In this paper, we propose a robust transmission strategy for multi-cell networks equipped with multiple-antenna base stations (BSs) under universal frequency reuse and in the presence of channel estimation error. We propose a distributed optimization scheme, where each BS individually minimizes a combination of its total transmit power and its resulting overall interference inflicted on the users of the adjacent cells, subject to maintaining a desired quality of service at its local users. We transform the proposed scheme to a robust optimization problem for the worst case of errors and derive a semidefinite programming (SDP) using rank-relaxation. We prove that the derived SDP always yields exact rank-one optimal solutions. This is in contrast to the standard rank- relaxed SDP technique that requires an additionally high computational complexity to approximate the solutions with sufficient accuracies, required for an effective beamforming. A comparison of simulation results show that the proposed transmission strategy can expand the signal-to-interference-plus-noise-ratio operational range with significantly reduced power consumption levels at BSs and perform closely to its centralized counterpart.