Omer M. Abdelrhman

In this study, we present novel algorithms for the robust direction of arrival estimation (DOA) in systems whose input and output are contaminated with noise. Our approach involves the utilization of a Half-Quadratic criterion (HQC) cost function, which enables the development of a robust total HQC algorithm (THQC). Additionally, to achieve an optimal balance between convergence speed and steady-state error performance, we propose a variable step-size approach based on THQC (VSS-THQC). This adaptive method adjusts the step size according to the signal-to-noise ratio (SNR). We provide a comprehensive mean convergence and stability analysis of the THQC algorithm, and further, we validate its effectiveness through numerical simulations conducted in the impulsive noise distribution. These simulations serve to demonstrate the efficiency of our proposed methods compared to some competitive methods.

Recently, robust constrained adaptive filtering algorithms have garnered significant research attention and have been the subject of extensive investigation. Most of these methods utilize specific error nonlinearity cost functions, which have demonstrated superiority over traditional methods based on the least mean squared error cost function, particularly in environments contaminated by Gaussian and non-Gaussian noise. This paper introduces a generalized family of constrained robust least mean logarithmic square (CRLMLS) algorithms that optimize error nonlinearity called a relative logarithmic cost function. The proposed method offers a tradeoff between robustness and computational complexity in comparison with other recently developed competitive methods. Using an energy conservation approach, we establish a sufficient condition for mean-square stability. Additionally, we analyze the steady-state mean-square deviation performance of the standard CRLMLS algorithm under both Gaussian and non-Gaussian noise distributions. We validate the effectiveness of the proposed algorithms through numerical simulations in various impulsive noise scenarios, focusing on applications in system identification and beamforming.

In recent years, the spotlight of research in the adaptive learning era has turned towards distributed adaptive filtering algorithms for sparse systems over wireless sensor networks (WSN) leveraging error nonlinearities. This interest has been sparked by their exceptional efficiency in both Gaussian and non-Gaussian/impulsive noise environments, leading to the development of many adaptive filtering algorithms. Notably, among these approaches is the proportionate robust diffusion recursive exponential hyperbolic cosine (PR-DREHC) algorithm, a recent method based on the exponential hyperbolic cosine function (EHCF). While the PR-DREHC algorithm is robust against impulsive noise distortion, it remains afflicted by notable shortcomings such as pronounced computational burden and notable steady-state misalignment. To address these limitations, this study introduces a novel approach by introducing a new cost function termed the generalized correntropy-based modified sigmoid function (GCMSF). Our findings substantiate that the GCMSF holds the potential to engender robust algorithms distinguished by enhanced performance in terms of steady-state misalignment and expedited convergence. Capitalizing on this insight, we present novel robust diffusion recursive algorithms formulated through the maximization of the proposed GCMSF cost function. This ensemble encompasses the robust proportionate diffusion recursive generalized correntropy-based modified sigmoid function (RP-DRGCMSF) algorithm. The mean and mean square stability conditions of the introduced approach are also derived. Finally, the proposed algorithm is applied to practical simulation studies to examine its performance under different Gaussian and non-Gaussian noise environments and compare it to its respective competitors.

Recent advances in adaptive filtering have highlighted the effectiveness of the robust algorithms employing error nonlinearity cost functions such as the maximum versoria criterion (MVC), which utilizes stochastic gradient descent (SGD). Traditional SGD-based methods struggle with signals exhibiting sharp spikes and outliers, typical in many modern applications and cannot be adequately modeled by Gaussian processes. To address this issue, we model both the input and noise signals using a-stable distribution. We enhance the MVC method through a fractional-order SGD (FoSGD) approach, resulting in a new method called the fractional-order maximum versoria criterion (FoMVC) algorithm. Then, we rigorously analyze the algorithm’s mean stability and demonstrate its superior performance over existing methods through Monte Carlo simulations in diverse non-Gaussian environments.

In adaptive filtering for direction-of-arrival (DOA) estimation, traditional bias-compensated models often suffer from significant performance degradation in the presence of impulsive noise affecting both input and output signals. This paper addresses this challenge by introducing new algorithms for robust DOA estimation tailored for environments contaminated by impulsive noise. We initially employ the error-in-variable (EIV) model to derive a generalized framework for robust adaptive DOA estimation algorithms. Our methodology incorporates the Maximum Versoria (MV) criterion as a cost function, facilitating the development of the robust Gradient Total MV (GTMV) algorithm. To further enhance performance, we introduce a variable step-size mechanism within the GTMV framework (VSS-GTMV), which dynamically adjusts the step size based on the signal-to-noise ratio (SNR) to optimize the trade-off between convergence speed and steady-state error. The convergence properties of the GTMV algorithm are analytically examined, and its effectiveness is substantiated through extensive numerical simulations in impulsive noise environments. Comparative results demonstrate the superiority of our proposed methods over existing competitive approaches in terms of accuracy and robustness.

In recent years, algorithms based on the Maximum Versoria Criterion (MVC) and a relative logarithmic cost function have gained the attention of researchers because they improve the filtering accuracy and robustness towards non-Gaussian/impulsive noises. To further enhance the steady-state convergence behavior of these aforementioned algorithms in impulsive noise scenarios, we introduce a generalized, robust logarithmic family (GRLF) framework that underlies the relative logarithmic cost function and MVC, and the corresponding GRLF-based adaptive filters called least mean square based-GRLF (GRLF-LMS) and least absolute difference based-GRLF (GRLF-LAD) algorithms are designed. With an approximate solution using Taylors expansion, the steady-state behavior of the GRLF-LMS and GRLF-LAD methods is presented. Then, algorithms are used in practical simulation studies in system identification to compare the performance of GRLF-LMS and GRLF-LAD filtering in Gaussian and non-Gaussian impulsive environments in terms of accuracy and robustness to that of their competitors.