In this paper, we consider a two-tier network consisting of a macrocell and several closed-access femtocells sharing bandwidth with the macrocell. With multiple transmit antennas at both the macrocell and femtocell base stations, we propose a downlink power control and beamforming algorithm in two steps. In the first step, the beamformer of the macrocell base station is chosen to be the maximal ratio transmission beamformer, and we determine the power allocation at the macrocell and all femtocell base stations in a centralized manner by constraining that the signal power and leakage power associated with the femtocell beamformers satisfied certain predetermined thresholds. In the second step, the femtocell beamformers are obtained in a distributed manner by taking into account these thresholds. In the presence of imperfect channel state information, we further extend our proposed algorithm in a robust manner using robust optimization methodology.
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