• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.507-528
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• 2006

In this paper we show that the Koecher's Jordan automorphic generators of one variable on an irreducible symmetric cone are enough to determine the elements of scalar multiple of the Jordan identity on the attached simple Euclidean Jordan algebra. Its various geometric, Jordan and Lie theoretic interpretations associated to the Cartan-Hadamard metric and Cartan decomposition of the linear automorphisms group of a symmetric cone are given with validity on infinite-dimensional spin factors

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.3
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• pp.1156-1173
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• 2021

In this paper, we propose a new joint precoder and postcoder design strategy to support multiple streams per user in multiuser multiple-input multiple-output (MIMO) systems. We propose two step precoding strategies using equal channel gain decomposition and block diagonalization at the transmitter. With the proposed precoder, the multiuser MIMO channel can be decomposed into multiple parallel channels with equal channel gain per user. After applying receive postcoder which is generated and sent by the transmitter, we can use ML based decoder per stream to achieve full receive diversity. Achievable sum rate bound and diversity performance of the proposed algorithm are presented with feedback signaling design and quantitative complexity analysis. Simulation results show that the proposed algorithm asymptotically approaches to the sum rate capacity of the MIMO broadcast channel while maintaining full diversity order.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.48 no.8
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• pp.15-26
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• 2011

In this paper, we present a new beamforming scheme for a downlink of multiuser multiple-input multipleoutput (MIMO) communication systems. Recently, a block-diagonalization (BD) algorithm has been proposed for the multiuser MIMO downlink where both a base station and each user have multiple antennas. However, the BD algorithm is not efficient when the number of supported streams per user is smaller than that of receive antennas. Since the BD method utilizes the space based on the channel matrix without considering the receive combining, the degree of freedom for beamforming cannot be fully exploited at the transmitter. In this paper, we optimize the receive beamforming vector under a zero forcing (ZF) constraint, where all inter-user interference is driven to zero. We propose an efficient algorithm to find the optimum receive vector by an iterative procedure. The proposed algorithm requires two phase values feedforward information for the receive combining vector. Also, we present another algorithm which needs only one phase value by using a decomposition of the complex general unitary matrix. Simulation results show that the proposed beamforming scheme outperforms the conventional BD algorithm in terms of error probability and obtains the diversity enhancement by utilizing the degree of freedom at the base station.

• Journal of Korean Society of Transportation
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• v.20 no.1
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• pp.77-90
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• 2002

Network expansion has been an inevitable method for most traffic equilibrium assignments to consider intersection movements such as intersection delays. The drawback of network expansion is that because it dramatically increases network sizes to emulate possible directional movements as corresponding links, not only is complexities for building network amplified, but computational performance is shrunk. This paper Proposes a new variational inequality formulation for a user-optimal traffic equilibrium assignment model to explicitly consider directional delays without building expanded network structures. In the formulation, directional delay functions are directly embedded into the objective function, thus any modification of networks is not required. By applying a vine-based shortest Path algorithm into the diagonalization algorithm to solve the problem, it is additionally demonstrated that various loop-related movements such as U-Turn, P-Turn, etc., which are frequently witnessed near urban intersections, can also be imitated by blocking some turning movements of intersections. The proposed formulation expects to augment computational performance through reduction of network-building complexities.

• Journal of the Korean Chemical Society
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• v.27 no.4
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• pp.244-254
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• 1983

Single crystals of sodium thiosulfate $(Na_2S_2O_3) have been grown from the saturated solution by the evaporation method at the optimum condition. Radiation damages in the crystal by ${\gamma}$-irradiation of $20{\times}10^6$ Rontgen have given rise to paramagnetic centers. The anisotropic spectra of each paramagnetic species have been obtained with the X-band EPR spectrometer at room temperature. When an isotropic D.P.P.H. at g value of 2.0036 is based on. ESR Spectra of the single crystal are recorded for each rotation about the perpendicular a, b and c axis with intervals of $10^{\circ}$ from $0^{\circ}$to $180^{\circ}$ in order to find out the properties of the crystal for anglar variation of the anisotropic peaks. The g values are calculated from the line position between the anisotropic peaks and the isotropic peaks of D.P.P.H. and then principal g values and their direction cosines of the species is obtained by the diagonalization of 9 matrix elements of the corresponding g values. From the analysis of the characteristic principal g values and direction cosines for ${\gamma}$-irradiated $Na_2S_2O_3$ crystal, anisotropic peaks corresponding to $SO_2^+, SO_2^- $are identified and the existences of unidentified and unstable paramagnetic defects are verified.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.12
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• pp.3-11
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• 2014

