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

A theorem that describes the high signal-to-noise ratio outage behavior of fixed-gain amplify-and-forward 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.