Max-Min Rate Optimization of Low-Complexity Hybrid Multi-User Beamforming Maintaining Rate-Fairness

A wireless network serving multiple users in the millimeter-wave or the sub-terahertz band by a base station is considered. High-throughput multi-user hybrid-transmit beamforming is conceived by maximizing the minimum rate of the users. For the sake of energy-efficient signal transmission, the array-of-subarrays structure is used for analog beamforming relying on low-resolution phase shifters. We develop a convex-solver based algorithm, which iteratively invokes a convex problem of the same beamformer size for its solution. We then introduce the soft max-min rate objective function and develop a scalable algorithm for its optimization. Our simulation results demonstrate the striking fact that soft max-min rate optimization not only approaches the minimum user rate obtained by max-min rate optimization but it also achieves a sum rate similar to that of sum-rate maximization. Thus, the soft max-min rate optimization based beamforming design conceived offers a new technique of simultaneously achieving a high individual quality-of-service for all users and a high total network throughput.