Mode Of Energy Transfer Research Articles

Preparation and characterization of a new orange-red phosphor Ba2LaTaO6:Eu3+ with abnormal thermal quenching

Herein, double-perovskite Ba2LaTaO6 Eu-doped orange-red phosphors were successfully synthesized using a high-temperature solid-phase method. The phosphor phase purity was investigated using X-ray diffraction and microscopic morphology analyses. Their luminescence properties were investigated using absorption, emission, excitation, and temperature-dependent spectra. The transition mechanism mainly involves a magnetic–dipole transition with an energy transfer mode featuring multipole–multipole interactions, and concentration quenching is achieved via dipole–dipole interactions. In addition, the intensity of the temperature-dependent spectrum increases abnormally between 298 and 373 K, with the luminous intensity at 373 K increasing to 110% of that observed at room temperature. This phenomenon can be attributed to lattice defects in Ba2LaTaO6:Eu3+, and the phosphor luminous intensity at 473 K remains at 80.62% of that at room temperature. In addition, white-light-emitting diode devices based on this novel Ba2LaTaO6:0.35Eu3+ phosphor were fabricated to evaluate the potential applications of the as-prepared phosphor.

A Charge/Discharge Plan for Electric Vehicles in an Intelligent Parking Lot Considering Destructive Random Decisions, and V2G and V2V Energy Transfer Modes

The random decisions of electric vehicle (EV) drivers, together with the vehicle-to-vehicle (V2V) and vehicle-to-grid (V2G) energy transfer modes, make scheduling for an intelligent parking lot (IPL) more complex; thus, they have not been considered simultaneously during IPL planning in other studies. To fill this gap, this paper presents a complete optimal schedule for an IPL in which all the above-mentioned items are considered simultaneously. Additionally, using a complete objective function—including charging/discharging rates and prices, together with penalties, discounts, and reward sets—increases the profits of IPL and EV owners. In addition, during peak times, the demand for energy from the distribution system is decreased. The performance of the proposed schedule is validated by comparing three different scenarios during numerical simulations. The results confirm that the proposed algorithm can improve the IPL’s benefits up to USD 1000 and USD 2500 compared to the cases that do not consider the V2V and V2G energy transfer modes, respectively.

What are the fundamental modes of energy transfer and partitioning in the coupled Magnetosphere-Ionosphere system?

The fundamental processes responsible for energy exchange between large-scale electromagnetic fields and plasma are well understood theoretically, but in practice these theories have not been tested. These processes are ubiquitous in all plasmas, especially at the interface between high and low beta plasmas in planetary magnetospheres and other magnetic environments. Although such boundaries pervade the plasma Universe, the processes responsible for the release of the stored magnetic and thermal plasma energy have not been fully identified and the importance of the relative impact of each process is unknown. Despite advances in understanding energy release through the conversion of magnetic to kinetic energy in magnetic reconnection, how the extreme pressures in the regions between stretched and more relaxed field lines in the transition region are balanced and released through adiabatic convection of plasma and fields is still a mystery. Recent theoretical advances and the predictions of large-scale instabilities must be tested. In essence, the processes responsible remain poorly understood and the problem unresolved. The aim of the White Paper submitted to ESA’s Voyage 2050 call, and the contents of this paper, is to highlight three outstanding open science questions that are of clear international interest: (i) the interplay of local and global plasma physics processes: (ii) the partitioning during energy conversion between electromagnetic and plasma energy: and (iii) what processes drive the coupling between low and high beta plasmas. We present a discussion of the new measurements and technological advances required from current state-of-the-art, and several candidate mission profiles with which these international high-priority science goals could be significantly advanced.

Deciphering modes of long-range energy transfer in perovskite crystals using confocal excitation and wide-field fluorescence spectral imaging

