A Theorem on the Asymptotic Outage Behavior of Fixed-Gain Amplify-and-Forward Relay Systems

TL;DR

This paper presents a theorem characterizing the asymptotic outage probability decay in fixed-gain amplify-and-forward relay systems at high SNR, revealing a power law behavior influenced by the fading distribution's poles.

Contribution

It introduces a new theorem that describes the high-SNR outage behavior of FGAF relay systems, linking decay rate to the poles of the fading distribution's moments.

Findings

Outage probability decays as a power law at high SNR.

Logarithmic damping occurs when the dominant pole has order two or more.

The theorem is straightforward to apply to various fading scenarios.

Abstract

A theorem that describes the high signal-to-noise ratio (SNR) outage behavior of fixed-gain amplify-and-forward (FGAF) relay systems is given. Qualitatively, the theorem states that the outage probability decays according to a power law, where the power is dictated by the poles of the moments of the underlying per-hop fading distributions. The power law decay is dampened by a logarithmic factor when the leading pole (furthest to the right in the plane) is of order two or more. The theorem is easy to apply and several examples are presented to this effect.