Adaptive beamforming based on linearly constrained maximum correntropy learning algorithm

Underdetermined inverse sparse signal reconstruction problems in the presence of non-Gaussian noise interference are often encountered in high-mobility wireless communications and signal processing. These problems can be solved by finding the minimizer of a suitable objective function which consists of a data-fitting term and a regularization term with different mixed-norms. Based on the Gaussian-noise assumption, two mixed norms (i.e. l 2 /l 1 and l ∞ /l 1 ) were confirmed as effective as well as stable algorithms for reconstructing sparse signals. However, the two algorithms are unable to reconstruct signal stable under non-Gaussian noise environments. In this paper, we propose a stable least absolute deviation (LAD) algorithm (i.e., l 1 /l 1 ) for achieving two aspects: exploiting signal sparse structure information as well as mitigating the non-Gaussian noise interference. First of all, regularization parameter of the proposed algorithm is selected via Monte Carlo simulations. Then, experimental results in different non-Gaussian environments are used to demonstrate the effectiveness of the proposed algorithm.

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.

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

Constrained least lncosh adaptive filtering algorithm

Linear adaptive interference suppression is an effective approach in mitigating Multiple Access Interference (MAI) in CDMA communications channels under Gaussian noise. However, applying Gaussian-based linear receivers to realistic communications channels affected by impulsive noise can result in performance degradation and is therefore a suboptimal solution. The linear adaptive receiver is limited by its structural formulation as a simple linear combiner with a hyperplanar decision boundary that is unable to form arbitrarily non-linear boundaries inherent in CDMA communications, particularly under hostile channel conditions. In this paper, we consider the use of a multilayer perceptron (MLP) for robust single-user detection in multiuser non-Gaussian channels; the receiver is trained via the back-propagation (BP) algorithm using a known training sequence. Theoretical arguments supported by simulation suggest that the perceptron-based receiver, which combines the basic attributes of nonlinearity, adaptivity and non-parametric approach, shows promise as a near-far resistant receiver in non-Gaussian environments.

Robust adaptive sparse channel estimation problem has been attracted highly attention in the next-generation wireless communications systems. Re-weighted L1-norm penalized sign least mean square error (RL1-SLMS) algorithm is considered as one of attractive methods to estimate unknown sparse system as well as to mitigate impulsive noises. However, the convergence performance of RL1-SLMS is very ambiguous comparing with its preliminary version. This paper provides comprehensive convergence analysis for the RL1-SLMS algorithm under non-Gaussian impulsive noise environment. Numerical simulations are given to show the fast convergence and robustness with respect to system sparsity as well as non-Gaussian noise.

In this paper, the non-recursive estimation algorithm using a batch filter based on particle filtering is developed and utilized for one-dimensional nonlinear example. For comparison study, algorithms of a batch filter based on unscented transformation and generic particle filtering are briefly reviewed and new algorithm of a batch filter based on particle filtering is presented. For verification of presented batch filter's performance, the numerical simulations and the accuracy assessment are achieved and results are compared with those of a batch filter based on unscented transformation for various nonlinear and non-Gaussian environments. The root mean square value of differences between observational values and computed values after convergence is used for precision check of filtering process, estimated initial state value and the difference between true initial state value and estimated initial state value are used for state accuracy check of nonlinear estimation. Large initial state and various type of measurement noise are used for nonlinear and non-Gaussian environments, respectively. Under large initial state error or large non-Gaussian measurement noise, the developed non-recursive estimation algorithm give more robust and accurate estimation results than those of a batch filter based on unscented transformation easily. Finally, the non-recursive batch filter based on particle filtering is effectively applicable for batch estimation problems under nonlinear and non-Gaussian environments.

This paper investigates the kernel entropy based extended Kalman filter (EKF) as the navigation processor for the Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS). The algorithm is effective for dealing with non-Gaussian errors or heavy-tailed (or impulsive) interference errors, such as the multipath. The kernel minimum error entropy (MEE) and maximum correntropy criterion (MCC) based filtering for satellite navigation system is involved for dealing with non-Gaussian errors or heavy-tailed interference errors or outliers of the GPS. The standard EKF method is derived based on minimization of mean square error (MSE) and is optimal only under Gaussian assumption in case the system models are precisely established. The GPS navigation algorithm based on kernel entropy related principles, including the MEE criterion and the MCC will be performed, which is utilized not only for the time-varying adaptation but the outlier type of interference errors. The kernel entropy based design is a new approach using information from higher-order signal statistics. In information theoretic learning (ITL), the entropy principle based measure uses information from higher-order signal statistics and captures more statistical information as compared to MSE. To improve the performance under non-Gaussian environments, the proposed filter which adopts the MEE/MCC as the optimization criterion instead of using the minimum mean square error (MMSE) is utilized for mitigation of the heavy-tailed type of multipath errors. Performance assessment will be carried out to show the effectiveness of the proposed approach for positioning improvement in GPS navigation processing.

