Dynamic rate adaptation and multiuser downlink beamforming using mixed integer conic programming

This paper considers jointly optimized rate adaptation and beamforming (JRAB) to achieve maximum weighted sum-rate in a multiuser downlink network. In our approach the rate adaptation consists in assigning modulation and coding schemes (MCSs) for the users which are modeled by multiple-choice constraints. The challenge of the problem lies in its combinatorial nature of the MCS selection process. We address the JRAB problem within the mixed integer second order cone programming (MI-SOCP) framework. We propose a convenient MI-SOCP reformulation that is specifically suitable to reduce the run-time in branch-and-bound (BB) methods. Further, a preprocessing step and a novel branching prioritizing principle (BPP) are introduced to speed up the BB type solutions. To facilitate applications in large systems, a fast heuristic algorithm is developed. We show via simulations that the improved MI-SOCP formulation and the BPP can significantly reduce the run-time for solving the JRAB problem with BB. Numeric results also show that the heuristic algorithm yields weighted sum-rates that are larger than that computed by the state-of-the-art MI-SOCP solver IBM ILOG CPLEX under the given run-time limitations.