  We consider hierarchical beamforming in wireless networks. For a given
population of flows, we propose computationally efficient algorithms for fair
rate allocation including proportional fairness and max-min fairness. We next
propose closed-form formulas for flow level performance, for both elastic (with
either proportional fairness and max-min fairness) and streaming traffic. We
further assess the performance of hierarchical beamforming using numerical
experiments. Since the proposed solutions have low complexity compared to
conventional beamforming, our work suggests that hierarchical beamforming is a
promising candidate for the implementation of beamforming in future cellular
networks.
