Abstract-We investigate the performance of distributed leastmean square (LMS) algorithms for parameter estimation over sensor networks where the regression data of each node are corrupted by white measurement noise. Under this condition, we show that the estimates produced by distributed LMS algorithms will be biased if the regression noise is excluded from consideration. We propose a bias-elimination technique and develop a novel class of diffusion LMS algorithms that can mitigate the effect of regression noise and obtain an unbiased estimate of the unknown parameter vector over the network. In our development, we first assume that the variances of the regression noises are known a-priori. Later, we relax this assumption by estimating these variances in real-time. We analyze the stability and convergence of the proposed algorithms and derive closed-form expressions to characterize their mean-square error performance in transient and steady-state regimes. We further provide computer experiment results that illustrate the efficiency of the proposed algorithms and support the analytical findings.

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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.

In this paper, we propose and study the distributed blind adaptive algorithms for wireless sensor network applications. Specifically, we derive a distributed forms of the blind least mean square (LMS) and recursive least square (RLS) algorithms based on the constant modulus (CM) criterion. We assume that the inter-sensor communication is single-hop with Hamiltonian cycle to save the power and communication resources. The distributed blind adaptive algorithm runs in the network with the collaboration of nodes in time and space to estimate the parameters of an unknown system or a physical phenomenon. Simulation results demonstrate the effectiveness of the proposed algorithms, and show their superior performance over the corresponding non-cooperative adaptive algorithms.Index Terms-Distributed adaptive algorithms; wireless sensor networks; incremental cooperative strategy; constant modulus criterion.

Abstract-We study the problem of distributed adaptive estimation over networks where nodes cooperate to estimate physical parameters that can vary over both space and time domains. We use a set of basis functions to characterize the spacevarying nature of the parameters and propose a diffusion least mean-squares (LMS) strategy to recover these parameters from successive time measurements. We analyze the stability and convergence of the proposed algorithm, and derive closed-form expressions to predict its learning behavior and steady-state performance in terms of mean-square error. We find that in the estimation of the space-varying parameters using distributed approaches, the covariance matrix of the regression data at each node becomes rank-deficient. Our analysis reveals that the proposed algorithm can overcome this difficulty to a large extent by benefiting from the network stochastic matrices that are used to combine exchanged information between nodes. We provide computer experiments to illustrate and support the theoretical findings.