Excitation energy migration beyond mesoscale is of contemporary interest for both solar photovoltaic and light-emissive devices, especially in context of organometal halide perovskites (OMHPs) which have been shown to have very long (charge carrier) diffusion lengths. While understanding the energy propagation pathways in OMHPs is crucial for further advancement of material design and improvement of opto-electronic features, the simultaneous existence of multiple processes like carrier diffusion, photon recycling, and photon transport makes it often complex to differentiate them. In this study, we unravel the diverse yet dominant excitation energy transfer mode(s) in crystalline MAPbBr3 micron-sized 1D rods and plates by localized (confocal) laser excitation coupled with spectrally-resolved wide-field fluorescence imaging. While rarely used, this technique can efficiently probe excitation migration beyond the diffraction limit and can be realized by simple modification of existing epifluorescence microscopy setups. We find that in rods of length below ∼2 microns, carrier diffusion dominates amongst various energy transfer processes. However, the transient non-radiative defects severely inhibit the extent of carrier migration and also temporarily affect the radiative recombination dynamics of the photo-carriers. For MAPbBr3 plates of several tens of micrometers, we find that the photoluminescence (PL) spectral characteristics remain unaltered at short distances (< ∼3 μm) while at a larger distance, the spectral profile is gradually red-shifted. This implies that carrier diffusion dominates over small distances, while photon recycling, i.e., repeated re-absorption and re-emission of photons, propagates excitation energy transfer over extended length scales with assistance from wave-guided photon transport. Our findings can potentially be used for future studies on the characterization of energy transport mechanisms in semiconductor solids as well as for organic (molecular) self-assembled microstructures.

Macro-ecology of cold seeps in the South China Sea

• Overview of macro-ecology of cold seeps in the South China Sea. • Distribution of macrofauna in the active seep areas. • Mechanistic link between microbial and metazoan communities. • A time-integrated approach is critical for seep research in the future. After nearly 20 years of exploration, various areas of the seafloor with hydrocarbon seepage have been discovered in the South China Sea (SCS). Through linking subsurface and seafloor biospheres, seeps have become natural laboratories to enhance our knowledge on the processes of hydrocarbon migration and associated hydrocarbon-based ecosystems in the marine environment. This review summarizes the distribution of macrofauna in the active seep areas of the SCS and describes the physiological characteristics of three groups of representative macrofauna (bathymodioline mussels, pliocardiine clams, siboglinid tubeworms). In addition, a comparison is made between the seep macrofauna of the SCS and the Northwest Pacific Ocean. Modes of energy transfer and microbial processes are elucidated by integrating trace element, stable isotope, and lipid biomarker data of macrofaunal soft tissues. Our aims are to provide an overview of the macro-ecology of the SCS seeps and to underscore aspects which desire more research efforts in the future.

Growth and Temperature-Dependent Spectral Properties of Yb3+, Tm3+ Co-Doped NaY(MoO4)2 Crystal

The NaY(MoO4)2:Yb3+/Tm3+ single crystal was grown by the vertical Bridgman method using spontaneous crystallization. After annealing at 850 °C for 24 h in a muffle furnace under an air atmosphere, the obtained light black crystal became transparent and optically clear. Powder X-ray diffraction (PXRD) confirmed that the as-grown crystal had the structure of scheelite. The segregation coefficients of Tm3+ and Yb3+ were 0.589 and 0.588, respectively. Under 980 nm excitation, the temperature dependence of the emission intensity of the crystal in the temperature range of 298–473 K was measured. The results show that, because of the thermal quenching effect, the emission intensity decreases as the temperature rises. The possible energy transfer modes between Yb3+ and Tm3+ ions were analyzed. The emission cross section was calculated to be 1.97 × 10-20 cm2 by the Füchtabauer-Ladeburg formula, and the fluorescence lifetime was fitted to be 166.67 μs.

Energy extraction in the dynamic modes of flow for airfoil's laminar separation flutter

This paper aims to gain new insight into the physical mechanism of laminar separation flutter (LSF) from the perspective of energy transfer and dynamic mode decomposition (DMD) modes of flow. An online DMD method accounting for the airfoil's pitch motion is developed, and the relationship between the topology of energy map and DMD modes is established. Simulation results indicate that there are two limit cycle branches in energy map, but only one branch is stable. The LSF time response state can be predicted accurately by the stable limit cycle branch. The topology of an energy map is dominated by the DMD mode corresponding to the airfoil's pitch frequency. The developed DMD method can extract the variation of flow structures effectively. The pressure distribution of DMD mode corresponding to the pitch frequency is dominated by the leading-edge suction and bubble's suction. The bubble's suction is induced by the trailing-edge laminar separation bubble or laminar separation bubble (LSB). When the pitch amplitude is larger than 4°, the trailing-edge laminar separation bubble transforms to LSB. The inherent mechanism is that increasing the trailing-edge separation bubble's intensity promotes the energy extraction while the occurrence of LSB mitigates it.