The statistical characteristics of impulsive noise differ greatly from those of Gaussian noise. Hence, the performance of conventional decoders, optimized for AWGN channels is not promising in non-Gaussian environments. In order to achieve improved performance in impulsive environments the decoder structure needs to be adapted in accordance with the impulsive noise model. This paper provides performance analysis of turbo codes over fully interleaved Nakagami-m fading channels with Mid- dleton's additive white Class-A impulsive noise (MAWCAIN). Simulation results for memoryless Nakagami-m fading channels under coherent BPSK signaling are provided for the cases of ideal channel state information (ICSI) and no channel state information (NCSI) at the decoder. As in the 3GPP UMTS forward link an eight state turbo encoder having (1, 13/15,13/15) generator polynomial is used throughout the analysis. The novelty of this work lies in the fact that this is an initial attempt to provide a detailed analysis of turbo codes over Nakagami-m fading channels with impulsive noise rather than fading channels with AWGN.

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.

Traditionally, Kalman filter (KF) is designed with the assumptions of non-delayed measurements and additive white Gaussian noises. However, practical problems often fail to satisfy these assumptions and the conventional Kalman filter suffers from poor estimation accuracy. This paper proposes a modified Kalman filter to address both the problems of delayed measurements and non-Gaussian noises. The proposed filter is updated using correntropy maximization criterion, which is suitable for non-Gaussian noise environments. It falls short of a closed-form solution due to analytically complex equations that appear during the filtering. We use fixed-point iterative method to find an approximate solution. The delayed measurement problem is addressed by implementing a likelihood-based approach to identify the delay. Based on the identified delay information, the measurement is used to update the desired state in the subsequent past instant. To perform real-time filtering, the estimated state is further updated up to the current time instant using the process dynamics. The performance analysis validates the improved accuracy of the proposed method compared to the ordinary Kalman filter and its existing extensions.

<div> <h2>Abstract</h2> <p><strong>Background:</strong> Spectrum sensing is a crucial step to realize the Cognitive Radio technology. The spectrum sensing schemes at low signal-to-noise ratio, noise uncertainty and especially under the background of non-Gaussian noise, provide low detection of the primary user. This results in missed detection or false alarm and increases higher interference to the primary user. <strong>Objectives:</strong> Detection schemes designed for additive Gaussian noise exhibit poor performance in the non-Gaussian environment. This study considers the problem of spectrum sensing with the assumption that the noise follows a non-Gaussian distribution with heavier tails. <strong>Methods/findings:</strong> A fuzzy logicbased method is proposed for primary user detection under non Gaussian Noise. The results are highlighted for the Laplacian noise. Through Monte Carlo simulations it is observed that Laplacian noise noticeably affects the performance of energy detector. Also, a fractional change in noise uncertainty degrades the performance of energy detector. The performance of the proposed scheme is presented through receiver operating characteristic (ROC) and plot of the detection probability versus signal-to-noise ratio (SNR) using simulations. It is shown that by appropriately choosing the membership functions and the fuzzy rule base in the fuzzy inference system the proposed fuzzy logic method for spectrum sensing provides reliable detection.</p> <p><strong>Keywords:</strong> NonGaussian noise; Fuzzy logic; Spectrum sensing; noise uncertainty</p> </div> <div></div> <div> </div>

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.

This study addresses the state estimation problem for the preceding vehicle in vehicle-to-vehicle (V2V) cooperative perception, with the objective of balancing estimation accuracy against communication load under constraints of limited bandwidth and non-Gaussian noise interference. To this end, an extended Kalman filtering algorithm is proposed that integrates an event-triggered (ET) mechanism with the maximum correntropy criterion (MCC). The event-triggered mechanism adaptively regulates communication frequency, significantly reducing network load while preserving estimation performance. Meanwhile, the maximum correntropy criterion enhances the filter’s robustness against non-Gaussian noise, enabling high-precision state estimation under limited communication resources. Simulation results under double lane-change and continuous sinusoidal steering scenarios show that, compared to conventional extended Kalman filtering and existing event-triggered robust filtering methods, the proposed algorithm achieves better estimation accuracy and stability in non-Gaussian noise environments. Moreover, it reduces the average communication load by approximately 68% without compromising estimation performance. This work provides an effective solution for state estimation in V2V cooperative perception that combines high robustness with high communication efficiency.

Filtered-x generalized mixed norm (FXGMN) algorithm for active noise control