Uplink-Downlink Duality of Multi-Cell Non-Orthogonal Multiple Access Systems

Towards the sixth generation (6G) wireless communications, multiple access is a potential technology to achieve thousand times of traffic capacity enhancement comparing with 5G. This paper investigates the feasible signal-to-interference-plus-noise-ratio (SINR) region for the multi-cell downlink and uplink non-orthogonal multiple access (NOMA) systems. Within a cell, the signals of different users are multiplexed on a channel with different power levels and successive interference cancellation is applied at the receivers to decode the signals. For the downlink, based on Perron-Frobenius Theory, we first derive a necessary and sufficient condition for an SINR vector to be feasible under a fixed decoding order. Then, a closed-form expression for the feasible SINR region is given by the union of the SINR regions under all possible decoding orders. Following a similar idea, the expression of the feasible SINR region for the uplink is also derived. Furthermore, the duality between the multi-cell downlink and uplink NOMA systems is explored. It is proved that the two systems have same feasible SINR region under dual channels. Finally, we propose an efficient algorithm to approximate the SINR region boundary. Simulation results are provided to validate the efficiency of the algorithm and compare the performance with orthogonal multiple access scheme.