Weighted Sum-Rate Maximization in Wireless Networks: A Review

A wide variety of resource management problems of recent interest, including power/rate control, link scheduling, cross-layer control, network utility maximization, beamformer design of multiple-input multiple-output networks, and many others are directly or indirectly reliant on the weighted sum-rate maximization (WSRMax) problem. In general, this problem is very difficult to solve and is NP-hard. In this review, we provide a cohesive discussion of the existing solution methods associated with the WSRMax problem, including global, fast local, as well as decentralized methods. We also discuss in depth the applications of general optimization techniques, such as branch and bound methods, homotopy methods, complementary geometric programming, primal decomposition methods, subgradient methods, and sequential approximation strategies, in order to develop algorithms for the WSRMax problem. We show, through a number of numerical examples, the applicability of these algorithms in various application domains.