The convective heat transfer analysis of the casson nanofluid jet flow under the influence of the movement of gyrotactic microorganisms

Jet flows provide an effective mode of energy transfer or mass transfer in industrial applications. When compared to traditional cooling through convection, jet flows have high heat and mass transfer coefficients. Further, the devices equipped with jet flow provides efficient use of fluid and also offers enhanced heat and mass transfer rates. Hence in this study, the jet flow of Casson nanofluid containing gyrotactic microorganisms that stabilises the nanoparticle suspension is discussed. To control the fluid from outside external magnetic field is imposed. The model with these characteristics are useful in the appliances like coolants in automobiles, nuclear reactors, micro-manufacturing, metallurgical process etc. Such a model is created by employing PDE, which are then transformed into a system of ODE. The DTM is employed to obtain the solution to system of equations, and the results are interpreted using graphs. It is perceived that the velocity of the nanofluid flow is decreased because of the increased yield stress created by the greater values of the Casson parameter. As a result, the temperature profile is found to be increasing. Meanwhile, it is observed that for increased value of chemical reaction parameter diminishes the nanoparticle concentration. The motile density is found to decrease for increase in the Peclet number and the bioconvection Schmidt number. Further, the thermophoresis improves the temperature and concentration profile of the nanofluid.

Analysis of hybrid Adiabatic Compressed Air Energy Storage - Reverse Osmosis desalination system with different topological structures

Given the high energy consumption in the traditional Reverse Osmosis (RO) desalination system, it is necessary to enable energy-efficient and sustainable water production. This study proposed four hybrid systems of Adiabatic Compressed Air Energy Storage (ACAES) and RO desalination with different topological structures. By establishing mathematical models of each sub-system, the steady-state simulation of the hybrid system was carried out. Energy transfer modes of four different hybrid system topological structures were proposed and analyzed. Then, the effects of the storage pressure and ambient temperature variation on the system performance were analyzed. The results show that the hybrid system without electric power has a 10% reduction in energy consumption. In all simulated working conditions, when the End Pressure of Charge (EPC) varies from 8 to 12 MPa, an optimal value of 5 MPa exists for EPD, enabling the lowest Specific Energy Consumption (SEC) of the hybrid system. In comparison, system SEC can be reduced by about 30% at a high ambient gas temperature of 40 °C than at a lower temperature of 0 °C. In all simulated working conditions, when EPC and EPD are respectively 12 MPa and 5 MPa, SEC has a minimum value of 3.18 kWh/m3. This study is helpful to promote the application of ACAES in the field of RO desalination and provides a theoretical reference for the system design.

A Secure and Efficient Wireless Charging Scheme for Electric Vehicles in Vehicular Energy Networks

To address the limited driving range of electric vehicles (EVs) and promote EVs’ penetration, vehicular energy networks (VENs) have emerged and opened possibility to charge EVs in motion via dynamic wireless power transfer (DWPT) technology. However, security and efficiency concerns arise due to the untrusted operating environment and EVs’ selfish charging/discharging behaviors. Existing trust models rely on the personal recommendations from neighboring EVs to identify malicious entities in VENs, which may cause potential privacy breaches and data misuse for recommenders. Besides, it is challenging to optimally schedule EVs’ energy behaviors by considering complex interactions among three energy entities (i.e., energy nodes, charging EVs, and discharging EVs). To this end, by leveraging blockchain technology and game theory, this paper proposes a secure and efficient wireless charging scheme to address these issues in VENs. Firstly, a blockchain-based fine-grained access control mechanism with traceability and auditability is presented to enable EV users to fully control and audit their personal rating data usage during trust management by logging data activities and issuing access tokens into decentralized ledgers. In this manner, the privacy of recommenders can be preserved by fully controlling the access and usage of personal rating data. Furthermore, by introducing cooperative wireless energy transfer mode, a hierarchical game-based energy scheduling algorithm is developed to optimize the strategies of three energy parties tier by tier, while considering their cooperation and competition. Finally, extensive simulations are conducted, which demonstrate that the proposed scheme can effectively improve users’ utility and security of energy transmission for EVs, compared with existing representative approaches.

