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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 …