Closed-loop linear model validation and order estimation usingpolyspectral analysis

Suppose that we perform closed-loop linear system identification using polyspectral analysis given noisy time-domain input-output measurements. In this setup, it is assumed that various disturbances affecting the system are zero-mean stationary Gaussian, whereas the closed-loop system operates under an external (possibly noisy) non-Gaussian input. The closed-loop system must be stable, but it is allowed to be unstable in the open loop. Various techniques have been proposed for system identification using polyspectral analysis. Having obtained a model, how do we know if the fitted model is “good?” This paper is devoted to the problem of statistical model validation using polyspectral analysis. We propose simple statistical tests based on the estimated polyspectrum (integrated bispectrum and/or integrated trispectrum) of an output error signal or the estimated cross-polyspectrum between the external reference and the output error signal. Model order estimation is performed by repeatedly using the model validation procedure. Computer simulation examples are presented in support of the proposed approaches     

Narrowband weak signal detection by higher order spectrum

A study of narrowband weak signal detection by higher order spectrum (HOS) using real signals and real noise, rather than just Gaussian noise, is presented. Noisy real signals are processed using various HOS techniques. We propose to look at the diagonal slices of the bispectrum and the trispectrum as possible substitutes for the power spectrum. The result of applying these slices to weak, real signals is surprisingly good. The dramatic improvements are presented for visual inspection. The performance of the various techniques are then compared quantitatively for different signal-to-noise ratios. The diagonal slices prove to be fast and robust techniques for weak signal detection     

基于高阶统计量的多模噪声中的信号检测

按照概率密度函数形状,给出了一种比较通用的非高斯噪声模型——多模噪声。多模噪声总体上属于非高斯噪声,但兼容了高斯噪声。改进了高阶统计量的双谱算法,给出一种基于双谱的多模噪声中信号的检测方法,并在此基础上结合无惯性非线性变换器和双谱技术,改进了传统的自适应幅频干扰抑制器,可以精确估计或检测信号。仿真表明该方法可以抑制高斯噪声,同时在强噪声和复杂背景下可以以较高的检测概率检测出信号,优于传统的似然比检测。     

Detection of non-Gaussian signals by bispectrum-U detector

A method for detecting non-Gaussian stationary signals in additive Gaussian noise using a bispectrum-U test is presented. The performance of the proposed detection statistic is compared to the conventional bispectrum χ² detector     

Detection of weak signals in non-Gaussian noise

A locally optimum detector structure is derived for the detection of weak signals in non-Gaussian environments. Optimum performance is obtained by employing a zero-memory nonlinearity prior to the matched filter that would be optimum for detecting the signal were the noise Gaussian. The asymptotic detection performance of the locally optimum detector under non-Gaussian conditions is derived and compared with that for the corresponding detector optimized for operations in Gaussian noise. Numerical results for the asymptotic detection performance are shown for signal detection in noise environments of practical interest.     

Detecting a transient signal by integrated polyspectrum

A method for detecting a transient signal in additive Gaussian noise via an integrated polyspectrum is presented. The performance of the proposed detection statistic, relative to a conventional energy detector and a bispectral detector is demonstrated     

Generalized compressive detection of stochastic signals using Neyman–Pearson theorem

Compressive sensing (CS) enables reconstructing a sparse signal from fewer samples than those required by the classic Nyquist sampling theorem. In general, CS signal recovery algorithms have high computational complexity. However, several signal processing problems such as signal detection and classification can be tackled directly in the compressive measurement domain. This makes recovering the original signal from its compressive measurements not necessary in these applications. We consider in this paper detecting stochastic signals with known probability density function from their compressive measurements. We refer to it as the compressive detection problem to highlight that the detection task can be achieved via directly exploring the compressive measurements. The Neyman–Pearson (NP) theorem is applied to derive the NP detectors for Gaussian and non-Gaussian signals. Our work is more general over many existing literature in the sense that we do not require the orthonormality of the measurement matrix, and the compressive detection problem for stochastic signals is generalized from the case of Gaussian signals to the case of non-Gaussian signals. Theoretical performance results of the proposed NP detectors in terms of their detection probability and the false alarm rate averaged over the random measurement matrix are established. They are verified via extensive computer simulations.     

