# Simulated Annealing for Resource Allocation in Downlink NOMA Systems in 5G Networks
## 1 Introduction
### Related Work
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Reference** & **Objective** & **Proposed Algorithm** \\ \hline
[5] & To maximize the sum rate for SISO and MIMO NOMA system. & Closed-form solution for power allocation with KKT condition. \\
[6] & Maximize the sum rate for the NOMA system with imperfect & Optimal power using KKT condition. \\
[7] & Maximalization of the ergodic capacity. & Bisection search-based power allocation. \\
[8] & Maximize the weighted sum rate of a downlink NOMA system. & Minimum mean square error (MMSE). \\
[9] & Maximize the total sum rate for orthogonal frequency-division multiple-access (OFDM) based NOMA. & User, channel matching, and iterative power allocation scheme based on the difference of convex (DC) programming. \\
[10] & Improve Throughput and energy efficiency for the NOMA system. & Subchannel matching for user and subchannel assignment and DC. \\
[11] & Maximize the Throughput for the NOMA-enhanced relay network. & Simulated annealing (SA) for subcarrier and user assignment and DC for power allocation \\
[12] & Maximize the NOMA’s system total sum rate. & Two closed-form suboptimal solutions using the Lagrange multiplier. \\
[13] & Maximize the sum rate with minimum rate constraint for downlink NOMA with two users. & The proportional fairness scheduling (PFS). \\
[14] & Maximize the weighted sum rate (WSR). & Iterative fractional quadratic transformation algorithm. \\
[15] & Maximize the sum rate and investigate the BER performance in the NOMA system. & Generalized power allocation (GPA). \\
[16] & Maximize the sum rate by evaluating the impact of user pairing. & Channel gain difference with fixed power allocation. \\
[17] & Maximize the Throughput in the NOMA system. & Lyapunov optimization framework. \\
[18] & Improve the Throughput for the NOMA system. & Two-sided matching scheme combining the power allocation and maximum fairness (MMF). \\
[19] & Sum-rate maximization under constraints of total power and proportional rate. & Hierarchical pairing power allocation (HPPA). \\
[20] & Maximize the sum rate for MC-NOMA. & Projected gradient descent algorithm and greedy heuristic search. \\
[21] & Maximize the sum rate for NOMA. & Ant colony optimization (ACO) and LTE bandwidth division. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Literature Review Summary. network's Throughput and energy efficiency. The DC achieved a suboptimal solution for power allocation, also outperforming the OFDMA scheme. [PERSON] et al. [11] proposed a joint allocation scheme based on simulated annealing (SA) for subcarrier assignment and DC for power allocation to maximize the throughput for the NOMA-enhanced relay network. The joint resource allocation is divided into two subproblems to reduce the coupled resources' complexity between the subcarrier and power allocation. The SA is used for the subcarrier assignment with fixed power, then replaces the fixed power with the power obtained DC-based Lagrangian dual method to optimize the power allocation. The authors in [12] proposed an optimal transmission power for each user by deriving two closed-form suboptimal solutions using the Lagrange multiplier to maximize the NOMA's system total sum rate. In terms of complexity, the work initially derived the suboptimal power for two-user configuration and was then extended for multi-user by subbands transmission using bandwidth division. [PERSON] et al. [13] proposed a proportional fairness scheduling (PFS) approach to achieving optimal power allocation and maximize the sum-rate under the minimum rate constraint for downlink NOMA with two users. The PFS scheme maximized the minimum rate with a 0.1% variation of the transmission rate. The authors in [14] proposed a power allocation scheme based on the iterative fractional quadratic transformation to solve the non-convexity complexity and employed user scheduling to maximize the weighted sum-rate (WSR) while considering imperfect SIC in multi-carrier NOMA (MC-NOMA) system. [PERSON] et al.