Weighted-sum-rate maximization in certain half-duplex cooperative systems

In half-duplex cooperative systems the problem of finding the jointly optimal power and channel resource allocation that maximizes the weighted sum rate (WSR) can be difficult to solve. Algorithms to solve that problem are provided herein for two classes of orthogonal half-duplex systems. For a class of systems in which the set of rates that can be achieved without time sharing is convex, the WSR problem is decomposed into a direct search in which a target rate problem is solved at each step. The target rate problem involves maximizing one of the rates subject to target values for the others, and can often be efficiently solved. For a subclass of those systems, the notion of perspective is used to transform the WSR problem into \revrev{an efficiently-solvable} convex optimization problem. Numerical examples involving a multiple access relay system and a pairwise cooperation scheme show that joint optimization can result in significantly larger weighted sum rates than optimization over the powers alone with a fixed channel resource allocation.