Alpha-stable Noise Environments Research Articles

CML based parameter estimation of FH signals in alpha stable noise environment

CML based parameter estimation of FH signals in alpha stable noise environment

Research on geometric algebra-based robust adaptive filtering algorithms in wireless communication systems

Noise and interference are the two most common and basic problems in wireless communication systems. The noise in wireless communication channels has the characteristics of randomness and impulsivity, so the performance of adaptive filtering algorithms based on geometric algebra (GA) and second-order statistics is greatly reduced in the wireless communication systems. In order to improve the performance of adaptive filtering algorithms in wireless communication systems, this paper proposes two novel GA-based adaptive filtering algorithms, which are deduced from the robust algorithms based on the minimum error entropy (MEE) criterion and the joint criterion (MSEMEE) of the MEE and the mean square error (MSE) with the help of GA theory. The noise interference in wireless communication is modeled by alpha-stable distribution which is in good agreement with the actual data in this paper. Simulation results show that for the mean square deviation (MSD) learning curve, the GA-based MEE (GA-MEE) algorithm has faster convergence rate and better steady-state accuracy compared to the GA-based maximum correntropy criterion algorithm (GA-MCC) under the same generalized signal-to-noise ratio (GSNR). The GA-MEE algorithm reduces the convergence rate, but improves the steady-state accuracy by 10–15 dB compared to the adaptive filtering algorithms based on GA and second-order statistics. For GA-based MSEMEE (GA-MSEMEE) algorithm, when GA-MSEMEE and the adaptive filtering algorithms based on GA and second-order statistics keep the same convergence rate, its steady-state accuracy is improved by 10–15 dB, and when GA-MSEMEE and GA-MEE maintain approximately steady-state accuracy, its convergence rate is improved by nearly 100 iterations. In addition, when the algorithms are applied to noise cancellation, the average recovery error of the two proposed algorithms is 7 points lower than that of other GA-based adaptive filtering algorithms. The results validate the effectiveness and superiority of the GA-MEE and GA-MSEMEE algorithms in the alpha-stable noise environment, providing new methods to deal with multi-channel interference in wireless networks.

Robust detection and motion parameter estimation for weak maneuvering target in the alpha-stable noise environment

This paper focuses on the weak maneuvering target detection problem in the alpha-stable noise (ASN) environment. A novel coherent integration framework is proposed, where the range migration (RM) is first removed via approximate linear methods to make the noise distribution character remain unchanged, and then the ASN suppression, Doppler frequency migration (DFM) compensation, and coherent integration are simultaneously achieved in the proper transform domain. Based on this framework, a robust detection method is developed. First, the second-order keystone transform (SoKT) is employed to correct the range curve (RC) induced by the target's acceleration. Thereafter, the centroid axis rotation (CAR) is presented to remove the residual range walk (RW) by rotating the slow time axis parallel to the RW line in the fast-time and slow-time domain. Finally, the phase fractional lower-order Lv's distribution (PFLOLVD) is proposed to compensate the DFM and realize the energy accumulation of the target in the ASN environment. Furthermore, the performance of proposed algorithm in aspects of coherent integration time, computational complexity, and multiple targets detection are analyzed in detail. Compared with the existing coherent integration detection methods, the proposed method is both robust for ASN environments and superior in the detection performance.

Kernel Affine Projection P-norm (KAPP) Filtering under Alpha Stable Distribution Noise Environment

Aiming at improving the performance of the nonlinear adaptive filtering under the alpha-stable distribution noise environment, Kernel Affine Projection P-norm (KAPP) algorithm based on the minimum dispersion coefficient criterion and the affine projection is deduced. The accuracy of the gradient estimation is enhanced by using the input signals and the error signals at multiple times. The simulation results on Mackey–Glass chaotic time series prediction show that the KAPP algorithm has faster convergence speed, better steady-state performance and stronger robustness under the Gaussian noise and stable distributed noise environment.

