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Publication# Diffusion LMS strategies for parameter estimation over fading wireless channels

Abstract

We propose a modified diffusion strategy for parameter estimation in sensor networks where nodes exchange information over fading wireless channels. We show that the effect of fading can be mitigated by incorporating local equalization coefficients into the diffusion process. We explain how the equalization coefficients are chosen and show that the (mean) stability of the network continues to be insensitive to the choice of the combination weights and to the network topology. Our computer experiments demonstrate that the performance of the modified diffusion algorithm in fading scenario is nearly identical to that of centralized least-mean square (LMS) with equalized input data.

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Ontological neighbourhood

Fading

In wireless communications, fading is variation of the attenuation of a signal with the various variables. These variables include time, geographical position, and radio frequency. Fading is often modeled as a random process. A fading channel is a communication channel that experiences fading. In wireless systems, fading may either be due to multipath propagation, referred to as multipath-induced fading, weather (particularly rain), or shadowing from obstacles affecting the wave propagation, sometimes referred to as shadow fading.

Rayleigh fading

Rayleigh fading is a statistical model for the effect of a propagation environment on a radio signal, such as that used by wireless devices. Rayleigh fading models assume that the magnitude of a signal that has passed through such a transmission medium (also called a communication channel) will vary randomly, or fade, according to a Rayleigh distribution — the radial component of the sum of two uncorrelated Gaussian random variables.

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

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