  We investigate the performance of distributed least-mean 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.
