An energy-efficient power allocation scheme for millimeter-wave MIMO-NOMA systems

There are many challenges in fifth generation (5G) telecommunication systems, due to the increasing demands and applications. The most important of which are need to have higher energy efficiency (EE) and spectral efficiency (SE). They are critical in the practical multiple-input multiple-output (MIMO) telecommunication systems. Non-orthogonal multiple access (NOMA) methods and millimeter-waves can be used in conjunction with MIMO systems to improve their EE and SE performance. In this paper, we investigate the application of NOMA and mm-Wave transmission in the downlink of MIMO systems. Then, we formulate the optimization problem for users in MIMO-NOMA systems to maximize the EE that is subject to minimum data rate to satisfy required quality of service (QoS) and maximum transmission power. To achieve the optimal power allocation for users, we reach a problem for the EE maximization that is non-convex and solution of the optimization problem is not trivial. We exploit a lower bound of the data rate and the Lagrange dual function to convert it to a convex and unconstrained problem, which is easy to solve. In the next step, we derive a relation for determining the optimal power allocation of users. In addition, a numerical algorithm is presented that can be used to solve the problem. According to the simulation results of the proposed algorithm, our method performs better and provides higher EE than both orthogonal multiple access and equal power allocation schemes.     

Optimal user selection and power allocation for revenue maximization in non‐orthogonal multiple access systems

A novel algorithm for joint user selection and optimal power allocation for Stackelberg game‐based revenue maximization in a downlink non‐orthogonal multiple access (NOMA) network is proposed in this study. The condition for the existence of optimal solution is derived by assuming perfect channel state information (CSI) at the transmitter. The Lagrange multiplier method is used to convert the revenue maximization problem into a set of quadratic equations that are reduced to a regular chain of expressions. The optimal solution is obtained via a univariate iterative procedure. A simple algorithm for joint optimal user selection and power calculation is presented and exhibits extremely low complexity. Furthermore, an outage analysis is presented to evaluate the performance degradation when perfect CSI is not available. The simulation results indicate that at 5‐dB signal‐to‐noise ratio (SNR), revenue of the base station improves by at least 15.2% for the proposed algorithm when compared to suboptimal schemes. Other performance metrics of NOMA, such as individual user‐rates, fairness index, and outage probability, approach near‐optimal values at moderate to high SNRs.     

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.     

User clustering and robust beamforming design in multicell MIMO-NOMA system for 5G communications

In this paper, we present a robust beamforming design to tackle the weighted sum-rate maximization (WSRM) problem in a multicell multiple-input multiple-output (MIMO) – non-orthogonal multiple access (NOMA) downlink system for 5G wireless communications. This work consider the imperfect channel state information (CSI) at the base station (BS) by adding uncertainties to channel estimation matrices as the worst-case model i.e., singular value uncertainty model (SVUM). With this observation, the WSRM problem is formulated subject to the transmit power constraints at the BS. The objective problem is known as non-deterministic polynomial (NP) problem which is difficult to solve. We propose an robust beamforming design which establishes on majorization minimization (MM) technique to find the optimal transmit beamforming matrix, as well as efficiently solve the objective problem. In addition, we also propose a joint user clustering and power allocation (JUCPA) algorithm in which the best user pair is selected as a cluster to attain a higher sum-rate. Extensive numerical results are provided to show that the proposed robust beamforming design together with the proposed JUCPA algorithm significantly increases the performance in term of sum-rate as compared with the existing NOMA schemes and the conventional orthogonal multiple access (OMA) scheme.     

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.     

