Downlink Beamforming for Weighted Sum-Rate Maximization

A monotonic optimization approach to downlink beamforming is developed to maximize the weighted sum of user rates. After formulating the problem as a monotonic program (MP), a polyblock outer approximation algorithm is devised to construct a nested sequence of polyblocks, and search for the optimal MP solution among the vertices of these polyblocks. In the downlink beamforming context, construction of such a nested sequence of polyblocks is enabled by solving a series of signal-to-interference-plus-noise ratio (SINR) balancing problems. Leveraging uplink-downlink duality, efficient algorithms are introduced to solve these SINR balancing problems, yielding throughout maximizing beamformers with guaranteed convergence and global optimality. The novel approach provides a benchmark for downlink beamforming schemes designed for throughput maximization.