Power minimization in parallel vector broadcast channels with separate linear precoding

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 sub-channel. 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, we 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. We also discuss a suboptimal algorithm, which is based on a recently proposed gradient-projection method for power minimization in multiple-input multiple-output (MIMO) broadcast channels. In numerical simulations, the gradient-based method turns out to perform close to the globally optimal solution if a good initialization is chosen.