Clairvoyant and adaptive signal detection in non-Gaussian clutter:a data-dependent threshold interpretation

This paper addresses the problem of signal detection in correlated non-Gaussian clutter modeled as a spherically invariant random process. The optimum strategy to detect a constant signal, with either known or unknown complex amplitude, embedded in correlated Gaussian clutter is given by comparing the whitening-matched filter output with a fixed threshold. When the clutter is non-Gaussian, the performance of the matched filter sensibly degrades. The optimum strategy is the classical whitening-matched filter output compared with a data-dependent threshold. This interpretation provides a deeper insight into the structure of the optimum detector and allows us to single out a family of suboptimum detectors based on a polynomial approximation of the data-dependent threshold. They are easy to implement and have performance that is really close to the optimal. The adaptive implementation of the polynomial detectors is also investigated, and their performance is analyzed by means of Monte Carlo simulation for various clutter scenarios     

Signal Activity Detection of Phase-Shift Keying Signals

We propose computationally inexpensive and efficient solutions for signal activity detection of phase-shift keying (PSK) signals in additive white Gaussian noise. We consider the complex amplitude of the signal as well as the information sequence as the unknown parameters. In addition, the noise variance is assumed unknown. We derive the generalized likelihood ratio test (GLRT) and suggest a computationally efficient implementation thereof. Furthermore, we develop a new inexpensive detector for binary PSK signals, which we will refer to as the generalized energy detector. To evaluate the performance of these detectors, we attempt to derive a uniformly most powerful invariant test (UMPI) as an optimal detector. It turns out that the UMPI test exists only if the signal-to-noise ratio is known. We use this UMPI test in order to obtain an upper-bound performance for the evaluation of invariant detectors, such as the above-mentioned GLRT. Simulation results illustrate and compare the performance and the efficiency of the proposed signal activity detectors.     

A CFAR adaptive subspace detector for second-order Gaussian signals

We study the problem of detecting subspace signals described by the Second-Order Gaussian (SOG) model in the presence of noise whose covariance structure and level are both unknown. Such a detection problem is often called Gauss-Gauss problem in that both the signal and the noise are assumed to have Gaussian distributions. We propose adaptive detectors for the SOG model signals based on a single observation and multiple observations. With a single observation, the detector can be derived in a manner similar to that of the generalized likelihood ratio test (GLRT), but the unknown covariance structure is replaced by sample covariance matrix based on training data. The proposed detectors are constant false alarm rate (CFAR) detectors. As a comparison, we also derive adaptive detectors for the First-Order Gaussian (FOG) model based on multiple observations under the same noise condition as for the SOG model. With a single observation, the seemingly ad hoc CFAR detector for the SOG model is a true GLRT in that it has the same form as the GLRT CFAR detector for the FOG model. We give an approximate closed form of the probability of detection and false alarm in this case. Furthermore, we study the proposed CFAR detectors and compute the performance curves.     

Signal detection using third-order moments

The noise suppression capability of higher-order moments and spectra has made them attractive when the goal is to extract or reconstruct a signal that is contaminated by multivariate Gaussian noise or certain types of non-Gaussian noise. Two new detectors, one centralized and one distributed, which are based on the third-order moment of the data are proposed. The asymptotic performance of the centralized detector and the asymptotic distribution of the components of the distributed detector are analyzed. Further, the performance of these detectors is simulated and compared to that of the matched filter for three different types of interference: Gaussian noise, Gaussian noise corrupted by a sinusoid with random phase, and Arctic under-ice noise.     

基于分数低阶统计量的双谱及其估计方法

稳定分布可更好地描述实际中所遇到的具有显著脉冲特性的随机噪声.为了更好地抑制信号背景中的非高斯噪声,本文提出了基于分数低阶的双谱定义,并给出在分数低阶有色噪声背景下双谱非参数和参数模型的估计方法.仿真结果表明,同传统的双谱估计相比较,非参数法分数低阶双谱估计能有效的识别信号,保留了信号的幅度和相位信息,但存在较大的估计方差.基于AR模型的分数低阶双谱估计具有最大的谱平坦度,能够有效地抑制噪声,具有良好的韧性.     

高阶累积量在红外热像损伤检测信号分析中的应用

针对常规红外检测信号的脉冲相位法没有考虑测量噪音,简单的Fourier变换对数据信息的挖掘不足、利用率不高的问题,提出在处理中引入非高斯特性分析,应用三阶累积量和双谱估计对信号进行分析,提取发生损伤时信号的特性信息,得到分辨完好区域与损伤区域的特征判据。给出信号分析中三阶累积量和双谱的定义,分析其幅值和相位的对角切片谱在提取损伤特征方面的优势,最后对比分析两者在实际检测中的效果。结果表明:利用该方法具有良好的抗高斯和非高斯对称分布型噪音的优点,且运算量小、计算速度快。同时,弥补了传统脉冲相位法中幅值谱不宜使用的缺点。     

A note on power-law devices and their effect on signal-to-noise ratio

The effect of power-law devices, used as either band-pass nonlinear amplifiers or envelope detectors, on the signal-to-noise ratio is determined for both limiting cases of very large and very small input signal-to-noise ratio. Expressions are derived for the degradation in signal-to-noise ratio in terms of the envelopes and phases of the signal and noise. The results are general, applying to Gaussian and non-Gaussian noises and modulated and unmodulated signals, and allow important conclusions to be reached concerning the value of power-law devices in communications systems in various signal and noise environments. It is found that band-pass nonlinear amplifiers can generally be chosen to improve the signal-to-noise ratio if the input signal-to-noise ratio is small and the noise is non-Gaussian. Envelope detectors usually degrade the signal-to-noise ratio since they exhibit a "small-signal suppression" effect in all noise environments except for the special case of unmodulated sine-wave interference.     

