Optimality of Received Energy in Decision Fusion Over Rayleigh Fading Diversity MAC With Non-Identical Sensors

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 [C. R. Berger, M. Guerriero, S. Zhou, and P. Willett, "PAC vs. MAC for Decentralized Detection Using Noncoherent Modulation," IEEE Trans. Signal Process., vol. 57, no. 9, pp. 3562-2575, Sep. 2009], [F. Li, J. S. Evans, and S. Dey, "Decision Fusion Over Noncoherent Fading Multiaccess Channels," IEEE Trans. Signal Process., vol. 59, no. 9, pp. 4367-4380, Sep. 2011]. 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 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.