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Performance of MIMO Systems Using Space Time Block Codes (STBC) 被引量:1
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作者 Christopher M. Lau 《Open Journal of Applied Sciences》 2021年第3期273-286,共14页
Digital Communications, in relation to wireless networks, have taken off in recent years due to the expanding need to communicate faster and more efficiently. A popular way to achieve this is by using wireless Multipl... Digital Communications, in relation to wireless networks, have taken off in recent years due to the expanding need to communicate faster and more efficiently. A popular way to achieve this is by using wireless Multiple Input Multiple Output (MIMO) communication systems. MIMO systems utilize Space Time Block Codes (STBC) as one of the leading ways to obtain higher data rates with limited bandwidth and power. With several STBC methods currently available, this paper analyzes simulations using Orthogonal Space Time Block Codes (OSTBC) in Rayleigh fading channels to evaluate the performance of MIMO systems. The selection to use a Rayleigh fading channel as a model for a non-line-of-sight (nLOS) environment is selected to mimic installations where a large number of signal paths and reflections are expected. All simulations are coded, generated and plotted using MATLAB resulting in graphical data representing the bit-error rate (BER) to signal-to-noise ratio (Eb/N<sub>0</sub>) or SNR. Each simulation captures how different configurations of key variables including code rate, diversity and antenna count can impact system performance. Four modulation schemes (BPSK, QPSK, 16-QAM and 64-QAM) are included in each simulation. Conclusive evidence based upon these simulations suggests higher diversity gains were achieved with a greater number of antennas. The most significant factor for increasing system performance was using a lower count of transmit antennas with a higher count of receive antennas. 展开更多
关键词 Computer Analysis Digital Communications MATLAB MIMO Modulation Techniques Multiple Input Multiple Output Systems Orthogonal space time Block Codes OSTBC Rayleigh Fading Channels space time Block Codes STBC Wireless Communications Wireless Networks
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Traffic condition estimation with pre-selection space time model 被引量:5
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作者 DONG Hong-hui SUN Xiao-liang +2 位作者 JIA Li-min LI Hai-jian QIN Yong 《Journal of Central South University》 SCIE EI CAS 2012年第1期206-212,共7页
A pre-selection space time model was proposed to estimate the traffic condition at poor-data-detector,especially non-detector locations.The space time model is better to integrate the spatial and temporal information ... A pre-selection space time model was proposed to estimate the traffic condition at poor-data-detector,especially non-detector locations.The space time model is better to integrate the spatial and temporal information comprehensibly.Firstly,the influencing factors of the "cause nodes" were studied,and then the pre-selection "cause nodes" procedure which utilizes the Pearson correlation coefficient to evaluate the relevancy of the traffic data was introduced.Finally,only the most relevant data were collected to compose the space time model.The experimental results with the actual data demonstrate that the model performs better than other three models. 展开更多
关键词 traffic condition ESTIMATION space time model pre-selection
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A Method for Improving Power Distribution Characteristics of Space Time Block Codes 被引量:3
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作者 Vahid Abbasi Mahrokh GShayesteh 《China Communications》 SCIE CSCD 2020年第6期223-234,共12页
Improving power distribution characteristics of space time block codes(STBCs),namely peak to average power ratio(PAPR),average to minimum power ratio(Ave/min),and probability of transmitting"zero"by antenna,... Improving power distribution characteristics of space time block codes(STBCs),namely peak to average power ratio(PAPR),average to minimum power ratio(Ave/min),and probability of transmitting"zero"by antenna,makes easier their practical implementation.To this end,this study proposes to multiply full diversity STB C with a non-singular matrix in multiple input multiple output(MIMO)or multiple input single output(MISO)systems with linear or maximum likelihood(ML)receivers.It is proved that the obtained code achieves full diversity and the order of detection complexity does not change.The proposed method is applied to different types of STBCs.The bit error rate(BER)and power distribution characteristics of the new codes demonstrate the superiority of the introduced method.Further,lower and upper bounds on the BER of the obtained STBCs are derived for all receivers.The proposed method provides trade-off among PAPR,spectral efficiency,energy efficiency,and BER. 展开更多
