• Journal of the Korean Statistical Society
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• 제16권1호
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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.

• 디지털산업정보학회논문지
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• 제14권3호
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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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• 제17권1호
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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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• 제14권1_2호
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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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• 제5권2호
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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.

• 한국통신학회논문지
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• 제33권1C호
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• pp.79-85
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• 2008

본 논문에서는 다중사용자 multiple-input-multiple output(MIMO) 하향링크 채널 환경에서 시스템 용량을 향상시키기 위한 프리코딩(preceding) 기법에 관해 논의한다. 다중사용자 MIMO 시스템에서는 시스템 용량을 향상시키기 위한 다양한 프리코딩 기법들이 연구되어 왔다. 블록 대각화(Block Diagonalization) 프리코딩 기법은 다중사용자 MIMO broadcast 채널 환경에서 만들어진 여러 가지 프리코딩 기법 중 하나로 특이값 분해를 이용하여 제로-포싱(zero-forcing)을 하는 간단한 방법으로 구성되어 있다. 그러나 블록 대각화 기법은 복잡도가 낮아진 만큼 시스템 용량이 저하되는 단점을 갖고 있으며, 이러한 현상은 시스템 용량의 저하는 안테나들 사이에 상관도가 높을 때 더 심각해진다. 따라서 본 논문에서는 블록 대각화 기법을 수정하여 시스템 용량을 향상시킬 수 있는 프리코딩 기법을 제안한다. 실험 결과를 통해 본 논문에서 제안하는 방법이 기존의 블록 대각화 기법에 비해 높은 시스템 용량 성능을 보임을 확인할 수 있다.

• Journal of Communications and Networks
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• 제16권1호
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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.

• 전자공학회논문지SC
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• 제48권6호
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• pp.8-14
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• 2011

본 연구에서는 불확실 단일 입력 시스템의 경우에 대하여 Utkin 정리의 증명을 제시한다. 소위 두가지의 대각화 방법(Diagonalization Method)이라 불리는 Utkin 정리의 두 변환 방법에 대한 불변 정리를 비교적으로 분명히 증명한다. 슬라이딩모드의 수식 즉 슬라이딩 면은 두가지 대각화 변환에 대하여 변화 없고 두 인가된 제어입력은 같은 이득을 갖는다. 두가지 대각화 방법에 의하여 같은 결과를 얻는다. 설계 예와 시뮬레이션 연구를 통하여 제안된 결과의 효용성을 입증한다.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2009년도 추계학술대회
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• pp.481-484
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• 2009

본 논문에서는 다중 안테나를 갖는 릴레이 (relay)의 양방향 (full-duplex) 동작을 위한 프리코딩(precoding) 기법을 제안한다. 양방향 릴레이는 기존의 반이중 (half-duplex) 릴레이와 달리 같은 주파수 대역에서 동일한 시간에 송수신을 수행하기 때문에, 릴레이의 송신 안테나로부터 수신 안테나로 유입되는 자기 간섭 (self interference)이 발생한다. 제안한 프리코딩 기법은 이러한 자기 간섭을 블록 대각화 (block diagonalization) 기법을 통해 제거하여 릴레이의 양방향 동작이 가능하도록 한다. 또한, 모의 실험을 통해 양방향 릴레이가 기존의 반이중 릴레이에 비해 향상된 채널 용량을 가짐을 증명한다.

• 전기학회논문지
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• 제59권9호
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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.