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Steady-State Analysis of Incremental LMS Adaptive Networks With Noisy Links

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3 Author(s)
Khalili, A. ; Fac. of Electr. & Comput. Eng., Univ. of Tabriz, Tabriz, Iran ; Tinati, M.A. ; Rastegarnia, A.

Recently proposed adaptive networks assume perfect communication among the nodes. In this correspondence, we extend existing analysis to study the performance of incremental least mean square (LMS) adaptive networks in a more realistic case in which communication links between nodes are considered noisy. More precisely, using weighted spatial-temporal energy conservation relation, we arrive a variance relation which contains moments that represent the effects of noisy links. We evaluate these moments and derive closed-form expressions for the mean-square deviation (MSD), excess mean-square error (EMSE) and mean-square error (MSE) to explain the steady-state performance at each individual node. The derived expressions have good match with simulations. However, the main result is that unlike the ideal link case, the steady-state MSD, EMSE, and MSE curves are not monotonically increasing functions of the step-size parameter when links are noisy. We illustrate this behavior and also find the optimal step-size in a closed-form (for a special case) which minimizes the steady-state values of MSD, EMSE, and MSE in each node. Simulations are also provided to clarify the derived theoretical results.

Published in:

Signal Processing, IEEE Transactions on  (Volume:59 ,  Issue: 5 )

Date of Publication:

May 2011

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