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     

Noncoherent Detection of Sinusoidal Signals in Sinusoidal Clutter

Probability density expressions associated with the noncoherent detection of a sinusoidal signal have been obtained. The signal is assumed to be imbedded in sinusoidal clutter at the same frequency and narrow-band Gaussian noise. The density expressions are shown to be a function of the signal-to-noise power ratio and the clutter-to-noise power ratio. The expressions have been numerically evaluated for a number of conditions, and the results under each reception hypothesis are presented graphically. Under large-sample conditions, the probability density for a multisample test statistic is shown to be Gaussian, and the probability of detection expression is written such that commonly available tabulated data can be utilized to determine the probabilities.     

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.     

Asymptotic Performance of Sparse Signal Detection Using Convex Programming Method

The detection of sparse signals against background noise is considered. Detecting signals of such kind is difficult since only a small portion of the signal carries information. Prior knowledge is usually assumed to ease detection. In this paper, we consider the general unknown and arbitrary sparse signal detection problem when no prior knowledge is available. Under a Neyman-Pearson hypothesis-testing framework, a new detection scheme is proposed by combining a generalized likelihood ratio test (GLRT)-like test statistic and convex programming methods which directly exploit sparsity in an underdetermined system of linear equations. We characterize large sample behavior of the proposed method by analyzing its asymptotic performance. Specifically, we give the condition for the Chernoff-consistent detection which shows that the proposed method is very sensitive to the 2 norm energy of the sparse signals. Both the false alarm rate and the miss rate tend to zero at vanishing signal-to-noise ratio (SNR), as long as the signal energy grows at least logarithmically with the problem dimension. Next we give a large deviation analysis to characterize the error exponent for the Neyman-Pearson detection. We derive the oracle error exponent assuming signal knowledge. Then we explicitly derive the error exponent of the proposed scheme and compare it with the oracle exponent. We complement our study with numerical experiments, showing that the proposed method performs in the vicinity of the likelihood ratio test (LRT) method in the finite sample scenario and the error probability degrades exponentially with the number of observations.     

An Adaptive Threshold System for Nonstationary Noise Backgrounds

The problem of detecting target signals in an ocean environment using active sonar is complicated by the nonstationary background which usually consists of both ambient ocean noise and reverberation. on. In this paper a signal processing system capable of detecting a signal in nonstationary noise is introduced. This system makes use of the mean and variance time functions of the nonstationary noise background in order to design estimation filters which will cope with the nonstationarity. Appropriate statistics of the noise and signal (tone burst) plus noise have been obtained and are used to determine the probabilities of false alarm and detection and the receiver operating characteristics.     

Multiple-Tone Signals and Detection Probabillities

An analysis technique is presented for multiple-tone signals insystems employing noncoherent integration of a square-law detectoroutput. It is shown how the characteristic function for the teststatistic can be found from the easily determined "coherent"characteristic function defined in the two-dimensional signal space.This result is applied to two detection problems, the detection of multiple-tone signals in Gaussian noise and the detection of a Gaussian signal in multiple-tone plus Gaussian noise interference.The detection curves are compared to an approximation that is often used in practice to estimate performance. It is found that detection performance in the presence of multiple-tone interferences can be significantly different from that in the presence of Gaussian noise alone.     

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.     

Detection probabilities for correlated Rayleigh fading signals

Both the method of saddlepoint integration and its associated saddlepoint approximation are applied to calculating the probability of detecting correlated Rayleigh-fading signals in Gaussian noise by means of a detector that integrates M samples of the output of a quadratic rectifier. The quadrature components of the signal samples are modeled as an autoregressive moving-average process, and specific results are exhibited for a first-order Markov process. By these methods the fluctuation loss can be computed for much larger values of M and for larger values of the detection probability than previously. Values calculated by the saddlepoint approximation prove to be close enough to the exact values to be useful over a broad range of signal parameters     

Imperfect Carrier Recovery Effect on Filtered PSK Signals

Coherent demodulation of a PSK signal requires the generation of a local carrier phase reference. Methods are given to determine the detection loss caused by noisy phase recovery and its use in the coherent detection of filtered BPSK and QPSK signals. It is assumed that the phase noise can have a static part and a random component with a Tikhonov-type distribution. The static part is mostly due to offset frequency tracking of the PLL used to recover the carrier, while the random component is due to thermal noise present in the carrier recovery loop and is also due to the random nature of the phase modulation. It is shown that the probability of error of BPSK and QPSK can be expressed as a finite sum of a set of strictly alternating converging series when the number of ISI terms is finite. Upper and lower bounds on the probability of error have been derived when this number becomes infinite and we show how this error rate can be computed with any desired accuracy. Numerical results are presented for various values of static error and phase noise variance when the transmit and receive filters are 4-pole Butterworth filters. For filtered PSK signals and for a bit error rate of 10-6, our results show that the additional degradation in presentday receiver systems due to imperfect carrier recovery can be less than 0.1 dB for BPSK and less than 1 dB for QPSK.     

