quantum rate, and input SNR, are discussed. In addition, the difference in performance between amplitude and intensity modulation is discussed. The detection characteristics of the homodyne system are also considered.     

Signal Sequence Detection Given Noisy, Common Background Image Sets

The optimum processing (likelihood functional) is found for a set of M images {Zm = Sm + Y + Nm}, each the sum of a member Sm of a signal sequence {Sm}, due to an object to be detected and its parameters estimated, a sample function Nm of a noise field {Nm}, and a sample function Y of a common background field {Y}. The noise fields {{Nm}} are independent, zero mean, white Gaussian fields, all independent of the background field {Y}; the latter is assumed to be either 1} completely unknown or of known mean and covariance functions with 2) a certain fluctuation property or 3) Gaussian. Three equivalent forms of the optimum processing are found: 1) a summation of generalized matched filterings of the images, 2) a summation of matched filtering of certain generalized differences of the images, 3) a summation of ?estimator-correlator? type filterings. The detection performance and optimum signal/image selection under the Neyman-Pearson criterion is given and the singularity of the ({{Nm = O}} and M > 1) case noted. It is shown that optimum processor and signal design can completely eliminate any effect of the background on detectability (M > 1). The Cramer-Rao lower bound for the signal parameter estimates meansquare error is given along with an example; optimum signal/image selection in the single parameter case is discussed.     

Envelope Threshold Detection in a Class of Non-Gaussian Interference

This paper considers the detection of a sinusoidal or chirp signal imbedded in wideband FM interference (as might be generated by some types of active jamming), such that after pulse compression or other integration, the interference can be approximated by a sum of sinusoids of independent phase. The detection probability in such non-Gaussian noise is compared to that for Gaussian noise, with the Gaussian result approached, as required, in the limit that the number of sinusoids in the sum increases without bound. For detection using a comparison of the envelope with a threshold which yields a given false-alarm probability (CFAR detection), the detection probability is improved over the case of Gaussian noise, so that the usual approach basing the design on Gaussian noise would be conservative. Using a threshold determined from the envelope mean, the FM interference yields a lower false-alarm probability than for Gaussian noise, with detection probability only slightly degraded.     

Data-Adaptive Detection of a Weak Signal

Motivated by a form of the likelihood-ratio-tesf statistic for detection of a rank-one Gaussian signal in colored Gaussian noise, we apply our earlier technique for estimation of a low-rank signal to the problem of estimating and subtracting the waveform of a strong sinusoidal interference prior to detection of a weak sinusoidal signal. We consider the difficult case in which samples of data are taken over a short interval of time or space and the frequencies of the sinusoidal signal and sinusoidal interference are more closely spaced than the reciprocal of the extent of the aperture. The method can be applied to cases of nonsinusoidal and/or random signals and interference. The most important assumption is that when the samples of the interference are arranged in matrix form the matrix is approximately of low rank in the sense that, with high probability, the interference-only matrix can be well approximated by a matrix of low rank.     

Signal to Noise Ratio Improvement by Frequency Division in the Presence of Bandpass Noise

The performance of a wide band frequency divider in the presence of additive Gaussian noise is presented. It is shown that the same theoretical signal to noise ratio improvement is attainable in this case as in the case where the spurious signal is a sine wave.     

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.     

基于周期Wigner-Hough变换多相编码连续波雷达信号检测算法

为提高雷达侦察截获接收机对多相编码连续波弱信号截获能力,提出了一种基于周期Wigner-Hough变换（Periodic Wigner-Hough Transform,PWHT）的多相编码连续波信号检测算法。研究了线性调频连续波信号的PWHT及性质;分析了多相编码连续波信号时频主脊线的类似线性调频连续波特征;推导了高斯白噪声在PWHT域的统计分布特征,根据多相编码连续波信号与线性调频连续波的相似性,提出了基于PWHT的多相编码连续波信号检测算法,给出了实现流程,并计算出其检测性能和参数估计性能仿真的仿真结果。仿真结果表明：该算法较已有的其他多相编码信号检测算法有更好的弱信号检测能力,最小可检测信噪比至少可以降低3dB,并随着观测时间延长而进一步降低;其参数估计精度具有渐进最优的性质。     

Limitations of radiometer performance in spherically invariantnoise

The radiometer is a common method for detection of unknown signals in noise. Most analyses of radiometer performance are based on assumptions of stationary Gaussian noise with known marginal statistics. In this note, we use a spherically invariant noise model to derive simple expressions for radiometer performance degradation in noise variance uncertainty. Numerical examples are provided to show that channel uncertainty imposes a substantial penalty in detection performance