Nonlinear Hybrid Precoding for Multi-User Weighted Sum-Rate Maximization

Characterizing rate regions provides a critical theoretical foundation for evaluating multi-user communication system performance, yet this aspect remains underexplored in hybrid precoding (HP) research. To bridge this gap, we develop a nonlinear HP scheme incorporating dirty-paper coding (DPC) for weighted sum-rate maximization (max-WSR) in massive multiple-input multiple-output broadcast channels (MIMO-BC), enabling characterization of achievable rate regions in hybrid architectures. Exploiting uplink-downlink duality, we reformulate the intractable downlink nonlinear HP as an equivalent more tractable uplink hybrid combining problem. Subsequently, the downlink nonlinear HP is derived from the dual uplink hybrid combiner through joint transceiver optimization. Formulating the max-WSR problem in this manner facilitates the characterization of achievable rate regions. The ergodic rate region quantifies the average rate vectors over channel fading states, thereby establishing a theoretical foundation for multi-user system analysis. Numerical results demonstrate that the achievable rate region of the proposed DPC-based nonlinear HP closely approaches the optimal capacity boundary.