On the correlation function of signal plus Gaussian noise passed through nonlinear devices (Corresp.)

This correspondence discusses the transformations between the output autocorrelation functions of functionally related zero-memory nonlinear devices excited by signal plus Gaussian noise. The results are applied to show how output autocorrelation functions can easily be obtained for exponential and half-wave power law devices.     

The correlation function of Gaussian noise passed through nonlinear devices

This paper is concerned with the output autocorrelation functionR^{y}of Gaussian noise passed through a nonlinear device. An attempt is made to investigate in a systematic way the changes inR^{y}when certain mathematical manipulations are performed on some given device whose correlation function is known. These manipulations are the "elementary combinations and transformations" used in the theory of Fourier integrals, such as addition, differentiation, integration, shifting, etc. To each of these, the corresponding law governingR^{y}is established. The same laws are shown to hold for the envelope of signal plus noise for narrow-band noise with spectrum symmetric about signal frequency. Throughout the text and in the Appendix it is shown how the results can be used to establish unknown correlation function quickly with main emphasis on power-law devicesy = x^{m}withmeither an integer or half integer. Some interesting recurrence formulas are given. A second-order differential equation is derived which serves as an alternative means for calculatingR^{y}.     

Robust detection of a known signal in nearly Gaussian noise

A detector that is not nonparametric, but that nevertheless performs well over a broad class of noise distributions is termed a robust detector. One possible way to obtain a certain degree of robustness or stability is to look for a min-max solution. For the problem of detecting a signal of known form in additive, nearly Gaussian noise, the solution to the min-max problem is obtained when the signal amplitude is known and the nearly Gaussian noise is specified by a mixture model. The solution takes the form of a correlator-limiter detector. For a constant signal, the correlator-limiter detector reduces to a limiter detector, which is shown to be robust in terms of power and false alarm. By adding a symmetry constraint to the nearly normal noise and formulating the problem as one of local detection, the limiter-correlator is obtained as the local min-max solution. The limiter-correlator is shown to be robust in terms of asymptotic relative efficiency (ARE). For a pulse train of unknown phase, a limiter-envelope sum detector is also shown to be robust in terms of ARE.     

Two-dimensional memoryless detection of a random signal inphi-mixing non-Gaussian noise (Corresp.)

The problem is considered of designing memoryless detection systems for detecting random signals in qb-mixing noise environments. Assuming that the bivariate densities of the noise can be expressed in an infinite series expansion, the nonlinearity is expressed as a series expansion and the coefficients are found that maximize the asymptotic relative efficiency.     

Interaction of a post-threshold signal and a weak microwave signal during passage through a ferrite-film noise suppressor

The interaction of a post-threshold signal and a weak signal in a noise suppressor based on a microstrip line loaded with an yttrium-iron-garnet (YIG) epitaxial film is studied experimentally. It is demonstrated that anomalous fragments may emerge in the weak-signal transmission spectrum at frequencies that correspond to the excitation of magnetostatic surface waves (MSSWs) in the YIG film in the presence of a post-threshold signal with supercriticality C of ≈ 7–30 dB. The frequencies that correspond to these fragments may differ from the frequency of the post-threshold signal by 10–400 MHz and are equal to the frequencies corresponding to the anomalous fragments in the dispersion relation of a weak MSSW.     

Optimal detection of a BPSK signal contaminated by interference andnoise

The problem of detecting a desired binary phase-shift keying (BPSK) modulated bit in the presence of a second BPSK modulated interfering signal and additive white Gaussian noise is considered. Given knowledge of the amplitudes and phases of the unmodulated signals received from the two transmitters, the minimum achievable bit error rate is obtained and compared with that for a conventional matched filter detector. It is shown that the performance difference can be quite large when the interfering signal is strong     

Innovations informational equivalence for a class of observationswith independent non-Gaussian noise

The problem of innovations informational equivalence for observations with non-Gaussian additive noise is addressed. It is assumed that the additive noise is a non-Gaussian continuous martingale with an almost surely absolutely continuous quadratic covariation process. Under the assumptions of stochastic independence between the signal and the noise and of square integrability conditions on them, it is shown that the non-Gaussian innovations process, i.e., a non-Gaussian martingale adapted to the observation, is informationally equivalent to the observation     

Robust watermarking against print and scan attack through efficient modeling algorithm