基于双向中继和网络编码的NOMA网络性能分析

针对实际场景中存在的具有上下行双向传输任务的通信系统,本文提出了一种双向中继协作非正交多址接入(NOMA, non-orthogonal multiple access)传输方案,基于解码转发(DF, Decode and Forward)协议研究信号的上行和下行双向传输技术,与现有NOMA方案不同,本方案为近端用户分配较大的功率,利用网络编码(NC, network coding)原理在两个时隙内实现基站和用户之间的双向信息交换。进一步考虑不完美信道状态信息(CSI, Channel State Information)条件,分析系统的传输性能并推导了系统中断概率以及遍历和速率闭合表达式。仿真结果表明,在完美CSI和不完美CSI条件下,相比于现有文献所提方案、单向中继(OWR,One-Way Relay)和正交多址(OMA, Orthogonal Multiple Access)网络,本文所提方案有效降低了系统的传输中断概率,提高了系统的遍历和速率以及系统吞吐量。      

NOMA系统中利用共轭梯度法的功率分配方案

通过功率分配,5G通信的关键技术——非正交多址（NOMA）实现发射功率域的多用户复用,有效提高了频谱效率。不同的功率分配方案直接影响系统的吞吐量,针对NOMA下行链路现有功率分配算法存在的局部最优问题,提出了一种利用共轭梯度法的最优功率分配方案,采用共轭梯度法求解用户的加权和速率最大化的优化问题。现有理论证明,该方法可以收敛到全局最优解。仿真结果表明,该方法性能优于已有的固定功率分配（FPA）算法和分数阶发射功率分配（FTPA）算法,且此非正交多址（NOMA）系统性能明显优于正交多址（OMA）系统。      

Low‐complexity energy efficient power allocation scheme for DAS with maximum power constraint

In this paper, a low‐complexity optimal power allocation (PA) scheme is developed to maximize energy efficiency (EE) in a distributed antenna system (DAS) under maximum power constraint and target bit error rate (BER) requirement. Composite Rayleigh fading, multiple receive antennas, and dynamic circuit power consumption are all considered in the system. Unlike conventional schemes, the presented scheme provides a closed‐form expression of PA. Firstly, the optimization problem is formulated according to the definition of EE. Using the Karush‐Kuhn‐Tucker conditions, a general form of the optimal PA, in which the number of active antennas and corresponding power allocation are required only, is then proposed. With this general form, an effective algorithm is presented to yield the closed‐form PA. The proposed scheme can be applied to the system with static circuit power consumption and/or without target BER constraint to obtain optimal PA. Simulation results corroborate the effectiveness of the developed scheme, and the scheme can achieve the same EE performance as the existing optimal schemes with lower complexity. Moreover, the distributed antenna system with multiple receive antennas has higher EE than that with single receive antenna.     

Capacity Performance of Polarized Distributed MIMO System on Rician Channel

The analytical upper bound and lower bound on the ergodic capacity of polarized distributed antenna system and their relation with antenna polarization on Rician channel are deduced by applying properties of complex non-central Wishart matrices and matrix-variate non-central quadratic forms. Compared to the related studies, our analysis is extended to account for the polarized distributed system with Rician fading where a line-of-sight component exists and both ends are affected by spatial correlation. The antenna polarization has some impacts on the capacity bounds according to the expressions of capacity bounds. Both the transmitter and the receiver are equipped with multiple polarization antennas, and the transmitters are of linear layout. A power allocation scheme based on the path loss fading is presented by maximizing the capacity upper bound. The power allocation scheme is feedback efficient compared with those power allocation schemes based on statistical parameters of the channel which need a large amount of feedback. In the simulations, the ergodic capacity of polarized distributed MIMO is analyzed. Comparisons are taken on the effects of angle spread, Rician factor and power on the ergodic capacity. The proposed power allocation scheme is superior to the equal power allocation scheme and has very close performance to the optimal power allocation scheme.     