Detection of weak random signals in IID non-Gaussian noise

This paper considers the detection of weak random signals in circularly symmetric, independent, identically distributed noise. Locally optimum detectors and ad hoc nonlinearities are considered, with asymptotic expressions provided for evaluation of detection performance. The analytical expressions are used to evaluate the robustness of detectors to mismatch in the noise models. Finite-sample Monte Carlo simulation results indicate the reliability of these asymptotic measures in cases of practical interest. The results show that, as has been found for detection of weak known signals in non-Gaussian noise, reasonably configured ad hoc nonlinearities are nearly optimum and robust to modest errors in the noise statistics     

Suboptimum detection of weak signals in non-Gaussian noise (Corresp.)

A suboptimum detector structure is developed for the detection of weak signals in non-Gaussian noise. In contrast to locally optimum detectors, the suboptimum detector structure is relatively easy to implement and is shown to perform well for a wide range of underlying noise distributions. The robustness of simple limiter detectors is discussed. The extension of the concept of a suboptimum detector to an adaptive detector for operating in an unknown noise environment is also discussed.     

A geometrical interpretation of signal detection and estimation (Corresp.)

By introducing an appropriate representation of the observation, detection problems may be interpreted in terms of estimation. The case of the detection of a deterministic signal in Gaussian noise is associated with two orthogonal subspaces: the first is the signal subspace which is generally one dimensional and the second is called a reference noise alone (RNA) space because it contains only the noise component and no signal. The detection problem can then be solved in the signal subspace, while the use of the RNA space is reduced to the estimation of the noise in the signal subspace. This decomposition leads to a very simple interpretation of singular detection, even in the non-Gaussian case, in terms of perfect estimation. The method is also extended to multiple signal detection problems and to some special cases of detection of random signals.     

威伯尔和对数正态噪声中的检测问题

本文研究窄带非高斯(non-Gaussian)噪声中窄带相参和非相参脉冲串信号的离散时间检测。导出了局部最佳(LO)检测器结构,它具有在窄带高斯噪声中的尼曼-皮尔逊(Neyman-Pearson)最佳检测器里引入局部最佳零记忆非线性(LOZNL)的形式。许多实用检测器属于与LO检测器相同类型的结构,导出了这些检测器功效的表达式,特别研究了威伯尔(Weibull)和对数正态噪声模型。导出了LOZNL和检测器功效,并用曲线给出了数值结果。说明在皮特曼(Pitman)的渐近相对效率(ARE)意义上,许多具有能更多抑制噪声包络分布尾部的非线性的检测器,其渐近性能明显优于窄带高斯噪声中的尼曼-皮尔逊最佳检测器。     

Detection in weibull and log-normal noises

The discrete-time detection of narrowband coherent and incoherent pulse train signals in narrowband non-Gaussian noise is investigated. The locally optimum (LO) detector structures are developed and found to be in the form of incorporating a locally optimum zero-memory nonlinearity (LOZNL) into the Neyman-Pearson optimum detector for narrowband Gaussian noise. Many practical detectors belong in the same class of structures with the LO detector. The expressions for the efficacies of the detectors are derived. In particular, Weibull and log-normal noise models are considered. The LOZNL’s, and the efficacies of the detectors are given, and numerical results are graphically presented. It is shown that, in the sense of the Pitman asymptotic relative efficiency (ARE), the asymptotic performance of many detectors whose nonlinearity can more effectively suppress the tail of the noise envelope distribution is apparently better than that of the Neyman-Pearson optimum detector for narrowband Gaussian noise.     

ARMA modeling of fourth-order cumulants and phase estimation

A new procedure is proposed for ARMA modeling of fourth-order cumulants and trispectrum estimation of non-Gaussian stationary random processes. The new procedure is applied to the identification of nonminimum phase systems for both phase and magnitude response estimation. It is demonstrated by means of comprehensive simulation examples that the ARMA approach exhibits improved performance over conventional trispectrum methods. ARMA model order selection criteria based on fourth-order cumulants are presented and their performance evaluated. The computational complexity of the ARMA and conventional trispectrum methods is also examined. The new procedure does not require knowledge of the non-Gaussian distribution.This work was supported by the Office of Naval Research under Contract No. ONR-N00014-86-K-0219.