Pyrylium salts acting as both energy transfer and electron transfer photocatalysts for E → Z isomerization of activated alkenes and cyclization of cinnamic or biaryl carboxylic acids

Here we report that 2,4,6-triarylpyrylium salts could perform both energy transfer and electron transfer photocatalysis modes for E → Z isomerization of activated alkenes and cyclization of cinnamic or biaryl carboxylic acids.

Direct fabrication of high-performance multi-response e-skin based on a graphene nanosheet film

With the increasing popularity of wearable devices, lightweight electronic skin (e-skin) has attracted significant attention. However, current fabrication technologies make it difficult to directly fabricate sensing materials on flexible substrates at low temperatures. Hence, we propose a flexible graphene nanosheet-embedded carbon (F-GNEC) film, which is directly grown on a flexible substrate using an electron cyclotron resonance low-temperature sputtering system. The direct batch manufacturing of e-skin is obtained by the unique plasma generation mode of electron cyclotron resonance and the polariton energy transfer mode between the plasma and substrate surface. The F-GNEC film contains a large number of graphene nanosheets grown vertically and the graphene edges can serve as electron capture centers, thereby enabling the multi-response properties. We achieve a high gauge factor of 14,699 under a tensile strain of ε = 0.5% and the changing rate of the resistance reaches to 113.2% when the e-skin is bent to 120°. Furthermore, the e-skin achieves a photocurrent of 1.2 μA under 532 nm laser illumination. The F-GNEC film exhibits a sensitive temperature response and achieves a coefficient of -0.58%/°C in a wide temperature range (30-100 °C). The directly fabricated F-GNEC film-based e-skin is stable and firm and exhibits multi-response detection capabilities, which enable its potential application in virtual reality technology and flexible robots.

Organic Semiconductor–Organism Interfaces for Augmenting Natural and Artificial Photosynthesis

Carbon neutrality is increasingly broadly recognized as a vehicle for climate action and sustainable development. Photosynthesis contributes to maintaining a suitable carbon-oxygen balance for survival and plays an irreplaceable role in mitigating the greenhouse effect. However, the energy conversion efficiency of photosynthesis is only about 1%, far below the theoretical maximum. With the ecological demand of carbon neutrality, it is wise and necessary to further improve the efficiency of photosynthesis. Among methods to do so, the most direct and original one is improving the utilization of photosynthetic pigments to the weak absorption region of the spectrum and thus enhancing the solar energy utilization efficiency.This Account summarizes our group's work on constructing conjugated polymer-photosynthetic organism interfaces to augment photosynthetic efficiency. Side chain modification of ionic groups or preparation of nanoparticles makes conjugated polymers water-soluble and electrically charged, which allows them to bind to the surface of photosynthetic microorganisms through electrostatic interactions or be absorbed by plant roots. Owing to the designable and unparalleled light capture and emission capabilities, funnel-like excitation energy transfer mode, and enviable biocompatibility, organic semiconductor conjugated polymers can be used as "artificial antennas" to make up for the lack of natural antenna pigments and expand the photosynthetically active radiation (PAR) range. With this strategy, we achieved enhancement of the photosynthetic efficiency of a broad range of organisms, including oxygenic photosynthetic organisms, from organelle to prokaryotic cyanobacteria, eukaryotic lower plants, and higher plants, as well as anoxygenic photosynthetic organisms. Unlike conventional semiconductors, conjugated polymers have not only electronic conductivity but also ionic conductivity, which is the main means of bioelectrical signal transduction. Therefore, they are able to act as "electron bridges" to accelerate the electron transfer rate at the material-organism interface. On this basis, we introduced conjugated polymers into artificial photosynthesis systems, including biological photovoltaics and artificial carbon sequestration, to increase energy conversion efficiency. These studies open a new frontier for functional studies of conjugated molecules and provide inspirations for the design of photosynthesis systems in the future.

