Analytical power allocation for a full duplex decode-and-forward relay channel

For a Rayleigh fading full-duplex decode-and-forward relay channel, we analytically derive optimum power allocation schemes subject to individual power constraints for the source and the relay. The optimization problem is taken over the source power and the relay power. It is proven that the optimization problem is concave for this scenario, and optimum power allocations are derived in a closed-form. Finally, the implications of the theoretical results are discussed through the graphs.