  In this work we analyze the mean-square performance of different strategies
for distributed estimation over least-mean-squares (LMS) adaptive networks. The
results highlight some useful properties for distributed adaptation in
comparison to fusion-based centralized solutions. The analysis establishes
that, by optimizing over the combination weights, diffusion strategies can
deliver lower excess-mean-square-error than centralized solutions employing
traditional block or incremental LMS strategies. We first study in some detail
the situation involving combinations of two adaptive agents and then extend the
results to generic N-node ad-hoc networks. In the later case, we establish
that, for sufficiently small step-sizes, diffusion strategies can outperform
centralized block or incremental LMS strategies by optimizing over
left-stochastic combination weighting matrices. The results suggest more
efficient ways for organizing and processing data at fusion centers, and
present useful adaptive strategies that are able to enhance performance when
implemented in a distributed manner.
