• Korean Journal of Mathematics
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• v.3 no.1
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• pp.1-4
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• 1995

• Honam Mathematical Journal
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• v.14 no.1
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• pp.25-35
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• 1992

• International Journal of Contents
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• v.11 no.4
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• pp.38-43
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• 2015

Non-orthogonal multiple access (NOMA) where all users share the entire time and frequency resource has paid attention as one of the key technologies to enhance the spectral efficiency and the total throughput. Nevertheless, as the number of users and SIC error increase, the inter-user interference and the residual interference due to the SIC error also increase, resulting in performance degradation. In order to mitigate the performance degradation, we propose grouping-based NOMA system. In the proposed scheme, all users are divided into two groups based on the distance between the BS and each user, where one utilizes the first half of the bandwidth and the other utilizes the rest in the orthogonal manner. On the other hand, users in each group share the spectrum in the non-orthogonal manner. Grouping users can reduce both the inter-user interference and residual interference due to the SIC error, so it can outperform conventional NOMA system, especially in case that the number of users and the SIC error increase. Based on that, we also present the hybrid operation of the conventional and the proposed NOMA systems. In numerical results, the total throughput of the proposed NOMA systems is compared with that of the conventional NOMA systems with regard to the number of users and SIC error. It is confirmed that the proposed NOMA system outperforms the conventional NOMA system as the number of users and the SIC error increase.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1705-1723
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• 2008

Let n be a 2-step nilpotent Lie algebra which has an inner product <, > and has an orthogonal decomposition $n\;=z\;{\oplus}v$ for its center z and the orthogonal complement v of z. Then Each element z of z defines a skew symmetric linear map $J_z\;:\;v\;{\longrightarrow}\;v$ given by <$J_zx$, y> = for all x, $y\;{\in}\;v$. In this paper we characterize Jacobi fields and calculate all conjugate points of a simply connected 2-step nilpotent Lie group N with its Lie algebra n satisfying $J^2_z$ = A for all $z\;{\in}\;z$, where S is a positive definite symmetric operator on z and A is a negative definite symmetric operator on v.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.6
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• pp.2054-2061
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• 2010

This paper suggests an algorithm for optimal positioning individuals(or observations) with p-dimensional measurements into coordinates of a two dimensional space. A criterion for optimizing the rotation is taken as the consistency of the grouping result obtained by the cluster analysis. This paper introduces the criterion and a transformation matrix for the orthogonal rotation. The criterion of the optimal positioning is that standard groups are placed in each quadrant of the positioning. An optimal angle of the orthogonal rotation is investigated and found by this criterions.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.585-602
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• 2020

In this paper, we construct four infinite families of binary linear codes associated with double cosets with respect to a certain maximal parabolic subgroup of the orthogonal group O⁺(2n, 2^r). And we obtain two infinite families of recursive formulas for the power moments of Kloosterman sums and those of 2-dimensional Kloosterman sums in terms of the frequencies of weights in the codes. This is done via Pless' power moment identity and by utilizing the explicit expressions of exponential sums over those double cosets related to the evaluations of "Gauss sums" for the orthogonal groups O⁺(2n, 2^r).

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.4
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• pp.1837-1860
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• 2020

We propose a general framework for studying resource allocation problem and the tradeoff between spectral efficiency (SE) and energy efficiency (EE) for downlink traffic in power domain-non-orthogonal multiple access (PD-NOMA) and device to device (D2D) based heterogeneous cloud radio access networks (H-CRANs) under imperfect channel state information (CSI). The aim is jointly optimize radio remote head (RRH) selection, spectrum allocation and power control, which is formulated as a multi-objective optimization (MOO) problem that can be solved with weighted Tchebycheff method. We propose a low-complexity algorithm to solve user association, spectrum allocation and power coordination separately. We first compute the CSI for RRHs. Then we study allocating the cell users (CUs) and D2D groups to different subchannels by constructing a bipartite graph and Hungrarian algorithm. To solve the power control and EE-SE tradeoff problems, we decompose the target function into two subproblems. Then, we utilize successive convex program approach to lower the computational complexity. Moreover, we use Lagrangian method and KKT conditions to find the global optimum with low complexity, and get a fast convergence by subgradient method. Numerical simulation results demonstrate that by using PD-NOMA technique and H-CRAN with D2D communications, the system gets good EE-SE tradeoff performance.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.7
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• pp.1533-1546
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• 2013

Wireless multicast is considered as an effective transmission mode for the future mobile social contact services supported by Long Time Evolution (LTE). Though wireless multicast has an excellent resource efficiency, its performance suffers deterioration from the channel condition and wireless resource availability. Cognitive Radio (CR) and Device to Device (D2D) are two solutions to provide potential resource. However, resource allocation for cognitive wireless multicast based on D2D is still a great challenge for LTE social networks. In this paper, a joint sub-carriers and power allocation model based on D2D for general cognitive radio multicast (CR-D2D-MC) is proposed for Orthogonal Frequency-Division Multiplexing (OFDM) LTE systems. By opportunistically accessing the licensed spectrum, the maximized capacity for multiple cognitive multicast groups is achieved with the condition of the general scenario of imperfect spectrum sensing, the constrains of interference to primary users (PUs) and an upper-bound power of secondary users (SUs) acting as multicast source nodes. Furthermore, the fairness for multicast groups or unicast terminals is guaranteed by setting a lower-bound number of the subcarriers allocated to cognitive multicast groups. Lagrange duality algorithm is adopted to obtain the optimal solution to the proposed CR-D2D-MC model. The simulation results show that the proposed algorithm improves the performance of cognitive multicast groups and achieves a good balance between capacity and fairness.

• Journal of Communications and Networks
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• v.14 no.3
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• pp.257-266
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• 2012

A decode-and-forward two-way relay system benefits from orthogonal frequency division multiplexing (OFDM) and relay transmission. In this paper, we consider a decode-and-forward two-way relay system over OFDMwith two strategies: A joint subcarrier matching algorithm and a power allocation algorithm operating with a total power constraint for all subcarriers. The two strategies are studied based on average capacity using numerical analysis by uniformly allocating power constraints for each subcarrier matching group. An optimal subcarrier matching algorithm is proposed to match subcarriers in order of channel power gain for both transmission sides. Power allocation is defined based on equally distributing the capacity of each hop in each matching group. Afterward, a modified water-filling algorithm is also considered to allocate the power among all matching groups in order to increase the overall capacity of the network. Finally, Monte Carlo simulations are completed to confirm the numerical results and show the advantages of the joint subcarrier matching, power allocation and water filling algorithms, respectively.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.257-268
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• 2008

Let G and K be compact subgroups of orthogonal groups and $0{\leq}r<x<{\infty}$. We prove that every topological fiber bundle over a definable $C^r$ manifold whose structure group is K admits a unique strongly definable $C^r$ fiber bundle structure up to definable $C^r$ fiber bundle isomorphism. We prove that every G vector bundle over an affine definable $C^rG$ manifold admits a unique strongly definable $C^rG$ vector bundle structure up to definable $C^rG$ vector bundle isomorphism.