Robust detection of known signals in asymmetric noise

The detection of signals in noise with possibly asymmetric probability density functions is considered. The noise density model allows a symmetric contaminated-nominal central part and an arbitrary tail behavior. For detection of known signals, the robust nonlinear-correlator (NC) detector is obtained based on detector efficacy as performance criterion. The robustM-detector structure for constant-signal detection is also explicitly obtained.     

The good, bad and ugly: distributed detection of a known signal in dependent Gaussian noise

Most results about quantized detection rely strongly on an assumption of independence among random variables. With this assumption removed, little is known. Thus, in this paper, Bayes-optimal binary quantization for the detection of a shift in mean in a pair of dependent Gaussian random variables is studied. This is arguably the simplest meaningful problem one could consider. If results and rules are to be found, they ought to make themselves plain in this problem. For certain problem parametrizations (meaning the signals and correlation coefficient), optimal quantization is achievable via a single threshold applied to each observation-the same as under independence. In other cases, one observation is best ignored or is quantized with two thresholds; neither behavior is seen under independence. Further, and again in distinction from the case of independence, it is seen that in certain situations, an XOR fusion rule is optimal, and in these cases, the implied decision rule is bizarre. The analysis is extended to the multivariate Gaussian problem.     

Comparison of known signal detection schemes under a weaklydependent noise model

The authors consider the discrete-time signal detection problem under the presence of additive noise exhibiting weak dependence. They first propose a weakly dependent noise model, in which the additive noise is modelled as a moving average process. They derive the locally optimum, memoryless, and one-memory detector test statistics under the model. The asymptotic performance of the one-memory detector is compared with that of the locally optimum and memoryless detectors. Specific examples for the asymptotic performance comparison of these detectors are considered. The authors also investigate the finite sample-size performance of several detectors through Monte-Carlo simulation. It is observed that the one-memory detector can achieve almost optimum performance at the expense of only one memory unit under the weakly dependent noise model, and is rather insensitive to slight model change     

A projection method for signal detection in colored Gaussian noise

The problem of the detection of known signals in colored Gaussian noise is usually studied through infinite-series representations for the signals and noise. In particular, the Karhunen-Loève (K-L) expansion is often used for this purpose. Such infinite-series methods, while elegant, often introduce mathematical complications because they raise questions of convergence, interchange of orders of integration, etc. The resolution of these problems is difficult and has led, when the K-L expansion is used, to the introduction of subsidiary conditions whose physical meaning is often unclear. We present a method of reducing the detection problem to a finite-dimensional form where many of the difficulties with the infinite-series K-L expansion do not arise. The resulting simplicity provides more direct derivations of and more physical insights into several earlier results. It has also suggested some new results. The method is essentially based on the use of a projection in a special kind of Hilbert space called a reproducing kernel Hilbert space.     

On the detection of known binary signals in Gaussian noise of exponential covariance

The optimum test statistic for the detection of binary sure signals in stationary Gaussian noise takes a particularly simple form, that of a correlation integral, when the solution, denoted byq(t), of a given integral equation is well behaved(L_{2}). For the case of a rational noise spectrum, a solution of the integral equation can always be obtained if delta functions are admitted. However, it cannot be argued that the test statistic obtained by formally correlating the receiver input with aq(t)which is notL_{2}is optimum. In this paper, a rigorous derivation of the optimum test statistic for the case of exponentially correlated Gaussian noiseR(tau) = sigma^{2} e^{-alpha|tau|}is obtained. It is proved that for the correlation integral solution to yield the optimum test statistic whenq(t)is notL_{2}, it is sufficient that the binary signals have continuous third derivatives. Consideration is then given to the case where a, the bandwidth parameter of the exponentially correlated noise, is described statistically. The test statistic which is optimum in the Neyman-Pearson sense is formulated. Except for the fact that the receiver employsalpha_{infty}(which in general depends on the observed sample function) in place ofalpha, the operations of the optimum detector are unchanged by the uncertainty inalpha. It is then shown that almost all sample functions can be used to yield a perfect estimate ofalpha. Using this estimate ofalpha, a test statistic equivalent to the Neyman-Pearson statistic is obtained.     

