An optimum step-size assignment for incremental LMS adaptive networks based on average convergence rate constraint

This paper presents an optimum step-size assignment for incremental least-mean square adaptive networks in order to improve its robustness against the spatial variation of observation noise statistics over the network. We show that when the quality of measurement information (in terms of observation noise variances) is available, we can exploit it to adjust the step-size parameter in an adaptive network to obtain better performance. We formulate the optimum step-size assignment as a constrained optimization problem and then solve it via the Lagrange multipliers approach. The derived optimum step-size for each node requires information from other nodes, thus with some justifiable assumptions, near-optimum solutions are derived that depend only on local information. We show that the incremental LMS adaptive network with near-optimal step sizes has improved robustness and steady-state performance. Simulation results are also presented to support the theoretical results.