关键词 full diversity linear receiver maximum likelihood peak to average power ratio power distribution space time block codes
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Joint multi-user space time block coding and beamforming via convolutional weighting 被引量:1
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作者 邢志强 Zhou Tingxian Meng Weixiao 《High Technology Letters》 EI CAS 2006年第2期119-123,共5页
A convolutional weighting (CW) scheme applied to a half-wavelength spacing array was proposed for multi-user system to joint STBC (space time block ceding) and beam forming (BF). The transmitting beam is equival... A convolutional weighting (CW) scheme applied to a half-wavelength spacing array was proposed for multi-user system to joint STBC (space time block ceding) and beam forming (BF). The transmitting beam is equivalent to the product of two sub-beams. One is used to realize interference suppression, while the other is employed to form a couple of uncorrelated channels from base station (BS) to the desited user (to meet the requirement of STBC) and to maximize SINR (signal-to-interference-plus noise ratio) at the desired receiver. As an optimum combination of STBC and beam forming, the proposed scheme can achieve both full diversity order of STBC and array gain of BF. Meanwhile, it can also effec- tively restrain multi-user interference by nulling. Simulation results show that the proposed scheme can significantly improve the BER (Bit Error Rate) performance and enhance system capacity as compared with the conventional eigen-beamforming (EBF) technique applied to a half-wavelength spacing array. 展开更多
关键词 space time block ceding beam forming convolutional weighting multi-user interference
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Performance and EXIT analysis of parallel concatenated space time trellis codes
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作者 Yang Haifen Li Guangjun +1 位作者 Guo Zhiyong Xiong Yong 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2009年第6期1193-1197,共5页
Space time trellis coding (STTC) techniques have been proposed to achieve both diversity and coding gains in multiple input multiple output (MIMO) fading channels. But with more transmit antennas STTCs suffer from... Space time trellis coding (STTC) techniques have been proposed to achieve both diversity and coding gains in multiple input multiple output (MIMO) fading channels. But with more transmit antennas STTCs suffer from the design dificulty and complexity increasing. This paper proposes a scheme, named parallel concatenated space time trellis codes (PC-STTC), to achieve the tradeoff between the performances and complexity of STTCs for a large number of transmit antennas. Simulation results and complexity comparison are provided to demonstrate the performance and superiority of the proposed scheme over conventional schemes in fast fading channels in low signal-to-noise ratio (SNR) regions. And an EXIT (extrinsic information transform) chart is given to analyze the iterative convergence of the proposed scheme. It shows that PC-STTC has better iterative convergence in low SNR regions. 展开更多
关键词 space time trellis coding EXIT chart Log-MAP decoder convergence.
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SPACE TIME ON THE POINCARE DIAGRAMS
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作者 林金 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第9期835-847,共13页
Relations between the experience of space technology and theory of space and time are found in this paper. A nontraditional approach to the concepts of space and time is introduced. The approach is based upon the the ... Relations between the experience of space technology and theory of space and time are found in this paper. A nontraditional approach to the concepts of space and time is introduced. The approach is based upon the the analysis of the detailed mechanism of radar measurement and nonlinear Doppler effects as measured by an astronaut. The Lorentz factor and four-dimensional interval may be interpreted from the point of view of a space technologist. A 'geometrical mean' notion for computing time interval is introduced parallelly with the usual arithmetic mean formulas, giving results comparable with those of special relativity theory. Space time relationships are demonstrated on the Poincare diagrams. 展开更多
关键词 space time Poincare diagrams relativity theory
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Space time clock:An on-chip clock with 10^(-12) instability
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作者 Zhendong XU Yingchun ZHANG +3 位作者 Pengfei LI Yongsheng WANG Limin DONG Guodong XU 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2022年第10期247-253,共7页
