Energy Efficiency Optimization Problem Research Articles

Hybrid Precoding Design for Energy Efficient Millimeter-Wave Massive MIMO Systems

In this letter, we propose a hybrid precoding design algorithm by utilizing RF chain selection to optimize the number of RF chains to achieve high energy efficiency (EE) with slightly spectral efficiency (SE) performance degradation. In this algorithm, we firstly reformulate the energy efficiency optimization problem, and resolve the hybrid precoding optimization problem with alternating minimization method to seek the approximate optimal analog precoder and digital precoder under the proposed structure. Then, we perform the transmitter RF chain selection to find the optimal RF chain set corresponding to better EE and SE performance. Simulation results show the proposed algorithm achieves the good trade-off between EE and SE performance when the transmit power constraint is no larger than 30 dBm.

Robust THP Design for Energy Efficiency of Multibeam Satellite Systems with Imperfect CSI

In this letter, we investigate a robust zero-forcing (ZF) Tomlinson-Harashima Precoding (THP) scheme for multibeam satellite downlink systems to improve the energy efficiency (EE) when the channel state information (CSI) at the transmitter is imperfect. By using a norm-bounded error (NBE) model with unknown statistical characterization, the worst case EE optimization problem under transmit power constraint is solved with two steps. Firstly, the optimal CSI uncertainty parameter minimizing the EE is obtained, then sequential convex approximation (SCA) is used to obtain the solution via a nested iteration method. The proposed robust algorithm achieves better EE performance in comparison with the nonrobust one in the literature in the presence of CSI error, which can be shown from simulation results.

Codebook-Based Max–Min Energy-Efficient Resource Allocation for Uplink mmWave MIMO-NOMA Systems

In this paper, we investigate the energy-efficient resource allocation problem in an uplink non-orthogonal multiple access (NOMA) millimeter wave system, where the fully-connected-based sparse radio frequency chain antenna structure is applied at the base station (BS). To relieve the pilot overhead for channel estimation, we propose a codebook-based analog beam design scheme, which only requires to obtain the equivalent channel gain. On this basis, users belonging to the same analog beam are served via NOMA. Meanwhile, an advanced NOMA decoding scheme is proposed by exploiting the global information available at the BS. Under predefined minimum rate and maximum transmit power constraints for each user, we formulate a max-min user energy efficiency (EE) optimization problem by jointly optimizing the detection matrix at the BS and transmit power at the users. We first transform the original fractional objective function into a subtractive one. Then, we propose a two-loop iterative algorithm to solve the reformulated problem. Specifically, the inner loop updates the detection matrix and transmit power iteratively, while the outer loop adopts the bi-section method. Meanwhile, to decrease the complexity of the inner loop, we propose a zero-forcing (ZF)-based iterative algorithm, where the detection matrix is designed via the ZF technique. Finally, simulation results show that the proposed schemes obtain a better performance in terms of spectral efficiency and EE than the conventional schemes.

Energy Efficient Resource Management in SWIPT Enabled Heterogeneous Networks With NOMA

Non-orthogonal multiple access (NOMA) in heterogeneous network (HetNet) is a very promising scheme to meet the exponential growth of mobile data expected in the coming years. However, since wireless networks are becoming denser, the energy consumption of such networks is increasingly severe. Therefore, it is necessary to design novel energy efficiency (EE) maximization technologies under the constraint of limited energy supply. This paper investigates the resource optimization problem of NOMA heterogeneous small cell networks with simultaneous wireless information and power transfer (SWIPT). By decoupling subchannel allocation and power control, a low-complexity subchannel matching algorithm is designed. Furthermore, to maximize the energy efficiency, a power optimization algorithm is proposed using Langrangian duality. Aiming at the power allocation problem, the original non-convex and non-linear energy efficiency optimization problem is transformed into a more tractable one. Simulation results demonstrate the effectiveness and convergence of the proposed optimization scheme in terms of system energy efficiency.

