Optimal Zero-Forcing Hybrid Downlink Precoding for Sum-Rate Maximization

This letter studies zero-forcing (ZF) hybrid precoding for maximizing the sum-rate of a downlink multi-user massive multi-input multi-output (mMIMO) system. Assuming the water-filling power allocation across different users, we derive the optimal digital precoder based on the Karush-Kuhn-Tucker (KKT) condition. We then formulate the optimization of the analog precoder as an unconstrained nonlinear problem, which can be efficiently solved by the conjugate gradient method. The resultant hybrid precoder is optimal in the sense that it uses no approximation to the objective function of sum-rate. Therefore, it outperforms the state-of-the-art methods as verified by the numerical simulations.