Energy-Efficient Multi-cell NOMA Design via Coalition Formation Game

Abstract

In this work, we consider a downlink non-orthogonal multiple access (NOMA) network where multiple single-antenna users are served by multiple multi-antenna base stations (BSs). For practical considerations, we assume that only the imperfect channel state information (CSI) of each user is available at the BSs. Based on this model, the problem of joint user grouping and robust beamforming design is formulated to minimize the sum transmission power, and meanwhile, guarantee the quality of service requirements of users. Due to the integer variables of user grouping, coupling effects of beamformers, and infinitely many constraints caused by the imperfect CSI, the formulated problem is challenging to solve. For computational complexity reduction, the original problem is divided into a user grouping subproblem and a robust beamforming design subproblem. First, the user grouping problem is efficiently solved by a coalition formation game based algorithm. Then, for the robust beamforming design problem, a semidefinite relaxation (SDR) based method is proposed to produce a suboptimal solution efficiently. Moreover, we provide a sufficient condition under which the SDR based approach can guarantee to obtain an optimal rank-one solution, which is theoretically analyzed. Simulation results demonstrate the efficacy of the proposed algorithms.