On the Ergodic Capacity and Energy Efficiency for Fading MIMO NOMA Systems

Non-orthogonal multiple access (NOMA) is expected to be a promising multiple access techniques for 5G networks due to its superior spectral efficiency (SE). Previous research mainly focus on the design to improve the SE performance with instantaneous channel state information (CSI). In this paper, we consider the fading MIMO channels with only statistical CSI at the transmitter, and explore the potential gains of MIMO NOMA scheme in terms of both ergodic capacity and energy efficiency (EE). The ergodic capacity maximization problem is first studied for the fading multiple-input multiple-output (MIMO) NOMA systems. We derive the optimal input covariance structure and propose both optimal and low complexity suboptimal power allocation schemes to maximize the ergodic capacity of MIMO NOMA system. For the EE maximization, the optimization problem is formulated to maximize the system EE (defined by ergodic capacity under unit power consumption) under the total transmit power constraint and the minimum rate constraint of the weak user. By transforming the EE maximization problem into an equivalent one-dimensional optimization problem, the optimal power allocation for EE design is proposed. To further reduce the computation complexity, a near-optimal solution based on golden section search and suboptimal closed form solution are proposed as well. Numerical results show that the proposed NOMA schemes significantly outperform the traditional orthogonal multiple access scheme with traditional orthogonal multiple access transmission in terms of both SE and EE.     

Energy efficient power allocation in MIMO relaying systems with the MRT precoding

Multiple-input multiple-output (MIMO) systems perform well from the energy efficiency (EE) and the spectral efficiency (SE) points of view in fifth generation (5G) communication systems. This paper considers the operation of a MIMO system with a relay. The optimization problem relates to the EE maximization. This problem has two types of limitations, which provide a maximum transmission power and a minimum data rate for users. The encountered objective function is in a fractional form and thus it is a non-convex function. Besides, the problem is constrained. We utilize a lower bound analysis for the data rates, some properties of the linear programming, and the maximum ratio transmission (MRT) precoding scheme to obtain a convex objective function. Using the Lagrange dual function, we obliterate the constraints of the problem and then it is easy to solve. To improve system performance, users are divided into two groups based on their channel gains, and the maximum transmission power is reasonably divided between them. Two iterative algorithms are proposed to solve the optimization problem numerically, and finally we investigate performance of the proposed method.     

Power allocation scheme for maximizing spectrum efficiency and energy efficiency tradeoff for multi-cluster NOMA system

In this paper, a power allocation to maximize tradeoff between spectrum efficiency (SE) and energy efficiency (EE) is considered for the downlink non-orthogonal multiple access (NOMA) system with arbitrarily clusters and arbitrarily users, where the subcarriers of clusters are mutually orthogonal to each other. Specifically, an optimization problem of maximizing SE-EE tradeoff is formulated by optimizing power allocation among users under the constraints of user rate requirements. Then, the optimization problem is decomposed into a group of sub-problems with the aim of maximizing SE-EE tradeoff for each cluster, which is solved by using bisection method and monotonicity of function. Finally, the power allocation optimization problem among users is transformed into that between clusters, and a two steps inter-cluster power allocation algorithm is developed to solve this problem. Simulation results show that SE-EE tradeoff of the proposed scheme is better than that of the existing schemes.     

Energy efficiency and spectral efficiency tradeoff in downlink OFDMA systems with imperfect CSI

In this paper, we investigate the tradeoff between energy efficiency (EE) and spectral efficiency (SE) in downlink orthogonal frequency division multiplexing access (OFDMA) systems, whilst considering the channel estimation cost and the corresponding effect of imperfect channel state information (CSI) on SE and EE. The problem is formulated as a multi-objective optimization to determine the optimal pilot transmission power, data transmission power and subcarrier assignment, and then transformed into a single-objective optimization problem, which is a non-convex mixed-integer nonlinear programming (NCMINP) and NP-hard. To address it, we propose an efficient algorithm by adopting alternating optimization and convex optimization methods in lower power region as well as approximate conversion and branch-and-bound methods in high power region. Simulation results analyze and validate the performance of EE-SE tradeoff.     

