Non-orthogonal multiple access (NOMA) is a promising technology to increase the spectral efficiency and enable massive connectivity in 5G and future wireless networks. In contrast to orthogonal schemes, such as OFDMA, NOMA multiplexes several users on the same frequency and time resource. Joint subcarrier and power allocation problems (JSPA) in NOMA are NP-hard to solve in general. In this family of problems, we consider the weighted sum-rate (WSR) objective function as it can achieve various tradeoffs between sum-rate performance and user fairness. Because of JSPA's intractability, a common approach in the literature is to solve separately the power control and subcarrier allocation (also known as user selection) problems, therefore achieving sub-optimal result. In this work, we first improve the computational complexity of existing single-carrier power control and user selection schemes. These improved procedures are then used as basic building blocks to design new algorithms, namely Opt-JSPA, $\varepsilon$-JSPA and Grad-JSPA. Opt-JSPA computes an optimal solution with lower complexity than current optimal schemes in the literature. It can be used as a benchmark for optimal WSR performance in simulations. However, its pseudo-polynomial time complexity remains impractical for real-world systems with low latency requirements. To further reduce the complexity, we propose a fully polynomial-time approximation scheme called $\varepsilon$-JSPA. Since, no approximation has been studied in the literature, $\varepsilon$-JSPA stands out by allowing to control a tight trade-off between performance guarantee and complexity. Finally, Grad-JSPA is a heuristic based on gradient descent. Numerical results show that it achieves near-optimal WSR with much lower complexity than existing optimal methods.

中文翻译：

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NOMA 中的联合副载波和功率分配：最优和近似算法

非正交多址 (NOMA) 是一项很有前途的技术，可提高频谱效率并在 5G 和未来无线网络中实现大规模连接。与正交方案（例如 OFDMA）相比，NOMA 在相同的频率和时间资源上复用多个用户。NOMA 中的联合子载波和功率分配问题 (JSPA) 通常是 NP 难解决的。在这一系列问题中，我们考虑加权和速率 (WSR) 目标函数，因为它可以在和速率性能和用户公平性之间实现各种权衡。由于JSPA的难处理性，文献中常用的方法是分别解决功率控制和子载波分配（也称为用户选择）问题，从而达到次优结果。在这项工作中，我们首先提高现有单载波功率控制和用户选择方案的计算复杂度。然后将这些改进的过程用作设计新算法的基本构建块，即 Opt-JSPA、$\varepsilon$-JSPA 和 Grad-JSPA。Opt-JSPA 计算的最佳解决方案的复杂度低于文献中当前的最佳方案。它可以用作模拟中最佳 WSR 性能的基准。然而，它的伪多项式时间复杂度对于具有低延迟要求的现实世界系统来说仍然不切实际。为了进一步降低复杂性，我们提出了一个名为 $\varepsilon$-JSPA 的完全多项式时间近似方案。由于在文献中没有研究过近似值，$\varepsilon$-JSPA 通过允许控制性能保证和复杂性之间的严格权衡而脱颖而出。最后，Grad-JSPA 是一种基于梯度下降的启发式算法。数值结果表明，它以比现有优化方法低得多的复杂度实现了接近最优的 WSR。