Distributed Diffusion-Based LMS for Node-Specific Adaptive Parameter Estimation

A distributed adaptive algorithm is proposed to solve a node-specific parameter estimation problem where the nodes are interested in estimating parameters that can be of local interest, common interest to a subset of nodes and 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, yet coupled Least Mean Squares (LMS) algorithms, each associated with the estimation of a specific set of local, common or global parameters. The study of convergence in the mean sense reveals that the proposed algorithm is asymptotically unbiased. Moreover, a spatial-temporal energy conservation relation is provided to evaluate the steady-state performance at each node in the mean-square sense. Finally, the theoretical results and the effectiveness of the proposed technique are validated through computer simulations in the context of cooperative spectrum sensing in Cognitive Radio networks.