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In this paper, a new analytical expression of the max-min SINR duality between the multi-cell downlink and the virtual uplink subject to per-BS power constraints is firstly given. Based on that, a hierarchical iterative scheme is proposed to solve the virtual uplink optimization problem. The uplink solution is then converted to achieve the solution to the multi-cell downlink beamforming problem. Simulation results show that, in contrast to existing multi-cell beamforming schemes, the proposed scheme achieves better performance in terms of both the worst-user rate and the rate per energy.
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