Performance Analysis of Incremental LMS over Flat Fading Channels

TL;DR

This paper analyzes how fading channels affect the performance of the incremental LMS algorithm in sensor networks, deriving stability conditions and showing that fading can cause bias and increased error metrics.

Contribution

It provides a detailed steady-state performance analysis of ILMS over fading channels, including stability conditions and the impact of channel gain variances.

Findings

ILMS is asymptotically biased under fading channels.

Mean stability depends only on mean channel gain.

Performance metrics worsen with higher channel gain variances.

Abstract

We study the effect of fading in the communication channels between sensor nodes on the performance of the incremental least mean square (ILMS) algorithm, and derive steady state performance metrics, including the mean-square deviation (MSD), excess mean-square error (EMSE) and meansquare error (MSE). We obtain conditions for mean convergence of the ILMS algorithm, and show that in the presence of fading channels, the ILMS algorithm is asymptotically biased. Furthermore, the dynamic range for mean stability depends only on the mean channel gain, and under simplifying technical assumptions, we show that the MSD, EMSE and MSE are non-decreasing functions of the channel gain variances, with mean-square convergence to the steady states possible only if the channel gain variances are limited. We derive sufficient conditions to ensure mean-square convergence, and verify our results through simulations.