Joint Subcarrier and Power Allocation in NOMA: Optimal and Approximate Algorithms

Abstract

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