Optimality of Received Energy in Decision Fusion over Rayleigh Fading Diversity MAC with Non-Identical Sensors

TL;DR

This paper generalizes the optimality of the received-energy test for decision fusion over Rayleigh fading MAC, accommodating non-identical sensors and diversity, and analyzes the impact on large-system performance.

Contribution

It extends the optimality results to non-identical sensors and introduces diversity, providing a general method to verify optimality with correlated sensor decisions.

Findings

Diversity improves large-system performance under power constraints.

The received-energy test remains optimal in generalized scenarios.

Analytical expressions quantify diversity effects on system performance.

Abstract

Received-energy test for non-coherent decision fusion over a Rayleigh fading multiple access channel (MAC) without diversity was recently shown to be optimum in the case of conditionally mutually independent and identically distributed (i.i.d.) sensor decisions under specific conditions [1], [2]. Here, we provide a twofold generalization, allowing sensors to be non identical on one hand and introducing diversity on the other hand. Along with the derivation, we provide also a general tool to verify optimality of the the received energy test in scenarios with correlated sensor decisions. Finally, we derive an analytical expression of the effect of the diversity on the large-system performances, under both individual and total power constraints.