Transient analysis of diffusion least‐mean squares adaptive networks with noisy channels

Abstract

In this paper, we study the effect of noisy channels on the transient performance of diffusion adaptive network with least-mean squares (LMS) learning rule. We first drive the update equation of diffusion LMS which incorporates the effects of noisy channels. Then, using the framework of fundamental weighted energy conservation relation, we derive closed-form expressions for learning curves in terms of mean-square deviation and excess mean-square error. We also find the mean and mean-square stability bounds of step-size for diffusion LMS with noisy channels. We show that although noisy channels affect the performance of the diffusion LMS network, the stability bounds of the step-size are the same form as in the ideal channels case. The derived closed-form expressions are shown to provide a good match with values found by simulation.

Adaptive Estimation over Networks with Link Failures and Channel Noise

“…However, the performance of adaptive networks can be affected by the presence of communication noise. This issue motivated our study of adaptive networks with noisy links [12][13][14][15]. In this paper, we extend the previous work in [10,14,15] and study the steady-state performance of a diffusion LMS adaptive network in a more realistic case, where the network topology is random due to link failures and communication between nodes happen in the presence of noise.…”

Adaptive multitask network based on maximum correntropy learning algorithm

“…The adapt-then-combine diffusion strategy based on minimum mean-square-error criterion has been developed in previous studies [1][2][3][4][5][6][7][8] to minimize Equation 1 in a cooperative manner. Each agent k of the network tries to learn its optimum vector w o k through a 2-step process including adaptation and combination steps:…”

“…1 Among several strategies for distributed optimization and learning over networks, [1][2][3][4][5][6][7][8] diffusion strategy 7 is an impressive approach due to its scalability and robustness. 1 Among several strategies for distributed optimization and learning over networks, [1][2][3][4][5][6][7][8] diffusion strategy 7 is an impressive approach due to its scalability and robustness.…”

“…Adaptation and learning over distributed networks allow a collection of interconnected agents to estimate and track an objective in a cooperative manner. 1 Among several strategies for distributed optimization and learning over networks, [1][2][3][4][5][6][7][8] diffusion strategy 7 is an impressive approach due to its scalability and robustness.…”

Nonlinear diffusion adaptation with bounded transmission over distributed networks

“…The diffusion LMS of [6] is generalized in [7] where measurement data are exchanged as well as parameter estimates. When the linear diffusion is performed with wireless communications, noisy links are considered in [8], [10], [11], and fading channels in [12]. Further variations of linear diffusion strategies in 1 Each node k has access to data {d k (i), u k,i } and estimates w o using an adaptive learning algorithm.…”