• Title/Summary/Keyword: orthogonal basis matrix

Search Result 18, Processing Time 0.024 seconds

A Mathematical Implementation of OFDM System with Orthogonal Basis Matrix (직교 기저행렬을 이용하는 직교 주파수분할다중화의 수학적 구현)

  • Kang, Seog-Geun
    • Journal of the Korea Institute of Information and Communication Engineering
    • /
    • v.13 no.12
    • /
    • pp.2731-2736
    • /
    • 2009
  • In this paper, a new implementation method of OFDM (orthogonal frequency division multiplexing) system with an orthogonal basis matrix is developed mathematically. The basis matrix is based on the Haar basis but has an appropriate form for modulation of multiple subchannel signals of OFDM. It is verified that the new basis matrix can be expanded with a simple recursive algorithm. The order of synthesis matrix in the transmitter is increased by the factor of two with every expansion. Demodulation in the receiver is carried out by its inverse matrix, which can be generated recursively with the orthogonal basis matrix. It is shown that perfect reconstruction of original signals is possibly achieved in the proposed OFDMsystem.

On the Design of the Linear Phase Lapped Orthogonal Transform Bases Using the Prefilter Approach (전처리 필터를 이용한 선형 위성 LOT 기저의 설계에 관한 연구)

  • 이창우;이상욱
    • Journal of the Korean Institute of Telematics and Electronics B
    • /
    • v.31B no.7
    • /
    • pp.91-100
    • /
    • 1994
  • The lapped orthogonal transform(LOT) has been recently proposed to alleviate the blocking effects in transform coding. The LOT is known to provide an improved coding gain than the conventional transform. In this paper, we propose a prefilter approach to design the LOT bases with the view of maximizing the transform coding gain. Since the nonlinear phase basis is inappropriate to the image coding only the linear phase basis is considered in this paper. Our approach is mainly based on decomposing the transform matrix into the orthogonal matrix and the prefilter matrix. And by assuming that the input is the 1st order Markov source we design the prefilter matrix and the orthogonal matirx maximizing the transform coding gain. The computer simulation results show that the proposed LOT provides about 0.6~0.8 dB PSNR gain over the DCT and about 0.2~0.3 dB PSNR gain over the conventional LOT [7]. Also, the subjective test reveals that the proposed LOT shows less blocking effect than the DCT.

  • PDF

On the Design of Orthogonal Pulse-Shape Modulation for UWB Systems Using Hermite Pulses

  • Giuseppe, Thadeu Freitas de Abreu;Mitchell, Craig-John;Kohno, Ryuji
    • Journal of Communications and Networks
    • /
    • v.5 no.4
    • /
    • pp.328-343
    • /
    • 2003
  • Orthogonal pulse-shape modulation using Hermite pulses for ultra-wideband communications is reviewed. Closedform expressions of cross-correlations among Hermite pulses and their corresponding transmit and receive waveforms are provided. These show that the pulses lose orthogonality at the receiver in the presence of differentiating antennas. Using these expressions, an algebraic model is established based on the projections of distorted receive waveforms onto the orthonormal basis given by the set of normalized orthogonal Hermite pulses. Using this new matrix model, a number of pulse-shape modulation schemes are analyzed and a novel orthogonal design is proposed. In the proposed orthogonal design, transmit waveforms are constructed as combinations of elementary Hermites with weighting coefficients derived by employing the Gram-Schmidt (QR) factorization of the differentiating distortion model’s matrix. The design ensures orthogonality of the vectors at the output of the receiver bank of correlators, without requiring compensation for the distortion introduced by the antennas. In addition, a new set of elementary Hermite Pulses is proposed which further enhances the performance of the new design while enabling a simplified hardware implementation.

The DOA Estimation of Wide Band Moving Sources

  • Cho, Mun-Hyeong
    • Journal of information and communication convergence engineering
    • /
    • v.5 no.1
    • /
    • pp.12-16
    • /
    • 2007
  • In this paper, a new method is proposed for tracking the direction-of-arrival (DOA) of the wideband moving source incident on uniform linear array sensors. DOA is estimated by focusing transformation matrices. To update focusing matrices along with new data snap shots, we use the FAST (Fast Approximate Subspace Tracking) method. Present focusing matrices are constructed by previous signal and its orthogonal basis vectors as well as present signal and its orthogonal basis vectors, which are the left and right singular vectors of the inner product of two approximated matrices. Simulation results are shown to illustrate the performance of the proposed method.

Research on Camouflaged Encryption Scheme Based on Hadamard Matrix and Ghost Imaging Algorithm

  • Leihong, Zhang;Yang, Wang;Hualong, Ye;Runchu, Xu;Dawei, Zhang
    • Current Optics and Photonics
    • /
    • v.5 no.6
    • /
    • pp.686-698
    • /
    • 2021
  • A camouflaged encryption scheme based on Hadamard matrix and ghost imaging is proposed. In the process of the encryption, an orthogonal matrix is used as the projection pattern of ghost imaging to improve the definition of the reconstructed images. The ciphertext of the secret image is constrained to the camouflaged image. The key of the camouflaged image is obtained by the method of sparse decomposition by principal component orthogonal basis and the constrained ciphertext. The information of the secret image is hidden into the information of the camouflaged image which can improve the security of the system. In the decryption process, the authorized user needs to extract the key of the secret image according to the obtained random sequences. The real encrypted information can be obtained. Otherwise, the obtained image is the camouflaged image. In order to verify the feasibility, security and robustness of the encryption system, binary images and gray-scale images are selected for simulation and experiment. The results show that the proposed encryption system simplifies the calculation process, and also improves the definition of the reconstructed images and the security of the encryption system.

