• Bulletin of the Korean Chemical Society
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• v.12 no.1
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• pp.39-47
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• 1991

A cluster made of $N_A,\;N_B\;and\;N_C$ atoms in the x, y and z directions respectively, is treated with Huckel method. We obtain the approximate expressions for the eigenvalues and eigenvectors of f.c.c., b.c.c. and h.c.p. clusters in closed forms. The maximum and minimum values of the band so obtained converge to those derived from the Bloch sum in the limit of infinite extension. For a small cluster (of $9{\times}9{\times}5$ atoms, for instance), LDOS from the analytical (approximate) solution manifests better agreement at the surface, than inside the bulk.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.12
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• pp.2317-2323
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• 2015

In this paper, we analyze the performance of dual-hop amplify-and-forward (AF) relaying in cooperative networks with partial relay selection. An AF relay gain considered in this paper includes channel-noise-assisted relay gain. Leveraging a received signal-to-noise ratio (SNR) model, we derive exact closed-form expressions for the probability density function (pdf) and cumulative distribution function (cdf) of the end-to-end SNR. Moreover, an exact closed-form expression of the ergodic capacity for dual-hop AF relaying with channel-noise-assisted relay gain and partial relay selection is investigated. The analytical results shown in this paper are confirmed by Monte-Carlo simulations.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.11
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• pp.5410-5426
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• 2019

With the advent of the fifth-generation (5G) era, Massive multiple-input multiple-output (MIMO) relay systems have experienced the rapid development. Recently, the performance analysis models of Massive MIMO relay systems have been proposed, which are mostly based on Rayleigh fading channels. In order to create a more suitable model for 5G Internet of Things scenarios, our study is based on the Rician fading channels, where line-of-sight (LOS) path exists in the channels. In this paper, we assume the channel state information (CSI) is perfect. In this case, we use statistical information to derive the analytical exact closed-form expression for the achievable sum rate of the uplink for the Massive MIMO two-hop relay system over Rician fading channels. Moreover, considering the different communication scenarios, we derive the analytical exact closed-form expression for the achievable sum rates of the uplink for other three scenarios. Finally, based on these expressions, we make simulations and analyze the performance under different transmit powers and Rician-factors, which provides a theoretical basis and reference for further research.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.6C
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• pp.561-569
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• 2003

In this paper, for my linear orthogonal space-time block including the orthogonal space-time codes introduced by Alamouti［1］, Tarokh［14］, and Xia［11］, the exact expression for the pairwise error probability in the slow Rayleigh fading channel is derived in terms of the message symbol distance between two message vectors rather than the codeword symbol distance between two transmitted codeword matrices. Using the one-dimensional component symbol error probability, the exact closed form expressions for the symbol error probability of linear orthogonal space-time codes are derived for QPSK, 16-QAM, 64-QAM, and 256-QAM.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.5
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• pp.1682-1701
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• 2015

In this paper, we propose an intergraded unified imperfect CSI model and investigate the joined effects of feedback delay and channel estimation errors (CEE) for two-hop relaying systems with transmit beamforming and relay selection. We derived closed-form expressions for important performance measures including the exact analysis and lower bounds of outage probability as well as error performance. The ergodic capacity is also included with closed-form results. Furthermore, diversity and coding gains based on the asymptotic analysis at high SNRs are also presented, which are simple and concise and provide new analytical insights into the corresponding power allocation scheme. The analysis indicates that delay effect results in the coding gain loss and the diversity order loss, while CEE will merely cause the coding gain loss. Numerical results verify the theoretical analysis and illustrate the system is more sensitive to transmit beamforming delay compared with relay selection delay and also verify the superiority of optimum power allocation. We further investigate the outage loss due to the CEE and feedback delays, which indicates that the effect of the CEE is more influential at low-to-medium SNR, and then it will hand over the dominate role to the feedback delay.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.11C
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• pp.1070-1076
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• 2003

