This paper investigates the joint subcarrier and power allocation problem for the downlink of a multi-carrier non-orthogonal multiple access (MC-NOMA) system. A novel three-step resource allocation framework is designed to deal with the sum rate maximization problem. In Step 1, we relax the problem by assuming each of the users can use all subcarriers simultaneously. With this assumption, we prove the convexity of the resultant power control problem and solve it via convex programming tools to get a power vector for each user; In Step 2, we allocate subcarriers to users by a heuristic greedy manner with the obtained power vectors in Step 1; In Step 3, the proposed power control schemes used in Step 1 are applied once more to further improve the system performance with the obtained subcarrier assignment of Step 2. To solve the maximization problem with fixed subcarrier assignments in both Step 1 and Step 3, a centralized power allocation method based on projected gradient descent algorithm and two distributed power control strategies based respectively on pseudo-gradient algorithm and iterative waterfilling algorithm are investigated. Numerical results show that our proposed three-step resource allocation algorithm could achieve comparable sum rate performance to the existing nearoptimal solution with much lower computational complexity and outperforms power controlled OMA scheme. Besides, a tradeoff between user fairness and sum rate performance can be achieved via applying different user power constraint strategies in the proposed algorithm.
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, ε-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 ε-JSPA. Since, no approximation has been studied in the literature, ε-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.
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