Multiple antennas can provide huge capacity gains when the transmitter knows the channel state information (CSI). Precoding is a technique that exploits CSI at the transmitter side. In this paper, an adaptive precoding scheme is proposed, called a hybrid multiple-input multiple-output (MIMO) precoding (HMP). HMP is a combination of linear and nonlinear precoding. The number of transmit antennas less than or equal to four is as same as the conventional antenna selection scheme. Therefore, the HMP scheme uses more than four transmit antennas. The good channel means that the channels must be selected to maximize the channel capacity among the given channels, and the rest channels are called bad channel. In HMP scheme, we use the nonlinear precoding in the good channels and the linear precoding in the bad channels. The well-known Tomlinson-Harashima precoding (THP) is considered as nonlinear precoding. The system throughput and MSE (minimum square error) are shown for the performance of HMP scheme compared to the conventional schemes which are BD (block diagonalization), antenna selection and THP.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.46 no.4
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• pp.95-103
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• 2009

In this paper, a generation method of transmit and receive beamforming vectors based on base station cooperation is proposed which maximizes the user SINR in mobile cellular multi-user MIMO systems. There are two main sources of interference which deteriorate the performance of the system, i.e. the inter-user interference caused by the usage of the same radio resource for multiple users in the system, and the inter-cluster interference from neighboring base stations which are not participating in cooperative transmission. The proposed scheme cancels out the inter-user interference by using the block diagonalization(BD) method, and mitigate the inter-cluster interference by using optimal transmit and receive beamforming vectors based on optimal combining(OC) with the statistic information of inter-cluster interference. We perform computer simulations to verify the performance of the proposed scheme, and compare the result to the conventional performance obtained from utilizing the receiver side information only or utilizing the information from neither sides. The performance evaluations are conducted not only over the independent MIMO channels, but over correlated MIMO channels to demonstrate the robustness of the proposed scheme over the channels with correlation among antennas.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.11
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• pp.97-108
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• 1994

A modified Karhunen-Loeve transformation technique using normalization and simultaneous diagonalization of two sample covariance matrices is proposed to separate the object from the background. The transformation technique for the separation of local data structure through maximizing the ratio of sample variances between two classes was identified as a promising one for a preprocessing of multi-variate signal processing algorithms using neighborhood operators including morphological filtering. To relate the separation quality of the proposed technique to a morphological measure, average height was defined by using morphological pattern spectrum. A practical implementation of the transformation technique was tested experimentally and the theoretical results were confirmed.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.11
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• pp.2616-2635
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• 2013

In this paper, we propose an iterative transceiver design in a multi-relay multi-user multiple-input multiple-output (MIMO) system. The design criterion is to minimize sum mean squared error (SMSE) under relay sum power constraint (RSPC) where only local channel state information (CSI)s are available at relays. Local CSI at a relay is defined as the CSI of the channel between BS and the relay in the $1^{st}$ hop link, and the CSI of the channel between the relay and all users in the $2^{nd}$ hop link. Exploiting BS transmitter structure which is concatenated with block diagonalization (BD) precoder, each relay's precoder can be determined using local CSI at the relay. The proposed scheme is based on sequential iteration of two stages; stage 1 determines BS transmitter and relay precoders jointly with SMSE duality, and stage 2 determines user receivers. We verify that the proposed scheme outperforms simple amplify-and-forward (SAF), minimum mean squared error (MMSE) relay, and an existing good scheme of [13] in terms of both SMSE and sum-rate performances.

• Journal of Satellite, Information and Communications
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• v.6 no.1
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• pp.19-27
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• 2011

In this paper, we propose the data stream allocation algorithms for maximizing sum capacity of downlink multiuser MIMO (Multiple-input Multiple-output) systems with BD (Block Diagonalization). The conventional BD precoding algorithms maximize the capacity by controlling power against channel gain of each user. In multiuser MIMO systems, however, the number of data streams for each user can be used to as another control parameter, which determines the capacity. This paper proposes the data stream allocation algorithm of BD for increasing capacity in multiuser MIMO systems. The proposed algorithm allocates unequal bit stream to each user based on channel matrix of each user for maximizing sum capacity. It is proved that proposed algorithm can achieve the significantly improved sum capacity by computer simulation.