Effect of Tb3+ ion concentration on the up-conversion and down-conversion luminescence properties of the Yb3+/Ho3+/Tb3+ tri-doped SiO2–Al2O3–Y2O3–NaF–CaF2 glasses

Yb 3+ -Ho 3+ -Tb 3+ co-doped SiO 2 –Al 2 O 3 –Y 2 O 3 –NaF–CaF 2 glasses were prepared. The XRD of the glass was obtained, which proved the amorphous state of the glass. The crystallization temperature of glass was measured by differential scanning calorimetry, and the crystallization activation energy was obtained. The absorption spectrum of glass was investigated. The network structure of glass was studied. The up-conversion and down-conversion spectra of the glass were obtained under 980 nm and 369 nm excitation, respectively, and the fluorescence decay lifetime of Tb 3+ : 5 D 4 was measured. The influence of laser power on up-conversion luminescence intensity was investigated by changing the laser power. The energy transfer relationship among Yb 3+ , Ho 3+ , and Tb 3+ was researched. The CIE chromaticity coordinate was calculated according to the emission spectrum. It shows that this series of glasses have possible applications in the field of the green light display. • Yb 3+ -Ho 3+ -Tb 3+ tri-doped SiO 2 –Al 2 O 3 –Y 2 O 3 –NaF–CaF 2 glass was prepared. • Intensity of the up-conversion and down-conversion emission peaks was dominated by Tb 3+ ions. • Energy level transitions and energy transfer modes between Yb 3+ -Ho 3+ -Tb 3+ ions were discussed. • This series of glass has potential applications in the field of green light display elements.

Obvious phase transition status induced by He+-ions implantation in KTN crystal

We report on the formation of a critical ferroelectric state induced by the He+ ion implantation in potassium tantalate niobate crystal. Obvious phase change has been observed in the ion irradiated region, which is mostly related to the stable polarized nanometric regions formed during the ion implantation process. Under the irradiation of 2 MeV He+ ions, two distinguishable layers corresponding to different energy transfer modes (elastic nuclear collision and inelastic electronic collision, respectively) between the incident He+ ions and the intrinsic lattices have been formed beneath the irradiated surface. Lattice dynamics before and after the ion implantation process are investigated by the confocal µ-Raman system. And the variations of typical Raman-active vibrational modes demonstrate the presence of lattice distortion in the irradiated region. X-ray diffraction experiments further suggest the mostly uniform lattice elongation in this region. Piezo-response force characteristic measurements reveal the existence of stable polarized nanometric regions with more intense polarization and verify that the crystal with such a phase status possesses extraordinary microscopic disorders, which is different from the traditional ferroelectric or paraelectric phase. Optical transmission experiments demonstrate that the irradiated region possesses relatively low propagation loss. The ion implantation method provides a new approach to form a temperature-stable critical ferroelectric state in relaxor ferroelectric materials. Analyses of the modification on the lattice dynamics of the irradiated region can help us build a clear awareness of the physical essence of this critical state and the relaxor ferroelectricity. Also, with good optical transmittance, the irradiated region is capable of promising optical functional devices.

Computational Study of Hypersonic Rarefied Gas Flow over Re-Entry Vehicles Using the Second-Order Boltzmann-Curtiss Constitutive Model

The aerothermodynamics of re-entry vehicles vary significantly upon re-entry, descent, and landing, because of the drastic changes in atmospheric density and velocity. In highly rarefied regimes, the conventional Navier-Stokes-Fourier equations may not provide an accurate prediction of aerothermodynamic loads acting on these vehicles. To tackle these challenges, an explicit mixed-type modal discontinuous Galerkin method was developed, based on the second-order Boltzmann-Curtiss constitutive model and the Maxwell slip and Smoluchowski jump conditions. A comprehensive analysis was conducted for different configurations of re-entry vehicles under various degrees of rarefaction. The computational results show that the rotational mode of energy transfer for diatomic gases substantially affects the lift-to-drag ratio and stability of re-entry vehicles. The total drag and heat transfer rate of the second-order constitutive model remained smaller than those of the first-order constitutive model in the rarefied regime, which makes the second-order results in better agreement with the direct simulation Monte Carlo.

Analysis of energy separation inside a Ranque-Hilsch vortex tube using RANS based CFD

The primary aim of this study was to investigate the role of turbulent structure in energy separation inside Vortex Tube. The important flow features were identified using RANS based CFD. The flow was divided into two parts above and below the cross-over region which is the radial location where the axial velocity is zero i.e., the flows above and below this region are oppositely directed. The Reynolds stress analysis revealed the stresses to be maximum at the cross-over region. In addition, the reversing and expanding core flow was found to have a temperature drop greater than that computed assuming an isentropic expansion process. This was also confirmed in the Control Volume (CV) analysis of the energy in the core flow wherein the core flow at the outlet of the CV was found to have experienced an energy loss compared to when it entered the CV. This was then correlated with the assumed work and heat interactions across the control surface bounding the CV of the core flow. The energy difference in the core flow computed by the two methods were found to agree within an accuracy of 10 %, thus validating our assumptions regarding the presence of heat and work transfer between the core and annular flows. The analysis also revealed that the turbulent shear work to be the dominant mode of energy transfer between the core and annular flows, comprising about 80 % of the energy transfer, and remaining 20 % attributed to heat transfer.