Energy-Efficiency Optimization for IoT-Distributed Antenna Systems With SWIPT Over Composite Fading Channels

Due to the requirement of low-power network devices for the proliferation of high data communication, enabling technologies for energy sustainable Internet of Things (IoT) are of great significance. In this article, we investigate the energy-efficiency (EE) optimization of IoT-distributed antenna (DA) system with simultaneous wireless information and power transfer (SWIPT) technique over fading channels, where the IoT device is equipped with power splitter to integrate the energy harvesting and information decoding processes via adjusting the transmit power of each DA port and power splitting (PS) ratio of IoT device. According to the analysis of EE, an optimization problem with the aim of maximizing the system EE is formulated under the constraints of maximum transmit power of each DA port as well as minimum harvested energy. Through analyzing the structure of the objective problem, it is found that the EE optimization problem, which combines transmit power allocation (PA) with PS problem, can be predigested to a PA problem. Then, the amount of valid DA ports and the corresponding PA are achieved by utilizing the Karush–Kuhn–Tucker conditions and Lambert function. Based on this, we propose an optimal resource allocation scheme without iteration to obtain the optimal PA and PS ratio, and the resulting closed-form expressions are provided. Considering that perfect channel state information (CSI) is hard to achieve, we also study the resource allocation scheme based on the imperfect CSI (i.e., statistical CSI with large-scale fading information), two suboptimal schemes are proposed. These two schemes have better robustness and lower complexity than the optimal scheme with perfect CSI because they only need partial channel information, but the performances are worse than the latter, as expected. Computer simulation indicates that proposed schemes are valid and can obtain superior EE performance with lower complexity.

Optimizing Design Parameters for Relay-Aided Massive MIMO Systems

Utilization of relay stations (RSs) in massive multiple input multiple output (MIMO) systems is a challenging task. This paper proposes a relay-aided massive MIMO system under realistic circuit power consumption. The main focus is to search the optimal design parameters (i.e., number of RSs N, the number of RS antennas R, the number of BS antennas M, the number of user equipments K, the transmit power at base station (BS) pBS, and the transmit power at RS pRS for maximum energy efficiency (EE). The channel estimation and an arbitrary path loss with perfect and imperfect channel state information are considered. EE optimization problem is formulated with the objective of finding optimal design parameters. This paper also solves an optimization problem using three optimization algorithms, which are standard alternating algorithm, the Charnes-Cooper transform method-based scheme and the Dinkelbach's method-based scheme. Results are used to demonstrate the impacts of various system parameters on the EE performance.

Enabling Security and High Energy Efficiency in the Internet of Things With Massive MIMO Hybrid Precoding

Recently, the security of Internet of Things (IoT) has been an issue of great concern. Physical layer security methods can help IoT networks achieve information-theoretical secrecy. Nevertheless, utilizing physical security methods, such as artificial noise (AN) may cost extra power, which leads to low secure energy efficiency. In this paper, the hybrid precoding technique is employed to improve the secure energy efficiency of the IoT network. A secure energy efficiency optimization problem is formulated for the IoT network. Due to the non-convexity of the problem and the feasible domain, the problem is firstly transformed into a tractable suboptimal form. Then a secure hybrid precoding energy efficient (SEEHP) algorithm is proposed to tackle the problem. Numerical results indicate that the proposed SEEHP algorithm achieves higher secure energy efficiency compared with three existing physical layer security algorithms, especially when the number of transmit antennas is large.

Time and Power Allocation for Energy Efficiency Maximization in Wireless-Powered Full-Duplex Relay Systems

In this paper, we propose an optimal time and power allocation scheme in a wireless power supply full-duplex (FD) relay system, where we consider the number of relay antennas in the energy harvesting stage. At the same time, the energy efficiency optimization problem of the system is structured, where optimization issues related to time allocation factors and power allocation are established. For the FD dual-antenna and the FD single-antenna energy harvesting system, energy efficiency function is proven to be a concave function over the time-switch factor, and the optimal time-switching factor is theoretically obtained using the Lambert function. Then, according to the given value range of the optimal time switching factor, the optimal power distribution scheme is obtained by analyzing the derivative function of the system energy efficiency and using the properties of the Lambert function. The time-switching factor and transmission power are optimally selected at the wireless power supply FD relay. Results reveal that the performance of energy efficiency of the dual-antenna energy harvesting at the FD relay outperforms that of the single-antenna. Moreover, our results demonstrate that FD relay systems always substantially boost the energy efficiency compared with half-duplex (HD) relay systems.

