On the optimality of beamformer design for zero-forcing DPC with QR decomposition

We consider the beamformer design for zero-forcing dirty paper coding (ZF-DPC), a suboptimal transmission technique for MISO broadcast channels (MISO BCs). Beamformers for ZF-DPC are designed to maximize a performance measure, subject to some power constraints and zero-interference constraints. For the sum rate maximization problem under a total power constraint, the existing beamformer designs in the literature are based on the QR decomposition (QRD), which is used to satisfy the ZF constraints. However, the optimality of the QRD-based design is still unknown. First, we prove that the QRD-based design is indeed optimal for ZF-DPC for any performance measure under a sum power constraint. For the per-antenna power constraints, the QRD-based designs become suboptimal, and we propose an optimal design, using a convex optimization framework. Low-complexity suboptimal designs are also presented.