This article proposes a blind discrete wavelet transform-discrete cosine transform (DWT-DCT) composite watermarking scheme that is robust against print and scan distortions. First, two-dimensional DWT is applied to the original image to obtain the mid-frequency subbands. Then, a one-dimensional DCT is applied to the selected mid-frequency subbands to extract the final coefficients for embedding the watermark. To specify watermarking parameters, we utilize a Genetic Algorithm to achieve a predefined image quality after watermark insertion. Suitable locations for watermarking are determined by analyzing the effect of a modeling algorithm. This model simulates noise and nonlinear attacks in printers and scanners through noise estimation and system identification methods. The experimental results demonstrate that the proposed algorithm has a high robustness against print and scan attack such that its robustness is higher than related watermarking algorithms.     

DOA estimation in unknown colored noise using covariance differencing and sparse signal recovery

A direction-of-arrival （DOA） estimation algorithm is presented based on covariance differencing and sparse signal recovery, in which the desired signal is embedded in noise with unknown covariance. The key point of the algorithm is to eliminate the noise component by forming the difference of original and transformed covariance matrix, as well as cast the DOA estimation considered as a sparse signal recovery problem. Concerning accuracy and complexity of estimation, the authors take a vectorization operation on difference matrix, and further enforce sparsity by reweighted l1-norm penalty. We utilize data-validation to select the regularization parameter properly. Meanwhile, a kind of symmetric grid division and refinement strategy is introduced to make the proposed algorithm effective and also to mitigate the effects of limiting estimates to a grid of spatial locations. Compared with the covariance-differencing-based multiple signal classification （MUSIC） method, the proposed is of salient features, including increased resolution, improved robustness to colored noise, distinguishing the false peaks easily, but with no requiring of prior knowledge of the number of sources.     

Modeling and measurement of simultaneous switching noise coupling through signal via transition

The signal via is a heavily utilized interconnection structure in high-density System-on-Package (SoP) substrates and printed circuit boards (PCBs). Vias facilitate complicated routings in these multilayer structures. Significant simultaneous switching noise (SSN) coupling occurs through the signal via transition when the signal via suffers return current interruption caused by reference plane exchange. The coupled SSN decreases noise and timing margins of digital and analog circuits, resulting in reduction of achievable jitter performance, bit error ratio (BER), and system reliability. We introduce a modeling method to estimate SSN coupling based on a balanced transmission line matrix (TLM) method. The proposed modeling method is successfully verified by a series of time-domain and frequency-domain measurements of several via transition structures. First, it is clearly verified that SSN coupling causes considerable clock waveform distortion, increases jitter and noise, and reduces margins in pseudorandom bit sequence (PRBS) eye patterns. We also note that the major frequency spectrum component of the coupled noise is one of the plane pair resonance frequencies in the PCB power/ground pair. Furthermore, we demonstrate that the amount of SSN noise coupling is strongly dependent not only on the position of the signal via, but also on the layer configuration of the multilayer PCB. Finally, we have successfully proposed and confirmed a design methodology to minimize the SSN coupling based on an optimal via positioning approach.     

Robust spectrum sensing for orthogonal frequency division multiplexing signal without synchronization and prior noise knowledge

Spectrum sensing is defined as the task of detecting the presence of licensed users and is an essential prerequisite for opportunistic spectrum access in cognitive radio. Motivated by the infeasible assumptions of perfect synchronization and prior noise knowledge in most of the existing spectrum sensing algorithms, a robust orthogonal frequency division multiplexing (OFDM) signal sensing scheme, with the use of a noise power insensitive threshold, is investigated in this paper. Identification of primary OFDM signals is achieved by sliding the local pilot reference over the received signals and measuring the frequency domain correlations. The necessity of prior noise power knowledge for the sensing threshold determination is removed by employing the proposed interference insensitive test metric, which is a ratio of uniformly distorted correlations. As a result, no noise power information is required in the sensing process. In addition, the effects of both timing and frequency offsets are mitigated with a novel extended time domain segmentation as well as multiple frequency domain correlations via a frequency sliding window. Numerical results are provided to validate the theoretical analysis and estimate the performance of the proposed algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

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     

Multi-resolution fourier analysis: extraction and missing signal recovery of short buried signals in noise

In this paper, proposed multi-resolution Fourier analysis, relabeled NY-MFA, recovers as a function of resolution levels brief duration signals defined for low signal-to-noise ratios. These short noisy signals are restored with their missing parts independently of the nature of noise and its frequency extent. It is shown that the variance of resolved spectral estimates is reduced proportionally to the chosen level of frequency resolution. Extraction ability of NY-MFA using no more than a single realization of noisy simulated or experimental signals outperforms that of wavelets. Moreover, missing signal recovery of buried signals in the time domain, called here natural extrapolation, is achieved without errors. It is shown that NY-MFA is a promising signal processing tool.     

