Distortion limited amplify-and-forward relay networks and the ε-critical phase transition

摘要

We study amplify-and-forward (AF) relay networks operating with source and relay amplifier distortion, where the distortion dominates the noise power. The diversity order is shown to be 0 for fixed-gain (FG) and 1 for variable-gain (VG) if distortion occurs at the relay; if distortion occurs only at the source, the diversity order will be 1 for both. With ε = N/η (N the noise power, η the distortion power at node β ϵ {S, R}, the source or relay), we demonstrate the emergence of what we call an ε-critical signal-to-noise plus distortion ratio (SNDR) threshold (a threshold that emerges when min{ε} becomes small) for both forwarding protocols. We show that crossing this threshold in distortion limited regions will cause a phase transition (a dramatic drop) in the network's outage probability. Thus, small reductions in the required end-to-end transmission rate can have significant reductions in the network's outage probability.