Optimum Power Allocations for Fading Decode-and-Forward Relay Channel

 Abstract—In this paper optimum power allocations are derived for a fading decode-and-forward full-duplex relay channel, analytically. Individual power constraints for the source and the relay are assumed and the related optimization problem is analyzed for two scenarios. First, optimization is taken over the source power, the relay power, and the correlation coefficient between the transmitted signals of the source and the relay. Then, for a fixed value of correlation coefficient, the optimization problem is analyzed. It is also proved that the optimization problem is convex for these scenarios. The problem is analyzed in the three possible cases, and optimum power allocations are derived in closed-form for each case. Finally, theoretical results are evaluated through simulations, and for each scenario; we also show how the transition between the three cases takes place.