Distributed Downlink Power Control for the Non-Orthogonal Multiple Access System with Two Interfering Cells

This paper investigates the power control problem for the downlink of a non-orthogonal multiple access (NOMA) system with two cells. The problem, called P-OPT, aims to minimizes the total transmit power of the base stations subject to the data rate requirements of the users. The feasibility and optimality properties of P-OPT is first characterized. It is proved that the feasible power region of P-OPT can be represented by the feasible regions of four power control subproblems that constitute a related optimization problem called Q-OPT. Furthermore, the optimal solution to P-OPT can be obtained by solving the corresponding instance of Q-OPT. A distributed algorithm to solve Q-OPT is designed and the underlying iteration is shown to be a standard interference function. According to Yates's power control framework, the algorithm always converges to the optimal solution if exists. Numerical results validate the convergence of the distributed algorithm and quantify the improvement of NOMA over its orthogonal multiple access counterparts in terms of power consumption and outage probability.