In this paper, for a fading decode-and-forward full-duplex relay channel, we analytically derive optimum power allocations. 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 proven that the optimization problems are convex for these two scenarios. Finally, implications of theoretical results are discussed through simulations for each scenario.