Signals In non-Gaussian Noise Research Articles

Multi-Objective Grasshopper Optimization Based MPPT and VSC Control of Grid-Tied PV-Battery System

This article presents the control of a three-phase three-wire (3P-3W) dual-stage grid-tied PV-battery storage system using a multi-objective grass-hopper optimization (MOGHO) algorithm. The voltage source converter (VSC) control of the presented system is implemented with adaptive kernel width sixth-order maximum correntropy criteria (AKWSOMCC) and maximum power point tracking (MPPT) control is accomplished using the variable step-size incremental conductance (VSS-InC) technique. The proposed VSC control offers lower mean square error and better accuracy, convergence rate and speed as compared to peer adaptive algorithms, i.e., least mean square (LMS), least mean fourth (LMF), maximum correntropy criteria (MCC), etc. The adaptive Gaussian kernel width is a function of the error signal, which changes to accommodate and filter Gaussian and non-Gaussian noise signals in each iteration. The VSS-InC based MPPT is provided with a MOGHO based modulation factor for better and faster tracking of the maximum power point during changing solar irradiation. Similarly, an optimized gain conventional PI controller regulates the DC bus to improve the power quality, and DC link stability during dynamic conditions. The optimized DC-link generates an accurate loss component of current, which further improves the VSC capability of fundamental load current component extraction. The VSC is designed to perform multi-functional operations, i.e., harmonics elimination, reactive power compensation, load balancing and power balancing at point of common coupling during diverse dynamic conditions. The MOSHO based VSS-InC, and DC bus performance is compared to particle swarm optimization (PSO) and genetic algorithm (GA). The proposed system operates satisfactorily as per IEEE519 standards in the MATLAB simulation environment.

A KNN-Based Radar Detector for Coherent Targets in Non-Gaussian Noise

This paper proposes a decision scheme based on the $k$ -nearest neighbors rule to detect coherent signals in non-Gaussian noise modeled as the sum of K-distributed clutter plus thermal noise. The analysis is conducted also on real data recordings and shows that the proposed detector can outperform natural competitors.

Establishing the significance of continuous gravitational-wave detections from known pulsars

We present a method for assigning a statistical significance to detection candidates in targeted searches for continuous gravitational waves from known pulsars, without assuming the detector noise is Gaussian and stationary. We take advantage of the expected Doppler phase modulation of the signal induced by Earth's orbital motion, as well as the amplitude modulation induced by Earth's spin, to effectively blind the search to real astrophysical signals from a given location in the sky. We use this "sky-shifting" to produce a large number of noise-only data realizations to empirically estimate the background of a search and assign detection significances, in a similar fashion to the use of timeslides in searches for compact binaries. We demonstrate the potential of this approach by means of simulated signals, as well as hardware injections into real detector data. In a study of simulated signals in non-Gaussian noise, we find that our method outperforms another common strategy for evaluating detection significance. We thus demonstrate that this and similar techniques have the potential to enable a first confident detection of continuous gravitational waves.

Improving the frequency response of Savitzky-Golay filters via colored-noise models

Savitzky-Golay (SG) filters are finite impulse response (FIR) realizations of least-squares polynomial regression and they are widely used for filtering (e.g. smoothing, interpolating, predicting, differentiating) and processing (e.g. detecting and classifying) non-stationary signals in non-Gaussian noise. For such inputs, the Wiener filter is biased and the Kalman filter is sub-optimal. Sequentially-correlated (i.e. ‘colored’) noise models are an integral part of the Wiener filter and an optional addition to the Kalman filter; however, their use in SG-filters has been overlooked in recent times. It is shown here that colored (wide-band and narrow-band) noise models are readily incorporated into a standard SG-filter and that this also addresses the well-known deficiency of their poor frequency-selectivity/configurability. A wide-band noise model sets the main-lobe/side-lobe width/height and provides physical justification for band-limited design procedures described elsewhere. The proposed narrow-band noise model, with arbitrarily placed side-lobe nulls, has the potential to outperform other SG filters when sinusoidal interferers of known frequency are present. The utility of these ‘whitened’ SG-filters is illustrated in a hypothetical pulse/peak-detection application using a test statistic that is shaped by the noise model.