This paper presents and analyses the exact and general closed-form expression for the average bit error probability of M-ary square quadrature amplitude modulation (QAM) for maximal ratio combining (MRC) diversity reception in frequency-nonselective Nakagami-m fading. An L-branch Maximal ratio combining diversity technique with independent or correlated fading cases is considered. Numerical results demonstrate the error performance improvement by employing with the use of MRC diversity reception. The new expressions presented here can offer a convenient way to evaluate the performance of an arbitrary square M-W square QAM with an MRC diversity combiner for various cases of practical interest.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.12
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• pp.5898-5916
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• 2018

In this paper, the downlink performance of multi-cell distributed antenna systems (DAS) with a single user in each cell is investigated. Assuming the channel state information is available at the transmitter, four transmission modes are formulated as combinations of remote antenna units (RAUs) selection and cooperative transmission, namely, non-cooperative transmission without RAU selection (NCT), cooperative transmission without RAU selection (CT), non-cooperative transmission with RAU selection (NCT_RAUS), and cooperative transmission with RAU selection (CT_RAUS). By using probability theory, the cumulative distribution function (CDF) of a user's signal to interference plus noise ratio (SINR) and the system ergodic capacity under the above four modes are determined, and their closed-form expressions are obtained. Furthermore, the system energy efficiency (EE) is studied by introducing a realistic power consumption model of DAS. An expression for determining EE is formulated, and the closed-form tradeoff relationship between spectral efficiency (SE) and EE is derived as well. Simulation results demonstrate their consistency with the theoretical analysis and reveal the factors constraining system EE, which provide a scientific basis for future design and optimization of DAS.

• Geomechanics and Engineering
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• v.10 no.2
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• pp.189-205
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• 2016

Soils are subjected to additional stresses due to the loads transferred by the foundations of the buildings. The distribution of stress in soil has great importance in geotechnical engineering projects such as stress, settlement and liquefaction analyses. The purpose of this study is to examine the shear stresses on horizontal plane below the rectangular foundations subjected to biaxial bending on an elastic soil. In this study, closed-form analytical solutions for shear stresses in x and y directions were obtained from Boussinesq's stress equations. The expressions of analytical solutions were simplified by defining the shear stress influence values ($I_1$, $I_2$, $I_3$), and solution charts were presented for obtaining these values. For some special loading conditions, the expressions for shear stresses in the soil below the corners of a rectangular foundation were also given. In addition, a computer program was developed to calculate the shear stress increment at any point below the rectangular foundations. A numerical example for illustrating the use of the presented solution charts was given and, finally, shear stress isobars were obtained for the same example by a developed computer program. The shear stress expressions obtained in this work can be used to determine monotonic and cyclic behavior of soils below rectangular foundations subjected to biaxial bending.

• International Journal of Contents
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• v.14 no.1
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• pp.18-27
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• 2018

The objective of this study was to derive approximate closed-form error rates for M-ary burst symbol transmission (MBST) of dual-hop adaptive decode-and-forward (ADF) cooperative relay systems over quasi-static Rayleigh fading channels. Within a burst, there are pilot symbols and data symbols. Pilot symbols are used for channel estimation schemes and each relay node's transmission mode selection schemes. At first, our focus was on ADF relay systems' error-events at relay nodes. Each event's occurrence probability and probability density function (PDF) were then derived. With error-event based approach, we derived a tractable form of PDF for combined signal-to-noise ratio (SNR). Averaged error rates were then derived as approximate expressions for arbitrary link SNR with different modulation orders and numbers of relays. Its accuracy was verified by comparison with simulation results.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.11C
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• pp.1045-1052
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• 2005

The symbol error probability of M-ary PSK (MPSK) and QAM (MQAM) systems using the branch with the largest signal-to-noise ratio (SNR) at the output of L-branch selection combining (SC) in frequency-nonselective slow Nakagami fading channels with an additive white Gaussian noise (AWGN) is derived theoretically For integer values of the Nakagami fading parameter m, the general formula for evaluating symbol error rate (SER) of MPSK signals in the independent branch diversity system comprises numerical analyses with the integral-form expressions. An exact closed-form SER performance of MQAM signals under the effect of SC diversity via numerical integration is presented. These performance evaluations allow designers to determine M-ary modulation methods for Nakagami fading channels.