Structure and Performance Evaluation of Fractional Lower-Order Covariance Method in Alpha-Stable Noise Environments

Background: All existing time delay estimation methods, i.e. correlation and covariance, depend on second or higher-order statistics which are inapplicable for the correlation of alpha-stable noise signals. Therefore, fractional lower order covariance is the most appropriate method to measure the similarity between the alpha-stable noise signals. Methods: In this paper, the effects of skewness and impulsiveness parameters of alpha-stable distributed noise on fractional lower order covariance method have been analyzed. Results: It has been found that auto-correlation, i.e. auto fractional lower order covariance,\ of non delayed alpha-stable noise signals follows a specific trend for specific ranges of impulsiveness and skewness parameters of alpha-stable distributed noise. The results also depict that, by maintaining the skewness and impulsiveness parameters of α-stable noise signals in a certain suggested range, better auto-correlation can be obtained between the transmitted and the received alpha-stable noise signals in the absence and presence of additive white Gaussian noise. Conclusion: The obtained results would improve signal processing in alpha-stable noise environment which is used extensively to model impulsive noise in many noise-based systems. Mainly, it would optimize the performance of random noise-based covert communication, i.e. random communication.

A Novel Parameter Estimation Method Based on a Tuneable Sigmoid in Alpha-Stable Distribution Noise Environments.

In this paper, a novel method, that employs a fractional Fourier transform and a tuneable Sigmoid transform, is proposed, in order to estimate the Doppler stretch and time delay of wideband echoes for a linear frequency modulation (LFM) pulse radar in an alpha-stable distribution noise environment. Two novel functions, a tuneable Sigmoid fractional correlation function (TS-FC) and a tuneable Sigmoid fractional power spectrum density (TS-FPSD), are presented in this paper. The novel algorithm based on the TS-FPSD is then proposed to estimate the Doppler stretch and the time delay. Then, the derivation of unbiasedness and consistency is presented. Furthermore, the boundness of the TS-FPSD to the symmetric alpha stable () noise, the parameter selection of the TS-FPSD, and the feasibility analysis of the TS-FPSD, are presented to evaluate the performance of the proposed method. In addition, the Cramér–Rao bound for parameter estimation is derived and computed in closed form, which shows that better performance has been achieved. Simulation results and theoretical analysis are presented, to demonstrate the applicability of the forgoing method. It is shown that the proposed method can not only effectively suppress impulsive noise interference, but it also does not need a priori knowledge of the noise with higher estimation accuracy in alpha-stable distribution noise environments.

Kernel Recursive Generalized Maximum Correntropy

In this letter, a novel kernel adaptive algorithm, called kernel recursive generalized maximum correntropy algorithm (KRGMC), is derived in a kernel space and under the generalized maximum correntropy (GMC) criterion. The proposed kernel algorithm can effectively scale down the dynamic recursive weight coefficients influenced by the impulsive estimate error to avoid the significant performance degradation. The superior performance of the proposed algorithm is verified by numerical simulations about short-time series prediction in alpha-stable noise environment.

A novel cauchy score function based DOA estimation method under alpha-stable noise environments

Based on the study of alpha-stable distribution and its score function, by combining M-estimation theory and maximum likelihood estimation theory, this paper proposes a novel Cauchy score function based cost function of the residual fitting error matrix. And then, this cost function is employed as a substitute for the ℓp-norm based cost function of the residual fitting error matrix which is utilized in the ℓp-MUSIC algorithm. To solve the cost function, alternating convex optimization is applied. And the complex-valued Newton's method with optimal step size is developed to solve the resulting convex problem. With the obtained signal subspace, the direction of arrival (DOA) estimates are retrieved by the MUSIC technique. Comprehensive simulation results demonstrate that, the proposed algorithm can achieve more robust performance than its counterpart both in terms of resolution probability and root mean square error (RMSE), especially when the generalized signal to noise ratio (GSNR) is fairly low, or the underlying noise is extremely impulsive.

A robust DOA estimator based on the correntropy in alpha-stable noise environments

By introducing correntropy as the robust statistics, a novel direction of arrival estimator for α-stable noise is proposed. In this method, the signal subspace is estimated by solving the correntropy based optimization problem under the maximum correntropy criterion. An optimal step size based iterative algorithm is developed and the convergence of it is proved. Comprehensive simulation results demonstrate that the proposed method is superior to several existing algorithms in terms of the probability of resolution and the estimation accuracy, especially in the highly impulsive noise environments.

