Stochastic analysis of the diffusion least mean square and normalized least mean square algorithms for cyclostationary white Gaussian and non‐Gaussian inputs

Abstract

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 except for distributions with infinite variance. 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.

Gamelan Data Repository: The Implementation of Information and Communication Technology Preserving the Balinese Traditional Musical Orchestra

“…By knowing the frequency of a note, you can tell which tone it came from. Adaptive filter Least Mean Square (LMS) is a digital filter that is able to adjust the filter parameters to the given signal using the least mean square adaptive algorithm (Eweda et al, 2021;Xu et al, 2021). So that this filter can be used to detect the frequency of various gamelan device signals.…”

Stochastic Model for the LMS Algorithm with Symmetric/Antisymmetric Properties

“…In this context, stochastic models may serve as a theoretical basis for studying the behavior of adaptive algorithms without relying only on extensive Monte Carlo (MC) simulations [15][16][17][18][19][20][21][22][23]. Such models are useful to establish (through mathematical expressions) stability conditions for the algorithm and a suitable range of values for its parameters, as well as interesting cause-and-effect relationships between performance metrics and algorithm parameters, which can then help the designer [24][25][26][27][28][29].…”

“…which depends on (13); hence, the characteristics observed in the convergence of the (virtual) adaptive filters hold also for the convergence of the (global) adaptive filter. Therefore, the mean weight behavior of h 1 (n), h 2 (n), and h(n) can be predicted [from (13) and (23)] if the evolution of (20) is known.…”