non-Gaussian Impulsive Noise Research Articles

Discrimination between random signals and impulse noise in images which is optimal according to the criterion of minimum combined losses

An algorithm is proposed for discriminating between random image signals and non-Gaussian impulse noise with a uniform brightness distribution which is based on a new optimality criterion combining the minimization of weighted unconditional probabilities of wrong decisions of the first and second kind and maximization of the probabilities of making correct decisions. Results of numerical studies of the proposed and the well-known Bayes algorithms are given showing that the use of the new algorithm reduces the discrimination error under conditions of complete a priori uncertainty of the image signal distribution.

Detecting unmodeled GW bursts in non-Gaussian (glitchy) noise: two locally optimum network detectors

Two locally optimum interferometer-network statistics for detecting unmodeled gravitational wave bursts in a non-Gaussian impulsive (glitchy) noise background are introduced. These follow from two possible approaches, where the sought transient signals are alternatively assumed as (i) unknown but deterministic or (ii) random. The first approach yields a locally optimum generalized likelihood ratio test detector, based on the maximum likelihood estimate of the gravitational wave signal. The second makes only minimal (least informative) assumptions about the sought signals, and yields a special version of Kassam's generalized-cross-correlation test detector. Both outperform the standard coherent network detector based on the Gaussian noise assumption. In the realistic case where the glitch noise distribution is non-stationary in time, or incompletely characterized, robust versions of these locally optimum network detectors can be effectively used.

Adaptive blind equalization for MIMO systems uadaptive blind equalization for MIMO systems under α-stable noise environmentnder α-stable noise environment

The presence of non-Gaussian impulsive noise in wireless system can degrade the performance of existing equalizers and signal detectors. In this paper, the problem of blind source separation and equalization for MIMO systems in heavy-tailed impulsive noise is studied. A generalized multiuser constant modulus cost function by employing the fractional lower-order statistic of the equalizer input signal is proposed. The associated adaptive blind equalization algorithm based on a stochastic gradient descent method is defined as fractional lower-order multi-user constant modulus algorithm (FLOS MU CMA). Computer simulations are presented to illustrate the performance of the new algorithm.

Constant Modulus Algorithm for Cochannel Signal Separation in Non-Gaussian Impulsive Noise Environments

The separation of cochannel signals is of interest in communication community. Some algorithms based on constant modulus (CM) have been previously developed to separate cochannel signals with the assumption of Gaussian channel noise. The mismatches of noise models between the assumed channel noise and the practical noise may occur. These mismatches will inevitably lead the performance of cochannel signals separation to degrade. In this paper the alpha-stable distribution is employed as noise model to simulate impulsive noise occurring in wireless channel. A constant modulus algorithm is proposed to separate the cochannel signals based on fractional lower-order statistics (FLOS). The convergence of the CM array is analyzed. Numerical simulations are presented to verify the accuracy of the analytical results.

Optimal estimation of the position of non-Gaussian impulse noise in images

An algorithm for optimal estimation (in the sense of the minimum average risk criterion) of the spatial position of non-Gaussian impulse noise in digital images is proposed based on the signal difference between the center of the slide aperture and its other elements. An expression for the boundary values of the admissible signal interval is obtained that provides the potentially achievable zero probability of noise estimation error. Results of numerical studies of the efficiency of the synthesized algorithm show its advantages over the well-known nonoptimal algorithm.

Space–time blind equalisation in impulsive noise

The presence of non-Gaussian impulsive noise in wireless system can degrade the performance of existing equalisers and signal detectors. The problem of blind source separation and equalisation for multiple-input/multiple-output (MIMO) channels under heavy-tailed impulsive noise environment is studied. A generalised multi-user constant modulus (CM) cost function is proposed by employing the fractional lower order CM property of the equaliser input signals as well as the fractional lower order cross-correlations between them. The associated adaptive blind equalisation algorithm based on a stochastic gradient descent method is defined as fractional lower order multi-user constant modulus algorithm (FMU_CMA), which is able to mitigate impulsive channel noise while recovering all input signals simultaneously. The steady-state mean-square error (MSE) performance of the FMU_CMA is studied in a noise-free environment; the approximate expression is derived based on the energy-preserving relation and the Taylor series expansion. Simulation studies are undertaken to support the analysis with CM and non-CM signal.

Joint Erasure Marking and Viterbi Decoding Algorithm for Unknown Impulsive Noise Channels

In many real-world communication systems, the extent of non-Gaussian impulsive noise (IN) rather than Gaussian noise poses practical limits on the achievable system performance. The decoding of IN-corrupted signals is complicated by the fact that accurate IN statistics are typically unavailable at the receiver. Without exploiting the IN statistics, the conventional method is to try to mark the IN-corrupted symbols as erasures preceding a Euclidean metric based decoder. In this work, a novel joint erasure marking and Viterbi algorithm (JEVA) is proposed to decode the convolutionally coded data transmitted over an unknown impulsive noise channel. Based on the Bernoulli-Gaussian IN model, it is empirically demonstrated that JEVA not only can offer significant performance improvement over the conventional separate erasure marking and Viterbi decoding method, but also can almost achieve the optimal performance of the maximum likelihood decoder that fully exploits the perfect knowledge of the IN probability density function. Various implementations of JEVA are proposed to provide different performance-complexity trade-offs.

