Weighted sum-rate maximization for MISO downlink cellular networks via branch and bound

The problem of weighted sum-rate maximization (WSRMax) in multicell downlink multi-input single-output (MISO) systems is considered. The problem is known to be NP-hard. We propose a solution method, based on branch and bound technique, which solves globally the nonconvex WSRMax problem with an optimality certificate. Specifically, the algorithm computes a sequence of asymptotically tight upper and lower bounds and it terminates when the difference between the upper and lower bound is smaller than a pre-specified tolerance. Novel bounding techniques via conic optimization are introduced and their efficiency is demonstrated via numerical simulations. The proposed method can be used to provide performance benchmarks by back-substituting it into many existing network design problems which relies on solving WSRMax problem. The method proposed here is not restricted to WSRMax; it can also be used to maximize any system performance metric that can be expressed as a Lipschitz continuous and increasing function of signal-to-interference-plus-noise ratio.