Abstract-Coordinated beamforming can significantly improve the performance of cellular systems through joint interference management. Unfortunately, such beamforming optimization problems are typically NP-hard in multicell scenarios, making heuristic beamforming the only feasible choice in practice. This paper proposes a new branch-reduce-and-bound algorithm that solves such optimization problems globally, with a complexity suitable for benchmarking and analysis. Compared to prior work, the framework handles robustness to uncertain intercell interference and numerical analysis shows higher efficiency.
I. INTRODUCTIONMost resource allocation problems in multiantenna multicell systems are non-convex and NP-hard [1], meaning that the optimal solution cannot be obtained in polynomial time. Thus, only heuristic suboptimal beamforming strategies can be applied in practice when trying to optimize, for example, the sum performance, proportional fairness, or harmonic mean. Still, it is very important to compute the optimal solution to use it as a benchmark and to study its properties.The key to solve non-convex resource allocation problems systematically is to find a suitable parameter space that represents all feasible and some infeasible strategies, and then apply some global optimization technique to iteratively reduce this space with guaranteed convergence to a global optimum In addition, all of these papers assume perfect channel state information (CSI) between all transmitters and all users in the system, which is almost impossible to achieve in practice.Herein, we propose a framework for computing optimal coordinated beamforming with robustness to CSI uncertainty. We use a new branch-reduce-and-bound (BRB) algorithm and operate in the space of the robust performance region. At each iteration, we solve a quasi-convex resource allocation problem that we call robust fairness-profile optimization (RFO). We show by simulations that the BRB algorithm is more efficient than the polyblock approximation algorithm.