Distributed remote estimation over the collision channel with and without local communication

TL;DR

This paper studies distributed sensor communication over collision channels, proposing threshold-based strategies and learning methods to optimize estimation accuracy with limited communication and coordination.

Contribution

It introduces a quasi-convex optimization framework for threshold design, analyzes decentralization loss, and develops hybrid strategies for improved convergence and performance.

Findings

Decentralized threshold strategies nearly match centralized bounds.

Local communication enables online parameter learning and improved thresholds.

Hybrid strategies achieve fast convergence and high estimation accuracy.

Abstract

The emergence of the Internet-of-Things and cyber-physical systems necessitates the coordination of access to limited communication resources in an autonomous and distributed fashion. Herein, the optimal design of a wireless sensing system with n sensors communicating with a fusion center via a collision channel of limited capacity k (k < n) is considered. In particular, it is shown that the problem of minimizing the mean-squared error subject to a threshold-based strategy at the transmitters is quasi-convex. As such, low complexity, numerical optimization methods can be applied. When coordination among sensors is not possible, the performance of the optimal threshold strategy is close to that of a centralized lower bound. The loss due to decentralization is thoroughly characterized. Local communication among sensors (using a sparsely connected graph), enables the on-line learning of unknown parameters of the statistical model. These learned parameters are employed to compute the desired thresholds locally and autonomously. Consensus-based strategies are investigated and analyzed for parameter estimation. One strategy approaches the performance of the decentralized approach with fast convergence and a second strategy approaches the performance of the centralized approach, albeit with slower convergence. A hybrid scheme that combines the best of both approaches is proposed offering a fast convergence and excellent convergent performance.