Approximate Joint MAP Detection of Co-Channel Signals in Non-Gaussian Noise

Detection of co-channel signals is important as wireless communication systems become increasingly dense. A particularly challenging case is single antenna reception in both the presence of inter-symbol interference and co-channel interference. Optimal joint maximum a posteriori probability (MAP) detection of the co-channel signals is prohibitively complex. Therefore, in this paper, we propose a factor graph-based iterative receiver which approximates joint MAP detection. In the receiver, noise is modeled with a Gaussian mixture distribution since studies have shown that the noise affecting wireless communication systems is often impulsive. Furthermore, the parameters of the factor graph model (channel and noise parameters) are iteratively estimated within the receiver. The proposed receiver is shown to the outperform state-of-the-art receiver algorithms while having a lower complexity in both Gaussian and impulsive noise. We also show significant gains from iterative parameter estimation, especially in non-Gaussian noise.

Recognition Method of Digital Modulation Signals in NonGaussian Noise

针对传统数字调制识别方法在非高斯Alpha稳定分布噪声下识别性能差的问题，该文提出一种基于广义分数阶傅里叶变换和分数低阶Wigner-Ville分布的数字调制识别新方法。该方法提取广义分数阶傅里叶变换的零中心归一化瞬时幅度谱密度的最大值和分数低阶Wigner-Ville分布幅度的最大值作为识别特征参数，并采用判决树分类器，实现了非高斯噪声下数字调制信号识别。仿真结果表明，在非高斯Alpha稳定分布噪声下，该识别方法不仅性能明显优于传统方法并且具有较高的识别率和良好的稳健性。

A robust detector of known signal in non-Gaussian noise using threshold systems

In this paper, we propose a threshold-system-based detector (TD) for detecting a known deterministic signal in independent non-Gaussian noise whose probability density function (pdf) is unknown but is symmetric and unimodal. The optimality of the proposed TD is proved under the assumptions of white noise, small signal, and a large number of samples. While previous TD designs need accurate information of the noise pdf, the proposed TD is independent of the noise pdf, and thus is robust to the noise pdf. The detection probability and the receiver operating characteristic (ROC) of the proposed TD are analyzed both theoretically and numerically. It is shown that even without knowing the noise pdf, the proposed TD has close performance to the optimal detector designed with the noise pdf information. It also performs significantly better than the matched filter (MF) when the noise pdf has heavy tails. The practical implementation, robustness to both the noise pdf and the signal, and region of validity of the proposed TD are also investigated.

Simple Detection Based on Soft-Limiting for Binary Transmission in a Mixture of Generalized Normal-Laplace Distributed Noise and Gaussian Noise

In this letter, a simplified suboptimum receiver based on soft-limiting for the detection of binary antipodal signals in non-Gaussian noise modeled as a generalized normal-Laplace (GNL) distribution combined with Gaussian noise is presented. The suboptimum receiver has low computational complexity. Furthermore, when the number of diversity branches is small, its performance is very close to that of the Neyman-Pearson optimum receiver based on the probability density function obtained by the Fourier inversion of the characteristic function of the GNL-plus-Gaussian distribution.

Robust detection of ultra-wideband signals in non-Gaussian noise

A robust receiver is proposed for time-hopping pulse-position-modulation impulse radio systems transmitting over frequency-selective ultra-wideband channels, which aims to remove large-amplitude outliers that occur due to impulsive noise. The proposed system contains a rake structure for collecting the signal energy, which is dispersed over a large number of paths as a result of the wide channel bandwidth. Before the paths are merged via maximal ratio combining, they are passed through nonlinearities to trim the outlier noise components. The robust receiver so designed is shown to outperform the conventional linear rake receiver that consists of only matched filters at its fingers.

Reading a Pulsed, Fluctuating-Amplitude Radio Signal in Non-Gaussian Noise at Non-Coherent Reception

Algorithms are suggested for synthesizing detectors capable of reading pulsed signals through the non-Gaussian noise under non-coherent reception. Using the moment and cumulant description of a random variable, the decision rules are built to be optimum according to the criterion of lowest upper bounds of the error probability. The synthesizing detectors have been analyzed, the quality of the detectors based on the non-Gaussian noise consideration has been estimated.