Energy Efficiency Optimization for Secure Transmission in MISO Cognitive Radio Network with Energy Harvesting

In this paper, we investigate different secrecy energy efficiency (SEE) optimization problems in a multiple-input single-output underlay cognitive radio (CR) network in the presence of an energy harvesting receiver. In particular, these energy efficient designs are developed with different assumptions of channels state information (CSI) at the transmitter, namely perfect CSI, statistical CSI and imperfect CSI with bounded channel uncertainties. In particular, the overarching objective here is to design a beamforming technique maximizing the SEE while satisfying all relevant constraints linked to interference and harvested energy between transmitters and receivers. We show that the original problems are non-convex and their solutions are intractable. By using a number of techniques, such as non-linear fractional programming and difference of concave (DC) functions, we reformulate the original problems so as to render them tractable. We then combine these techniques with the Dinkelbach's algorithm to derive iterative algorithms to determine relevant beamforming vectors which lead to the SEE maximization. In doing this, we investigate the robust design with ellipsoidal bounded channel uncertainties, by mapping the original problem into a sequence of semidefinite programs by employing the semidefinite relaxation, non-linear fractional programming and S-procedure. Furthermore, we show that the maximum SEE can be achieved through a search algorithm in the single dimensional space. Numerical results, when compared with those obtained with existing techniques in the literature, show the effectiveness of the proposed designs for SEE maximization.

A resource allocation and cell association algorithm for energy efficiency in HetNets

SummaryAiming at further improving the energy efficiency of system while meeting the data rate requirement of the users, in this paper, a network energy efficiency optimization problem by jointly optimizing the resource allocation of macrocells and small cells is formulated and proven to be an NP‐hard problem, which cannot be worked out by direct methods in polynomial time. Considering the effectiveness of the modified particle swarm optimization (MPSO) algorithm, an MPSO‐based resource allocation and cell association algorithm is employed to solve the proposed joint optimization problem where the frequency resource partitioning of the macrocells, the transmission power, and the cell‐association bias of the small cells are jointly optimized. During the implementation of the optimization algorithm, the cell association alters with the transmission power and cell‐association bias adjustment, and the small cells where there are no active users associating with them will be turned off. The data rate requirement of the users is an indispensable metric in the communication system. Taking no account of the data rate requirement of the users, the frequency resource partitioning and cell association alteration will deteriorate the data rate of a few of users. Under such circumstances, we take the users' data rate requirement as a constraint of the joint optimization problem. The system level simulation results show that, by jointly optimizing the resource allocation of macrocells and small cells while guaranteeing the users' data rate requirement, the energy efficiency and system throughput can be further improved, and energy consumption can be further reduced.

Energy Efficiency Optimization for Massive MIMO Non-Orthogonal Unicast and Multicast Transmission with Statistical CSI

We study the energy efficiency (EE) optimization problem in non-orthogonal unicast and multicast transmission for massive multiple-input multiple-output (MIMO) systems with statistical channel state information of all receivers available at the transmitter. Firstly, we formulate the EE maximization problem. We reduce the number of variables to be solved and simplify this large-dimensional-matrix-valued problem into a real-vector-valued problem. Next, we lower the computational complexity significantly by replacing the objective with its deterministic equivalent to avoid the high-complex expectation operation. With guaranteed convergence, we propose an iterative algorithm on beam domain power allocation using the minorize maximize algorithm and Dinkelbach’s transform and derive the locally optimal power allocation strategy to achieve the optimal EE. Finally, we illustrate the significant EE performance gain of our EE maximization algorithm compared with the conventional approach through conducting numerical simulations.

An energy efficiency integration optimization scheme for ethylene production with respect to multiple working conditions

Ethylene production is an energy-intensive process, hence energy management and optimization play a crucial role in saving energy and increasing economic benefits. In industrial-scale ethylene production, the energy efficiency level is greatly influenced by different working conditions and multiple energy arrangements in different sub-processes. Energy efficiency optimization is a more direct and scientific way to improve efficiency and reduce consumption. However, conventional energy optimization schemes are implemented without due consideration of the above two factors adequately, and energy efficiency indicators are not considered a key objective of optimization. Aiming at the energy efficiency optimization problem of ethylene plant under multiple working conditions, an energy efficiency integration optimization scheme is proposed, combining multi-level production process and multi-condition technology. The traditional single optimization model cannot achieve the energy efficiency improvement of the ethylene production process characterized by the multi-condition and hierarchical architecture. To this end, by establishing dynamic models of the system level, process level and equipment level, and considering the associations at different levels, energy efficiency optimization models of ethylene production for different working conditions are established to realize an energy optimization management that maximizes the overall energy utilization efficiency of production. For the solution of model, a multi-objective particle swarm optimization algorithm based on historical working condition knowledge base is proposed to improve the performance of the optimization algorithm by guiding the oriented local area search. The effectiveness of the proposed scheme is verified through the application in a Chinese ethylene plant. The optimization results show that the overall energy efficiency of ethylene production has been significantly improved despite frequent changes in working conditions.

