Robust downlink beamforming with imperfect CSI

In this paper, we consider an optimum multicell downlink beamforming that minimizes a combination of the sum-power, used by each base station (BS) to transmit data to its local users, and the worst-case of the resulting overall interference induced on the other users of the adjacent cells in the presence of imperfect channel state information (CSI). The aim is to ensure that the worst-cases of the signal-to-interference-plus-noise ratio (SINR) at each user remains above the required level. The imperfection in CSI is modeled to be bound within an ellipsoidal set, which is used to model the uncertainty between the true and the estimated channel coefficients. Using the S-procedure, we cast the original non-convex problem into a tractable formulation with convex constraints in linear matrix inequality (LMI) form and solve it using the standard semidefinite relaxation (SDR). The results confirm the effectiveness of the proposed robust scheme, in terms of power efficiency at BSs, compared with the conventional method in the presence of imperfect CSI.