Convergence analysis of RL1-SLMS-based robust adaptive sparse channel estimation

Spectrum sensing is important for a cognitive radio (CR) system to protect primary users (PUs) from harmful interference. At present, most of the existing sensing schemes are proposed in Gaussian noise environments. Nevertheless, a CR system actually also suffers from non-Gaussian noise, such as man-made impulsive noise, ultrawideband interference and co-channel interference. In this article, to handle the degradation of detection performance in non-Gaussian impulsive noise environments, a robust spectrum sensing scheme named hyperbolic tangent-based energy detector (HT-ED) is proposed. The hyperbolic tangent function is applied to suppress the impulsive noise by the nonlinear behavior, but without restraining the normal noise by the linear behavior. This property enables the new method to achieve the good detection performance in both Gaussian and non-Gaussian noise environments. In addition, it is similar to an energy detector, the new detector does not need to know the characteristics of the PU's signal. The performance analysis of the proposed HT-ED scheme is also presented. The simulation results show the HT-ED is robust against impulsive noise, which is modeled as Laplace or α-stable noise. Moreover, the HT-ED provides a superior detection performance compared with the other existing relative methods in a wide range of non-Gaussian noise.

In the next-generation wireless communication systems, the broadband signal transmission over wireless channel often incurs the frequency-selective channel fading behavior and also results in the channel sparse structure which is dominant by very few large coefficients. To ensure the stable wireless propagation, various linear adaptive channel estimation algorithms, e.g., recursive least square (RLS) and least mean square (LMS), have been developed. However, the traditional algorithms are unable to exploit the channel sparsity. Supporting by the compressive sensing (CS) theory, channel estimation performance can be further improved by taking advantage of the sparsity. In this paper, RLS based fast adaptive sparse channel estimation algorithm is proposed by introducing two sparse constraint functions, L1-norm and L0-norm. To improve the flexibility of the proposed algorithms, this paper introduces a regularization parameter selection method to adaptively exploit the channel sparsity. Finally, Monte Carlo based computer simulations are conducted to validate the effectiveness of the proposed algorithms based robust channel estimation either for sparse or non-sparse channel.

The purpose of this correspondence is to report on some nxasurements of output SNR (signal-to-noise ratio or S/N), characteristics for a square-law detector extracting signals from non-Gaussian noise, specifically, impulsive noise. Non-Garlssian noise arises in varioas communication media such as the atmosphere, wire lines, and under water. In experimental and theoretical investigations of the effects of non-Gaussian noise on various communications systems, a simple correlator is often considered because it is possible to obtain theoretical predictions of the (S/N), for signal and additive non-Gaussian noise at the correlator input if an appropriate noise model is available for calculating the required fourth-order moment. Middleton (1962), in his analysis of correlator performance in non-Gaussian background noise, employed the so-called Poisson impulse noise model. His theoretical predictions reveal that impulsive noise always degrades the (S/N), as compared with Gaussian noise backgrounds having the same spectral distribution for a given input SNR. However, his theoretical formulas are rather difficult to check experimentally in their full generality and assess the relative importance of various parameters. We compare a study restricted to the case of a square-law detector with Middleton's results.

Accurate channel-estimation algorithms are critical for enhancing the throughput of wireless communication systems, including millimetre wave (mmWave) multiple-input multiple-output (MIMO) systems, where precise channel knowledge enables reliable signal detection and beamforming. In practical wireless environments, impulsive non-Gaussian noise with unknown statistics often occurs due to electromagnetic interference and harsh propagation conditions, significantly degrading estimation accuracy and overall system performance. In this context, the maximum correntropy criterion (MCC) has emerged as an attractive solution for robust channel estimation that outperforms state-of-the-art algorithms. However, the MCC-based algorithm’s performance is sensitive to the tuning of hyperparameters, which is challenging in the presence of non-Gaussian noise, such as impulsive noise (IN). Furthermore, a recent genre of kernel width sampling methods makes MCC hyperparameter-free and allows for asymptotic convergence to the squared-error performance of MCC with the ideal kernel width. To ensure their practical applicability, convergence analysis is essential to theoretically guarantee stability and performance under various IN scenarios. This study presents convergence analysis of hyperparameter-free MCC-based channel estimation for mmWave MIMO systems considering various IN scenarios. To validate the theoretical analysis, simulations are conducted on practical mmWave MIMO system models. Simulation results closely match the analytical findings, which confirms the accuracy and effectiveness of the analysis we here present.

We use the Yosida approximation to find an Itô formula for mild solutions { X x ⁢ ( t ) , t ≥ 0 } {\{X^{x}(t),t\geq 0\}} of SPDEs with Gaussian and non-Gaussian colored noise, with the non-Gaussian noise being defined through a compensated Poisson random measure associated to a Lévy process. The functions to which we apply such Itô formula are in C 1 , 2 ⁢ ( [ 0 , T ] × H ) {C^{1,2}([0,T]\times H)} , as in the case considered for SDEs in [15]. Using this Itô formula, we prove exponential stability and exponential ultimate boundedness properties, in the mean square sense, for mild solutions. We also compare this Itô formula to an Itô formula for mild solutions introduced by Ichikawa in [12], and an Itô formula written in terms of the semigroup of the drift operator [5], which we extend to the non-Gaussian case.