Cramer–Rao Lower Bound for Estimating Quadrupole Resonance Signals in Non-Gaussian Noise

Quadrupole resonance (QR) technology for the detection of explosives is of crucial importance in an increasing number of applications. For landmine detection, where the detection system cannot be shielded, QR has proven to be highly effective if the QR sensor is not exposed to radio-frequency interference (RFI). However, strong non-Gaussian RFI in the field is unavoidable. A statistical model of such non-Gaussian RFI noise is given in this letter. In addition, the asymptotic Cramer-Rao lower bound for estimating a deterministic QR signal in this non-Gaussian noise is presented. The performance of several convenient estimators is compared to this bound.

Adaptive Antenna Array Receivers for Spread-Spectrum Signals in Non-Gaussian Noise

Pados, D. A., Medley, M. J., and Batalama, S. N., Adaptive Antenna Array Receivers for Spread-Spectrum Signals in Non-Gaussian Noise, Digital Signal Processing 11 (2001) 144–158 We consider the problem of recovering a spread-spectrum (SS) signal in the presence of unknown highly correlated spread-spectrum interference and impulsive noise. In terms of basic system and signal model considerations, we assume availability of a narrowband adaptive antenna array that experiences additive white Gaussian noise in time and across elements, as well as impulsive disturbance with direction-of-arrival (DOA) that changes at the chip rate. The space–time receiver design developed in this work is characterized by the following attributes: (i) Adaptive interference suppression is pursued in the joint space–time domain. (ii) An adaptive parametric nonlinear front end offers effective suppression of impulsive disturbances at low computational cost. (iii) An adaptive auxiliary-vector linear filter postprocessor offers effective, low-complexity suppression of SS interferers and leads to superior bit-error-rate (BER) performance under rapid, short-data-record system adaptation. Numerical and simulation comparisons with plain and outlier resistant space–time minimum-variance-distortionless-response (MVDR) filtering procedures are included to illustrate and support the theoretical developments.

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.

Maximum-likelihood array processing in non-Gaussian noise with Gaussian mixtures

Many approaches have been studied for the array processing problem when the additive noise is modeled with a Gaussian distribution, but these schemes typically perform poorly when the noise is non-Gaussian and/or impulsive. This paper is concerned with maximum likelihood array processing in non-Gaussian noise. We present the Cramer-Rao bound on the variance of angle-of-arrival estimates for arbitrary additive, independent, identically distributed (iid), symmetric, non-Gaussian noise. Then, we focus on non-Gaussian noise modeling with a finite Gaussian mixture distribution, which is capable of representing a broad class of non-Gaussian distributions that include heavy tailed, impulsive cases arising in wireless communications and other applications. Based on the Gaussian mixture model, we develop an expectation-maximization (EM) algorithm for estimating the source locations, the signal waveforms, and the noise distribution parameters. The important problems of detecting the number of sources and obtaining initial parameter estimates for the iterative EM algorithm are discussed in detail. The initialization procedure by itself is an effective algorithm for array processing in impulsive noise. Novel features of the EM algorithm and the associated maximum likelihood formulation include a nonlinear beamformer that separates multiple source signals in non-Gaussian noise and a robust covariance matrix estimate that suppresses impulsive noise while also performing a model-based interpolation to restore the low-rank signal subspace. The EM approach yields improvement over initial robust estimates and is valid for a wide SNR range. The results are also robust to PDF model mismatch and work well with infinite variance cases such as the symmetric stable distributions. Simulations confirm the optimality of the EM estimation procedure in a variety of cases, including a multiuser communications scenario. We also compare with existing array processing algorithms for non-Gaussian noise.

Adaptive detection of small sinusoidal signals in non-Gaussian noise using an RBF neural network

This paper addresses the application of locally optimum (LO) signal detection techniques to environments in which the noise density is not known a priori. For small signal levels, the LO detection rule is shown to involve a nonlinearity which depends on the noise density. The estimation of the noise density is a major part of the computational burden of LO detection rules. In this paper, adaptive estimation of the noise density is implemented using a radial basis function neural network. Unlike existing algorithms, the present technique places few assumptions on the properties of the noise, and performs well under a wide variety of circumstances. Experimental results are shown which illustrate the system performance as a variety of noise densities are encountered.

