In this paper, we investigate and reveal the ergodic sum-rate gain (ESG) of non-orthogonal multiple access (NOMA) over orthogonal multiple access (OMA) in uplink cellular communication systems. A base station equipped with a single-antenna, with multiple antennas, and with massive antenna arrays is considered both in single-cell and multi-cell deployments. In particular, in single-antenna systems, we identify two types of gains brought about by NOMA: 1) a large-scale near-far gain arising from the distance discrepancy between the base station and users; 2) a small-scale fading gain originating from the multipath channel fading. Furthermore, we reveal that the large-scale near-far gain increases with the normalized cell size, while the small-scale fading gain is a constant, given by $\gamma = 0.57721$ nat/s/Hz, in Rayleigh fading channels. When extending single-antenna NOMA to M-antenna NOMA, we prove that both the large-scale near-far gain and small-scale fading gain achieved by single-antenna NOMA can be increased by a factor of M for a large number of users. Moreover, given a massive antenna array at the base station and considering a fixed ratio between the number of antennas, M, and the number of users, K, the ESG of NOMA over OMA increases linearly with both M and K. We then further extend the analysis to a multi-cell scenario. Compared to the single-cell case, the ESG in multi-cell systems degrades as NOMA faces more severe inter-cell interference due to the non-orthogonal transmissions. Besides, we unveil that a large cell size is always beneficial to the ergodic sum-rate performance of NOMA in both single-cell and multi-cell systems. Numerical results verify the accuracy of the analytical results derived and confirm the insights revealed about the ESG of NOMA over OMA in different scenarios.

中文翻译：

---

上行通信系统中 NOMA 优于 OMA 的性能增益

在本文中，我们研究并揭示了上行蜂窝通信系统中非正交多址 (NOMA) 相对于正交多址 (OMA) 的遍历总速率增益 (ESG)。在单小区和多小区部署中都考虑配备单天线、多天线和大规模天线阵列的基站。特别是在单天线系统中，我们确定了 NOMA 带来的两种增益：1）基站与用户之间距离差异引起的大规模近远增益；2) 源自多径信道衰落的小规模衰落增益。此外，我们揭示了大规模近远增益随着归一化小区大小而增加，而小规模衰落增益是一个常数，在瑞利衰落信道中由 $\gamma = 0.57721 $ nat/s/Hz 给出。当将单天线 NOMA 扩展到 M-antenna NOMA 时，我们证明对于大量用户，单天线 NOMA 实现的大规模近远增益和小规模衰落增益都可以增加 M 倍. 此外，给定基站的大规模天线阵列，并考虑天线数量 M 和用户数量 K 之间的固定比率，NOMA 相对于 OMA 的 ESG 随 M 和 K 线性增加。然后我们进一步扩展对多小区场景的分析。与单小区情况相比，多小区系统中的 ESG 性能下降，因为 NOMA 由于非正交传输而面临更严重的小区间干扰。此外，我们揭示了大单元尺寸总是有利于 NOMA 在单单元和多单元系统中的遍历总速率性能。