System Sum Rate Research Articles

Dynamic Unequally Sub-Connected Hybrid Beamforming Architecture for Massive MIMO Systems

In this work, we propose a novel dynamic unequal sub-array (DUESA) architecture for massive multiple-input multiple-output (MIMO) systems with partially connected hybrid beamforming (PC-HBF) that relaxes the antenna-allocation constraint in the conventional unequal sub-array (UESA) architecture. The proposed DUESA architecture dynamically allocates antennas to sub-arrays based on channel state information, which leads to a combinatorial problem to optimize the sum rate. The exact solution to this problem requires an exhaustive search; however, the total number of candidates to search through can be extremely large in massive MIMO systems. To address this challenge, we propose three sub-optimal algorithms. The first is a tabu search-based algorithm, which examines the neighbors of the current solution to antenna-to-sub-array allocation and moves to the best one in each iteration. The second is a sequential antenna-reallocation algorithm with reduced complexity, which updates an antenna-to-sub-array assignment in each iteration. The third algorithm, that is, greedy antenna allocation, is composed of two sub-optimal algorithms. In its first part, only a single antenna is allocated to each sub-array based on a conventional algorithm. Then, in the second part, the antennas are added sequentially to each sub-array to optimize the system sum rate. The numerical results demonstrate that the DUESA architecture achieves substantially higher total achievable rates than conventional PC-HBF schemes. Furthermore, it has approximately 10%–20% higher energy efficiency than the conventional UESA architecture.

Machine Learning-Enabled Joint Antenna Selection and Precoding Design: From Offline Complexity to Online Performance

We investigate the performance of multi-user multiple-antenna downlink systems in which a base station (BS) serves multiple users via a shared wireless medium. In order to fully exploit the spatial diversity while minimizing the passive energy consumed by radio frequency (RF) components, the BS is equipped with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> RF chains and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> antennas, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M &lt; N$ </tex-math></inline-formula> . Upon receiving pilot sequences to obtain the channel state information (CSI), the BS determines the best subset of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> antennas for serving the users. We propose a joint antenna selection and precoding design (JASPD) algorithm to maximize the system sum rate subject to a transmit power constraint and quality of service (QoS) requirements. The JASPD algorithm overcomes the non-convexity of the formulated problem via a doubly iterative algorithm, in which an inner loop successively optimizes the precoding vectors, followed by an outer loop that tests all valid antenna subsets. Although approaching (near) global optimality, the JASPD suffers from a combinatorial complexity, which may limit its application in real-time network operations. To overcome this limitation, we propose a learning-based antenna selection and precoding design algorithm (L-ASPA), which employs a deep neural network (DNN) to establish underlaying relations between key system parameters and the selected antennas. The proposed L-ASPD algorithm is robust against the number of users and their locations, the transmit power of the BS, as well as the small-scale channel fading. With a well-trained learning model, it is shown that the L-ASPD algorithm significantly outperforms baseline schemes based on the block diagonalization and a learning-assisted solution for broadcasting systems and achieves a better effective sum rate than that of the JASPA under limited processing time. In addition, we observed that the proposed L-ASPD algorithm can reduce the computation complexity by 95% while retaining more than 95% of the optimal performance.

Supporting IoT With Rate-Splitting Multiple Access in Satellite and Aerial-Integrated Networks

To satisfy the explosive access demands of Internet-of-Things (IoT) devices, various kinds of multiple access techniques have received much attention. In this article, we investigate the multicast communication of a satellite and aerial-integrated network (SAIN) with rate-splitting multiple access (RSMA), where both satellite and unmanned aerial vehicle (UAV) components are controlled by network management center and operate in the same frequency band. Considering a content delivery scenario, the UAV subnetwork adopts the RSMA to support massive access of IoT devices (IoTDs) and achieve desired performances of interference suppression, spectral efficiency, and hardware complexity. We first formulate an optimization problem to maximize the sum rate of the considered system subject to the signal-interference-plus-noise-ratio requirements of IoTDs and per-antenna power constraints at the UAV and satellite. To solve this nonconvex optimization problem, we exploit the sequential convex approximation and the first-order Taylor expansion to convert the original optimization problem into a solvable one with the rank-one constraint, and then propose an iterative penalty function-based algorithm to solve it. Finally, simulation results verify that the proposed method can effectively suppress the mutual interference and improve the system sum rate compared to the benchmark schemes.