High precision and stable clock is extremely important in communication and navigation.The miniaturization of the clocks is considered to be the trend to satisfy the demand for5G and the next generation communications... High precision and stable clock is extremely important in communication and navigation.The miniaturization of the clocks is considered to be the trend to satisfy the demand for5G and the next generation communications.Based on the concept of meter bar and the principle of the constancy of light velocity,we designed a micro clock,Space Time Clock(STC),with the size smaller than 1 mm×1 mm and the power dissipation less than 2 m W.Designed in integrated circuit of 0.18μm technology,the instability of STC is assessed to be 2.23×10^(-12)and the trend of the instability is reversely proportional toτ.With the potential ability to reach the level of 10instability on chip in the future,the period of the STC’s signal is locked on the delay time defined by the meter bar which keeps the time reference constant.Because of its superior performance,the STC is more suitable for mobile communication,PNT(Positioning,Navigation and Timing),embedded processor and deep space application,and becomes the main payload of the ASRTU satellite scheduled to launch next year and investigate in space environment. 展开更多
关键词 Communication Embedded processor INSTABILITY Positioning navigation and timing space time clock
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The space time CE/SE method for solving one-dimensional batch crystallization model with fines dissolution 被引量:1
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作者 Saima Noor Shamsul Qamar 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2015年第2期337-341,共5页
This article is concerned with the numerical investigation of one-dimensional population balance models for batch crystallization process with fines dissolution.In batch crystallization,dissolution of smaller unwanted... This article is concerned with the numerical investigation of one-dimensional population balance models for batch crystallization process with fines dissolution.In batch crystallization,dissolution of smaller unwanted nuclei below some critical size is of vital importance as it improves the quality of product.The crystal growth rates for both size-independent and size-dependent cases are considered.A delay in recycle pipe is also included in the model.The space–time conservation element and solution element method,originally derived for non-reacting flows,is used to solve the model.This scheme has already been applied to a range of PDEs,mainly in the area of fluid mechanics.The numerical results are compared with those obtained from the Koren scheme,showing that the proposed scheme is more efficient. 展开更多
关键词 Population balances Batch process Crystallization Dissolution of fines spacetime conservation element and solution element method
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Space time fractional KdV Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions 被引量:2
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作者 Emad K.El-Shewy Abeer A.Mahmoud +2 位作者 Ashraf M.Tawfik Essam M.Abulwafa Ahmed Elgarayhi 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第7期316-322,共7页
The KdV-Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged non- thermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzma... The KdV-Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged non- thermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzmann distribution is used for electrons in the presence of the cold (hot) dust viscosity coefficients. The semi-inverse method and Agrawal variational technique are applied to formulate the space-time fractional KdV-Burgers equation which is solved using the fractional sub-equation method. The effect of the fractional parameter on the behavior of the dust acoustic shock waves in the dusty plasma is investigated. 展开更多
关键词 dust-acoustic waves reductive perturbation method modified Riemann-Liouville fractionalderivative space-time fractional KdV-Burgers equation
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Neutrino oscillation interference phase in Kerr space time
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作者 任军 贾孟文 袁常青 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第12期5575-5582,共8页
The mass neutrino interference phases along the null trajectory and the geodesic line in Kerr space-time are studied on the plane θ = π/2. Because of the rotation object in Kerr space-time, a particle travelling alo... The mass neutrino interference phases along the null trajectory and the geodesic line in Kerr space-time are studied on the plane θ = π/2. Because of the rotation object in Kerr space-time, a particle travelling along the radial geodesic must have a dragging effect produced by the angular momentum of the central object. We give the correction of the phase due to the rotation of the space-time. We find that the type-I interference phase along the geodesic remains the double of that along the null on the condition that the rotating quantity parameter a^2 is preserved and the higher order terms are negligible (e.g. a^4). In addition, we calculate the proper oscillation length in Kerr space-time. All of our results can return to those in Schwarzschild space-time as the rotating parameter a approaches zero. 展开更多
