Power allocation for orthogonal AF relay systems with outage-based QOS constraints

We consider the problem of minimizing the cost of the power required to achieve a specified level of quality-of-service (QoS) on a point-to-point link that may be assisted by an orthogonal amplify-and-forward (AF) relay. We consider a scenario in which only the distribution of the channel states is available for the design, and the QoS is specified in terms of a target rate that is to be achievable with a specified probability of outage. We assign prices to the power expended by the source and the relay, and we seek to minimize the cost of the power required to achieve the specified QoS. This chance-constrained problem appears to be difficult to solve in its direct form. Instead, we employ the Chebyshev inequality to obtain a deterministic formulation whose solution is guaranteed to provide the required QoS. Although that problem is non-convex, its structure enables the development of an effective algorithm. We apply this design methodology to a system with imperfect channel estimation and illustrate its performance.