Generalized User Grouping in NOMA: An Overlapping Perspective

Non-orthogonal multiple access (NOMA) is regarded as a promising technology to provide high spectral efficiency and support massive connectivity in 5G systems. Traditionally, NOMA user grouping is non-overlapping, leading to a waste of power resources within each NOMA group. Motivated by this, in this paper we propose a novel generalized user grouping (GuG) concept for NOMA from an overlapping perspective, which allows each user to participate in multiple user groups but subject to individual maximum power constraint. In order to achieve effective GuG and maximize the system sum rate, we formulate a joint power control and GuG optimization problem. Then we further provide a machine learning-based GuG scheme to obtain the optimized feasible GuG and the optimal power control solutions efficiently, in which the established machine learning-based model is exploited to explore the relative relationships of channel gains of users and obtain several fixed grouping patterns via Merge operation. Simulation results verify the efficiency of GuG in NOMA systems and indicate that compared with traditional NOMA user grouping schemes, our proposed GuG scheme achieves significant performance gains in terms of system sum rate.

Decentralized Beamforming Design for Intelligent Reflecting Surface-Enhanced Cell-Free Networks

Cell-free networks are considered to be a promising distributed network architecture to satisfy the increasing number of users and high rate expectations in beyond-5G systems. However, to further enhance network capacity, an increasing number of high-cost base stations (BSs) is required. To address this problem and inspired by the cost-effective intelligent reflecting surface (IRS) technique, we propose a fully decentralized design framework for cooperative beamforming in IRS-aided cell-free networks. We first transform the centralized weighted sum-rate maximization problem into a tractable consensus optimization problem, and then an incremental alternating direction method of multipliers (ADMM) algorithm is proposed to locally update the beamformer. The complexity and convergence of the proposed method are analyzed, and these results show that the performance of the new scheme can asymptotically approach that of the centralized one as the number of iterations increases. Results also show that IRSs can significantly increase the system sum-rate of cell-free networks and the proposed method outperforms existing decentralized methods.

On the performance of massive MIMO two-way relaying systems using double precision technique

The practical application for massive MIMO relaying system with a large number of antennas is considered a challenging problem. To solve this problem, a promising solution is to utilize double precision analog-to-digital converter (ADC) and digital-to-analog converter (DAC) at the relay. Depending on the additive quantization noise model, closed-form expression for system sum rate is analyzed. Furthermore, some asymptotic simplifications are utilized to reveal the effects of some parameters on the system performance. These parameters such as the proportion of full precision in the double precision architecture (κ), the number of quantization bits (b) and the number of relay antennas (N). In addition, a tradeoff between system sum rate and power consuming is discussed by deriving energy efficiency (EE). Moreover, the tradeoff between EE and the system sum rate is investigated with different numbers of full precision ADCs/DACs. Simulation results demonstrated that large antenna array with double precision ADCs/DACs can reduce hardware cost and power consuming for practical massive MIMO relaying systems.

Sum-Rate of Cell Free Massive MIMO Systems With Power Amplifier Non-Linearity

Cell free (CF) massive multiple input multiple output (mMIMO) has been suggested as a key solution to meet the high data rate demands of future wireless communications. Studying the performance of these systems in practical scenarios such as in the presence of hardware impairments is of vital importance. In this paper, we study the effect of power amplifier non-linearity on the uplink and downlink sum-rate of CF mMIMO systems. We derive closed form expressions for the uplink and downlink achievable sum-rates of orthogonal frequency division multiplexing (OFDM) based CF mMIMO systems. Our results show that in the uplink the sum-rate does not increase unlimitedly as the number of access points (AP) increases, being upper bounded, contrarily to the ideal linear case. In fact, the rate of each user is limited by the distortion signal of its power amplifier. However, in the downlink, the sum-rate of the system with non-linear power amplifiers is not bounded and increases unlimitedly with the number of APs. Our results also indicate that for the same signal to distortion ratio (SDR) at the power amplifier output or the same normalized saturation level of the power amplifiers, the relative downlink sum-rate degradation is lower than the relative uplink sum-rate degradation (both with respect to their corresponding values in the ideal linear case). In fact, our results confirm that the user side power amplifier non-linearity has higher impact on the system performance than the power amplifier non-linearity on the AP antennas.