Energy Efficient Optimization of Wireless-Powered 5G Full Duplex Cellular Networks: A Mean Field Game Approach

This paper studies the power allocation of an ultra-dense cellular network consisting of multiple full-duplex (FD) base stations (BSs) serving a large number of half-duplex (HD) user equipments (UEs) located in a wide geographical area. Each BS consists of a baseband unit (BBU) that is responsible for signal processing and BS control, and a radio remote unit (RRU) that corresponds to a radio transceiver remotely built closer to the UEs. We consider a wireless-powered cellular network in which the BBU can periodically charge the RRU. We model the energy efficiency and coverage optimization problem for this network as a mean field game. We consider the weighted energy efficiency of the BS as the main performance metrics and evaluate the optimal strategy that can be adopted by the FD BSs in an ultra-dense network setting. Based on the interference and network energy efficiency models of the mean field game theory, Nash equilibrium of our proposed game is derived. Utilizing solutions of Hamilton–Jacobi–Bellman (HJB) and Fokker–Planck–Kolmogorov (FPK) equations, a new power transmission strategy is developed for the BSs to optimize the energy efficiency of 5G cellular networks with full duplex transmissions. Simulation results indicate that the proposed strategy not only improves the energy efficiency but also ensures the average network coverage probability converges to a stable level.

Simulation and Robust Optimization Design for Electromagnetic Railgun Performance

Energy efficiency is a critical quantity of interest in the performance of electromagnetic railgun (EMRG). To improve the energy efficiency of EMRG with the presence of uncertainty, a hybrid robust optimization method is proposed. EMRG simulation model is developed to simulate the behavior of exterior ballistics and the corresponding robust optimization issue is formulated. With the help of the impact factor analysis, several significant factors of energy efficiency are selected as the design variables while the insignificant ones are not taken into account. In the robust optimization, the polynomial chaos expansion approach coupled with Latin hypercube design is proposed to propagate the uncertainty for alleviating the computational burden of fitness function (energy efficiency) evaluation. Then, the genetic algorithm is employed to solve the EMRG energy efficiency optimization problem with the constraint of mean miss distance. The optimization results illustrate that the hybrid robust optimization method is an efficient approach to improve the energy efficiency, which can be applied in the practical application of EMRG projectile design.

Robust Optimization for Energy Efficiency in MIMO Two-Way Relay Networks With SWIPT

Energy efficiency (EE) is a key issue in energy-constrained wireless networks because of the energy scarcity. In this paper, we present the robust energy-efficient optimization design for multiple-input–multiple-output two-way relay networks with simultaneous wireless information and power transfer, where the available channel state information is considered to be imperfect. We model the channel errors by using the norm bounded model, and aim to maximize the worst-case EE by jointly designing the precoders of the sources and relay, and the power splitting ratio of the relay under the worst-case transmit power constraints at the sources and relay. To solve the robust EE optimization problem, we propose an iterative optimization algorithm based on the weighted minimum mean-square-error method, where the $\mathcal {S}$ -procedure and sign-definiteness lemma are employed to eliminate the channel errors. To balance the performance and complexity, we propose a channel diagonalization algorithm based on the generalized singular value decomposition, which has lower complexity. The effectiveness of the proposed algorithms is shown by numerical results.

Energy Efficiency–Delay Tradeoff for a Cooperative NOMA System

The tradeoff between the energy efficiency (EE) and delay problem in the cooperative relaying system is studied by using non-orthogonal multiple access (NOMA) in this letter. To obtain an efficiency tradeoff between EE and delay, a stochastic-based EE optimization problem is formulated by considering the system queue stability. Then, the fractional programming and control parameter-based Lyapunov optimization method is proposed to solve the formulated problem. Furthermore, we derive the analytical bounds of EE and delay based on the control parameter. Finally, simulation results verify that the proposed cooperative NOMA system performs better than the traditional orthogonal multiple access cooperative system.