Spectral efficiency and energy efficiency of distributed antenna systems with virtual cells

In this paper, we consider user centric virtual cells model in distributed antenna systems (DAS). We investigate different power allocation optimization problems with interferences in DAS with and without user centric virtual cells model, respectively. The first objective problem is maximizing spectral efficiency (SE) of the DAS with user centric virtual cells model under the constraints of the minimum SE requirements of each user equipment (UE), maximum transmit power of each remote access unit (RAU). We firstly transform this non-convex objective function into a difference of convex functions (D.C.) problem, and then we obtain the optimal solutions by using the concave-convex procedure (CCCP) algorithm. The second objective problem is maximizing energy efficiency (EE) of the DAS with user centric virtual cells model under the same constraints as the first objective problem. Firstly, we exploit fractional programming theory to obtain the equivalent objective function of the second problem with subtract form, and then transform it into a D.C. problem and use CCCP algorithm to obtain the optimal power allocation. In each part, we propose the corresponding optimal power allocation algorithm and also use similar method to obtain optimal solutions of the same optimization problems in DAS without using user centric virtual cells model. Simulation results are provided to demonstrate the effectiveness of the DAS with user centric virtual cells model, which can significantly improve the SE and the EE of the communication systems.     

Energy‐Efficient Power Allocation for Cognitive Radio Networks with Joint Overlay and Underlay Spectrum Access Mechanism

Traditional designs of cognitive radio (CR) focus on maximizing system throughput. In this paper, we study the joint overlay and underlay power allocation problem for orthogonal frequency‐division multiple access–based CR. Instead of maximizing system throughput, we aim to maximize system energy efficiency (EE), measured by a “bit per Joule” metric, while maintaining the minimal rate requirement of a given CR system, under the total power constraint of a secondary user and interference constraints of primary users. The formulated energy‐efficient power allocation (EEPA) problem is nonconvex; to make it solvable, we first transform the original problem into a convex optimization problem via fractional programming, and then the Lagrange dual decomposition method is used to solve the equivalent convex optimization problem. Finally, an optimal EEPA allocation scheme is proposed. Numerical results show that the proposed method can achieve better EE performance.     

基于GSIC的上行链路毫米波大规模MIMO-NOMA系统低功耗传输方法

非正交多址接入（non-orthogonal multiple access,NOMA）和毫米波大规模多输入多输出（multiple-input multiple-output,MIMO）的结合能够支持未来无线通信网络的巨流量大连接需求。研究了上行链路毫米波大规模MIMO-NOMA系统中的功率最小化问题，提出了基于群体串行干扰消除（group-levelsuccessiveinterference cancellation,GSIC）的混合波束成形毫米波MIMO-NOMA上行传输系统新架构。具体来说，根据信道增益对用户进行群体划分，不同群体用户由NOMA服务，群体内用户采用空分多址区分。通过给不同群体设计模拟波束成形矩阵，对数字波束成形和功率控制进行联合优化，提出了一种并行迭代算法来解决优化问题。仿真结果表明，所提出的新架构在总功率方面优于传统的基于分簇和用户级串行干扰消除的毫米波大规模MIMO-NOMA。     

Energy‐Efficiency Power Allocation for Cognitive Radio MIMO‐OFDM Systems

This paper studies energy‐efficiency (EE) power allocation for cognitive radio MIMO‐OFDM systems. Our aim is to minimize energy efficiency, measured by “Joule per bit” metric, while maintaining the minimal rate requirement of a secondary user under a total power constraint and mutual interference power constraints. However, since the formulated EE problem in this paper is non‐convex, it is difficult to solve directly in general. To make it solvable, firstly we transform the original problem into an equivalent convex optimization problem via fractional programming. Then, the equivalent convex optimization problem is solved by a sequential quadratic programming algorithm. Finally, a new iterative energy‐ efficiency power allocation algorithm is presented. Numerical results show that the proposed method can obtain better EE performance than the maximizing capacity algorithm.     

