Robust Multicell Downlink Beamforming Based on Second-Order Statistics of Channel State Information

In this paper, we design downlink (DL) beamforming vectors for a multiuser multicell network when only imperfect knowledge of the channel covariance is available at base stations. Specifically, we consider two different models for covariance errors: (a)deterministic error bounded in a spherical region and (b) stochastic error with known probability distribution. Our objective is to minimize the total DL transmit power subject to quality of service (QoS) constraint of every user. It is shown that for both uncertainty models, the optimization can be formulated as a convex semidefinite programming (SDP) problem using the standard rank relaxation approach. Interestingly, numerical results show that the obtained solutions fulfill the rank constraint and are therefore exact.