Multi-hop Diffusion LMS for Energy-constrained Distributed Estimation

TL;DR

This paper introduces a multi-hop diffusion LMS strategy for energy-efficient distributed estimation in sensor networks, optimizing information exchange over multiple hops to reduce energy consumption while maintaining estimation accuracy.

Contribution

It develops a novel multi-hop diffusion approach with optimized combination rules and adaptive algorithms, enabling energy-efficient distributed estimation under local and global energy constraints.

Findings

Achieves same steady-state MSD as one-hop methods with lower energy use.

Provides offline and distributed algorithms for optimizing information neighborhoods.

Demonstrates effectiveness through numerical simulations.

Abstract

We propose a multi-hop diffusion strategy for a sensor network to perform distributed least mean-squares (LMS) estimation under local and network-wide energy constraints. At each iteration of the strategy, each node can combine intermediate parameter estimates from nodes other than its physical neighbors via a multi-hop relay path. We propose a rule to select combination weights for the multi-hop neighbors, which can balance between the transient and the steady-state network mean-square deviations (MSDs). We study two classes of networks: simple networks with a unique transmission path from one node to another, and arbitrary networks utilizing diffusion consultations over at most two hops. We propose a method to optimize each node's information neighborhood subject to local energy budgets and a network-wide energy budget for each diffusion iteration. This optimization requires the network topology, and the noise and data variance profiles of each node, and is performed offline before the diffusion process. In addition, we develop a fully distributed and adaptive algorithm that approximately optimizes the information neighborhood of each node with only local energy budget constraints in the case where diffusion consultations are performed over at most a predefined number of hops. Numerical results suggest that our proposed multi-hop diffusion strategy achieves the same steady-state MSD as the existing one-hop adapt-then-combine diffusion algorithm but with a lower energy budget.