Joint Beamforming and Scheduling for a Multi-Antenna Downlink with Imperfect Transmitter Channel Knowledge

We consider the downlink of a wireless system where the base-station has M ges 1 antennas and K user terminals have one antenna each. We study the weighted rate sum maximization in the case of non-perfect Channel State Information at the Transmitter (CSIT). Some relevant downlink optimization problems, such as the stabilization of the transmission queues under random packet arrivals and the proportional fair scheduling for infinite backlogged systems, can be solved as special cases of the proposed problem. We restrict the transmitter strategy to be based on Gaussian coding and beamforming. Even under this simplifying condition, the problem at hand is non-convex and it does not appear to lend itself to a simple algorithmic solution. Therefore, we introduce some approximations that yield a definition of signal-to-interference plus noise ratio (SINR) commonly used in the classical array- processing/beamforming literature. For the simpler (but still non-convex) approximated problem, we propose a powerful heuristic solution based on greedy user selection and a gradient iteration that converges to a local maximum of the objective function. This method yields very competitive results with relatively low computational complexity. Extensive simulations show that, in the case of perfect CSIT, the proposed heuristic scheme performs very closely to the optimal (dirty-paper coding) strategy while, in the case of non-perfect CSIT, it significantly outperforms previously proposed suboptimal approaches, such as random beamforming and approximated zero-forcing with greedy user selection.