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

We introduce an adaptive distributed technique that is suitable for parameter estimation in a network where nodes have different but overlapping interests. At each node, the parameters to be estimated can be of local interest, global interest to the whole network and common interest to a subset of nodes. To estimate each set of local, common and global parameters, a least mean squares (LMS) algorithm is implemented under an incremental mode of cooperation. Coupled with the estimation of the different sets of parameters, the implementation of each LMS algorithm is only undertaken by the nodes of the network interested in a specific set of local, common or global parameters. Besides obtaining the conditions under which the proposed strategy converges in the mean to the solution of a centralized unit that processes all the observations, a spatial-temporal energy conservation relation is provided to evaluate the steady-state performance at each node across the network. Finally, the theoretical results are validated through generic computer simulations as well as simulation results in the context of cooperative spectrum sensing in cognitive radio networks.