We study the effect of fading in the communication channels between nodes on the performance of the incremental least mean square (ILMS) algorithm. We derive steadystate performance metrics, including the mean-square deviation (MSD), excess mean-square error (EMSE), and mean-square error (MSE). We obtain the sufficient conditions to ensure meansquare convergence, and verify our results through ...

in the present paper, we introduce some new sequence spaces derived by riesz mean and the notions of almost and strongly almost convergence in a real 2-normed space. some topological properties of these spaces are investigated. further, new concepts of statistical convergence which will be called weighted almost statistical convergence, almost statistical convergence and statistical convergence...

An efficient and computationally linear algorithm is derived for total least squares solution of adaptive filtering problem, when both input and output signals are contaminated by noise. The proposed total least mean squares (TLMS) algorithm is designed by recursively computing an optimal solution of adaptive TLS problem by minimizing instantaneous value of weighted cost function. Convergence a...

LMS algorithm is simple and is well suited for continuous transmission systems since it is a continuously adaptive algorithm. However, it is not known for its convergence speed in the presence of Gaussian, spatially white, of null mean and variance which has prompted people to use other complicated algorithms. In the above scenario LMS has maximum mean square error and minimum error stability. ...

A version of the fundamental mean-square convergence theorem is proved for stochastic differential equations (SDEs) in which coefficients are allowed to grow polynomially at infinity and which satisfy a one-sided Lipschitz condition. The theorem is illustrated on a number of particular numerical methods, including a special balanced scheme and fully implicit methods. The proposed special balanc...

This paper provides a partial-update normalized sign least-mean square (NSLMS) algorithm with sparse updates. The proposed algorithm reduces the computational complexity compared with the conventional L∞-norm adaptive filtering algorithms by decreasing the frequency of updating the filter coefficients and updating only a part of the filter coefficients. And we develop a mean square analysis to ...

Abstract. A class of implicit methods is introduced for Ito stochastic differential equations with Poisson-driven jumps. A convergence proof shows that these implicit methods share the same strong finite-time convergence rate as the explicit Euler–Maruyama scheme. A mean-square linear stability analysis shows that implicitness offers benefits, and a natural analogue of mean-square A-stability i...

This paper presents a new variable step-size normalized subband adaptive filter (VSS-NSAF) algorithm. The proposed algorithm uses the prior knowledge of the system impulse response statistics and the optimal step-size vector is obtained by minimizing the mean-square deviation(MSD). In comparison with NSAF, the VSS-NSAF algorithm has faster convergence speed and lower MSD. To reduce the computa...

This paper is concerned with weighted least mean square design of two-dimensional (2-D) zero-phase FIR lters with quadrantally symmetric and antisymmetric frequency responses. The optimal solutions are rst characterized by certain integral equations, and the existence, and uniqueness of the weighted least mean square solution for 2-D FIR lter design are then established using contraction mappin...