关键词 gravitational field general relativity neutrino interference phase Kerr space-time geodesic line
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Efficiency Improvement of Space Time Block Codes
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作者 Zahoor Ahmed Baloch Mohammad Usman Baloch Noor Hussain 《International Journal of Communications, Network and System Sciences》 2010年第6期507-510,共4页
Unlike most of the existing methods in Space Time coding (STC) system which focus on design of STC gaining full rate and/or maximum diversity, we propose an approach to improve spectral efficiency of the code. The pro... Unlike most of the existing methods in Space Time coding (STC) system which focus on design of STC gaining full rate and/or maximum diversity, we propose an approach to improve spectral efficiency of the code. The proposed scheme carries more information symbols in each transmission block as compare to its counterpart code, and yet retains the property of simple decoding. Simulation results show that transmit diversity is retained with improvement of code efficiency. We mainly focus on Four transmit antenna scheme but it can be generalized for any number of transmit antennas. 展开更多
关键词 space time BLOCK CODE SPECTRAL EFFICIENCY
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Non-Vanishing Space Time Block Code for Three Time Slots and Two Transmit Antennas
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作者 Ali Azarbar 《Journal of Computer and Communications》 2015年第6期74-86,共13页
Recently, space time block codes (STBCs) are proposed for multi-input and multi-output (MIMO) antenna systems. Designing an STBC with both low decoding complexity and non-vanishing property for the Long Term Evolution... Recently, space time block codes (STBCs) are proposed for multi-input and multi-output (MIMO) antenna systems. Designing an STBC with both low decoding complexity and non-vanishing property for the Long Term Evolution Advanced (LTE-A) remains an open issue. In this paper, first our previously proposed STBC’s non-vanishing property will be completely described. The proposed STBC scheme has some interesting properties: 1) the scheme can achieve full rate and full diversity;2) its maximum likelihood (ML) decoding requires a joint detection of three real symbols;3) the minimum determinant values (MDVs) do not vanish by increasing signal constellation sizes;4) compatible with the single antenna transmission mode. The sentence has been dropped. Second, in order to improve BER performance, we propose a variant of proposed STBC. This scheme further decreases the detection complexity with a rate reduction of 33%;moreover, non-vanishing MDVs property is preserved. The simulation results show the second proposed STBC has better BER performance compared with other schemes. 展开更多
关键词 space time Block Codes Maximum LIKELIHOOD DECODING Non-Vanishing Minimum DETERMINANT Value
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Index modulation aided generalized space-time block coding:A unified MIMO framework 被引量:1
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作者 Zhiqin Wang Hui Liu +3 位作者 Lixia Xiao Liuke Li Guochao Song Tao Jiang 《Digital Communications and Networks》 CSCD 2024年第5期1459-1470,共12页
In this paper,Index Modulation(IM)aided Generalized Space-Time Block Coding(GSTBC)is proposed,which intrinsically exploits the benefits of IM concept,diversity gain and spatial multiplexing gain.Specifically,the infor... In this paper,Index Modulation(IM)aided Generalized Space-Time Block Coding(GSTBC)is proposed,which intrinsically exploits the benefits of IM concept,diversity gain and spatial multiplexing gain.Specifically,the information bits are partitioned into U groups,with each being modulated by IM symbols(i.e.Spatial Modulation(SM),Quadrature SM(QSM),etc).Next,the structure of GSTBC is invoked for each K IM symbol,and a total ofμ=U/K GSTBC codes are transmitted via T time slots.A Block Expectation Propagation(B-EP)detector is designed for the proposed IM-GSTBC structure.Moreover,the theoretical Average Bit Error Probability(ABEP)is derived for our IM-GSTBC system,which is confirmed by the simulation results and helpful for performance evaluation.Simulation results show that our proposed IM-GSTBC system is capable of striking an efficient trade-off between spatial multiplexing gain,spatial diversity gain as well as implementation cost imposed for both small-scale and large-scale MIMO antenna configurations. 展开更多
关键词 Index modulation(IM) Generalized space time block coding(GSTBC) Spatial multiplexing gain Diversity gain Block expectation propagation(B-EP)
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Curved Space-Time at the Planck Scale
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作者 Lewis Nash 《Journal of High Energy Physics, Gravitation and Cosmology》 CAS 2024年第1期167-179,共13页