Parameter estimation of frequency hopping signals based on the Robust S-transform algorithms in alpha stable noise environment

In many communication systems the noise is non-Gaussian and usually exhibits impulsive characteristics. The alpha stable distribution, which is the only distribution satisfies the generalized central-limit theorem and characterizes a range of behaviors from Gaussian to extremely impulsive signals, is appropriate to model this type of noise. Since the performance of the S-transform (ST) based frequency hopping (FH) signal parameter estimation methods, which are very effective in Gaussian noise, may deteriorate significantly in the presence of impulsive noise, two robust methods based on the ST, i.e., the fractional lower order ST (FLOST) and the iterative ST (IST), are proposed in this paper. Specifically, the FLOST is the combination of fractional lower order statistics and the ST, whereas the IST is the application of the minimax Huber's robust theory to the ST. Both robust ST algorithms exhibit higher time-frequency concentration in the presence of alpha stable noise. Simulation results show that the proposed algorithms are valid for FH signal parameter estimation, and they distinctively outperform the standard ST in impulsive noise environment.

Kernel recursive maximum correntropy

In this letter, a robust kernel adaptive algorithm, called the kernel recursive maximum correntropy (KRMC), is derived in kernel space and under the maximum correntropy criterion (MCC). The proposed algorithm is particularly useful for nonlinear and non-Gaussian signal processing, especially when data contain large outliers or disturbed by impulsive noises. The superior performance of KRMC is confirmed by simulation results about short-term chaotic time series prediction in alpha-stable noise environments.

Stochastic Resonance in a Simple Threshold Sensor System with Alpha Stable Noise

We investigate the effect of alpha stable noise on stochastic resonance in a single-threshold sensor system by analytic deduction and stochastic simulation. It is shown that stochastic resonance occurs in the threshold system in alpha stable noise environment, but the resonant effect becomes weakened as the alpha stable index decreases or the skewness parameter of alpha stable distribution increases. In particular, for Cauchy noise a nonlinear relation among the optimal noise deviation parameter, the signal amplitude and the threshold is analytically obtained and illustrated by using the extreme value condition for the output signal-to-noise ratio. The results presented in this communication should have application in signal detection and image restoration in the non-Gaussian noisy environment.

Robust Detection for Cooperative Communication System in Alpha-stable Noise Environments

Robust Detection for Cooperative Communication System in Alpha-stable Noise Environments

Diffusion least‐mean P‐power algorithms for distributed estimation in alpha‐stable noise environments

We propose a diffusion least mean p-power (LMP) algorithm for distributed estimation in alpha stable noise environments, which is one of the widely used models that appears in various environments. Compared with the diffusion least mean squares (LMS) algorithm, better performance is obtained for the diffusion LMP methods when the noise is with alpha-stable distribution.

Particle Filtering for Acoustic Source Tracking in Impulsive Noise With Alpha-Stable Process

NonGaussian impulsive noises distort the source signal and cause problems for direction of arrival (DOA) estimation of an acoustic source. In this paper, a Bayesian framework and its particle filtering (PF) implementation for DOA tracking in the presence of complex symmetric alpha-stable noise process are developed. A constant velocity model is employed to model the source dynamics, and spatial spectra are exploited to formulate a pseudo likelihood of particles. Since the second-order statistics of alpha-stable processes do not exist, the fractional lower order moment matrix of the received data is used to replace the covariance matrix in calculating the spatial spectra. The noise usually spreads and distorts the mainlobe of the likelihood function and the particles cannot be weighted accurately. Hence, the likelihood function is exponentially weighted to emphasize the particles in a high likelihood area and thus enhance the resampling efficiency. The performance of the proposed tracking algorithm is extensively studied under simulated alpha-stable noise environments. The results show that the proposed algorithm significantly outperforms the existing PF tracking approach and the traditional localization approaches in DOA estimation.

Capture Properties of the Generalized CMA in Alpha-Stable Noise Environment

Constant modulus algorithm (CMA) is an adaptive technique for correcting multipath and interference-induced degradations in constant envelope waveforms. The algorithm exploits the fact that both multipath and additive interference can disrupt the constant envelope of the received signal. By detecting the received envelope variations, the adaptive algorithm has the ability to reset the coefficients vector so as to remove the variations, and in the process, reject the various interference components from the desired signal. If both the interferer and the signal of interest have constant envelope and are spectrally non-overlapped, it is possible to find two different solutions for the coefficient vector, in which one suppresses the interferer and the other "captures" the interferer. The problem of how "capture" can occur and how it may be prevented in Gaussian noise environment has been perfectly developed in the previous work (Treichler, Larimore, IEEE Trans Acoust Speech Signal Process, 33:946---958, 1985). However, recent investigation on the physical channels in wireless communication shows that there is aggregate noise component exhibiting high amplitudes for small duration time interval. This paper proposes a GCMA (Generalized CMA) which generalizes the CMA by introducing the α-stable distribution as the noise model. Here the original CMA is only a special case of the GCMA. In order to describe the average behavior of the GCMA, a simple model consisting of only two sinusoids is presented. As assuming slow adaptation, the adaptive weight recursion is shown to compress into a two-by-two recursion in the tone output amplitudes. The simplified recursion is analyzed to determine what combination of signals power and initialization on coefficient vectors leads to "lock" and what leads to the capture of the interferer. The method to determine lock and capture zone boundaries is analyzed. These convergence properties of the GCMA are studied by computer simulations.