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     

Coherent detection in Laplace noise

The discrete-time detection of a time-varying, additive signal in independent Laplace noise is considered. Previous efforts in this area have been restricted to the constant signal, and identically distributed noise case. Theoretical (closed form) expressions for the false alarm and detection probabilities are developed for both the Neyman-Pearson optimal detector and the classical matched filter detector. Comparisons between the two detectors are made which illustrate the effects of signal-to-noise power ratio and sample size for certain false alarm and detection probability constraints. In view of the fact that the optimal Laplace detector is not UMP, we also investigate the effect of signal amplitude mismatch     

The Nonparametric Detection of Signals Embedded in Log-Normal Noise

The nonparametric detection of signals embedded in log-normal noise is discussed. The generalized sign (GS), Mann-Whitney (MW), modified Savage (MS), and modified rank squared (MRS) non-parametic detectors are considered and are compared with the mean and trimmed mean (TM) detectors when envelope detection is used. The detection of both nonfluctuating and Rayleigh fluctuating signals is considered.     

An Application of Radiometric Techniques to Precision Angle Tracking Radar Systems

A new technique is described which provides for precision angle tracking of celestial radio sources with a conventional monopulse antenna receiving system. It is shown that this technique is readily adapted to angle tracking radars. The features of conventional monopulse operation are preserved while permitting precise angle tracking of noise sources when signal to noise ratios are much less than unity. Measurements, using a four-horn monopulse feed with a 28-foot parabolic reflector and a "monopulse radiometer" produced the characteristic monopulse angle detection functions when using the sun, the moon, and Cassiopeia A as boresight reference sources. Precision measurements were made to 8 arc second under varying weather conditions using 28-foot radio astronomy antennas. The accuracy of the measurements were limited by the antenna angle encoders, consequently no conclusions are drawn with regard to the absolute accuracy of the measurements. The celestial coordinates of four discrete radio sources and the equations for coordinate transformation to local elevation and azimuth are contained in the Appendixes.     

Detection Performance of a Mean-Level Threshold

The problem of detecting signals in nonstationary clutter is met by presenting a mean-level or adaptive threshold which adjusts to the changing background level. Such a threshold performs better than a fixed threshold that must be set for the highest amplitude clutter. However, the mean-level threshold does not perform as well for stationary noise as a fixed threshold set at the proper value. One measure of effectiveness of an adaptive threshold is its performance in stationary noise (compared to the optimum fixed threshold) for a specified speed of response. For the mean-level threshold, a simple mathematical solution is found for the detection probability when the noise is stationary and the signal scintillates rapidly. The performance is evaluated for a wide range of mean-level-threshold time constants and for several false-alarm probabilities. The results are presented graphically. As an example, the mean-level threshold suffers 3 dB in detectability (equivalent signal-to-noise ratio) in the presence of stationary noise as compared to the optimum fixed threshold for 50-percent probability of detection, false-alarm probability of 10-8, and an adjustment time of 15 times the signal duration.     

基于预估-反馈联合处理的射频噪声干扰抑制算法

针对强射频（RF）噪声干扰下脉压雷达目标检测概率较低的问题,提出了一种基于预估-反馈联合处理的射频噪声干扰抑制算法。首先,对回波信号进行盲源分离预处理,并利用分数阶傅里叶变换（FRFT）的特性对目标回波信号进行参数估计以及窄带滤波处理,滤除大部分干扰和噪声的能量;然后,在数据层运用M/N逻辑法进行点迹处理,并结合径向速度方向判决,实现对目标航迹的预估检测;最后,利用数据层对航迹状态的反馈实时修正滤波器参数,从而在信号层更好地滤除干扰能量,并对中断航迹进行剔除,完成射频噪声干扰的抑制。仿真结果表明：与现有射频噪声干扰抑制技术相比,所提算法具有更优的干扰抑制效果。     