This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the me... This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the metric tensor, is considered to be made up of a dynamic lattice of extremely small, localized fields that form a perfectly elastic Lorentz symmetric space-time at the global (macroscopic) scale. This theoretical model of space-time at the Planck scale leads to a somewhat surprising result in which matter waves in curved space-time radiate thermal gravitational energy, as well as an equally intriguing relationship for the anomalous dispersion of light in a gravitational field. 展开更多
关键词 Schwarzschild space-time Continuum Mechanics Planck Lattice Gravitational Radiation
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Viscoacoustic prestack reverse time migration based onthe optimal time-space domain high-order finite-difference method 被引量:7
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作者 赵岩 刘洋 任志明 《Applied Geophysics》 SCIE CSCD 2014年第1期50-62,116,共14页
Prestack reverse time migration (RTM) is an accurate imaging method ofsubsurface media. The viscoacoustic prestack RTM is of practical significance because itconsiders the viscosity of the subsurface media. One of t... Prestack reverse time migration (RTM) is an accurate imaging method ofsubsurface media. The viscoacoustic prestack RTM is of practical significance because itconsiders the viscosity of the subsurface media. One of the steps of RTM is solving thewave equation and extrapolating the wave field forward and backward; therefore, solvingaccurately and efficiently the wave equation affects the imaging results and the efficiencyof RTM. In this study, we use the optimal time-space domain dispersion high-order finite-difference (FD) method to solve the viscoacoustic wave equation. Dispersion analysis andnumerical simulations show that the optimal time-space domain FD method is more accurateand suppresses the numerical dispersion. We use hybrid absorbing boundary conditions tohandle the boundary reflection. We also use source-normalized cross-correlation imagingconditions for migration and apply Laplace filtering to remove the low-frequency noise.Numerical modeling suggests that the viscoacoustic wave equation RTM has higher imagingresolution than the acoustic wave equation RTM when the viscosity of the subsurface isconsidered. In addition, for the wave field extrapolation, we use the adaptive variable-lengthFD operator to calculate the spatial derivatives and improve the computational efficiencywithout compromising the accuracy of the numerical solution. 展开更多
关键词 REVERSE time migration Viscoacoustic Optimization Adaptive time-spacedomain FINITE-DIFFERENCE
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基于space-time的二叉树表示动态环境中的路径规划
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作者 唐平 何卓华 杨宜民 《计算机工程》 CAS CSCD 北大核心 2002年第5期59-60,74,共3页
研究具有空间和时间的三维动态环境下的机器人路径规划分析了四叉树表示二维空间的搜索算法,在此基础上,提出采space-time,用二叉树表示二维空间的方法时间信息中增加加速度利用二叉树遍历方法和算法设计一个在动态障碍物环境下进行路... 研究具有空间和时间的三维动态环境下的机器人路径规划分析了四叉树表示二维空间的搜索算法,在此基础上,提出采space-time,用二叉树表示二维空间的方法时间信息中增加加速度利用二叉树遍历方法和算法设计一个在动态障碍物环境下进行路径规划的新算法并,,A*,,在足球机器人系统中进行仿真,实现了较好的路径规划。 展开更多
关键词 移动机器人 数据结构 space-time 二叉树 动态环境 路径规划
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Interference Phase of Neutrino Oscillation in Schwarzschild-de Sitter Space-Time
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作者 任军 耿金鹏 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第4期665-668,共4页
We study the mass neutrino interference phase in Schwarzschild-de Sitter space time along the null trajectory and the geodesic line and obtain the effects of cosmological constant A on the neutrino oscillation. Firstl... We study the mass neutrino interference phase in Schwarzschild-de Sitter space time along the null trajectory and the geodesic line and obtain the effects of cosmological constant A on the neutrino oscillation. Firstly, in the high energy limit, we find that the phase along the geodesic keeps the double of that along the null. Secondly, we calculate the phase on the condition that the cosmological constant, A, is a small quantity. The correction of the phase due to A is given. Finally, we calculate the proper oscillation length in Schwarzschild-de Sitter space-time, which increases because of the existence of A, compared with the result in Schwarzschild space-time. All of our results can be reduced to those in Schwarzschild space-time as A approaches to zero. 展开更多
关键词 gravitational field Schwarzschild-de Sitter space time neutrino interference phase cosmological constant geodesic line
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Thermodynamics of DBI Black Holes in Anti-de Sitter Spacetime
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作者 贾冬燕 岳瑞宏 黄仕明 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第1期75-79,共5页