高斯白噪声信道下的弱信号盲检测方法

在电子侦察领域中,由于信号先验信息的缺失,传统时域检测方法的检测效果并不理想,变换域检测方法被大量应用,其中频域检测方法是应用最多且性价比最高的。在由时域向频域的信号变换中,DFT运算虽然可以改善信噪比,但在信号较弱时,需要做点数较多的DFT运算以满足检测器要求。提出一种基于噪声迭代估计的虚拟杂波参考通道建立方法,以减少双通道频域CFAR检测方法对硬件条件的依赖。在频域CA-CFAR检测方法现有研究成果的基础上引入非相干积累方法,在经过一定次数的频域能量积累后,保持信号频域峰均比不变的同时降低噪声的频域峰均比,得到了较优的检测性能。通过仿真分析两种算法经过一定次数非相干积累以及对门限进行一定的经验修正后,可得到虚警率和漏警率均小于0.1%的检测门限。     

Robust detection of known signals

The problem of detection of known signals in additive noise is solved under the assumption that the unknown noise density is a member of some known family of symmetric densities. A general approach to the design of receivers that are asymptotically most robust is established. As an example, a detector is derived by applying the procedure to the special case obtained when the noise density family is defined byF=left{f left| int^{a}_{-a} f(x) dx = p, f mbox{symmetric} right}.Simulation results showing the detector's performance for small sample sizes are provided.     

An integral relevant to the detection of a signal in polarized Gaussian noise (Corresp.)

An integral is calculated that arises while determining the probability of detecting a signal in polarized Gaussian noise and the probability of hitting a particular elliptical target with an imperfect weapon.     

Optimum detection of Gaussian signal fields in the multipath-anisotropic noise environment and numerical evaluation of detection probabilities

The optimum detector of Gaussian signal fields in the multipath-anisotropic noise environment is derived. The optimum detector consists of a series of matched quadratic filters and a decisionmaker. The filters are spatially and temporally matched to the eigenwaves of the signal-to-noise covariance, and the decisionmaker compares a quadratic form with a preassigned threshold. The optimum detector for single-path signals in isotropic white noise is the well-known delay-and-sum beamformer, which is widely used because of its simple structure. In the case of multipath signals in anisotropic noise, a substantial improvement in detection performance is possible over the beamformer. This is shown by numerically comparing the detection probability of the beamformer with that of the optimum detector for this case. In addition, we numerically evaluate the sensitivity of such an improvement to accurate knowledge of the signal and noise parameters that are required by the optimum detector. We also show the possibility of further improvement by the addition of a vertical segment to the commonly used horizontal linear array to provide sensitivity to the elevation angles of multipath signals.     

Optimal, causal, simultaneous detection and estimation of random signal fields in a Gaussian noise field

Two methods are presented for simultaneously detecting a random signal field and estimating its Markovian parameters in the qq prurience of a white Gaussian noise field. The first method provides the Neyman-Pearson decision rule for determining the absence-or-presence of the signal and the maximum {em a posteriori} likelihood estimators of the parameters. The second provides the Bayes decision rule for the absence-or-presence of the signal and the minimum mean-square error estimators of the parameters. Both methods allow continual causal detection and estimation based on the continuous space-time data, and their detection and estimation statistics are given in terms of a single statistic, which is the solution of a certain stochastic integral equation. Furthermore, an approximate scheme is developed for recursively generating this statistic by using spatially and temporally sampled data.     

Robust detection of signals in dependent noise

The robust detection of signals in additive dependent noise is considered. The solution to the finite-sample problem is obtained when the Bayes risk is used as the performance measure. For the multivariate densities involved we assume that they belong to an e-contamination model. The robust detection structure is shown to be optimum for the least-favorable density and is a censored version of the nominal likelihood ratio.     

