Research on Robustness of Geometric Algebra Based Adaptive Filtering Algorithms In Non-Gaussian Environment

In this paper, two new geometric algebra (GA) based adaptive filtering algorithms in non-Gaussian environment are proposed, which are deduced from the robust algorithms based on the minimum error entropy (MEE) criterion and the joint criterion of the MEE and the mean square error (MSE) with the help of GA theory. Some experiments validate the effectiveness and superiority of the GA-MEE and GA-MSEMEE algorithms in α-stable noise environment. At the same time, the GA-MSEMEE algorithm has faster convergence speed compared with the GA-MEE.

Isotropic and Non-Isotropic Signaling in Multivariate α-Stable Noise

A wide range of communication systems are corrupted by non-Gaussian noise, ranging from wireless to power line. In some cases, including interference in uncoordinated OFDM-based wireless networks, the noise is both impulsive and multivariate. At present, little is known about the information capacity and corresponding optimal input distributions. In this paper, we derive upper and lower bounds of the information capacity by exploiting non-isotropic inputs. For the special case of sub-Gaussian α-stable noise models, a numerical study reveals that isotropic Gaussian inputs can remain a viable choice, although the performance depends heavily on the dependence structure of the noise.

Spatial components dependence for bidimensional time-constant AR(1) model with $$\alpha $$-stable noise and triangular coefficients matrix

In this paper, we examine the bidimensional time-constant autoregressive model of order 1 with $$\alpha $$ α -stable noise. We focus on the case of the triangular coefficients matrix for which one of the spatial components of the model simplifies to the one-dimensional autoregressive time series. We study the asymptotic behaviour of the cross-codifference and the cross-covariation applied to describe the dependence in time between the spatial components of the model. As a result, we formulate the theorem about the asymptotic relation between both measures, which is consistent with the result that is correct for the case of the non-triangular coefficients matrix.