  The important problem of weighted sum rate maximization (WSRM) in a
multicellular environment is intrinsically sensitive to channel estimation
errors. In this paper, we study ways to maximize the weighted sum rate in a
linearly precoded multicellular downlink system where the receivers are
equipped with a single antenna. With perfect channel information available at
the base stations, we first present a novel fast converging algorithm that
solves the WSRM problem. Then, the assumption is relaxed to the case where the
error vectors in the channel estimates are assumed to lie in an uncertainty set
formed by the intersection of finite ellipsoids. As our main contributions, we
present two procedures to solve the intractable nonconvex robust designs based
on the worst case principle. The proposed iterative algorithms solve the
semidefinite programs in each of their steps and provably converge to a locally
optimal solution of the robust WSRM problem. The proposed approaches are
numerically compared against each other to ascertain their robustness towards
channel estimation imperfections. The results clearly indicate the performance
gain compared to the case when channel uncertainties are ignored in the design
process. For certain scenarios, we also quantify the gap between the proposed
approximations and exact solutions.
