• Title/Summary/Keyword: Sparse linear system

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Sweep Nonlinearity Estimation for High Range Resolution Millimeter-Wave Seeker Using Least Squares Method (최소 자승법을 이용한 고해상도 밀리미터파 탐색기의 비선형 위상 오차의 추정)

  • Yang, Hee-Seong;Chun, Joo-Hwan;Song, Sung-Chan
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.23 no.1
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    • pp.56-67
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    • 2012
  • In this thesis, to compensate the sweep nonlinearity occurring in the high resolution radar system using FMICW or FMCW, the method of the estimation of the nonlinearity is proposed. The nonlinear phase component caused by the nonlinear characteristic of the radar system is modelled as a linear combination of the sinusoidal functions consisting of various magnitudes and phases(systematic nonlinear phase error) and a random component(stochastic nonlinear phase error). From two IF signals that are measured respectively independently for two reference point targets lying in different distances which are known, a sparse linear equation is made and solved by least squares method to estimate the nonlinear phase component. The estimated component can be used for predistortion method to compensate the sweep nonlinearity.

High Data Rate Ultra Wideband Space Time Coded OFDM (고속 전송률 UWB 시공간 부호화 OFDM)

  • Lee Kwang-Jae;Chen Hsiao-Hwa;Lee Moon-Ho
    • Journal of the Institute of Electronics Engineers of Korea TC
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    • v.43 no.7 s.349
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    • pp.132-142
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    • 2006
  • In this paper, we present a candidate high data rate space time coded OFDM system for short range personal networking. The system transmits the complex space time coded signals with a hybrid orthogonal frequency division multiplexing (OFDM) based on ultra wideband (UWB) pulses. The transmitted signals are sparse pulse trains modulated by a frequency selected from a properly designed set of frequencies. Additionally, a widely linear (WL) receive filter and a space time frequency transmission are designed by using two simple parallel linear detectors. To overcome the deeply fade in the propagation system, a beamforming combined with space time block codes also 따 e briefly discussed.

ITERATIVE ALGORITHMS AND DOMAIN DECOMPOSITION METHODS IN PARTIAL DIFFERENTIAL EQUATIONS

  • Lee, Jun Yull
    • Korean Journal of Mathematics
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    • v.13 no.1
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    • pp.113-122
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    • 2005
  • We consider the iterative schemes for the large sparse linear system to solve partial differential equations. Using spectral radius of iteration matrices, the optimal relaxation parameters and good parameters can be obtained. With those parameters we compare the effectiveness of the SOR and SSOR algorithms. Applying Crank-Nicolson approximation, we observe the error distribution according to domain decomposition. The number of processors due to domain decomposition affects time and error. Numerical experiments show that effectiveness of SOR and SSOR can be reversed as time size varies, which is not the usual case. Finally, these phenomena suggest conjectures about equilibrium time grid for SOR and SSOR.

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TeT: Distributed Tera-Scale Tensor Generator (분산 테라스케일 텐서 생성기)

  • Jeon, ByungSoo;Lee, JungWoo;Kang, U
    • Journal of KIISE
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    • v.43 no.8
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    • pp.910-918
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    • 2016
  • A tensor is a multi-dimensional array that represents many data such as (user, user, time) in the social network system. A tensor generator is an important tool for multi-dimensional data mining research with various applications including simulation, multi-dimensional data modeling/understanding, and sampling/extrapolation. However, existing tensor generators cannot generate sparse tensors like real-world tensors that obey power law. In addition, they have limitations such as tensor sizes that can be processed and additional time required to upload generated tensor to distributed systems for further analysis. In this study, we propose TeT, a distributed tera-scale tensor generator to solve these problems. TeT generates sparse random tensor as well as sparse R-MAT and Kronecker tensor without any limitation on tensor sizes. In addition, a TeT-generated tensor is immediately ready for further tensor analysis on the same distributed system. The careful design of TeT facilitates nearly linear scalability on the number of machines.

