Optimal power allocation for orthogonal relay systems with quality-of-service constraints

In this paper, we address the problem of minimizing the cost of the power required to achieve reliable communication at a specified rate on a link that is assisted by an orthogonal half-duplex relay. The considered scenario is that of a narrowband channel with a long coherence time, single-antenna nodes, and the availability of perfect channel state information. We consider the regenerative decode-and-forward and amplify-and-forward relaying strategies, and for both of these strategies we obtain closed-form expressions for the optimal powers. These expressions yield insight into the design of relay-assisted communication schemes with quality-of-service requirements.