异构蜂窝网络中基于能效的非正交多址接入下行功率分配算法

该文针对应用非正交多址接入(NOMA)技术的异构蜂窝网络,在考虑层间层内干扰的情况下,提出一种能效最大化的功率分配算法。该算法主要包括两部分,一部分为子信道内用户功率分配因子的求解,主要利用差分优化的方法,迭代求解。另一部分为子信道间的功率分配,主要利用凹凸程序法将原有的非凸问题简化为可解的凸问题,最后利用拉格朗日求解法得出功率最优解。仿真结果表明该算法有良好的迭代性,且新算法表明利用NOMA技术得到的系统能效较利用正交技术得到的系统能效提高了至少44%以上。     

QoS-based optimal and fair resource allocation for energy-efficiency uplink NOMA networks

The energy-efficiency(EE) optimization problem was studied for resource allocation in an uplink single-cell network, in which multiple mobile users with different quality of service (QoS) requirements operate under a non-orthogonal multiple access (NOMA) scheme. Firstly, a multi-user feasible power allocation region is derived as a multidimensional body that provides an efficient scheme to determine the feasibility of original channel and power assignment problem. Then, the size of feasible power allocation region was first introduced as utility function of the subchannel-user matching game in order to get high EE of the system and fairness among the users. Moreover, the power allocation optimization to the EE maximization is proved to be a monotonous decline function. The simulation results show that compared with the conventional schemes, the network connectivity of the proposed scheme is significantly enhanced and besides, for low rate massive connectivity networks, the proposed scheme obtains performance gains in the EE of the system.     

Energy-aware power allocation using Ladybug Beetle Honey Badger Optimization in multiple-input multiple-output-non-orthogonal multiple access with multiple users

The non-orthogonal multiple access (NOMA) is highly capable of serving multiple users at similar times and frequencies. The power allocation (PA) is widely considered as a main factor in NOMA for efficient communication. Here, the application of multiple-input multiple-output (MIMO) is added to NOMA to fulfill demands of enriched spectral efficiencies and extra user data. In this research, the Ladybug Beetle Honey Badger Optimization (LBHBO) is proposed for efficient PA in MIMO-NOMA. Initially, the received signals from the user are modulated for amplitude and frequency. Then, user grouping is conducted by fuzzy local information c-means (FLICM) clustering followed by using PA done by proposed LBHBO. This power is then moved to the transmitter and then to the channel estimation process. Moreover, cyclic prefix (CP) removal is carried out that tends to discrete Fourier transform (DFT). Finally, quadrature amplitude modulation (QAM) demodulation is performed for reallocated output. Furthermore, LBHBO is formed by combining Ladybug Beetle Optimization (LBO) and Honey Badger Algorithm (HBA). The performance offered by the LBHBO-PA with maximal values with energy efficiency (EE) of 25.38 Mbits/s, sum rate of 1.29 Mbits/s, and achievable rate of 100.47 Mbits/s.     

Power allocation criteria for distributed antenna systems with D2D communication

In this paper, we discuss four different optimization problems for distributed antenna systems (DAS) with and without D2D communication, respectively. The first and the third problems are maximizing spectral efficiency (SE) and energy efficiency (EE) of the DAS with D2D communication on the conditions of the minimum SE of DAS as well as D2D pair, the maximum transmit power of each remote access unit (RAU) and maximum transmit power of D2D transmitter. The second and the forth problems are maximizing SE of the DAS on the conditions of the minimum SE as well as the maximum transmit power of RAUs. We exploit the sub-gradient iteration method to obtain the optimal power allocation and summarize optimal power allocation algorithms for the first and second problems. We exploit fractional programming method to investigate the third and fourth problems and develop corresponding optimal power allocation algorithms. Simulation results demonstrate the effectiveness of the proposed power allocation algorithms and show the SE and EE of the DAS by using D2D communication are much better than DAS without D2D communication.     