Multi-Operator Cooperation for Green Cellular Networks With Spatially Separated Base Stations Under Dynamic User Associations

This paper presents a cooperation framework for sharing base stations (BSs) among ${N}$ number of collocated radio-access networks (RANs) for improving energy efficiency (EE). The proposed framework is equally applicable for collocated and non-collocated BSs belonging to multiple RANs. To the best of our knowledge, this paper is the first for developing such cooperation mechanisms among the spatially separated BSs of ${N}$ RANs. Independent hard-core Poisson point process (PPP) is used for modeling the locations of BSs with a minimal inter-BS distance, while locations of user equipment devices (UEs) are modeled using PPP. The proposed cooperation mechanisms enable the networks to serve UEs of other RANs allowing some BSs to switch into sleep mode for better EE. Call continuity, signal quality and call blocking limits are guaranteed during this dynamic BS switching. For avoiding high complexity of the generalized EE optimization problem, heuristically guided algorithms with different dynamic UE association policies are proposed. Network performance including fairness of the proposed cooperation under a wide range of system settings is thoroughly investigated. Simulation results clearly demonstrate a substantial improvement in EE as well as an extremely fair cooperation. Comparisons with the other works further validate the proposed framework.

Energy Efficiency Optimization for NOMA With SWIPT

The combination of simultaneous wireless information and power transfer (SWIPT) and non-orthogonal multiple access (NOMA) is a potential solution to improve spectral efficiency and energy efficiency (EE) of the upcoming fifth generation (5G) networks, especially in order to support the functionality of the Internet of things (IoT) and the massive machine-type communications (mMTC) scenarios. In this paper, we investigate joint power allocation and time switching (TS) control for EE optimization in a TS-based SWIPT NOMA system. Our aim is to optimize the EE of the system whilst satisfying the constraints on maximum transmit power budget, minimum data rate, and minimum harvested energy per terminal. The considered EE optimization problem is neither linear nor convex involving joint optimization of power allocation and time switching factors and, thus, is extremely difficult to solve directly. In order to tackle this problem, we develop a dual-layer algorithm where Dinkelbach method is employed both in the inner layer to optimize the power allocation and in the outer layer to control the time switching assignment. Furthermore, a simplified but practical special case with equal time switching factors in all terminals is considered. Numerical results validate the theoretical findings and demonstrate that significant performance gain over orthogonal multiple access scheme in terms of EE can be achieved by the proposed algorithms in a SWIPT-enabled NOMA system.

Energy-Efficient Resource Allocation in Heterogeneous Cloud Radio Access Networks via BBU Offloading

Energy efficient resource allocation in heterogeneous cloud radio access networks (H-CRANs) is considered in this paper where a set of users within a specific region is served by femto-cell access points (FAPs) and remote radio heads (RRHs) connected to the base-band unit (BBU) pool through front-haul links. For orthogonal frequency division multiple access (OFDMA) based uplink H-CRANs, we formulate an energy efficient optimization problem with the novel utility function in order to jointly assign the access point (RRH/FAP), sub-carrier, transmit power, RRH, front-haul link and BBU. Due to highly complex relation between diverse optimization variables and their effects on each other, the formulated optimization problem is non-convex and NP-hard, suffering from high computational complexity. To tackle this issue, we develop an efficient two-step iterative algorithm with low computational complexity to solve the proposed problem based on the successive convex approximation (SCA) and complementary geometric programming (CGP). The simulation results reveal that our proposed approach can effectively offload the traffic from C-RAN to low-power femto-cells, and reduce the energy consumption cost by switching off the under-utilized BBUs.

Joint Antenna Selection and Power Allocation for an Energy-efficient Massive MIMO System

A joint antenna selection and power allocation scheme is proposed for a downlink massive multiple-input multiple-output system under perfect channel state information. Based on a tractable lower bound of the achievable downlink rate with linear zero-forcing precoding, a nonconvex energy efficiency optimization problem is formulated with nonlinear constraints. Since the optimization variables are highly interrelated, it is impractical to directly derive the closed-form solution to the original problem. To solve this problem, an effective iterative algorithm that maximizes energy efficiency is proposed according to the Lagrangian dual method, where the optimal number of transmit antennas and power allocation are solved iteratively until convergence. Numerical results demonstrate the effectiveness of the proposed algorithm.