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

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

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