Service outage based power and rate allocation for parallel fading channels

The service outage based allocation problem explores variable-rate transmission schemes and combines the concepts of ergodic capacity and outage capacity for fading channels. A service outage occurs when the transmission rate is below a given basic rate r/sub o/. The allocation problem is to maximize the expected rate subject to the average power constraint and the constraint that the outage probability is less than /spl epsi/. A general class of probabilistic power allocation schemes is considered for an M-parallel fading channel model. The optimum power allocation scheme is derived and shown to be deterministic except at channel states of a boundary set. The resulting service outage achievable rate ranges from 1-/spl epsi/ of the outage capacity up to the ergodic capacity with increasing average power. Two near-optimum schemes are also derived by exploiting the fact that the outage probability is usually small. The second near-optimum scheme significantly reduces the computational complexity of the optimum solution; moreover, it has a simple structure for the implementation of transmission of mixed real-time and non-real-time services.     

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。     

Energy-efficient power allocation for NOMA heterogeneous networks with imperfect CSI

In this paper, an optimal user power allocation scheme is proposed to maximize the energy efficiency for downlink non-orthogonal multiple access (NOMA) heterogeneous networks (HetNets). Considering channel estimation errors and inter-user interference under imperfect channel state information (CSI), the energy efficiency optimization problem is formulated, which is non-deterministic polynomial (NP)-hard and non-convex. To cope with this intractable problem, the optimization problem is converted into a convex problem and address it by the Lagrangian dual method. However, it is difficult to obtain closed-form solutions since the variables are coupled with each other. Therefore, a Lagrangian and sub-gradient based algorithm is proposed. In the inner layer loop, optimal powers are derived by the sub-gradient method. In the outer layer loop, optimal Lagrangian dual variables are obtained. Simulation results show that the proposed algorithm can significantly improve energy efficiency compared with traditional power allocation algorithms.     

Space–Time Power Schedule for Distributed MIMO Links Without Instantaneous Channel State Information at the Transmitting Nodes

A space-time optimal power schedule for multiple distributed multiple-input multiple-output (MIMO) links without the knowledge of the instantaneous channel state information (CSI) at the transmitting nodes is proposed. A readily computable expression for the ergodic sum capacity of the MIMO links is derived. Based on this expression, which is a non-convex function of power allocation vectors, a projected gradient algorithm is developed to optimize the power allocation. For a symmetric set of MIMO links with independent identically distributed channels, it is observed that the space-time optimal power schedule reduces to a uniform isotropic power schedule when nominal interference is low, or to an orthogonal isotropic power schedule when nominal interference is high. Furthermore, the transition region between the latter two schedules is seen to be very sharp in terms of nominal interference-to-noise ratio (INR). For MIMO links with correlated channels, the corresponding space-time optimal power schedule is developed based on the knowledge of the channel correlation matrices. It is shown that the channel correlation has a great impact on the ergodic capacity and the optimality of different power scheduling approaches.     

Energy-efficient power allocation scheme for distributed MISO system with transmit correlation

The energy efficiency (EE) of distributed multiple-input single-output (MISO) system is investigated in spatially-correlated Rayleigh channels, where large-scale fading including the path loss and the shadow fading is considered. The target is to maximize the EE which is defined as the ratio of the transmission rate to the total power consumed by the system subject to the maximum transmit power of each remote antenna unit (RAU) constraint. The EE optimization can be formulated as a nonlinear fractional programming problem. An optimal power allocation (PA) scheme for maximizing the EE is proposed. With this scheme, an iterative algorithm using Dinkelbach method is presented. To avoid iterative calculation, a low-complexity simplified PA scheme is developed based on the good channel information for antenna selection; it can provide a computational efficient method to acquire the optimal numbers of active RAUs. Therefore, the multidimensional optimization problem is converted to a single-dimensional optimization problem. As a result, the closed-form PA is attained. The simulation results validate the effectiveness of the proposed two schemes. The results indicate that these two schemes can achieve very similar performance, and the simplified scheme has lower complexity because no iteration is required.     

