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The problem of power-efficient communication with guaranteed quality of service (expressed in terms of per-user rate constraints) is considered in a set of parallel vector broadcast channels with separate linear precoding on each subchannel. With the restriction to use linear precoding without time-sharing, the arising optimization problem is non-convex due to the non-concavity of the rate equations. Choosing a rate-space formulation, the authors derive an algorithm to compute the globally optimal solution, which is based on a branch-and-bound strategy to solve a Difference of Monotonic functions (DM) reformulation of the problem. Despite its exponential complexity, the method is of theoretical interest as it can be used as a benchmark for heuristic algorithm.
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