Optimal Power Allocation in Downlink Non-Orthogonal Multiple Access (NOMA)

Fifth generation of wireless cellular networks promise to enable better services anytime and anywhere. Non-orthogonal multiple access (NOMA) stands as a suitable multiple accessing scheme due to the ability to allow multiple users to share the same radio resource simultaneously via different domains (power, code, etc.). Through the introduced power domain, users multiplexed at the radio resource within different power levels. This paper studies power allocation in downlink NOMA, an optimization problem formulated that aims to maximize the system's sum rate. To solve the problem, a genetic algorithm based power allocation (GAPA) was proposed that uses genetic algorithm (GA) that employs heuristics to search for suitable solutions. The performance of the proposed power allocation algorithm compared with full search power allocation (FSPA) that gives an optimal performance. Results show that GAPA reaches a performance near to FSPA with lower complexity. In addition, GAPA simulated with various user paring algorithms. Channel state sorting based user pairing with GAPA achieves the best performance comparing to random user pairing algorithm and exhaustive user pairing.

Reconfigurable Intelligent Surface Aided Multi-User Communications: State-of-the-Art Techniques and Open Issues

Reconfigurable intelligent surface (RIS)-aided communication is considered as an exciting research topic in academic and industrial communities since it provides an emerging affordable solution to achieve high quality and secure next-generation wireless systems. Especially, the deployment of RIS in multi-user wireless networks promises to reduce system hardware costs, signal processing complexity, as well as energy consumption due to small size, lightweight and ability to actively shape the wireless propagation environment. Further, by realizing a cost-effective radio environment, RIS-aided communication can be implemented to be an appealing technology for future integration with other emerging wireless applications and communication systems. Despite the positive appeal, RISs face new challenges that hinder integrating efficiently into wireless networks, such as network secrecy performance and system sum-rates, as well as achieving efficient deployment design in highly dynamic and time-varying wireless environments. To this end, we overview recent state-of-the-art techniques to address the above issues faced in the integration of RISs with various emerging multi-user communication techniques, such as Unmanned Aerial Vehicles (UAVs), Non-Orthogonal Multiple Access (NOMA), Millimeter Wave (mmWave) and Terahertz (THz) communications, Physical Layer Security (PLS), massive antennas, and Simultaneous Wireless Information and Power Transfer (SWIPT). Finally, we highlight promising future research directions of RIS-aided communication in Cell-Free Massive Multiple-Input-Multiple-Output (MIMO) systems, Rate-Splitting Multiple Access (RSMA), Light Fidelity (LiFi), and Cognitive Radio (CR) systems.

Energy‐Spectral Efficiency Trade‐Offs in Full‐Duplex MU‐MIMO Cloud‐RANs with SWIPT

The present paper investigates the trade‐offs between the energy efficiency (EE) and spectral efficiency (SE) in the full‐duplex (FD) multiuser multi‐input multioutput (MU‐MIMO) cloud radio access networks (CRANs) with simultaneous wireless information and power transfer (SWIPT). In the considered network, the central unit (CU) intends to concurrently not only transfer both energy and information toward downlink (DL) users using power splitting structures but also receive signals from uplink (UL) users. This communication is executed via FD radio units (RUs) which are distributed nearby users and connected to the CU through limited capacity fronthaul (FH) links. In order to unveil interesting trade‐offs between the EE and SE metrics, we first introduce three conventional single‐objective optimization problems (SOOPs) including (i) system sum rate maximization, (ii) total power minimization, and (iii) fractional energy efficiency maximization. Then, by making use of the multiobjective optimization (MOO) framework, the MOO problem (MOOP) with the objective vector of the achievable rate and power consumption is addressed. All considered problems are nonconvex with respect to designing variables comprising precoding matrices, compression matrices, and DL power splitting factors; thus, it is extremely intractable to solve these problems directly. To overcome these issues, we develop iterative algorithms by utilizing the sequential convex approximation (SCA) approach for the first two SOO problems and the SCA‐based Dinkelbach method for the fractional EE problem. Regarding the MOOP, we first rewrite it as an SOOP by applying the modified weighted Tchebycheff method and, then, propose the iterative algorithm‐based SCA to find its optimal Pareto set. Various numerical simulations are conducted to study the system performance and appealing EE‐SE trade‐offs in the considered system.