射频连接器振动对信号相位噪声的影响

振动环境作用于射频连接器会影响信号的相位噪声。为了提高通信质量,研究了振动对射频连接器相位噪声的影响。分析了振动条件下射频连接器对通过其中的高频信号产生相位噪声的基本原理,推导出了机械振动参数与其产生的相噪功率谱之间的数学关系,验证了振动对不同频率信号的影响关系,并在相应的试验中验证了推导结果的正确性。相关研究结果对分析射频连接器的工程应用中振动对信号的影响具有指导作用。     

Enhanced sequence detector in the presence of intersymbol interference and non-Gaussian noise

A new Viterbi equaliser is proposed for joint mitigation of intersymbol interference and impulsive noise. The new equaliser uses a robust branch metric incorporating the Talwar penalty function. It is shown that the proposed equaliser facilitates considerable performance improvements.     

Detection of non-Gaussian signals: a paradigm for modernstatistical signal processing [and prolog]

Non-Gaussian signals arise in a wide variety of applications, including sonar, digital communications, seismology, and radio astronomy. In this tutorial overview, a hierarchical approach to signal modeling and detector design for non-Gaussian signals is described. In addition to being of interest in applications, this problem serves as a paradigm within which most of the areas of active research in statistical signal processing arise. In particular, the methodologies of nonlinear signal processing, higher order statistical analysis, signal representations, and learning algorithms, all can be juxtaposed quite naturally in this framework     

Phase and logarithm of amplitude of a signal plus noise

The mean and variance of the logarithm of the amplitude of a signal plus noise are discussed. Ward and Tough's (see ibid., vol.24, no.2, p.85-7, 1988) explanation for the very small bias of this mean at high signal-to-noise ratios is shown to be closely related to the capture effect in FM reception     

Robust parameter estimation of a deterministic signal in impulsivenoise

This paper presents a robust class of estimators for the parameters of a deterministic signal in impulsive noise. The proposed technique has the structure of the maximum likelihood estimator (MLE) but has an extra degree of freedom: the choice of a nonlinear function (which is different from the score function suggested by the MLE) that can be adjusted to improve robustness. The effect of this nonlinear function is studied analytically via an asymptotic performance analysis. We investigate the covariance of the estimates and the loss of efficiency induced by nonoptimal choices of the nonlinear function, giving special attention to the case of α-stable noise. Finally, we apply the theoretical results to the problem of estimating the parameters of a sinusoidal signal in impulsive noise     

Detection and estimation of signals in noise when one or both are non-Gaussian

An examination is made of the basic principles and results of the theory of detection and estimation of signals in noise, which is not limited to the condition that the useful signal and noise be Gaussian and that the noise be additive. Formulas are obtained [(23) and (25)] for likelihood ratios which are useful in the Markovian as well as in the non-Markovian case. The results are specialized for the case of diffusion noise and fixed but unknown signal parameters, when it is possible to effectively utilize the theory of conditional Markov processes. Estimation by the quasi-linear theory is also discussed, the applicability of which is limited not by the Markovian condition, but by the condition of high a posteriori accuracy. In conclusion, a generalization is given of the theory for the case of adaptive detection and estimation, when the a priori information is replaced by learning. In this case, application of the theory of conditional Markov processes makes it possible to obtain, besides the previous equations of Gaussian approximation, similar equations for the unknown parameters.     

一种低噪声微弱信号调理电路设计

水下主动声纳探测系统是通过发射换能器发射主动声信号,水听器检测回波信号完成目标探测和方位估计等任务。由于水听器输出信号微弱,易被复杂的海洋环境噪声干扰不能直接用于后续采集电路,要求信号调理电路具有高增益并且自噪声远低于水听器输出信号。而且主动声呐工作在近距离时,水听器接收到的混响信号远高于目标的回波信号,水听器接收到的信号动态范围大。本文提出的一种低噪声微弱信号调理电路,是一种低噪声、高增益、大动态范围、高一致性的信号调理电路。