On the detection of a signal in colored noise

A modeling approach is used in the detection of a random signal in colored noise. The received sequence is modeled as a regressive/autoregressive time series, and the presence or absence of the desired signal is determined through a hypothesis testing procedure. The test is based on the construction of anF-statistic using likelihood functions. The statistic can be easily incorporated into the computation of the probability of a false alarm, such as required in the processing of radar signals. Results based on simulated data and actual radar data are presented.This research was supported by NSERC Grant No. A3635.     

Partition noise in CCD signal detection

Reset noise in CCD signal charge detection is analyzed experimentally and theoretically. From a reset noise measurement experiment, it has been inferred that reset noise consists of two parts: the sensing capacitance (Cs) dependent part and the effective reset channel length (L) dependent part. Conventional reset noise theory, where the Johnson noise in the reset MOS channel was regarded as the only noise source, agrees with the Csdependent part of measured reset noise. However, it cannot explain the L dependent part. To explain theLdependence, the authors propose "partition noise" caused by carrier partition in the reset MOS channel. Partition noise is analyzed by the unique technique of solving the one-dimensional diffusion equation. As a result, a reset channel capacitance dependent characteristic for partition noise has been derived, which agrees with theLdependent part for measured reset noise. Consequently, in addition to Johnson noise, partition noise is found to be a noise source in CCD signal detection.     

Asymptotic performance of a distributed detection system incorrelated Gaussian noise

The authors consider the detection of a constant signal in noise with a large set of geographically dispersed sensors. The noise at the sensors is correlated Gaussian. Two correlation models are considered: one where the correlation coefficient between any two sensors decreases geometrically as the sensor separation increases, and one in which the correlation coefficient between any two sensors is a constant. For both correlation models, the asymptotic (as the number of sensors becomes large) performances of a distributed detection system and a central system are examined     

Detection of a known signal in colored Gaussian noise---A new coordinate approach (Corresp.)

The classical problem of detecting a known signal in additive colored Gaussian noise on a finite interval is considered by using as "coordinates" (observables) the inner products formed between the received waveform and the elements of a simply constructed complete set of functions defined on the observation interval. Results of the Karhunen-Loève (K-L) approach are thereby obtained without the K-L expansion or any appeal to results from integral equation theory.     

Robust Gaussian and non-Gaussian matched subspace detection

We address the problem of matched filter and subspace detection in the presence of arbitrary noise and interference or interfering signals that may lie in an arbitrary unknown subspace of the measurement space. A minmax methodology developed to deal with this uncertainty can also be adapted to situations where partial information on the interference or other uncertainties is available. This methodology leads to a hypothesis test with adequate levels of false alarm robustness and signal detection sensitivity. The robust test is applicable to a large class of noise density functions. In addition, generalized likelihood ratio (GLR) detectors are derived for the class of generalized Gaussian noise. The detectors are generalizations of the /spl chi//sup 2/, t, and F statistics used with Gaussian noise, which are themselves motivated in a new way by the robust test. For matched filter detection, these expressions are simpler and computationally efficient. The robust test reduces to the conventional test when unlearned subspace interference is known to be absent. The results demonstrate that when compared with the conventional detector, the robust one trades off some detection performance in the absence of interference for the sake of robustness in its presence.     

Phase derivative distribution of signal and Gaussian noise sum

Characteristic function and integral function of the phase derivative distribution of harmonic signal and narrowband Gaussian noise sum are obtained for the case when the signal’s central frequency coincides with the central frequency of noise spectrum. It is shown that the power series for the distribution density of the phase derivative is determined by odd moments of the envelope.     

Robust noise detection for speech detection and enhancement

A simple and robust method of reliably detecting stationary noise periods in a mobile telephony environment is presented. Such noise detection techniques are useful for updating parameters in adaptive voice activity detectors and for speech enhancement techniques, such as spectral subtraction, which require accurate noise models