Through the gauge field theory, we obtain the solution of the DBI-AdS black hole, In the meantime, according to the relations between the action and the grand partition function, we obtain the grand partition function... Through the gauge field theory, we obtain the solution of the DBI-AdS black hole, In the meantime, according to the relations between the action and the grand partition function, we obtain the grand partition function in the DBI-AdS black hole. The temperature and the potential of the DBI-AdS black hole are gained from differential of the grand partition function. With the thermodynamic relations, other thermodynamics are also obtained. The solution and the thermodynamics of the DBI-AdS black hole are turned out that they can reduce to the case of a charged black hole in four-dimensional spacetimes. 展开更多
关键词 THERMODYNAMICS anti-de sitter space time DBI black hole
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A novel repetition space-time coding scheme for mobile FSO systems
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作者 黎明 曹阳 +1 位作者 李书明 杨绍文 《Optoelectronics Letters》 EI 2015年第2期125-129,共5页
Considering the influence of more random atmospheric turbulence, worse pointing errors and highly dynamic link on the transmission performance of mobile multiple-input multiple-output (MIMO) free space optics (FSO... Considering the influence of more random atmospheric turbulence, worse pointing errors and highly dynamic link on the transmission performance of mobile multiple-input multiple-output (MIMO) free space optics (FSO) communica- tion systems, this paper establishes a channel model for the mobile platform. Based on the combination of Alamouti space-time code and time hopping ultra-wide band (TH-UWB) communications, a novel repetition space-time coding (RSTC) method for mobile 2x2 free-space optical communications with pulse position modulation (PPM) is devel- oped. In particular, two decoding methods of equal gain combining (EGC) maximum likelihood detection (MLD) and correlation matrix detection (CMD) are derived. When a quasi-static fading and weak turbulence channel model are considered, simulation results show that whether the channel state information (CSI) is known or not, the coding sys- tem demonstrates more significant performance of the symbol error rate (SER) than the uncoding. In other words, transmitting diversity can be achieved while conveying the information only through the time delays of the modulated signals transmitted from different antennas. CMD has almost the same effect of signal combining with maximal ratio combining (MRC). However, when the channel correlation increases, SER performance of the coding 2×2 system de- grades significantly. 展开更多
关键词 Atmospheric turbulence Broadband networks Channel capacity Channel state information Codes (symbols) Communication channels (information theory) Fading channels Iterative decoding Maximum likelihood MIMO systems Optical communication Pulse position modulation Radio communication Random errors Signal detection Signal encoding space time adaptive processing Telecommunication networks time delay Ultra wideband (UWB)
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Energy-Momentum Density of Non-Diagonal Bianchi Type Space-Time in General Relativity and Teleparallel Gravity
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作者 Ragab M. Gad Haifaa A. Alharbi 《Journal of Applied Mathematics and Physics》 2021年第9期2355-2375,共21页
We calculated the energy-momentum density of non-diagonal Bianchi type space-time in two different theories of gravity, General relativity (GR) and the theory of Teleparallel gravity (TG). Firstly, by applying Einstei... We calculated the energy-momentum density of non-diagonal Bianchi type space-time in two different theories of gravity, General relativity (GR) and the theory of Teleparallel gravity (TG). Firstly, by applying Einstein, Landau-Lifshitz, Bergmann-Thomson and M<span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">&#248;</span></span></span>ller prescriptions, using double index complexes in <strong>GR</strong>. Secondly, in the frame work of <strong>TG</strong>, we used the energy momentum complexes of Einstein, Bergmann-Thomson and Landau-Lifshitz. We also study the spacial cases of non-diagonal Bianchi type space-time <strong>BII</strong>, <strong>BVIII</strong> and <strong>BIX</strong>. We obtained the same energy-momentum density components for Einstein and Bergmann-Thomson prescriptions for the above four mentioned space-times that we considered in our work. Also, we found that the energy density component in M<span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">&#248;</span></span></span>ller prescription is zero for all Bianchi types space-times in GR. Furthermore, we show that if the metric components are functions of time t alone, then the total gravitational energy is identically zero. 展开更多
关键词 Energy-Momentum Densities Double Index Complexes Teleparallel Gravity Bianchi Type space time
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