Achievable rates and power allocation for two-way AF relaying over Rayleigh fading channels

In this paper, achievable rates and power allocation (PA) schemes are studied for a two-way (TW) amplify-and-forward (AF) relaying system over Rayleigh fading channels in high and low signal-to-noise ratio (SNR) regimes. We consider three different AF techniques: i) the channel inversion (CI) scheme where the relay has full channel side information (CSI) of the two incoming links; ii) the fixed-gain scheme where the relay has only channel distribution information (CDI); and iii) a mixed (MX) scheme where the relay has CSI of one link but only CDI of the other. First, focusing on high SNR regimes, approximations to the achievable rates of the three systems are derived. The approximations are shown to be tight and can be used to analyze the systems under consideration. In particular, it is demonstrated that the CI system provides the best sum rate performance, followed by the MX and CDI techniques. A suboptimal yet effective PA scheme to maximize the sum rate at high SNR is then proposed. In low SNR regimes, we first derive rate approximations for the considered AF systems. It is then shown that the three systems achieve a similar sum rate. An asymptotically optimal PA is then proposed to maximize the sum rate at low SNRs. Finally, the sum rate of the direct transmission (DT) scheme is compared to that of the TWAF system. Although the TWAF is proved to be inferior at low SNRs, it outperforms the DT at high SNRs in various network configurations.