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Utility (e.g., sum-rate) maximization for multiantenna broadcast andinterference channels (with one antenna at the receivers) is known to be ingeneral a non-convex problem, if one limits the scope to linear (beamforming)strategies at transmitter and receivers. In this paper, it is shown that, undersome standard assumptions, most notably that the utility function is decreasingwith the interference levels at the receivers, a global optimal solution can befound with reduced complexity via a suitably designed Branch-and-Bound method.Although infeasible for real-time implementation, this procedure enables anon-heuristic and systematic assessment of suboptimal techniques. A suboptimalstrategy is then proposed that, when applied to sum-rate maximization, reducesto the well-known distributed pricing techniques. Finally, numerical resultsare provided that compare global optimal solutions with suboptimal (pricing)techniques for sum-rate maximization problems, leading to insight into issuessuch as the robustness against bad initializations.

Non-Convex Utility Maximization in Gaussian MISO Broadcast and Interference Channels