Robust and power efficient interference management in downlink multi-cell networks

In this paper, we focus on robust design of downlink beamforming vectors for multiple antenna base stations (BSs) in a multi-cell interference network. We formulate a robust optimization problem where an individual BS within a cell designs its beamforming vectors to minimize a combination of its sum-power, used for assuring a desired quality of service at its local users, and its aggregate induced interference on the users of the other cells, to balance inter-cell interference across the multiple cells. The proposed robust formulation uses spherical uncertainty sets to model imperfections in the second-order statistical channel knowledge between the BS and the users. To maintain tractability of the robust solutions, we derive an equivalent semidefinite programming (SDP) formulation that is convex under standard rank relaxation. The numerical results confirm the effectiveness of the proposed algorithm under various sizes of uncertainty set and the fact that the attained robust solutions always satisfy the rank constraint.