One of the key challenges in cognitive radio (CR) networks is to perform spectrum sensing in environments characterized by shadowing and fading effects as well as non-Gaussian noise distributions. Existing literature on spectrum sensing focuses mainly on the Gaussian noise model assumption, which does not properly characterize all the various noise types found in practical CR systems. This paper addresses the problem of spectrum sensing in the presence of non-Gaussian noise and interference for cognitive radio systems. A novel detector based on the Rao test is proposed for the detection of a primary user in the non-Gaussian noise environments described by the generalized Gaussian distribution (GGD). The test statistic of the proposed Rao detector is derived and its detection performance is analyzed and compared to that of the traditional energy detection. The Rao-based detection is then extended to a multi-user cooperative framework based on an improved decision fusion rule. It is shown through computer simulations that for a given probability of false alarm, the Rao detector can significantly enhance the spectrum sensing performance over conventional energy detection in non-Gaussian noise. Furthermore, the proposed cooperative detection scheme has a significantly higher global probability of detection than the non-cooperative scheme.

Local damage detection based on vibration data analysis in the presence of Gaussian and heavy-tailed impulsive noise

In wireless communication systems, the ambient channel noise is known through experimental measurements to be decidedly non-Gaussian, due largely to impulse phenomena. It is known, too, that when data are contaminated by non-Gaussian noise, the conventional MMSE channel estimation method may perform poorly. We develop robust channel estimation algorithms to combat the impulse noise in multiple input multiple output (MIMO) systems. Simulation results show that the robust channel estimation (RCE) method offers significant performance gain with little attendant increase in computational complexity compared with the MMSE channel estimation method in non-Gaussian channels. To implement RCE in practice, we also develop two approximate robust channel estimation (ARCE) methods.

Time-difference-of-arrival estimation algorithms for cyclostationary signals in impulsive noise

Constrained least lncosh adaptive filtering algorithm

The Gaussian noise profile has been demonstrated to be an inaccurate model in several antenna beamforming problems. Many available beamformers are based on second-order statistics and their efficiency degrades significantly due to impulsive noise existed in the received signal. Therefore, a demand exists for attention to address beamforming problems under nonGaussian noise environments. According to the robust performance of information theoretic learning (ITL) criteria in nonGaussian environments, we propose a linearly constrained version of maximum correntropy learning algorithm in order to solve beamforming problem in presence of nonGaussian and impulsive noises. Simulation results of the proposed adaptive beamformer are provided to illustrate its accurate and resistant performance in comparison with conventional second-order-moment-based beamformers.

Communication systems are affected by channel distortions. Impulsive noise is one of the significant factors for channel impairments. The standard additive white Gaussian noise (AWGN) channel model and conventional estimation algorithms like least mean square (LMS) and its variants tend to be ineffective under such conditions. This paper presents a robust adaptive channel estimation algorithm using the Geman-McClure estimator in a diffusion-based distributed network. The analytical study on mean stability and mean square analysis is carried out under two separate noise statistics: Symmetric α-stable ( SαS) and Bernoulli-Gaussian (BG) distribution. The computer simulations confirm the proposed algorithm's competitive robustness compared to the Maximum Correntropy Criterion and Minimum Kernel Risk Sensitive Loss algorithms at a high impulsive noise environment without exponential cost function. Further, the efficiency is also verified by simulating the bit error rate by designing a minimum mean square error (MMSE) equalizer with the estimated coefficients.

In wireless communication systems, the ambient channel noise is known through experimental measurements to be decidedly non-Gaussian, due largely to impulse phenomena. It is known that when data are contaminated by non-Gaussian noise, the conventional MMSE channel estimation method may perform poorly. We develop robust channel estimation algorithms to combat the impulse noise in multiple input multiple output (MIMO) systems. Simulation results show that the robust channel estimation (RCE) method offers significant performance gain with little attendant increase in computational complexity compared with the MMSE channel estimation method in non-Gaussian channels. To implement RCE in practice, we also develop two approximate robust channel estimation (ARCE) methods.

We employ the circular cumulant approach to construct a low dimensional description of the macroscopic dynamics of populations of phase oscillators (elements) subject to non-Gaussian white noise. Two-cumulant reduction equations for α-stable noises are derived. The implementation of the approach is demonstrated for the case of the Kuramoto ensemble with non-Gaussian noise. The results of direct numerical simulation of the ensemble of N=1500 oscillators and the "exact" numerical solution for the fractional Fokker-Planck equation in the Fourier space are found to be in good agreement with the analytical solutions for two feasible circular cumulant model reductions. We also illustrate that the two-cumulant model reduction is useful for studying the bifurcations of chimera states in hierarchical populations of coupled noisy phase oscillators.

State of Charge (SOC) estimation plays a crucial role in lithium battery energy storage systems (LBESS). In this paper, we describes a Correntropy Adaptive Unscented Kalman Filter (UKF) algorithms that is able to solve the problem of non-Gaussian noise interference in SOC estimation of LBESS. We believe that the problem of non-Gaussian noise interference will appear widely in power system because Equipment failure or serious electromagnetic interference are increasing common and can cause negative effect for grid. Whereas previous algorithms used mean Square Error (MSE) as the cost function of the UKF too inefficient to deal with non-Gaussian in practice, the algorithm described in this practical: a robust Correntropy Unscented Kalman Filter (UKF) is introduced to improve SOC estimation accuracy in the existence of non-Gaussian noise. Furthermore, this paper combines the advantages of Correntropy and Adaptive filter to improve UKF algorithm, and derives a new robust Kalman Filter, which is called Adaptive C-UKF. The experiment results show that the proposed Adaptive C-UKF method can efficiently improve the estimation accuracy in the non-Gaussian noise environment.