# Diffusion LMS with Communication Delays: Stability and Performance Analysis

arXiv: https://arxiv.org/abs/2004.08881 · HTML: https://mlsanity.com/paper/2004.08881/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2020.

## Built on by (most cited first, 2 of 2)

- [Continual Learning with Distributed Optimization: Does CoCoA Forget?](https://mlsanity.com/paper/2211.16994/) (2022)
- [Distributed Continual Learning with CoCoA in High-dimensional Linear Regression](https://mlsanity.com/paper/2312.01795/) (2023)

## Abstract (arXiv)

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 mean-square-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.