Sonar Array Detection of Gaussian Signals in Gaussian Noise of Unknown Power

A statistical test is postulated for detecting, with an M-element hydrophone array, a Gaussian signal in spatially independent Gaussian noise of unknown power. The test is an extension of the uniformly-most-powerful (UMP) unbiased test for a two-element array. The output signal-to-noise ratio of the test is calculated and, for a large number of independent space-time samples, is shown to be no better than a mean-level detector (MLD). Receiver operating characteristic curves (ROC) for the MLD are computed and compared to the ROC curves for the optimum (Bayes) parametric detector. The input signal-to-noise power ratios required to provide a detection probability of 0.5 differ by less than 0.2 dB for a fifty-element array with wide variation in false-alarm probability and time-bandwidth product. This result suggests that both the extended bivariate UMP unbiased test and the MLD perform close to the unknown UMP unbiased test for independence of a multivariate Gaussian distribution.     

An Upper Bound on Detection Probability for Fluctuating Signals

In the theory of signal detectability, the signal-to-noise ratio (SNR), defined as the quotient of the average received signal energy and the spectral density of the white Gaussian noise, is a fundamental parameter. For a signal which is exactly known, or known except for a random phase, this ratio uniquely defines the detection performance which can be achieved with a matched filter receiver. However, when the signal amplitude is a random parameter, the detection performance is changed and must be determined from the probability density function (pdf) of the amplitude. Relative to the case of a constant signal amplitude, such signal amplitude fluctuation usually degrades performance when a high probability of detection (Pd) is required, but improves performance at low values of Pd; the corresponding change in the required SNR is the so-called signal fluctuation loss Lf. Thus, since Lf in some cases represents an improvement in performance for low values of Pd, a question of at least theoretical interest is: how large might this improvement be, when the class of all signal amplitude pdf's is considered. The solution, presented here, results in a lower bound on the signal fluctuation loss Lf as a function of Pd, or equivalently an upper bound on Pd as a function of SNR. The corresponding most favorable pdf was determined using the Lagrange multiplier technique and results of a numerical maximization are included to provide insight into the general properties of the solution.     

Distributions of Radar Angels

A foremost characteristic of large dot radar angels is the wide variation of basic parameter values which they exhibit. This variation is traceable to the nature of the underlying phenomena, i.e., birds and flocks of birds. In this paper, statistical distribution models for the mean radar cross section (RCS) and density of radar angels are obtained, based on a combination of radar and direct ornithological data. The radar cross-section distribution model has been derived from a dimensionless RCS versus wavelength model for individual birds, obtained from measured RCS data which have been scaled to a dimensionless form. This model is applied to ornithological data on populations of birds. The density distribution model is based on statistical reduction of migratory bird data obtained by Lowery's moon watching experiment, and observed seasonal and diurnal variations of radar angel activity. Both resulting distribution models are closely appproximated by the log-normal distribution. The model parameters for these distributions are given.     

On Signal and Noise Level Estimation in a Coherent PCM Channel

Joint maximum likelihood estimators are presented for the signal amplitude and noise power density in a coherent PCM channel with white Gaussian noise and a correlation receiver. The estimates are based upon the correlation coefficient outputs of the receiver. From these estimators, an estimator for the quantity (received signal energy)/bit/,(noise power)/(unit bandwidth) upon which the error probabilities depend, is derived. This estimator is shown to be useful as 1) a point estimator for the signal-to-noise ratio for the higher values of this ratio (about 4 dB or greater), and 2) an easily calculated statistic upon which to base data acceptance or rejection criteria. The acceptance or rejection levels are obtained by the use of confidence interval curves in conjunction with word error probability data.     

Optimum Adaptive Reception for Binary Sequences

The a posteriori probability density function p(?|X1, X2,...,Xk), where the Xi, i=1, 2, ..., K, represent Kvector-valued observations statistically related to the random vector ?, appears in many applications of the methods of statistical inference to problems in pattern recognition and statistical communication theory. In this paper, it is shown that for equally likely binary sequences (M= 2) of anticorrelated patterns for signals observed in additive Gaussian noise, a device that computes p?|X1, X2, XK) can be synthesized from a correlator, a simple instantaneous nonlinearity, and a multiplier. These results are used to derive some equally simple structures for various optimum nonsupervised estimators, pattern recognition machines, and signal detectors.