Analysis on Full Duplex Amplify-and-Forward Relay Networks under Nakagami Fading Channels

A full duplex amplify-and-forward relay network is thoroughly investigated in this paper. To be practical and general, loop interference and Nakagami-$m$ fading channels are considered. Outage probability and ergodic capacity are particularly analyzed and exactly derived in close-forms. Asymptotic outage probability and bounds of the ergodic capacity are also derived in simple forms with clear insights. The analytical results unveil the impacts of loop interference and other system parameters in details. Specifically, it is found that the capacity and outage performance are enhanced via the increase of transmit power at the source, the average fading power and fading order associated with the source-to-relay link. However, under high signal- to-noise ratio (SNR), the increases of the transmit power at the relay and the average fading power corresponding to the loop interference would deteriorate the capacity and outage performance. The results also show that the outage probability obeys an inverse-$m_1$ law with respect to the ratio between the transmit powers in the source and relay, where $m_1$ is the fading order corresponding to the source-to-relay Nakagami fading channel. The accuracy of the analytical results is validated by Monte-Carlo simulations and they thus can serve as solid foundation for system design and optimization.