A Novel Subchannel and Power Allocation Algorithm in V2V Communication

This paper investigates resource allocation of latency constrained vehicle‐to‐vehicle (V2V) communication. When a subchannel of a vehicle‐to‐infrastructure (V2I) link can be reused by multiple V2V links, a nonlinear mixed integer optimization problem with the goal of maximizing the spectral efficiency of the system is derived under the constraints of minimum transmission rate of V2I links and transmission latency of V2V links. The subchannel allocation problem is solved by means of two‐sided exchange matching theory, optimal transmission power of V2I and V2V links is solved based on the poly‐block approximation (PBA) algorithm, and the system spectrum efficiency is maximized through loop iteration. In order to reduce the computational complexity of power allocation problem, a power allocation algorithm based on iterative convex optimization (ICO) is proposed. The convergence of the resource allocation algorithm is also proved. The simulation results show that the proposed algorithms can guarantee transmission latency requirements of V2V links and improve the system sum rate and access ratio of V2V links. Compared with two traditional algorithms, latency of poly‐block approximation combined with many to one matching (PBAMTO) is reduced by 30.41% and 20.43%, respectively.

Pilot Contamination Mitigation in Massive Multi-Input Multi-Output (MIMO) System

Massive MIMO is one of the key components in the technologies of the next generation wireless communication network; the fifth generation (5G). Although massive MIMO is considered a promising technology in 5G, its efficiency is limited by the challenge of the pilot contamination problem. Pilot contamination problem occurs when user terminals in different cells concurrently share the same control signal set (called pilot sets), which results in causing interference in the estimated channel. In this paper, a model to reduce the pilot contamination problem and to increase the system sum-rate is proposed. The proposed model is a combination of three schemes: 1) A time-shifting protocol where the pilots are transmitted by users without overlapping in time; 2) A directional pilot scheme where the users directionally transmit the pilot; 3) A pilot allocation scheme for channel estimation based on the greedy algorithm to optimize the system sum-rate and the signal to interference and noise ratio with low complexity, and to mitigate the pilot contamination. Simulation results show that significant improvements are achieved compared to existing directional, time shifting and pilot allocation schemes.

Performance enhancement for a non-orthogonal multiple access system using 4 × 4 multiple-input multiple-output visible-light communication

A multi-user visible-light communication (VLC) system based on 4 × 4 multiple-input multiple-output (MIMO) was investigated. The system consists of four light-emitting diodes (as a transmitter) and four photodetectors (as a receiver). The proposed system was simulated for two, three, and four users. The objective of this study is to optimize the system power consumption and to utilize the sum rate on the system coverage area. By expanding the system from a 2 × 2 MIMO-VLC to a 4 × 4 MIMO-VLC, the results demonstrate that the total sum rate of the system can be improved. The findings reveal that the 4 × 4 MIMO-VLC achieves a maximum sum-rate enhancement of 143% compared with the 2 × 2 MIMO-VLC. The results also show that the efficiency of 4 × 4 MIMO-VLC system with non-orthogonal multiple access (NOMA) and gain ratio power allocation (GRPA) was increased by around 181% compared to 2 × 2 MIMO-NOMA-based VLC with GRPA in combination. For the 4 × 4 MIMO-NOMA-VLC device with GRPA, the sum bit rate for two, three, and four users was increased by 40%, 33%, and 24%, respectively. Through this study, it can be concluded that GRPA scheme plays an important role in utilizing MIMO-VLC system sum rate of the MIMO-VLC system.