Underwater acoustic azimuth and elevation angle estimation using spatial invariance of two identically oriented vector hydrophones at unknown locations in impulsive noise

This paper proposes a new underwater acoustic 2-D direction finding algorithm using two identically oriented vector hydrophones at unknown locations in non-Gaussian impulsive noise. The two applied vector hydrophones are four-component, orienting identically in space with arbitrarily and possibly unknown displacement. Each vector hydrophone has three spatially co-located but orthogonally oriented velocity hydrophones plus another pressure hydrophone. The proposed algorithm employs the spatial invariance between the two vector hydrophones, but requires no a priori information of vector hydrophones' spatial factors and impinging sources' temporal forms. We apply ESPRIT to estimate vector hydrophones manifold and then to pair the x-axis direction cosines with y-axis direction cosines automatically and yield azimuth and elevation angle estimates. We also consider the additive noise be non-Gaussian impulsive, which is often encountered in underwater acoustics applications. Two typical impulsive noise model, Gaussian-mixture noise and symmetric @a-stable (S@aS) noise models are adopted. Instead of using conventional second order correlation of array output data, we define the vector hydrophone array sign covariance matrix (VSCM) for Gaussian-mixture noise and vector hydrophone array fractional lower order moment (VFLOM) matrix for S@aS noise with 1<@a=<2. These defined matrices may readily substitute customary vector hydrophone array covariance matrix for 2-D direction finding in impulsive noise.

Support vector machines for robust channel estimation in OFDM

A new support vector machine (SVM) algorithm for coherent robust demodulation in orthogonal frequency-division multiplexing (OFDM) systems is proposed. We present a complex regression SVM formulation specifically adapted to a pilots-based OFDM signal. This novel proposal provides a simpler scheme than an SVM classification method. The feasibility of our approach is substantiated by computer simulation results obtained for IEEE 802.16 broadband fixed wireless channel models. These experiments allow to scrutinize the performance of the OFDM-SVM system and the suitability of the epsiv-Huber cost function, in the presence of non-Gaussian impulse noise interfering with OFDM pilot symbols

Multiuser detection for DS-CDMA systems in non-Gaussian channels

An adaptive multi-user detector was developed for direct-sequence code division multiple access (DS-CDMA) systems corrupted by non-Gaussian channel noise, which can be quite detrimental to the performance of the multi-user detectors based on classical white Gaussian assumption. This receiver simultaneously combats multipleaccess interference (MAI) and non-Gaussian impulsive noise. The channel parameters are estimated and transmitted signals are jointly detected by a simple recursive algorithm derived from the EM/SAGE algorithm. Analytical and simulation results show that the proposed technique is robust with wider applicability than conventional multi-user detectors in terms of near-far resistance and bit-error ratio (BER) when either MAI or non-Gaussian impulsive noise is dominant.

Direction finding in non-Gaussian impulsive noise environments

The class of alpha-stable distributions is better for modeling impulsive noise than Gaussian distribution in array signal processing. This paper briefly introduces the statistical characteristics of stable distribution and its fractional lower-order statistics, covariation and fractional-order correlation, and proposes a new minimum norm method (FOC-MinNorm) of direction finding based on the fractional-order correlation and subspace technique under alpha-stable noise conditions. We analyze the performances of the FOC-MinNorm, including the accuracy in the estimation, the capability and probability of resolution, and the pseudo peaks of the FOC-MinNorm method. The analysis is based on the assumption that the additive noise can be modeled as a complex alpha-stable process. Simulation and analysis show that the proposed method is robust in a wide range of characteristic exponent values of stable distribution. Its resolution capability and probability of resolution are better than those of the conventional second-order statistics based MinNorm algorithm and covariation based ROC-MUSIC method, furthermore, fractional-order correlation is more suitable than covariation in practical applications.

Underwater sources location in non-Gaussian impulsive noise environments

The class of alpha-stable distributions is better for modeling impulsive noise than Gaussian distribution in array signal processing. After briefly introducing the statistical characteristics of stable distribution and the fractional lower order statistics, including the covariation and the fractional order correlation, this paper proposes a new FOC-ESPRIT method of 2-D direction finding based on the fractional order correlation and subspace technique for underwater 2-D source localization using a vector hydrophones array under alpha-stable noise conditions. A vector hydrophone comprises two or three spatially co-located, orthogonally oriented identical velocity hydrophones (each of which measures one Cartesian component of the underwater acoustical particle velocity vector-field) plus an optional pressure hydrophone. Simulation experiments show that the proposed method is robust in a wide range of characteristic exponent values of stable distribution. Its performances are better than those of the conventional second-order statistics based ESPRIT algorithm, furthermore, the fractional order correlation is more suitable than the covariation in practical applications.

