Distributed Detection of a Random Process over a Multiple Access Channel under Energy and Bandwidth Constraints

TL;DR

This paper studies a wireless sensor network's ability to detect a stationary Gaussian process using an energy-efficient analog scheme over a multiple access channel, optimizing detection performance under resource constraints.

Contribution

It introduces an asymptotically optimal linear analog transmission scheme for distributed detection under energy and bandwidth constraints, validated by theoretical analysis and simulations.

Findings

Achieves significant energy savings in low SNR conditions.

Proves asymptotic optimality of the proposed scheme among linear orthogonal strategies.

Validates analytical results with Monte Carlo simulations.

Abstract

We analyze a binary hypothesis testing problem built on a wireless sensor network (WSN) for detecting a stationary random process distributed both in space and time with circularly-symmetric complex Gaussian distribution under the Neyman-Pearson framework. Using an analog scheme, the sensors transmit different linear combinations of their measurements through a multiple access channel (MAC) to reach the fusion center (FC), whose task is to decide whether the process is present or not. Considering an energy constraint on each node transmission and a limited amount of channel uses, we compute the miss error exponent of the proposed scheme using Large Deviation Theory (LDT) and show that the proposed strategy is asymptotically optimal (when the number of sensors approaches to infinity) among linear orthogonal schemes. We also show that the proposed scheme obtains significant energy saving in the low signal-to-noise ratio regime, which is the typical scenario of WSNs. Finally, a Monte Carlo simulation of a 2-dimensional process in space validates the analytical results.