Detection of weak stochastic signals in double-sided exponential noise using generalized energy detector

Many locally optimum, suboptimum, and ad hoc detectors exploit knowledge of the noise probability density function (pdf) to obtain their test statistic for the detection of stochastic signals in non-Gaussian noise. These detectors appear to offer potential for highly improved performance for very small signal to noise ratios (asymptotically approaching zero). This paper studies a locally optimum detector namely the generalized energy detector, by deriving analytical expressions for a performance measure using a double-sided exponential noise pdf. The paper concludes that the apparently large gains predicted by the asymptotic theory may not be reachable within the practical range of signal-to-noise ratios.

A bivariate model for Arctic undersea noise

A bivariate model is developed for the impulsively contaminated noise of the Arctic undersea environment. It is based on one proposed by S. V. Czarnecki [‘‘Nearly Optimal Detection of Signals in Non-Gaussian Noise,’’ Ph.D. thesis, Dept. of EECS, Princeton Univ. (October 1983)] where impulsive and normal background noise regions are treated as coming from two independent Gaussian sources with differing variance. The noise is considered as the output of a switch that toggles between the two noise sources. In this paper, a statistical analysis is conducted on a 10-min time series of Arctic in-water noise data (Fram II) to provide a stochastic description of the real noise data within the framework of such a model. A median filter-based detector is developed to detect the state of the noise source selection switch and partition the time series into the impulsive and normal background regions. Goodness-of-fit tests are used to check the dual source noise distributions against the Gaussian hypothesis. A point process description of the operation of the source selection switch is also derived by statistically analyzing the switch transition inter-arrival times.

Signal interception in non-Gaussian noise

The interception of weak signals in nonGaussian noise is discussed. The spectral correlation property exhibited by all cyclostationary signals is exploited to synthesize multi-cycle and single-cycle detectors which assure a superior tolerance (as compared to radiometric techniques) to one of the most challenging problems in interception, namely accommodating unknown and changing noise level and interference activity. The proposed detectors perform a maximum likelihood estimate of the noise level and use the estimate to form the detection statistic. To obtain some analytical information about the performance of the multi-cycle and single-cycle detectors, the deflection, which is a useful measure of the output (signal-to-noise ratio), especially appropriate for weak-signal SNR interception, has been evaluated. The receiver operating characteristics, carried out via computer simulation, confirm the superiority of the proposed cycle detector with respect to the traditional radiometer.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A switched-source model for simulating Arctic undersea noise

A switched-source model is developed for simulating the impulsive character of Arctic undersea noise. The model is based on one proposed by S. V. Czarnecki [“Nearly optimal detection of signals in non-Gaussian noise,” Ph.D. thesis, Dept. of EECS, Princeton Univ. (October 1983)] where impulsive and normal background noise regions are treated as coming from two independent Gaussian sources with differing variance. P. K. Willet and J. B. Thomas [IEEE J. Ocean. Eng. OE-12, 29–37 (1987)] have suggested that the dual mode noise sequence can be treated as stationary and dependent if the state of the source selection switch is governed by a two-state Markov process. In this paper a statistical analysis is conducted on a 10-min time series of Fram 2 noise data in order to provide a complete stochastic description of real noise data within the framework of such a model. An earlier point process analysis is extended by examining the duration and amplitude of burst events. Results of the analysis are used to specify the dual source characteristics, and the terms of the transition matrix for the Markov process.

Detector design using a density fit to non-Gaussian noise

Suboptimal nonlinear detectors for known small signals in non-Gaussian noise are investigated. It is assumed that either the locally optimal nonlinearity is too complex to use or that the noise density is not known precisely. A memoryless suboptimal nonlinearity (ZNL) can be chosen, and the family of densities for which it is optimal is found. A member of this family is then fitted to the observed noise, and the corresponding detector is used. When a rational function is chosen for the nonlinearity, the Pearson family is the set of solution densities. This is not only a general family which contains many common univariate densities, but for nearly Gaussian noise the method of moments can be used efficiently to fit a member density to the noise. The coefficients of a ZNL are estimated for several (non-Pearson) densities using the first four noise moments. >