On Performance Comparison of Multi-Antenna HD-NOMA, SCMA, and PD-NOMA Schemes

In this letter, we study the uplink channel throughput performance of a proposed novel multiple-antenna hybrid-domain non-orthogonal multiple access (MA-HD-NOMA) scheme. This scheme combines the conventional sparse code multiple access (SCMA) and power-domain NOMA (PD-NOMA) schemes in order to increase the number of users served as compared to conventional NOMA schemes and uses multiple antennas at the base station. To this end, a joint resource allocation problem for the MA-HD-NOMA scheme is formulated that maximizes the sum rate of the entire system. For a comprehensive comparison, the joint resource allocation problems for the multi-antenna SCMA (MA-SCMA) and multi-antenna PD-NOMA (MA-PD-NOMA) schemes with the same overloading factor are formulated as well. Each of the formulated problems is a mixed-integer non-convex program, and hence, we apply successive convex approximation (SCA)- and reweighted ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> minimization-based approaches to obtain rapidly converging solutions. Numerical results reveal that the proposed MA-HD-NOMA scheme has superior performance compared to MA-SCMA and MA-PD-NOMA.

Unsupervised Learning-Based Joint Active and Passive Beamforming Design for Reconfigurable Intelligent Surfaces Aided Wireless Networks

This letter consider a reconfigurable intelligent surface (RIS) aided multi-user multiple-input single-output (MISO) downlink system, where transmit beamforming and phase shifts of RIS reflecting elements are jointly designed to maximize system sum rate. However, the unit modulus constraint of RIS phase shifts and coupling between active and passive beamforming make the optimal design a challenging task. Most of prior works adopt iterative optimization algorithms to get suboptimal solutions, which suffer from high computational complexity, hence are not applicable to practical scenarios. Responding to this, this letter proposes a deep learning based approach for joint active and passive beamforming design. Specifically, a two-stage neural network is trained offline in an unsupervised manner, which is then deployed online for real-time prediction. Simulation results indicate that the proposed approach is able to reduce computational complexity significantly with satisfactory performance compared to conventional iterative optimization algorithms.

Exploiting Intelligent Reflecting Surfaces in NOMA Networks: Joint Beamforming Optimization

This paper investigates a downlink multiple-input single-output intelligent reflecting surface (IRS) aided non-orthogonal multiple access (NOMA) system, where a base station (BS) serves multiple users with the aid of IRSs. Our goal is to maximize the sum rate of all users by jointly optimizing the active beamforming at the BS and the passive beamforming at the IRS, subject to successive interference cancellation decoding rate conditions and IRS reflecting elements constraints. In term of the characteristics of reflection amplitudes and phase shifts, we consider ideal and non-ideal IRS assumptions. To tackle the formulated non-convex problems, we propose efficient algorithms by invoking alternating optimization, which design the active beamforming and passive beamforming alternately. For the ideal IRS scenario, the two subproblems are solved by invoking the successive convex approximation technique. For the non-ideal IRS scenario, constant modulus IRS elements are further divided into continuous phase shifts and discrete phase shifts. To tackle the passive beamforming problem with continuous phase shifts, a novel algorithm is developed by utilizing the sequential rank-one constraint relaxation approach, which is guaranteed to find a locally optimal rank-one solution. Then, a quantization-based scheme is proposed for discrete phase shifts. Finally, numerical results illustrate that: i) the system sum rate can be significantly improved by deploying the IRS with the proposed algorithms; ii) 3-bit phase shifters are capable of achieving almost the same performance as the ideal IRS; iii) the proposed IRS-aided NOMA systems achieve higher system sum rate than the IRS-aided orthogonal multiple access system.

Hybrid Precoder Design With Minimum-Subspace-Distortion Quantization in Multiuser mmWave Communications

Hybrid precoding has been a promising technique in millimeter wave (mmWave) communications, providing a balanced tradeoff between system performance and hardware complexity. Existing hybrid precoding schemes either require full channel state information (CSI) or use codebook-based design, causing large feedback overhead or degraded system performance, respectively. In this paper, we propose a balanced scheme with limited feedback CSI and element-level quantization. Our key idea is to maximize the system sum rate by using an adaptive baseband precoder and an eigenbeam radio frequency (RF) precoder. The adaptive baseband precoder can balance the effective channel gain and the multiuser interference according to the transmitted power. The eigenbeam RF precoder is optimized with only requiring a limited length of feedback vector. Considering the practical constraints on RF precoders, we then propose a quantization algorithm that minimizes the subspace distortion between the optimized eigenbeam RF precoder and the quantized one. The quantization algorithm also works for the case when RF chains are more than users. Extensive simulation results are provided and validate the effectiveness of the proposed hybrid precoding scheme.