Robust propagation velocity estimation of gastric electrical activity by least mean p-norm blind channel identification

The propagation of the gastric slow wave is one of the most important spatial characteristics of gastric electrical activity (GEA). The time delay estimation (TDE) is an effective approach to quantitatively assessing the propagation velocity of GEA. Traditional TDE analyses are developed under the condition reported that the background noise in GEA analysis is Gaussian distributed. Due to the effects of spikes and/or motion artifacts, the GEA obtained from gastric serosal electrodes often contains sharp transitions. This paper proposes robust time delay estimation based on least mean p-norm blind channel identification (BCILMP) under alpha-stable noise condition. Compared with the least mean square time delay estimation (LMSTDE), the BCILMP provides better performance in the impulsive noise environments. The robustness of the proposed method is demonstrated through computer simulations in both Gaussian and alpha-stable noise environments. The results of the propagation velocity of real data obtained from gastric serosal electrodes in gastroparetic patients show that the propagation velocity in gastroparetic patients is slower than in the normal subjects reported in the literature, and the slow-wave propagation is directed proximally to distally from the corpus toward the pylorus but not all the variability of the propagation velocity increases monotonously.

Adaptive Bayesian decision feedback equaliser for alpha-stable noise environments

In some communication systems the channel noise is known to be non-Gaussian due, largely, to impulsive phenomena. The performance of signal processing algorithms designed under the Gaussian assumption may degrade seriously in such environments. In this paper we investigate the problem of adaptive channel equalisation in an impulsive noise environment. The impulsive interfering noise is modelled as an α-stable process. We first derive the optimum Bayesian decision feedback equaliser and present a novel analytical framework for the evaluation of systems in infinite variance environments. A family of generalised adaptive channel identification algorithms for this infinite variance noise environment is also presented. The combination of a Bayesian equaliser and a channel estimator operating as an adaptive channel equaliser is experimentally studied and its performance is compared with that of a traditional system designed under the Gaussian assumption. The experimental data suggest that the proposed combination of equaliser and channel estimator outperforms the traditionally designed adaptive equaliser in terms of error probability. We finally provide some useful approximations concerning the practical implementation of an α-stable adaptive equaliser.

Robust M-estimate adaptive filtering

An M-estimate adaptive filter for robust adaptive filtering in impulse noise is proposed. Instead of using the conventional least-square cost function, a new cost function based on an M-estimator is used to suppress the effect of impulse noise on the filter weights. The resulting optimal weight vector is governed by an M-estimate normal equation. A recursive least M-estimate (RLM) adaptive algorithm and a robust threshold estimation method are derived for solving this equation. The mean convergence performance of the proposed algorithm is also analysed using the modified Huber function (a simple but good approximation to the Hampel's three-parts-redescending M-estimate function) and the contaminated gaussian noise model. Simulation results show that the proposed RLM algorithm has better performance than other recursive least squares (RLS) like algorithms under either contaminated gaussian or alpha-stable noise environment. The initial convergence, steady-state error, robustness to system change and computational complexity are also found to be comparable to the conventional RLS algorithm under gaussian noise alone.

Adaptive estimation of latency change in evoked potentials by direct least mean p-norm time-delay estimation.

Evoked potentials (EP) have been widely used to quantify neurological system properties. Changes in EP latency may indicate impending neurological injury. Traditional EP analyses are developed under the condition that the background noise in EP analysis are Gaussian distributed. This paper proposes a latency change detection and estimation algorithm under alpha-stable noise condition, a generalization of Gaussian noise assumption. An analysis shows that the alpha-stable model fits the noises found in the impact acceleration experiment under study better than the Gaussian model. The robustness of the proposed algorithm is demonstrated through computer simulations and experimental data analysis under both Gaussian and alpha-stable noise environments.