This paper studies radio resource management (RRM) for the uplink of a multi-channel cellular system with hybrid beamforming based on analog beamforming using predefined codebooks and zero-forcing digital beamforming. We first formulate a per-time slot joint RRM optimization problem, which includes beam selection, user selection, power allocation, modulation and coding scheme selection, and digital beamforming. A per-time slot formulation of the RRM problem is necessary because the power budget of a user equipment (UE) needs to be allocated per time slot to its assigned channels which are not known a priori, and because we consider the case where the number of radio frequency chains is not large enough to select all possible analog beams, thereby requiring per-slot beam selection. This problem can be solved for at most a few UEs because the number of variables grows exponentially with the number of UEs. In order to obtain results with more UEs, we propose an offline heuristic that reduces the runtime to obtain results by two orders of magnitude, while achieving performance close to the joint optimization. This offline heuristic allows us to obtain engineering insights on the impact of different system parameters as well as a target performance that we use to validate the low-complexity online heuristic that we propose.

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