Joint beam allocation and scheduling for mmWave cellular networks

This paper provides capacity results for multi-user mm-wave hybrid-beamforming, and presents optimal joint beam allocation and user scheduling algorithms. We characterize the downlink capacity of a practical system with quantized analog beamforming code-books under the constraint that users cannot be scheduled at the same time if they are closer together than a beam width in angle. We show that the capacity region is determined by a small number of linear inequality constraints. We also present capacity-achieving scheduling algorithms that provide beam allocations guaranteeing that user rate requirements are met within each resource block. In particular, we propose “sand-filling” algorithms that are provably optimal and which have linear complexity. Intuitively, our schemes can be viewed in terms of filling containers with coloured sand, in such a way that the colours at any given height do not conflict with the colours in the other containers at the same height, where the containers represent the RF chains ( i.e . the beamforming resources), and the coloured sand represents the users (and their rate requirements). We show a numerical example where the capacity of our scheme is 82% higher than a traditional resource partitioning scheme.