• Journal of the Korean Statistical Society
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• v.16 no.1
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• pp.45-51
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• 1987

The condition that two hyper-ellipsoids have no points in common is derived using the simultaneous diagonalization of the two hyper-ellipsoids. It is observed that the simultaneous diagonalization is composed of rotation and extension followed by another rotation. An approximation to this condition in terms of the generalized distance is discussed.

• Journal of Korea Society of Digital Industry and Information Management
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• v.14 no.3
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• pp.77-85
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• 2018

Multi-User Multiple-Input Multiple-Output (MU-MIMO) is the core technology for improving the channel capacity compared to Single-User MIMO (SU-MIMO) by using multiuser gain and spatial diversity. Key problem for the MU-MIMO is the user selection which is the grouping the users optimally. To solve this problem, we adopt Extreme Value Theory (EVT) at the beginning of the proposed algorithm, which defines a primary user set instead of a single user that has maximum channel power according to a predetermined threshold. Each user in the primary set is then paired with all of the users in the system to define user groups. By comparing these user groups, the group that produces a maximum sum rate can be determined. Through computer simulations, we have found that the proposed method outperforms the conventional technique yielding a sum rate that is 0.81 bps/Hz higher when the transmit signal to noise ratio (SNR) is 30 dB and the total number of users is 100.

• Journal of information and communication convergence engineering
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• v.17 no.1
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• pp.1-7
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• 2019

In this paper, we present the block diagonalization (BD) algorithm for the multiple-user multiple input multiple output (MU-MIMO) $4{\times}4$ system using specific purpose processor (SPP) hardware. Our objective is to improve the single-user MIMO (SU-MIMO) system using the MU-MIMO technology, which is remarkably fast and allows more users to connect simultaneously. To that end, our MU-MIMO precoder uses the BD algorithm to ensure signal integrity when connecting multiple users; but remains accurate and stable. However, a precoder that uses the BD algorithm is computationally complex; therefore, we use an SPP with special functions designed to compute the BD algorithm. The implementation test results show that our SPP computes the BD algorithm faster than the software solution.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.81-96
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• 2004

The level-m scaled circulant factor matrix over the complex number field is introduced. Its diagonalization and spectral decomposition and representation are discussed. An explicit formula for the entries of the inverse of a level-m scaled circulant factor matrix is presented. Finally, an algorithm for finding the inverse of such matrices over the quaternion division algebra is given.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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• pp.137-147
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• 2001

Nonconvex Quadratic Optimization Problems (QOP) are solved approximately by SDP (semidefinite programming) relaxation and SOCP (second order cone programmming) relaxation. Nonconvex QOPs with special structures can be solved exactly by SDP and SOCP. We propose a method to formulate general nonconvex QOPs into the special form of the QOP, which can provide a way to find more accurate solutions. Numerical results are shown to illustrate advantages of the proposed method.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.1C
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• pp.79-85
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• 2008

Dirty Paper Coding(DPC) can achieve the sum capacity of a multiuser multiple-input multiple-output(MU MIMO) broadcast channels. However, due to the high computational complexity of the successive encoding and decoding, deploying DPC in real systems is impractical. As one of practical alternatives to DPC, Block Diagonalization(BD) was researched. BD is an extension of the zero-forcing preceding technique that eliminates interuser interference(IUI) in downlink MIMO systems. Though BD has lower complexity than DPC, BD shows poor sum capacity performance. We show that sum capacity performance of BD is degraded due to no IUI constraint. Then, we modify BD to improve its sum capacity performance with relaxing the constraint and sub optimal channel set searching. With simulation results, it can be verified that our modification in BD induces some improvement in sum capacity performance.

• Journal of Communications and Networks
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• v.16 no.1
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• pp.1-9
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• 2014

Block diagonalization (BD) has been proposed as a simple and effective technique in multiuser multiple-input multiple-output (MU-MIMO) broadcast channels. However, when channel state information (CSI) knowledge is limited at the transmitter, the performance of the BD may be degraded because inter-user interference cannot be completely eliminated. In this paper, we propose an efficient CSI quantization technique for BD precoded systems with limited feedback where users supported by a base station are selected by dynamic scheduling. First, we express the received signal-to-interference-plus-noise ratio (SINR) when multiple data streams are transmitted to the user, and derive a lower bound expression of the expected received SINR at each user. Then, based on this measure, each user determines its quantized CSI feedback information which maximizes the derived expected SINR, which comprises both the channel direction and the amplitude information. From simulations, we confirm that the proposed SINR-based channel quantization scheme achieves a significant sum rate gain over the conventional method in practical MU-MIMO systems.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.48 no.6
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• pp.8-14
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• 2011

In this note, a proof of Utkin's theorem is presented for SI(Single input) uncertain linear systems. The invariance theorem with respect to the two transformation methods so called the two diagonalization methods is proved clearly and comparatively for SI uncertain linear systems. With respect to the sliding surface transformation, the equation of the sliding mode i.e., the sliding surface is invariant. The control inputs by the two transformation methods both have the same gains. By means of the two transformation methods, the same results can be obtained. Through an illustrative example and simulation study, the usefulness of the main results is verified.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2009.10a
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• pp.481-484
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• 2009

In this paper, we suggest a precoding algorithm for full-duplex relay with multiple antennas. Because full-duplex relay performs transmission and reception at the same time in the same frequency band another existing half-duplex relay differently, self interference arise between transmit and receive antennas of relay. The proposed precoding algorithm eliminates self interference by block diagonalization algorithm and makes the relay perform full-duplex operation. Also we verify that full-duplex relay have improved channel capacity than existing half-duplex relay by computer simulation.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.9
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• pp.1680-1685
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• 2010

In this note, a proof of Utkin's theorem is presented for a MI(Multi Input) uncertain linear case. The invariance theorem with respect to the two transformation methods so called the two diagonalization methods are proved clearly and comparatively for MI uncertain linear systems. With respect to the sliding surface transformation and the control input transformation, the equation of the sliding mode i.e., the sliding surface is invariant. Both control inputs have the same gains. By means of the two transformation methods the same results can be obtained. Through an illustrative example and simulation study, the usefulness of the main results is verified.