Distributed Power Control for the Downlink of Multi-Cell NOMA Systems

This paper investigates the power control problem for the downlink of a multi-cell non-orthogonal multiple access system. The problem, called P-OPT, aims to minimize the total transmit power of all the base stations subject to the data rate requirements of the users. The feasibility and optimality properties of P-OPT are characterized through a related optimization problem, called Q-OPT, which is constituted by some relevant power control subproblems. First, we characterize the feasibility of Q-OPT and prove the uniqueness of its optimal solution. Next, we prove that the feasibility of P-OPT can be characterized by the Perron-Frobenius eigenvalues of the matrices arising from the power control subproblems. Subsequently, the relationship between the optimal solutions to P-OPT and that to Q-OPT is presented, which motivates us to obtain the optimal solution to P-OPT through solving the corresponding Q-OPT. Furthermore, 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 our proposed method over fractional transmit power control and orthogonal multiple access schemes in terms of power consumption and outage probability.