Beamformer designs for zero-forcing dirty paper coding

We consider the beamformer design for zero-forcing dirty paper coding (ZF-DPC), a suboptimal transmission technique for MISO broadcast channels (MISO BCs). 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 has been unknown previously. In this paper, we prove that the QRD-based design is 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, and numerically shown to achieve a significant fraction of the sum rate provided by the optimal design.