Distributed Dual Optimization for the Uplink of Multi-Cell NOMA

This paper studies distributed power control for the uplink of multi-cell non-orthogonal multiple access (NOMA) systems. Within a cell, the transmissions of different users are modeled as a Gaussian multiple access channel, treating inter-cell interference as additive Gaussian noise. By analyzing the geometry of the feasible power region, using successive interference cancellation at each base station is proved to be optimal in minimizing the total transmission power of all users under rate constraints. The decoding order at each base station, however, remains to be determined. If the decoding order is decided without base station cooperation, the overall control algorithm is fully distributed but is suboptimal in general. To achieve optimality, a partially distributed algorithm is designed, which requires base stations to exchange control messages. Given any feasible instance, the algorithm is proved to converge to the optimal solution. The performance of the fully distributed and partially distributed power control algorithms is compared by computer simulations. The fully distributed algorithm is nearly optimal in terms of outage probability. When a high data rate is required, the partially distributed algorithm is able to reduce the total power consumption by about 20%.