  The diffusion least mean square (DLMS) and the diffusion normalized least
mean square (DNLMS) algorithms are analyzed for a network having a fusion
center. This structure reduces the dimensionality of the resulting stochastic
models while preserving important diffusion properties. The analysis is done in
a system identification framework for cyclostationary white nodal inputs. The
system parameters vary according to a random walk model. The cyclostationarity
is modeled by periodic time variations of the nodal input powers. The analysis
holds for all types of nodal input distributions and nodal input power
variations. The derived models consist of simple scalar recursions. These
recursions facilitate the understanding of the network mean and mean-square
dependence upon the 1) nodal weighting coefficients, 2) nodal input kurtosis
and cyclostationarities, 3) nodal noise powers and 4) the unknown system
mean-square parameter increments. Optimization of the node weighting
coefficients is studied. Also investigated is the stability dependence of the
two algorithms upon the nodal input kurtosis and weighting coefficients.
Significant differences are found between the behaviors of the DLMS and DNLMS
algorithms for non-Gaussian nodal inputs. Simulations provide strong support
for the theory.
