Closed-Form MSE Performance of the Distributed LMS Algorithm

Mean-square error (MSE) performance analysis is conducted for a novel distributed least-mean square (D-LMS) algorithm, which is based on consensus, in-network, adaptive estimation using wireless sensor networks (WSNs). For sensor observations that are linearly related to the time-invariant parameter of interest and independent Gaussian data, exact closed-form expressions are derived for the global and sensor-level MSE evolution and steady-state limiting values. Tracking performance is also investigated when the true parameter adheres to a random-walk model. Remarkably for small step-sizes the results accurately extend to the pragmatic setup whereby sensors acquire temporally-correlated (non-)Gaussian data.