# Simulated Annealing for Resource Allocation in Downlink NOMA Systems in 5G Networks
## 1 Introduction
### Related Work
[15] proposed generalized power allocation (GPA) to calculate the different power for many users with no requirement to adjust any of the NOMA parameters based on the wireless communication system. The proposed power allocation scheme showed a slight variation percentage than the arbitrary power allocation and performed with similar behavior as the conventional power allocation for the NOMA system. The authors in [16] investigated user pairing schemes by testing the channel gain difference of the two users in the case of NOMA while allocating fixed power (F-NOMA) and another NOMA inspired by cognitive radio (CR-NOMA). The F-NOMA has shown a large Throughput that is better than the conventional OMA scheme where the user pairing is performed based on the two users experiencing good channel conditions. In CR-NOMA, the users with the best channel gain are paired with the second-best channel gain user, while the F-NOMA paired that user with the lowest channel gain. Thus, CR-NOMA showed different behavior than F-NOMA, but F-NOMA outperformed CR-NOMA because of the constraints on transmit power allocated to other users in the CR-NOMA. [PERSON]. et al. [17] proposed a joint optimization scheme to maximize throughput in the NOMA system by the Lyapunov optimization framework that converted the original long-term optimization problem into a series of online rate controls in the network layer and power allocation problems in each time slot in the physical layer. The work also obtained the optimal global solution with a polynomial computational complexity using a power allocation algorithm based on dynamic programming and it explored the two optimal solutions. The authors in [18] proposed a near-optimal solution using a two-sided matching scheme by combining the power allocation and maximum fairness (MMF) to improve throughput for the NOMA system. The proposed joint optimal resource allocation scheme is used iteratively to refine the solution. [PERSON] et al. [19] proposed hybrid multiple access schemes that combined the properties of NOMA and OFDMA for sum-rate maximization under constraints of total power and the proportional rate of the NOMA system. The suboptimal solution is obtained for two users, and the work is extended to serve the multiuser using a hierarchical pairing power allocation (HPPPA) process in the NOMA system. The authors in [20] proposed a projected gradient descent algorithm as a centralized power allocation method for a fixed subcarrier assignment, along with a greedy heuristic search for the user and subchannel matching to maximize the sum rate for MC-NOMA. The achieved solution is near-optimal with lower computational complexity than other near-optimal solutions. In [21], we proposed a power allocation scheme with two user configurations using the ant colony optimization (ACO) method to optimize the subchannel power and the power ratio among the multiplexed users. The proposed method is developed for a system with two users, and bandwidth division is adopted to extend the work to serve a larger number of users in the network. Therefore, the NOMA potentially enables the users to access the entire bandwidth, where the bandwidth division cannot meet that concept. Resource allocation is defined as a non-convex problem [9; 14; 17], where the direct numerical method is not efficient in solving it. A method is required to transform the non-convex problem into a convex problem in order to achieve an effective solution. However, no tractable solutions can be guaranteed for a non-convex optimization problem by converting it into a sub-problem. Furthermore, the optimal solution obtained by changing the non-convex into the convex may not be the optimal solution but can be the approximate solution. Most numerical optimization algorithms can only optimize the power allocation while requiring a user pairing scheme to achieve a comparable optimal resource allocation solution. Therefore, the optimal resource allocation can only be achieved in parallel with the optimal user pairing scheme.