Sealed Bid Single Price Auction Model (SBSPAM)-Based Resource Allocation for 5G Networks

The rapid increase in the number of devices associated with the cellular network; fulfilling their demands is one of the significant challenges for next-generation networks (5G). The existing schemes improve the network throughput by allowing to share the channels between the cellular user (CU) and device-to-device (D2D) users in one-to-one or one-to-many manners. However, none of the existing schemes does deal with minimizes the usage of resource blocks as well as improve network throughput. Therefore, in this paper, we propose a sealed bid single price auction model-based resource allocation scheme for 5G networks. The proposed scheme is divided into two steps. In the first step, cellular user broadcast a beacon packet into a network for identifying the nearby cellular users those are in the same mode. Nearby cellular users responded immediately to the broadcasted cellular user for forming a group. In the second step, the base station will perform a sealed bid single price auction model among participant cellular users with the amount of data to be transferred at the base station side and signal-to-interference plus noise ratio (SINR) as their valuations for bidding. The winner of this auction model forms a D2D pair with broadcasted cellular users, and both cellular users will send data with a single resource block. The proposed scheme not only reduces the usage of resource block it also increases the throughput of the network. Moreover, our results show that the proposed scheme achieves a performance gain in terms of the average system sum rate compared to existing resource allocation schemes.

Two-Timescale Hybrid Analog-Digital Beamforming for mmWave Full-Duplex MIMO Multiple-Relay Aided Systems

Due to the severe pathloss experienced by electromagnetic waves in the millimeter wave (mmWave) band, a substantial challenge in their design is to have an adequate coverage area. With the objective of improving the coverage area and the sum rate attained, we conceive new full-duplex (FD) mmWave multiple-input multiple-output (MIMO) multiple-relay systems. Specifically, we propose a novel two-timescale analog-digital hybrid beamforming scheme for maximizing the sum rate, while reducing the system's complexity and the channel state information (CSI) signalling overhead, as well as mitigating both the effects of self-interference and that of outdated CSIs caused by the associated delays. In the proposed scheme, the long-timescale analog beamforming matrices are designed based on the available channel statistics and updated in a frame-based manner, where a frame contains a fixed number of time slots. By contrast, the short-timescale digital beamforming matrices are optimized more frequently - namely for each time slot - based on the low-dimensional effective CSI matrices available on a real-time basis. We develop both an efficient analog beamforming algorithm based on the cut-set bound as well as on stochastic successive convex approximation (SSCA) and an innovative digital beamforming algorithm that relies on the theory of penalty dual decomposition (PDD), where our design objective is to maximize the system's sum rate. Both the convergence properties and the computational complexity of the proposed algorithms are also examined. Our simulation results show that the proposed two-timescale hybrid beamforming design significantly outperforms the conventional beamformers both in terms of requiring a lower CSI-signalling overhead and a higher sum rate in the face of realistic outdated CSIs.

Novel Resource Allocation Techniques for Downlink Non-Orthogonal Multiple Access Systems

Non-orthogonal multiple access (NOMA) plays an important role in achieving high capacity for fifth-generation (5G) networks. Efficient resource allocation is vital for NOMA system performance to maximize the sum rate and energy efficiency. In this context, this paper proposes optimal solutions for user pairing and power allocation to maximize the system sum rate and energy efficiency performance. We identify the power allocation problem as a nonconvex constrained problem for energy efficiency maximization. The closed-form solutions are derived using Karush–Kuhn–Tucker (KKT) conditions for maximizing the system sum rate and the Dinkelbach (DKL) algorithm for maximizing system energy efficiency. Moreover, the Hungarian (HNG) algorithm is utilized for pairing two users with different channel condition circumstances. The results show that with 20 users, the sum rate of the proposed NOMA with optimal power allocation using KKT conditions and HNG (NOMA-PKKT-HNG) is 6.7% higher than that of NOMA with difference of convex programming (NOMA-DC). The energy efficiency with optimal power allocation using DKL and HNG (NOMA-PDKL-HNG) is 66% higher than when using NOMA-DC.