Power allocation-Assisted secrecy analysis for NOMA enabled cooperative network under multiple eavesdroppers

In this work, the secrecy of a typical wireless cooperative dual-hop non-orthogonal multiple access (NOMA)-enabled decode-and-forward (DF) relay network is investigated with the impact of collaborative and non-collaborative eavesdropping. The system model consists of a source that broadcasts the multiplexed signal to two NOMA users via a DF relay, and information security against the eavesdropper nodes is provided by a helpful jammer. The performance metric is secrecy rate and ergodic secrecy capacity is approximated analytically. In addition, a differential evolution algorithm-based power allocation scheme is proposed to find the optimal power allocation factors for relay, jammer, and NOMA users by employing different jamming schemes. Furthermore, the secrecy rate analysis is validated at the NOMA users by adopting different jamming schemes such as without jamming (WJ) or conventional relaying, jamming (J), and with control jamming (CJ). Simulation results demonstrate the superiority of CJ over the J and WJ schemes. Finally, the proposed power allocation outperforms the fixed power allocation under all conditions considered in this work.     

Simplified transmitter design for MIMO systems with channel uncertainty

This article investigates transmitter design in Rayleigh fading multiple input multiple output (MIMO) channels with spatial correlation when there are channel uncertainties caused by a combined effect of channel estimation error and limited feedback. To overcome the high computational complexity of the optimal transmit power allocation, a simple and suboptimal allocation is proposed by exploiting the transmission constraint and differentiating a bound based on Jensen inequality on the channel capacity. The simulation results show that the mutual information corresponding to the proposed power allocation closely approaches the channel capacity corresponding to the optimal one and meanwhile the computational complexity is greatly reduced.     

Capacity and optimal power allocation for fading broadcast channels with minimum rates

We derive the capacity region and optimal power allocation scheme for a slowly fading broadcast channel in which minimum rates must be maintained for each user in all fading states, assuming perfect channel state information at the transmitter and at all receivers. We show that the minimum-rate capacity region can be written in terms of the ergodic capacity region of a broadcast channel with an effective noise determined by the minimum rate requirements. This allows us to characterize the optimal power allocation schemes for minimum-rate capacity in terms of the optimal power allocations schemes that maximize ergodic capacity of the broadcast channel with effective noise. Numerical results are provided for different fading broadcast channel models.     

Optimal resource allocation for multiple network‐coded two‐way relay in orthogonal frequency division multiplexing systems

This paper studies optimal resource allocation for multiple network‐coded two‐way relay in orthogonal frequency division multiplexing systems. All the two‐way relay nodes adopt amplify‐and‐forward and operate with analog network coding protocol. A joint optimization problem considering power allocation, relay selection, and subcarrier pairing to maximize the sum capacity under individual power constraints at each transmitter or total network power constraint is first formulated. By applying dual method, we provide a unified optimization framework to solve this problem. With this framework, we further propose three low‐complexity suboptimal algorithms. The complexity of the proposed optimal resource allocation (ORA) algorithm and three suboptimal algorithms are analyzed, and it is shown that the complexity of ORA is only a polynomial function of the number of subcarriers and relay nodes under both individual and total power constraints. Simulation results demonstrate that the proposed ORA scheme yields substantial performance improvement over a baseline scheme, and suboptimal algorithms can achieve a trade‐off between performance and complexity. The results also indicate that with the same total network transmit power, the performance of ORA under total power constraint can outperform that under individual power constraints. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

基于天线选择的MIMO系统能效功率分配优化

对MIMO系统在毫米波衰落信道下的能效功率分配进行研究,以期实现绿色传输。考虑发送端采用天线选择技术,接收端采用最大比合并技术,给出系统能量效率公式,并构建系统基于能效最大化的目标优化函数。利用拉格朗日乘子法,获得迭代功率分配方案。利用排序法及朗伯函数给出简单的闭式功率分配方案。利用Matlab软件验证所提功率分配方案的有效性。仿真结果表明,文章提出的功率分配方案较穷举搜索法EE性能得到了明显提升,是一种复杂度低的优化算法,能快速收敛到EE最大值。