  A distributed adaptive algorithm is proposed to solve a node-specific
parameter estimation problem where nodes are interested in estimating
parameters of local interest and parameters of global interest to the whole
network. To address the different node-specific parameter estimation problems,
this novel algorithm relies on a diffusion-based implementation of different
Least Mean Squares (LMS) algorithms, each associated with the estimation of a
specific set of local or global parameters. Although all the different LMS
algorithms are coupled, the diffusion-based implementation of each LMS
algorithm is exclusively undertaken by the nodes of the network interested in a
specific set of local or global parameters. To illustrate the effectiveness of
the proposed technique we provide simulation results in the context of
cooperative spectrum sensing in cognitive radio networks.
