Tracking Performance and Optimal Adaptation Step-Sizes of Diffusion-LMS Networks

In this paper, we investigate the effect of adaptation step sizes on the tracking performance of diffusion least-mean squares (DLMS) algorithms in networks under nonstationary signal conditions. We assume that the network parameter vector being estimated varies over time according to a first-order random walk model. To find the optimal adaptation step sizes over the network, we formulate a constrained nonlinear optimization problem and solve it through a log-barrier Newton algorithm in an iterative manner. Our studies reveal that the optimal step size of each node in the network not only depends on the statistics of the random walk and the energy profile of the node itself, but also on the energy and statistical profile of its neighboring nodes. The results show that the optimal step sizes can substantially improve the performance of DLMS algorithms in tracking time-varying parameters over networks. We also find that the DLMS algorithms have faster tracking ability and superior steady-state mean-square deviation (MSD) performance than the DLMS in noncorporative mode since the diffusion mode of cooperation, and each node at each iteration can take a larger step toward the network optimal parameters.