Performance Analysis of Diffusion LMS for Cyclostationary White Non-Gaussian Inputs

Abstract

This paper studies the transient behavior of the diffusion least-mean-square (LMS) algorithm over the single-task network for the non-stationary system using diverse types of cyclostationary white non-Gaussian inputs for an individual node. The analytical models of the recursive mean-weight-error vector and mean-square-deviation are derived for the system with random walk varying parameters and the white random process with periodically deterministic time-varying input variance. In addition, the approximated steady-state mean-square-deviation of the diffusion LMS is presented for the slow varying input variance. Monte Carlo simulations show excellent agreement with the theoretical prediction of mean-square-deviation validating the accuracy of derived analytical models and the tracking ability for non-stationary system and cyclostationary inputs simultaneously.INDEX TERMS Diffusion LMS, cyclostationary white non-Gaussian processes, adaptive network, tracking analysis.

Hidden Markov Model Decorrelated Diffusion Leaky LMS With Optimized Leaky Factor

“…For the minimum disturbance, we can replace (15) in (11). Then, we have the minimum disturbance equal to…”

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

“…This implies that different input distributions with the same kurtosis yield the same MSD for the FC-DLMS algorithm. Equation (26) implies that the MSD dependence on the type of input distribution is negligible for small 𝜇 and that the dependence increases as 𝜇 increases, since the kurtosis appears only in the 𝜇 2 term in the MSD recurrence. This is further detailed in part B of Section 4 below.…”

“…Professor Ali Sayed and his co-researchers have published a large variety of structural and stochastic analysis papers on the subject. [1][2][3][4][5][6][7][8][9][10][11][12] Examples of applications involving cyclostationary signals are mentioned in Eweda et al, 22(p. 4753) Existing studies of diffusion algorithms for cyclostationary inputs [24][25][26] involved a vector structure which gives rise to complex recursions for the adaptive weight error vector and the resultant mean square deviation (MSD). They use a Kronecker product formulation introduced in Lopes and Sayed, 6 resulting in block diagonal matrices of the size NM × NM where N is the adaptive filter length and M is the number of nodes.…”

“…There are two problems with this approach: 1) the energy principle 27,28 is only applicable if the filter converges, which is not the case for cyclostationary inputs; 2) the use of the Kronecker product formulation with the disadvantages listed above. Finally, Gao and Chen 26 studied the case of the DLMS algorithm for cyclostationary white non-Gaussian inputs. This is an extension of the work in Eweda et al 22 to the DLMS algorithm, which also uses Kronecker product formulation with the disadvantages listed above.…”

“…This is an extension of the work in Eweda et al 22 to the DLMS algorithm, which also uses Kronecker product formulation with the disadvantages listed above. In summary, the theory in Wang and Zhao 24,25 and Gao and Chen 26 makes analysis and design very difficult and reduces the advantages provided by generality. Most of the time, practical designs are based on the study of simplified structures.…”