Jointly Optimal Power and Resource Allocation for Orthogonal NDF Relay Systems with QoS Constraints

One of the advantages of relaying is that it offers the potential for a reduction the power required to achieve a specified level of quality-of-service (QoS). However, the problem of optimizing the available resources so as to minimize this power is often difficult to solve. In this paper we consider the case of a point-to-point link assisted by an orthogonal non-regenerative decode-and-forward (NDF) relay that is allocated a fraction of the time block. We assign prices to the powers of the source and the relay, and we consider the problem of jointly optimizing the source power, the relay power and the fraction of the time block so as to minimize the total cost of the power required to achieve a specified target rate. The natural formulation of that problem is not convex, but by analyzing the structure of the constraints we obtain a quasi-closed-form expression for the optimal solution that, at most, requires the solution of a simple one-dimensional zero-crossing problem for a monotonic function. This enables the problem to be efficiently solved, and clearly identifies when relaying is superior to direct transmission. Our numerical results illustrate the extent of the gains over regenerative decode-and-forward relaying, in which the resource allocation is, by definition, constrained to be equal.