Efficient Solutions for Weighted Sum Rate Maximization in Multicellular Networks With Channel Uncertainties

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 semidefinite programs in each of their steps and provably converge to a locally optimal solution of the robust WSRM problem. The proposed solutions are numerically compared against each other and known approaches in the literature 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.