基于速率约束的OFDM中继链路能效最优资源分配策略

该文研究解码转发(DF)模式的OFDM中继链路的能效最大化资源分配问题。与现有典型的固定速率最小化发射功率或无约束最大化能效算法不同,该文考虑电路功率消耗的前提下,将问题建模为以最大化系统能效为目标,同时考虑用户最小速率需求、源节点S和中继节点R各自总发射功率约束下的联合子载波配对和最优功率分配问题。证明了速率和功率联合约束条件下中继链路全局能效最优解的唯一性,在此基础上提出一种低复杂度联合最优资源分配策略。仿真结果表明,该文所提方案能够在最小速率和S/R节点最大发射功率约束下自适应分配功率资源,实现系统能效最优,并能够降低链路的中断概率。     

Resource optimization of secure energy efficiency based on mmWave massive MIMO-NOMA system with SWIPT

The secure energy efficiency (SEE) problem was investigated for the millimeter wave (mmWave) multiple input multiple output (MIMO) non-orthogonal multiplex access (NOMA) systems with simultaneous wireless information and power transfer (SWIPT) in the presence of multiple legitimate receiver (LR) and an eavesdropper.LR was first grouped according to the channel state information and the cluster heads of each group were selected,then the LR of each cluster was served by each beam with NOMA and hybrid precoding technology.Based on this,a SEE maximization problem was formulated by optimizing power allocation and power splitting factors.The Dinkelbach algorithm and first order Taylor approximation were proposed to transform the original non-convex problem into a convex one,and an iterative algorithm was developed to solve it.Finally,numerical results show that the proposed scheme can effectively improve the SEE.     

Energy efficiency optimization algorithm for heterogeneous NOMA network based on imperfect CSI

In order to improve the suppression capability of parametric perturbation and energy efficiency (EE) of heterogeneous networks (HetNets),a robust resource allocation algorithm was proposed to maximize system EE for reducing cross-tier interference power in non-orthogonal multiple access (NOMA) based HetNets.Firstly,the resource optimization problem was formulated as a mixed integer and nonlinear programming one under the constraints of the interference power of macrocell users,maximum transmit power of small cell base station (BS),resource block assignment and the quality of service (QoS) requirement of each small cell user.Then,based on ellipsoid bounded channel uncertainty models,the original problem was converted into the equivalent convex optimization problem by using the convex relaxation method,Dinkelbach method and the successive convex approximation (SCA) method.The analytical solutions were obtained by using the Lagrangian dual approach.Simulation results verifiy that the proposed algorithm had better EE and robustness by comparing it with the existing algorithm under perfect channel state information.     

多载波多用户下行NOMA系统的资源分配算法

非正交多址接入技术作为5G的候选技术之一受到了广泛关注。研究了以系统吞吐量优化为目标的多载波多用户NOMA系统下行链路的资源分配问题。在该问题的求解中,为了提高系统的吞吐量,子载波间采用线性注水算法,叠加用户间采用分数阶功率分配算法。同时,考虑了远近用户数目不等场景下能够调度更多的用户,在NOMA传输方案设计中引入时分的概念,将整个时间段t分为两个时隙,在不同时隙内实现不同远近用户分组的动态配对方案,从而在保证用户公平性的基础上,充分利用子信道资源,实现系统吞吐量的优化。仿真结果表明,对比于传统NOMA和OFDMA,提出的方法可以在相同的发射功率情况下传输更多的比特数。     

Optimal resource allocation for energy efficiency in coordinated multicell OFDMA networks

Because energy efficiency (EE) is inevitable in future wireless cellular networks, in this paper, we focus on improving the number of bits delivered to users for each unit energy consumption in the downlink of orthogonal frequency‐division multiple access cellular networks with base stations (BSs) coordination. Specifically, each BS shares the channel qualities of users with others and jointly choose the set of co‐channel users and the transmit power allocated to maximize the EE of the system subject to the transmit power ceiling of each BS and minimum required data rate. We formulate the problem as a nonlinear fractional optimization problem, using nonlinear fractional programming, the original hard‐to‐solve problem is transferred to a new one that has the same optimal solution and is easier to solve, this enables two iterative algorithms that achieve nearly the same maximum EE. Numerical results are provided to show the convergence and superiority of the two proposed. Copyright © 2014 John Wiley & Sons, Ltd.     

