Invited Article: A Multiple-Input and Multiple-Output Long-Term Evolution Precoding Based on Fast Diagonal-Weighted Jacket Matrices

Lee, Moon Ho; Khan, Md. Hashem Ali; Sarker, Md. Abdul Latif; Guo, Ying; Kim, Kyeong Jin

doi:10.1080/01468030.2012.663063

Cited by 4 publications

(1 citation statement)

References 21 publications

(9 reference statements)

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“…Jacket 행렬은 조합 분석(harmonic analysis) [8] 에서 부터 퀀텀 정보이론(quantum information theory) [5] 에 이르기까지 이론적으로 응용이 가능하며 또한 신호처 리 [9] 에도 응용된다. 특히, 최근에는 무선통신 네트워크 (wireless communication network) [10] 의 공간다중화를 실현하는데 이용되었고, [11]에서는 Jacket 행렬이 MIMO Multiple-Input ultiple-Output)시스템에서 unitary beamforming을 분석하는데 이용되었다.…”

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The Toeplitz Circulant Jacket Matrices

Park¹,

Kim²,

Szöllősi³

et al. 2013

Journal of the Institute of Electronics and Information Enginee

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본 논문에서는 모든 Toeplitz Jacket 행렬이 순환(circulant)하고 동치(equivalence)에 이름을 보여준다. 순환하고 동치에 이 르면 Toeplitz Jacket 행렬의 새로운 구조를 만들 수 있다. Toeplitz Jacket(TJ) 행렬의 구성법을 제시하고  ×  과  ×  의 Toeplitz Jacket 행렬의 예를 제시 하였다. 따라서 Toeplitz real Jacket 행렬은 순환하거나 negacycle임을 보여준다. AbstractIn this paper we prove that all Jacket matrices are circulant and up to equivalence. This result leads to new constructions of Toeplitz Jacket(TJ) matrices. We present the construction schemes of Toeplitz Jacket matrices and the examples of  ×  and  ×  Toeplitz Jacket matrices. As a corollary we show that a Toeplitz real Hadamard matrix is either circulant or negacyclic.

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The Toeplitz Circulant Jacket Matrices

Park¹,

Kim²,

Szöllősi³

et al. 2013

Journal of the Institute of Electronics and Information Enginee

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A fast hybrid Jacket–Hadamard matrix based diagonal block-wise transform

Lee

Khan

Kim

et al. 2014

Signal Processing: Image Communication

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In this paper, based on the block (element)-wise inverse Jacket matrix, a unified fast hybrid diagonal block-wise transform (FHDBT) algorithm is proposed. A new fast diagonal block matrix decomposition is made by the matrix product of successively lower order diagonal Jacket matrix and Hadamard matrix. Using a common lower order matrix in the form of 1 1, a fast recursive structure can be developed in the FHDBT, which is able to convert a newly developed discrete cosine transform (DCT)-II, discrete sine transform (DST)-II, discrete Fourier transform (DFT), and Haar-based wavelet transform (HWT). Since these DCT-II, DST-II, DFT, and HWT are widely used in different areas of applications, the proposed FHDBT can be applied to the heterogeneous system requiring several transforms simultaneously. Comparing with pre-existing DCT-II, DST-II, DFT, and HWT, it is shown that the proposed FHDBT exhibits less the complexity as its matrix size gets larger. The proposed algorithm is also well matched to circulant channel matrix. From the numerical experiments, it is shown that a better performance can be achieved by the use of DCT/DST-II compression scheme compared with the DCT-II only compression method. Signal Processing: Image CommunicationThis work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. , a fast recursive structure can be developed in the FHDBT, which is able to convert a newly developed discrete cosine transform (DCT)-II, discrete sine transform (DST)-II, discrete Fourier transform (DFT), and Haar-based wavelet transform (HWT). Since these DCT-II, DST-II, DFT, and HWT are widely used in different areas of applications, the proposed FHDBT can be applied to the heterogeneous system requiring several transforms simultaneously. Comparing with pre-existing DCT-II, DST-II, DFT, and HWT, it is shown that the proposed FHDBT exhibits less the complexity as its matrix size gets larger. The proposed algorithm is also well matched to circulant channel matrix. From the numerical experiments, it is shown that a better performance can be achieved by the use of DCT/ DST-II compression scheme compared with the DCT-II only compression method.

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Arikan and Alamouti matrices based on fast block-wise inverse Jacket transform

Lee

Khan

Kim

2013

EURASIP J. Adv. Signal Process.

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Recently, Lee and Hou (IEEE Signal Process Lett 13: 461-464, 2006) proposed one-dimensional and two-dimensional fast algorithms for block-wise inverse Jacket transforms (BIJTs). Their BIJTs are not real inverse Jacket transforms from mathematical point of view because their inverses do not satisfy the usual condition, i.e., the multiplication of a matrix with its inverse matrix is not equal to the identity matrix. Therefore, we mathematically propose a fast block-wise inverse Jacket transform of orders N = 2 k , 3 k , 5 k , and 6 k , where k is a positive integer. Based on the Kronecker product of the successive lower order Jacket matrices and the basis matrix, the fast algorithms for realizing these transforms are obtained. Due to the simple inverse and fast algorithms of Arikan polar binary and Alamouti multiple-input multiple-output (MIMO) non-binary matrices, which are obtained from BIJTs, they can be applied in areas such as 3GPP physical layer for ultra mobile broadband permutation matrices design, first-order q-ary Reed-Muller code design, diagonal channel design, diagonal subchannel decompose for interference alignment, and 4G MIMO long-term evolution Alamouti precoding design.

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Invited Article: A Multiple-Input and Multiple-Output Long-Term Evolution Precoding Based on Fast Diagonal-Weighted Jacket Matrices

Cited by 4 publications

References 21 publications

The Toeplitz Circulant Jacket Matrices

The Toeplitz Circulant Jacket Matrices

A fast hybrid Jacket–Hadamard matrix based diagonal block-wise transform

Arikan and Alamouti matrices based on fast block-wise inverse Jacket transform

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