Energy-Efficient Data and Energy Integrated Management Strategy for IoT Devices Based on RF Energy Harvesting

Considering not only reducing the energy consumption based on the fixed energy source but also capturing new energy by RF energy harvesting (EH) for Internet-of-Things (IoT) devices, an integrated energy-efficient strategy for IoT devices is proposed in this article. On the one hand, a node sampling scheduling algorithm based on matrix completion is designed. All the sampling data are handled as matrix elements. The basic idea is to reduce the sampling data and then reconstruct the complete data set with the technology of matrix completion by using the spatial-temporal correlation of all the sampling data. Thus, the IoT nodes can keep dormant more instead of working on data sampling. The energy consumption can be significantly reduced with very little data loss. On the other hand, an adaptive RF energy management strategy is introduced. Based on the self-designed data and energy integrated network (DEIN) system, both data and energy are transferred between the DEIN gateway (DEING) and the DEIN Node (DEINN). With the adaptive energy management strategy, they both automatically switch between the wireless information transfer (WIT) mode and the wireless energy transfer (WET) mode. Combining energy saving with EH, the energy efficiency can be greatly enhanced. The proposed integrated solution aims to decrease the energy consumption of IoT devices and provide them with constant new energy by RF EH. Thus, their battery lives can be prolonged. Both the effectiveness and the efficiency of the proposed integrated strategy have been validated with the simulation.

Holographic Optical Tweezers and Boosting Upconversion Luminescent Resonance Energy Transfer Combined Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR)/Cas12a Biosensors.

Taking advantage of outstanding precision in target recognition and trans-cleavage ability, the recently discovered CRISPR/Cas12a system provides an alternative opportunity for designing fluorescence biosensors. To fully exploit the analytical potential, we introduce here some meaningful concepts. First, the collateral cleavage of CRISPR/Cas12a is efficiently activated in a functional DNA regulation manner and the bottleneck which largely applicable to nucleic acids detection is broken. After selection of a representative aptamer and DNAzyme as the transduction pathways, the sensing coverage is extended to a small organic compound (ATP) and a metal ion (Na+). The assay sensitivity is significantly improved by utilizing a bead-supported enrichment strategy wherein emerging holographic optical tweezers are used to enhance imaging stability and simultaneously achieve multiflux analysis. Last, a sandwich-structured energy-concentrating upconversion nanoparticle triggered boosting luminescent resonance energy transfer mode is comined to face with complicated biological samples by skillfully confining the emitters into a very limited inner shell. Following the above attempts, the developed CRISPR/Cas12a biosensors not only present an ultrasensitive assay behavior toward these model non-nucleic acid analytes but also can serve as a formidable toolbox for determining real samples including single cell lysates and human plasma, proving a good practical application capacity.

Joint TS Beamforming and Hybrid TS-PS Receiving Design for SWIPT Systems

Simultaneously wireless information and power transfer technology enables information and energy to be transmitted over the same radio frequency (RF) signal. We investigate a multiple input simple output (MISO) system where the multiple-antenna base station not only transmits information to single-antenna users, but also supplies all power they need. The same beamforming at base station under two modes of energy transfer and information transmission causes the problem of low system energy efficiency. To solve this, we put forward a novel transmission scheme where beamforming is divided by time switching (TS) into two parts, energy beamforming and information beamforming, and users receive by hybrid time switching and power splitting (hybrid TS-PS) correspondingly. Under constraints of information and energy, we aim to achieve the maximal energy efficiency by jointly optimize power splitting, time allocation, beamforming for energy transfer and information transmission phase respectively. In the solving process, we transfer the maximal energy efficiency problem into the minimal energy consumption problem, analyze the feasibility, then prove the existing of optimal solution. Furthermore, we put forward a semidefinite relaxation (SDR) based algorithm to solve the problem optimally and two sub-optimal designs to simplify computing complexity. Simulation results illustrate that our proposed design can achieve the optimal energy efficiency and prove the asymptotic optimality of two sub-optimal solutions.