Distributed Decision-Making in Wireless Sensor Networks for Online Structural Health Monitoring

  • Ling, Qing;Tian, Zhi;Li, Yue
    • Journal of Communications and Networks
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    • v.11 no.4
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    • pp.350-358
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    • 2009
  • In a wireless sensor network (WSN) setting, this paper presents a distributed decision-making framework and illustrates its application in an online structural health monitoring (SHM) system. The objective is to recover a damage severity vector, which identifies, localizes, and quantifies damages in a structure, via distributive and collaborative decision-making among wireless sensors. Observing the fact that damages are generally scarce in a structure, this paper develops a nonlinear 0-norm minimization formulation to recover the sparse damage severity vector, then relaxes it to a linear and distributively tractable one. An optimal algorithm based on the alternating direction method of multipliers (ADMM) and a heuristic distributed linear programming (DLP) algorithm are proposed to estimate the damage severity vector distributively. By limiting sensors to exchange information among neighboring sensors, the distributed decision-making algorithms reduce communication costs, thus alleviate the channel interference and prolong the network lifetime. Simulation results in monitoring a steel frame structure prove the effectiveness of the proposed algorithms.

A PARALLEL PRECONDITIONER FOR GENERALIZED EIGENVALUE PROBLEMS BY CG-TYPE METHOD

  • MA, SANGBACK;JANG, HO-JONG
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.5 no.2
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    • pp.63-69
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    • 2001
  • In this study, we shall be concerned with computing in parallel a few of the smallest eigenvalues and their corresponding eigenvectors of the eigenvalue problem, $Ax={\lambda}Bx$, where A is symmetric, and B is symmetric positive definite. Both A and B are large and sparse. Recently iterative algorithms based on the optimization of the Rayleigh quotient have been developed, and CG scheme for the optimization of the Rayleigh quotient has been proven a very attractive and promising technique for large sparse eigenproblems for small extreme eigenvalues. As in the case of a system of linear equations, successful application of the CG scheme to eigenproblems depends also upon the preconditioning techniques. A proper choice of the preconditioner significantly improves the convergence of the CG scheme. The idea underlying the present work is a parallel computation of the Multi-Color Block SSOR preconditioning for the CG optimization of the Rayleigh quotient together with deflation techniques. Multi-Coloring is a simple technique to obatin the parallelism of order n, where n is the dimension of the matrix. Block SSOR is a symmetric preconditioner which is expected to minimize the interprocessor communication due to the blocking. We implemented the results on the CRAY-T3E with 128 nodes. The MPI(Message Passing Interface) library was adopted for the interprocessor communications. The test problems were drawn from the discretizations of partial differential equations by finite difference methods.

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A Study on Real-time State Estimation for Smart Microgrids (스마트 마이크로그리드 실시간 상태 추정에 관한 연구)

  • Bae, Jun-Hyung;Lee, Sang-Woo;Park, Tae-Joon;Lee, Dong-Ha;Kang, Jin-Kyu
    • 한국태양에너지학회:학술대회논문집
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    • 2012.03a
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    • pp.419-424
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    • 2012
  • This paper discusses the state-of-the-art techniques in real-time state estimation for the Smart Microgrids. The most popular method used in traditional power system state estimation is a Weighted Least Square(WLS) algorithm which is based on Maximum Likelihood(ML) estimation under the assumption of static system state being a set of deterministic variables. In this paper, we present a survey of dynamic state estimation techniques for Smart Microgrids based on Belief Propagation (BP) when the system state is a set of stochastic variables. The measurements are often too sparse to fulfill the system observability in the distribution network of microgrids. The BP algorithm calculates posterior distributions of the state variables for real-time sparse measurements. Smart Microgrids are modeled as a factor graph suitable for characterizing the linear correlations among the state variables. The state estimator performs the BP algorithm on the factor graph based the stochastic model. The factor graph model can integrate new models for solar and wind correlation. It provides the Smart Microgrids with a way of integrating the distributed renewable energy generation. Our study on Smart Microgrid state estimation can be extended to the estimation of unbalanced three phase distribution systems as well as the optimal placement of smart meters.

