Analysis of a Diffusion LMS Algorithm With Communication Delays for Cyclostationary White Gaussian Inputs

Available analyses of the diffusion LMS (DLMS) algorithm assume that the nodes probe the unknown system with zero delay. This assumption is unrealistic, since the unknown system is usually distant from the nodes. The present paper studies the behavior of the algorithm without this assumption. The analysis is done for a network having a central combiner. This structure reduces the dimensionality of the resulting stochastic models while preserving important diffusion properties. Communication delays between the nodes and the central combiner are also considered in the analysis. The analysis is done for system identification for cyclostationary white Gaussian nodal inputs. Mean and mean-square behaviors of the algorithm are analyzed. It is found that delays in probing the unknown system yield a bias in the algorithm without increasing its convergence time. The communication delays between the nodes and the central combiner increase the convergence time without affecting the steady-state behavior. The stability of the algorithm is not affected by either type of delay. The analysis exactly matches the simulations.