• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.11-18
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• 2004

In this paper, an efficient model reduction scheme is presented for large scale dynamic systems. The method is founded on a modal analysis in which optimal eigenvalue is extracted from time samples of the given system response. The techniques we discuss are based on classical theory such as the Karhunen-Loeve expansion. Only recently has it been applied to structural dynamics problems. It consists in obtaining a set of orthogonal eigenfunctions where the dynamics is to be projected. Practically, one constructs a spatial autocorrelation tensor and then performs its spectral decomposition. The resulting eigenfunctions will provide the required proper orthogonal modes(POMs) or empirical eigenmodes and the correspondent empirical eigenvalues (or proper orthogonal values, POVs) represent the mean energy contained in that projection. The purpose of this paper is to compare the reduced order model using Karhunen-Loeve expansion with the full model analysis. A cantilever beam and a simply supported plate subjected to sinusoidal force demonstrated the validity and efficiency of the reduced order technique by K-L method.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.9B
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• pp.1215-1225
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• 2001

통신 채널에서 블라인드 채널 인식은 매우 중요한 문제이다. 블라인드 채널 인식은 고차 통계를 이용하면 구할 수 있으나 최근에는 오버샘플링한 수신신호를 이용하거나 수신측의 안테나 어레이를 이용한 신호의 2차 통계값을 이용한 방법에 관한 많은 연구가 진행되고 있다. 기존의 알고리듬은 잡음이 없는 환경에서 LS 방법에 기반을 두고 있기 때문에 잡음이 강한 채널에서는 원하는 성능을 얻을 수 없는 단점이 있다. 수신신호의 상관행렬의 최소 고유값에 대응하는 고유벡터는 채널의 임펄스 응답에 관한 정보를 포함하고 있다. 본 논문에서는 이러한 고유벡터를 매 시간마다 갱신시키면서 구하는 적응 알고리듬을 제안하고 이를 이용하여 블라인드 채널 인식 알고리듬을 제안한다. 제안한 알고리듬은 잡음에 강인한 특성을 보일 뿐만 아니라 기존의 알고리듬들 보다 우수한 채널 추정 성능을 보임을 모의실험을 통하여 검증하였다.

• Nuclear Engineering and Technology
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• v.49 no.6
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• pp.1181-1188
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• 2017

This paper proposes the adoption of Monte Carlo perturbation theory to approximate the Jacobian matrix of coupled neutronics/thermal-hydraulics problems. The projected Jacobian is obtained from the eigenvalue decomposition of the fission matrix, and it is adopted to solve the coupled problem via the Newton method. This avoids numerical differentiations commonly adopted in Jacobian-free Newton-Krylov methods that tend to become expensive and inaccurate in the presence of Monte Carlo statistical errors in the residual. The proposed approach is presented and preliminarily demonstrated for a simple two-dimensional pressurized water reactor case study.

• Journal of Information Processing Systems
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• v.18 no.3
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• pp.293-301
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• 2022

Direction of arrival (DOA) estimation of space signals is a basic problem in array signal processing. DOA estimation based on the multiple signal classification (MUSIC) algorithm can theoretically overcome the Rayleigh limit and achieve super resolution. However, owing to its inadequate real-time performance and accuracy in practical engineering applications, its applications are limited. To address this problem, in this study, a DOA estimation algorithm with high parallelism and precision based on an analysis of the characteristics of complex matrix eigenvalue decomposition and the coordinate rotation digital computer (CORDIC) algorithm is proposed. For parallel and single precision, floating-point numbers are used to construct an orthogonal identity matrix. Thus, the efficiency and accuracy of the algorithm are guaranteed. Furthermore, the accuracy and computation of the fixed-point algorithm, double-precision floating-point algorithm, and proposed algorithm are compared. Without increasing complexity, the proposed algorithm can achieve remarkably higher accuracy and efficiency than the fixed-point algorithm and double-precision floating-point calculations, respectively.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.3
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• pp.15-24
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• 2015

Jacket matrices which are defined to be $m{\times}m$ matrices $J^{\dagger}=[J_{ik}^{-1}]^T$ over a Galois field F with the property $JJ^{\dagger}=mI_m$, $J^{\dagger}$ is the transpose matrix of element-wise inverse of J, i.e., $J^{\dagger}=[J_{ik}^{-1}]^T$, were introduced by Lee in 1984 and are used for Digital Signal Processing and Coding theory. This paper presents some square matrices $A_2$ which can be eigenvalue decomposed by Jacket matrices. Specially, $A_2$ and its extension $A_3$ can be used for modifying the properties of hyperbola and hyperboloid, respectively. Specially, when the hyperbola has n times transformation, the final matrices $A_2^n$ can be easily calculated by employing the EVD[7] of matrices $A_2$. The ideas that we will develop here have applications in computer graphics and used in many important numerical algorithms.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37 no.6A
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• pp.450-457
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• 2012