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Applications of Graph Theory for the Pipe Network Analysis (상수관망해석을 위한 도학의 적용)

  • Park, Jae-Hong;Han, Geon-Yeon
    • Journal of Korea Water Resources Association
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    • v.31 no.4
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    • pp.439-448
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    • 1998
  • There are many methods to calculate steady-state flowrate in a large water distribution system. Linear method which analyzes continuity equations and energy equations simultaneously is most widely used. Though it is theoretically simple, when it is applied to a practical water distribution system, it produces a very sparse coefficient matrix and most of its diagonal elements are to be zero. This sparsity characteristic of coefficient matrix makes it difficult to analyze pipe flow using the linear method. In this study, a graph theory is introduced to water distribution system analysis in order to prevent from producing ill-conditioned coefficient matrix and the technique is developed to produce positive-definite matrix. To test applicability of developed method, this method is applied to 22 pipes and 142 pipes system located nearby Taegu city. The results obtained from these applications show that the method can calculate flowrate effectively without failure in converage. Thus it is expected that the method can analyze steady state flowrate and pressure in pipe network systems efficiently. Keywords : pipe flow analysis, graph theory, linear method.

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Implementation of WCDMA Air Protocol Analyzer with An Effective Equalizer Design using Characteristic of Sparse Matrix (희소 행렬의 특성을 이용하여 효율적인 등화기 설계법이 적용된 WCDMA 무선 신호 분석기 구현)

  • Shin, Chang Eui;Choi, Seung Won
    • Journal of Korea Society of Digital Industry and Information Management
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    • v.9 no.1
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    • pp.111-118
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    • 2013
  • This paper presents implementation of Air protocol analyzer and physical layer design algorithm. The analyzer is a measurement system providing real-time analysis of wireless signals between User Equipment (UE) and Node-B. The implemented system proposed in this paper consists of Digital Signal Processors (DSPs) and Field Programmable Gate Arrays (FPGAs). The waveform of Wideband Code Division Multiple Access (WCDMA) has been selected for verification of the proposed system. We designed the analyzer using equalizer algorithm and rake-receiver algorithm. Among various algorithms of designing the equalizer, we have chosen Linear Minimum Mean Square Error (LMMSE) equalizer that uses the inverse of channel matrix. Since the LMMSE equalizer uses the inverse channel matrix, it suffers from a large amount of computational load, while it outperforms most conventional equalizers. In this paper, we introduce an efficient procedure of reducing the computational load required by LMMSE equalizer-based receiver.

Transmission waveform design for compressive sensing active sonar using the matrix projection from Gram matrix to identity matrix and a constraint for bandwidth (대역폭 제한 조건과 Gram 행렬의 단위행렬로의 사영을 이용한 압축센싱 능동소나 송신파형 설계)

  • Lee, Sehyun;Lee, Keunhwa;Lim, Jun-Seok;Cheong, Myoung-Jun
    • The Journal of the Acoustical Society of Korea
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    • v.38 no.5
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    • pp.522-533
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    • 2019
  • The compressive sensing model for range-Doppler estimation can be expressed as an under-determined linear system y = Ax. To find the solution of the linear system with the compressive sensing method, matrix A should be sufficiently incoherent and x to be sparse. In this paper, we propose a transmission waveform design method that maintains the bandwidth required by the sonar system while lowering the mutual coherence of the matrix A so that the matrix A is incoherent. The proposed method combines two methods of optimizing the sensing matrix with the alternating projection and suppressing unwanted frequency bands using the DFT (Discrete Fourier Transform) matrix. We compare range-Doppler estimation performance of existing waveform LFM(Linear Frequency Modulated) and designed waveform using the matched filter and the compressive sensing method. Simulation shows that the designed transmission waveform has better detection performance than the existing waveform LFM.