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Performance analysis of incremental LMS over flat fading channels
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 mean-square 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
Distributed Estimation and Control of Algebraic Connectivity over Random Graphs
In this paper we propose a distributed algorithm for the estimation and
control of the connectivity of ad-hoc networks in the presence of a random
topology. First, given a generic random graph, we introduce a novel stochastic
power iteration method that allows each node to estimate and track the
algebraic connectivity of the underlying expected graph. Using results from
stochastic approximation theory, we prove that the proposed method converges
almost surely (a.s.) to the desired value of connectivity even in the presence
of imperfect communication scenarios. The estimation strategy is then used as a
basic tool to adapt the power transmitted by each node of a wireless network,
in order to maximize the network connectivity in the presence of realistic
Medium Access Control (MAC) protocols or simply to drive the connectivity
toward a desired target value. Numerical results corroborate our theoretical
findings, thus illustrating the main features of the algorithm and its
robustness to fluctuations of the network graph due to the presence of random
link failures.Comment: To appear in IEEE Transactions on Signal Processin
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