  In this paper, we propose an optimal relay power allocation of an
Amplify-and-Forward relay networks with non-linear power amplifiers. Based on
Bussgang Linearization Theory, we depict the non-linear amplifying process into
a linear system, which lets analyzing system performance easier. To obtain
spatial diversity, we design a complete practical framework of a non-linear
distortion aware receiver. Consider a total relay power constraint, we propose
an optimal power allocation scheme to maximum the receiver signal-to-noise
ratio. Simulation results show that proposed optimal relay power allocation
indeed can improve the system capacity and resist the non-linear distortion. It
is also verified that the proposed transmission scheme outperforms other
transmission schemes without considering non-linear distortion.