For orthogonal frequency-division multiplexing (OFDM) systems, we propose a blind channel estimation scheme based on non-redundant precoding. In the proposed scheme, a modified covariance matrix is first obtained by dividing the covariance matrix of the received signal vector by the precoding matrix element-by-element. Then, the channel vector is estimated as an eigenvector corresponding to the largest eigenvalue of the modified covariance matrix. The eigenvector can be obtained by power method with low computational complexity instead of the complicated eigenvalue decomposition. We analytically derive a mean square error (MSE) of the proposed channel estimation scheme and show that the analysis result coincides well with the simulation result. Also, simulation results show that the proposed scheme has better MSE and bit error rate (BER) performance than conventional channel estimation schemes.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.6
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• pp.69-78
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• 2017

Shannon of the 5G smartphone and Fourier of the signal processing meet in the sampling theorem (2 times the highest frequency 1). In this paper, the initial Shannon Theorem finds the Shannon capacity at the point-to-point, but the 5G shows on the Relay channel that the technology has evolved into Multi Point MIMO. Fourier transforms are signal processing with fixed parameters. We analyzed the performance by proposing a 2N-1 multivariate Fourier-Jacket transform in the multimedia age. In this study, the authors tackle this signal processing complexity issue by proposing a Jacket-based fast method for reducing the precoding/decoding complexity in terms of time computation. Jacket transforms have shown to find applications in signal processing and coding theory. Jacket transforms are defined to be $n{\times}n$ matrices $A=(a_{jk})$ over a field F with the property $AA^{\dot{+}}=nl_n$, where $A^{\dot{+}}$ is the transpose matrix of the element-wise inverse of A, that is, $A^{\dot{+}}=(a^{-1}_{kj})$, which generalise Hadamard transforms and centre weighted Hadamard transforms. In particular, exploiting the Jacket transform properties, the authors propose a new eigenvalue decomposition (EVD) method with application in precoding and decoding of distributive multi-input multi-output channels in relay-based DF cooperative wireless networks in which the transmission is based on using single-symbol decodable space-time block codes. The authors show that the proposed Jacket-based method of EVD has significant reduction in its computational time as compared to the conventional-based EVD method. Performance in terms of computational time reduction is evaluated quantitatively through mathematical analysis and numerical results.

• Journal of IKEEE
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• v.27 no.4
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• pp.624-629
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• 2023

Estimation of signal parameters via rotational invariance techniques (ESPRIT) is an algorithm that estimates the angle of a signal arriving at an array antenna using the shift invariance property of an array antenna. ESPRIT offers the good trade-off between performance and complexity. However, the ESPRIT algorithm still requires high-complexity operations such as covariance matrix and eigenvalue decomposition, so implementation with a hardware processor is essential to estimate the angle of arrival in real time. In addition, ESPRIT processors should have high performance. The performance is related to the number of antennas, and the number of antennas required for each application are different. Therefore, we proposed an ESPRIT processor that provides 2 to 8 variable antenna configurations to meet the performance and complexity requirements according to the applied field. The proposed ESPRIT processor was designed using the Verilog-HDL and implemented on a field programmable gate array (FPGA).

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2003.05a
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• pp.111-114
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• 2003

It has well known that MUSIC and ESPRIT algorithms estimate angle of arrival(AOA) with high resolution by eigenvalue decomposition of the covariance matrix which were obtained from the array antennas. In the case that 2-D large-sized array antenna is required, however, one of the disadvantages of MUSIC and ESPRIT is that they are computationally ineffective, and then they are difficult to implement in real time. To alleviate the computational complexity, several method using neural model have been study. For multiple signals, those methods require huge training data prior to AOA estimation. This paper proposes the algorithm for AOA estimation by interconnected hopfield neural model. Computer simulations show the validity of the proposed algorithm.

• East Asian mathematical journal
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• v.22 no.2
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• pp.249-257
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• 2006

Let n be a 2-step nilpotent Lie algebra which has an inner product <,> and has an orthogonal decomposition $n=\delta{\oplus}\varsigma$ for its center $\delta$ and the orthogonal complement $\varsigma\;of\;\delta$. Then Each element Z of $\delta$ defines a skew symmetric linear map $J_Z:\varsigma{\rightarrow}\varsigma$ given by $=$ for all $X,\;Y{\in}\varsigma$. Let $\gamma$ be a unit speed geodesic in a 2-step nilpotent Lie group H(2, 1) with its Lie algebra n(2, 1) and let its initial velocity ${\gamma}$(0) be given by ${\gamma}(0)=Z_0+X_0{\in}\delta{\oplus}\varsigma=n(2,\;1)$ with its center component $Z_0$ nonzero. Then we showed that $\gamma(0)$ is conjugate to $\gamma(\frac{2n{\pi}}{\theta})$, where n is a nonzero intger and $-{\theta}^2$ is a nonzero eigenvalue of $J^2_{Z_0}$, along $\gamma$ if and only if either $X_0$ is an eigenvector of $J^2_{Z_0}$ or $adX_0:\varsigma{\rightarrow}\delta$ is not surjective.