Secrecy sum rate optimization in MISO nonorthogonal multiple access systems with orthogonal space‐time block coding

In this paper, we investigate the secrecy sum rate optimization problem for a multiple‐input single‐output (MISO) nonorthogonal multiple access (NOMA) system with orthogonal space‐time block codes (OSTBC). This system consists of a transmitter, two users, and a potential eavesdropper. The transmitter sends information by orthogonal space‐time block codes. The transmitter's precoder and the power allocation scheme are designed to maximize achievable secrecy sum rate subject to the power constraint at the transmitter and the minimum transmission rate requirement of the weak user. We consider two cases of the eavesdropper's channel condition to obtain positive secrecy sum rate. The first case is the eavesdropper's equivalent channel is the weakest, and the other is the eavesdropper's equivalent channel between the strong user and weak user. For the former case, we employ the constrained concave convex procedure (CCCP)‐based iterative algorithm with one‐dimensional search. While for the latter, we adopt the method of alternating optimization (AO) between precoder and power allocation. We solve a semidefinite programming to optimize the precoder and drive a closed‐form expression of power allocation. The simulation results obtained by our method demonstrate the superiority of our proposed scheme.     

基于NOMA的无线携能D2D通信鲁棒能效优化算法

针对频谱短缺、基站负荷过高、通信系统功耗较大等问题,考虑不完美的信道状态信息,该文提出一种基于非正交多址接入的无线携能(SWIPT)D2D网络鲁棒能效(EE)最大化资源分配算法(SREA).考虑用户的服务质量约束以及最大发射功率约束,基于随机信道不确定性建立鲁棒能效最大化资源分配模型.利用Dinkelbach和变量替换方法,将原NP-hard问题转换为确定性的凸优化问题,通过拉格朗日对偶理论求得解析解.仿真结果表明,所提算法在保证蜂窝用户通信质量的同时,能够有效提高D2D用户的能效性和鲁棒性能.     

Robust resource allocation for NOMA-assisted heterogeneous networks

As a promising technology to improve spectrum efficiency and transmission coverage, Heterogeneous Network (HetNet) has attracted the attention of many scholars in recent years. Additionally, with the introduction of the Non-Orthogonal Multiple Access (NOMA) technology, the NOMA-assisted HetNet cannot only improve the system capacity but also allow more users to utilize the same frequency band resource, which makes the NOMA-assisted HetNet a hot topic. However, traditional resource allocation schemes assume that base stations can exactly estimate direct link gains and cross-tier link gains, which is impractical for practical HetNets due to the impact of channel delays and random perturbation. To further improve energy utilization and system robustness, in this paper, we investigate a robust resource allocation problem to maximize the total Energy Efficiency (EE) of Small-Cell Users (SCUs) in NOMA-assisted HetNets under imperfect channel state information. By considering bounded channel uncertainties, the robust resource optimization problem is formulated as a mixed-integer and nonlinear programming problem under the constraints of the cross-tier interference power of macrocell users, the maximum transmit power of small base station, the Resource Block (RB) assignment, and the quality of service requirement of each SCU. The original problem is converted into an equivalent convex optimization problem by using Dinkelbach's method and the successive convex approximation method. A robust Dinkelbach-based iteration algorithm is designed by jointly optimizing the transmit power and the RB allocation. Simulation results verify that the proposed algorithm has better EE and robustness than the existing algorithms.