This paper addresses the problem of proportional fair beam allocation in millimeter wave (mmWave) switched-beam based systems. Working at the mmWave band facilitates using a massive number of antenna elements at the base station (BS). Usage of beamforming in large antenna arrays provides high directivity and increased SINR at the receivers. In this setting intelligent beam allocation over multiple time slots is required for fair rate allocation to users. Activating multiple beams simultaneously requires an algorithm that takes interbeam interference into account. We formulate the proportional fair beam allocation as a mixed integer nonlinear programming with an objective of logarithmic sum of average received rates. As for received rates at each time slot, Shannon capacity is used, taking the inter-beam interference into account. We also propose a near-MINLP-based solution as our interference-aware fair beam allocation algorithm. Numerical evaluation results reveal that proposed proportional fair beam allocation algorithm performs very close to the MINLP-based solution and performs much better than the considered benchmark algorithms.
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