Analytical Characterization of the Operational Diversity Order in Fading Channels

TL;DR

This paper introduces the operational diversity order (ODO) as a new way to analyze fading channels at any SNR, revealing insights into diversity gains in various scenarios including line-of-sight and Rayleigh channels.

Contribution

It defines and characterizes the operational diversity order, providing new insights into diversity gains at finite SNR in fading channels.

Findings

Increased diversity order in line-of-sight scenarios at finite SNR.

Attenuated but visible diversity effects with additional specular components.

Slow decay slope in Rayleigh product channels, never reaching unity at finite SNR.

Abstract

We introduce and characterize the operational diversity order (ODO) in fading channels, as a proxy to the classical notion of diversity order at any arbitrary operational signal-to-noise ratio (SNR). Thanks to this definition, relevant insights are brought up in a number of cases: (i) We quantify that in dominant line-of-sight scenarios an increased diversity order is attainable compared to that achieved asymptotically, even in the single-antenna case; (ii) this effect is attenuated, but still visible, in the presence of an additional dominant specular component; (iii) the decay slope in Rayleigh product channels increases very slowly, never fully achieving unitary slope for a finite SNR.