Inverse-Orthogonal Jacket-Haar and DCT Transform (Inverse-Orthogonal Jacket-Haar, DCT 변환)

  • Park, Ju Yong;Khan, Md. Hashem Ali;Kim, Jeong Su;Lee, Moon Ho
    • Journal of the Institute of Electronics and Information Engineers
    • /
    • v.51 no.9
    • /
    • pp.30-40
    • /
    • 2014
  • As the Hadamard transform can be generalized into the Jacket transform, in this paper, we generalize the Haar transform into the Jacket-Haar transform. The entries of the Jacket-Haar transform are 0 and ${\pm}2^k$. Compared with the original Haar transform, the basis of the Jacket-Haar transform is general and more suitable for signal processing. As an application, we present the DCT-II(discrete cosine transform-II) based on $2{\times}2$ Hadamard matrix and HWT(Haar Wavelete transform) based on $2{\times}2$ Haar matrix, analysis the performances of them and estimate them via the Lenna image simulation.

Low Pilot Ratio Channel Estimation for OFDM Systems Based on GCE-BEM

  • Wang, Lidong;Lim, Dong-Min
    • Journal of electromagnetic engineering and science
    • /
    • v.7 no.4
    • /
    • pp.195-200
    • /
    • 2007
  • Doubly-selective channel estimator for orthogonal frequency division multiplexing(OFDM) systems is proposed in this paper. Based on the generalized complex exponential basis expansion model(GCE-BEM), we describe the time-variant channel with time-invariant coefficients over multiple OFDM blocks. The time variation of the channel destroys the orthogonality between subcarriers, and the resulting channel matrix in the frequency domain is no longer diagonal, but the main interference comes from the near subcarriers. Based on this, we propose a channel estimator with low pilot ratio. We first develop a least-square(LS) estimator under the assumption that only the maximum Doppler frequency and the channel order are known at the receiver, and then verify that the correlation matrix of inter-channel interference(ICI) is a scaled identity matrix based on which we derive an optimal pilot insertion scheme for the LS estimator in the sense of minimum mean square error. The proposed estimator has the advantages of low pilot ratio and robustness against inter-carrier interference.

A fast M-band discrete wavelet transform algorithm using factorization of lossless matrix when the length of bases equals to 2M (기저의 길이 L=2M인 경우 무손실 행렬의 분해를 이용한 고속 M-대역 이산 웨이브렛 변환 알고리즘)

  • 권상근;이동식
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.22 no.12
    • /
    • pp.2706-2713
    • /
    • 1997
  • The fast implementation algorithm of M-band discrete wavelet transform is propsed using the factorization of lossless matrix when the length of discrete orthogonal wavelet bases equals to 2M. In computational complexity when direct filtering method is employed, the number of multiplicationand addition is (2M$^{2}$) and (2M$^{2}$ -M), respectively. But by proposed algorithm, it can be reduced to (M$^{2}$+M) and (M$^{2}$+2M-1), respectively. and it is possible to reduce the compuatational complexity further when unitary matrix employed to design the discrete or thogonal wavelet basis has the fast algorithm.

  • PDF

Computational performance and accuracy of compressive sensing algorithms for range-Doppler estimation (거리-도플러 추정을 위한 압축 센싱 알고리즘의 계산 성능과 정확도)

  • Lee, Hyunkyu;Lee, Keunhwa;Hong, Wooyoung;Lim, Jun-Seok;Cheong, Myoung-Jun
    • The Journal of the Acoustical Society of Korea
    • /
    • v.38 no.5
    • /
    • pp.534-542
    • /
    • 2019
  • In active SONAR, several different methods are used to detect range-Doppler information of the target. Compressive sensing based method is more accurate than conventional methods and shows superior performance. There are several compressive sensing algorithms for range-Doppler estimation of active sonar. The ability of each algorithm depends on algorithm type, mutual coherence of sensing matrix, and signal to noise ratio. In this paper, we compared and analyzed computational performance and accuracy of various compressive sensing algorithms for range-Doppler estimation of active sonar. The performance of OMP (Orthogonal Matching Pursuit), CoSaMP (Compressive Sampling Matching Pursuit), BPDN (CVX) (Basis Pursuit Denoising), LARS (Least Angle Regression) algorithms is respectively estimated for varying SNR (Signal to Noise Ratio), and mutual coherence. The optimal compressive sensing algorithm is presented according to the situation.

Development of an Inverse Method Using Orthogonal Basis Functions for the Evaluation of Boundary Tractions on an Elastic Body (탄성체 경계 트랙션을 구하는 문제에서 상호 수직 기저 함수를 사용한 역문제 해석 방법의 개발)

  • Kim, Sa-Young;Kim, Hyun-Gyu
    • Transactions of the Korean Society of Mechanical Engineers A
    • /
    • v.34 no.4
    • /
    • pp.487-493
    • /
    • 2010
  • Most structural analyses are concerned with the deformations and stresses in a body subjected to external loads. However, in many fields, inverse problems have to be interpreted to determine surface tractions or internal stresses from displacements measured on a remote surface. In this study, the inverse processes are studied by using the finite element method for the evaluation of internal stresses. Small errors in the measured displacements often result in a substantial loss of stability of an inverse system. In order to improve the stability of the inverse system, the displacements on a section near the region of the unknown tractions are predicted by using orthogonal basis functions. We use the Gram-Schmidt orthogonal technique to determine two bases for the displacements on a section near the region of the unknown tractions. Advantages over previous methods are discussed by using numerical examples.