Diffusion LMS with Communication Delays: Stability and Performance Analysis

Fei Hua (1) , Roula Nassif (2) , Cédric Richard (3) , Haiyan Wang (1) , Ali H Sayed (4)

1 NPU - Northwestern Polytechnical University [Xi'an]
2 AUB - American University of Beirut [Beyrouth]
3 LAGRANGE - Joseph Louis LAGRANGE
4 EPFL - Ecole Polytechnique Fédérale de Lausanne

We study the problem of distributed estimation over adaptive networks where communication delays exist between nodes. In particular, we investigate the diffusion Least-Mean-Square (LMS) strategy where delayed intermediate estimates (due to the communication channels) are employed during the combination step. One important question is: Do the delays affect the stability condition and performance? To answer this question, we conduct a detailed performance analysis in the mean and in the mean-square-error sense of the diffusion LMS with delayed estimates. Stability conditions, transient and steady-state meansquare-deviation (MSD) expressions are provided. One of the main findings is that diffusion LMS with delays can still converge under the same step-sizes condition of the diffusion LMS without delays. Finally, simulation results illustrate the theoretical findings.

Mots clés: Communication delays; distributed estimation; diffusion LMS; performance analysis; stability

Domaines: Traitement du signal et de l'image [eess.SP]; Intelligence artificielle [cs.AI]

Fei Hua, Roula Nassif, Cédric Richard, Haiyan Wang, Ali H Sayed. Diffusion LMS with Communication Delays: Stability and Performance Analysis. IEEE Signal Processing Letters, 2020, 27, pp.730 - 734. ⟨10.1109/lsp.2020.2990086⟩. ⟨hal-03347250⟩