Distributed Estimation and Detection with Bounded Transmissions over Gaussian Multiple Access Channels

TL;DR

This paper investigates distributed estimation and detection over Gaussian multiple access channels using bounded transmission functions, establishing conditions for consistency and reliability, and comparing robustness with amplify-and-forward methods.

Contribution

It characterizes conditions under which bounded transmission functions enable consistent estimation and reliable detection in distributed sensor networks.

Findings

Bounded transmission functions can achieve strong consistency with bounded noise variance.

Robustness of bounded transmissions is highlighted against impulsive noise.

Inconsistent estimates occur if sensing noise variance tends to infinity.

Abstract

A distributed inference scheme which uses bounded transmission functions over a Gaussian multiple access channel is considered. When the sensor measurements are decreasingly reliable as a function of the sensor index, the conditions on the transmission functions under which consistent estimation and reliable detection are possible is characterized. For the distributed estimation problem, an estimation scheme that uses bounded transmission functions is proved to be strongly consistent provided that the variance of the noise samples are bounded and that the transmission function is one-to-one. The proposed estimation scheme is compared with the amplify-and-forward technique and its robustness to impulsive sensing noise distributions is highlighted. In contrast to amplify-and-forward schemes, it is also shown that bounded transmissions suffer from inconsistent estimates if the sensing noise variance goes to infinity. For the distributed detection problem, similar results are obtained by studying the deflection coefficient. Simulations corroborate our analytical results.