Iterative multiuser detection for turbo-coded synchronous CDMA in Gaussian and non-Gaussian impulsive noise

We develop an iterative multiuser receiver for decoding turbo-coded synchronous code-division multiple-access signals in both Gaussian and non-Gaussian noise. A soft-input soft-output nonlinear multiuser detector is combined with a set of single-user channel decoders in an iterative detection/decoding structure. The nonlinear multiuser detector utilizes the prior probabilities of each user's bits to form soft estimates used for multiple-access interference cancellation. The channel decoders perform turbo-code decoding and produce posterior probabilities which are fed back to the multiuser detector for use as prior probabilities. Simulation results show that the proposed multiuser receiver performs well in both Gaussian and non-Gaussian noise. In particular, single-user turbo-code performance can be approached within a few iterations with medium to low cross correlation (/spl rho//spl les/0.5).

Nonlinear decorrelator for multiuser detectionin non-Gaussianimpulsive environments

A nonlinear decorrelator is proposed for robust multiuser detection in CDMA non-Gaussian channels. The new detector involves the use of a nonlinear front-end followed by a linear decorrelating stage. Simulation results show that the new detector exhibits good near-far resistance under both Gaussian and non-Gaussian impulsive noise environments.

Detection in correlated impulsive noise using fourth-order cumulants

We consider detection and estimation in correlated impulsive noise. The non-Gaussian impulsive noise is modeled as the sum of two linear processes: a nominal part and an impulsive part. This model admits correlated impulsive bursts lasting many data samples. Identifiability of the noise model is established using fourth- and second-order cumulants. Under this model, the correlated time series can be whitened and an appropriate memoryless nonlinearity applied to attenuate the impulsive events. A detection statistic is then formed from the output of the nonlinearity. In the threshold detection case, the use of cumulants allows identification of the noise in the presence of the signal to be detected, obviating the need for noise-only training records. Simulation results with a sample size of 512 show small loss in detector performance versus an ideal detector with no impulsive part present.

Joint estimation of time delay and frequency delay in impulsive noise using fractional lower order statistics

New methods for time delay estimation and joint estimation of time delay and frequency delay in the presence of impulsive noise are introduced. First, degradation of the conventional approaches based on second-order statistics is shown both theoretically and experimentally. Then, a new class of robust algorithms are developed using the theory of alpha-stable distributions, including the fractional lower order covariance (FLOC) method, which is formulated for the time delay estimation problem and the fractional lower order ambiguity function (FLOAF), which is defined for the joint estimation of time delay and frequency delay. It is shown that these new methods are robust for both Gaussian and non-Gaussian impulsive noise environments. The improved performance is clearly demonstrated through detailed analysis and comprehensive simulations with computer-generated data as well as actual radar and sonar clutter data.

Detection for binary transmission in a mixture of Gaussian noise and impulsive noise modeled as an alpha-stable process

The impact of nonGaussian impulsive noise combined with Gaussian noise on the performance of the binary transmission is analyzed. The impulsive noise is modeled as an alpha-stable process. The probability of error for optimum, linear and nonlinear receivers is derived. The proposed nonlinear detectors show substantial improvements in performance compared to linear ones. The obtained results will be useful in performance evaluation of digital communication links subject to Gaussian and impulsive noises.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Response distribution of non-linear systems excited by non-Gaussian impulsive noise

A perturbation scheme is devised to obtain an approximate stationary probability density for the response of a non-linear oscillator subjected to an impulsive-noise process which is statistically stationary but non-Gaussian. The excitation can be either additive or multiplicative. The effect of non-Gaussianity in the excitation process is found to be negligible if the product of the average arrival rate of the impulses and the relaxation time of the oscillator is of an order of 10 or greater. When this is not the case, the effect is not uniform; it may be more pronounced for one dynamic system than that of another. Numerical results are obtained for two examples, and they compare well with Monte Carlo simulations.

Performance of high level QAM in the presence of impulsive noise and co-channel interference in multipath fading environment

An analysis is presented for the performance of a high-level (e.g. 16, 64 and 256-QAM) QAM (quadrature amplitude modulation) system in the presence of Gaussian thermal noise combined with a non-Gaussian impulsive noise and cochannel continuous wave interference in the multipath fading environment. The system performance is evaluated in terms of CNR (carrier-to-noise power ratio), CIR (carrier-to-interference ratio), impulsive index of the noise, power ratio of the Gaussian noise-to-impulsive noise, and fading figure. >

Impact of Non-Gaussian Impulsive Noise and Multipath Fading on the Performance of Digital Mobile-Satellite Systems

The impact of non-Gaussian impulsive noise combined with that of Gaussian thermal noise on the performance of mobile-satellite systems is analyzed. The analysis if further extended with a co-channel carrier wave (CW) interference and/or multipath fading (m-distribution) presented in the transmission channels. The system performance is evaluated in terms of CNR, CIR (Carrier-to-interference Ratio), impulsive index of the noise, power ratio of the Gaussian noise-to-impulsive noise and fading figure. The impulsive noise may be caused by in-band or by out-of-band intermodulation noise which has a non-Gaussian probability density function.