Optimal power allocation for the chance-constrained vector broadcast channel and rank-one channel approximation

We address the linear precoder design problem based on chance constrained quality-of-service (QoS) power minimization in the vector broadcast channel (BC). We divide the problem into a two step optimization that separates the precoder design from the power allocation. For the power allocation, we propose a map that fits into the framework of standard interference functions. Therefore, we can compute the optimal power allocation for given beamformers and detect whether a tuple of beamformers is feasible. This allows us to test conservative and non-conservative approaches for the beamformer design, e.g., a design based on a rank-one channel approximation is used. Numerical results show that the approximation is adequate for the non-conservative calculation approach, i.e., the postprocessing power allocation is capable of compensating for the suboptimal beamforming. Thereby, a wider range of rate targets is achieved than with the conservative beamformer designs.