Maximization of Worst-Case Weighted Sum-Rate for MISO Downlink Systems With Imperfect Channel Knowledge

The problem of robust weighted sum-rate maximization (WSRMax) in multicell downlink multi-input single-output systems is considered. We assume that channel state information (CSI) of all users is imperfectly known at the base stations. The problem is known to be NP-hard even in the case of perfect CSI. We propose optimal and suboptimal but fast-converging algorithms for WSRMax problem with CSI errors. Assuming bounded ellipsoidal model for the CSI errors, we optimize the worst-case weighted sum-rate. The proposed optimal algorithm is based on branch and bound (BB) technique, and it globally solves the worst-case WSRMax problem with an optimality certificate. As the convergence speed of the BB method can be slow for large networks, we also provide a fast but possibly suboptimal algorithm based on alternating optimization technique and sequential convex programming. The optimal BB based algorithm can be used to provide performance benchmarks for any suboptimal algorithm. Numerical results show that the convergence speed of the suboptimal algorithm is fast, and it finds a close-to-optimal solution in only a few iterations.