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Block-Circulant Inverse Orthogonal Jacket Matrices and Its Applications to the Kronecker MIMO Channel

  • Han Hai
  • Moon Ho LeeEmail author
  • Xiao-Dong Zhang
Article
  • 14 Downloads

Abstract

This paper presents a note on the block-circulant generalized Hadamard matrices, which is called inverse orthogonal Jacket matrices of orders \(N=2p, 4p, 4^kp, np\), where k is a positive integer for the Kronecker MIMO channel. The class of block Toeplitz circulant Jacket matrices not only have many properties of the circulant Hadamard conjecture but also have the construction of block-circulant, which can be easily applied to fast algorithms for decomposition. The matrix decomposition is with the form of the products of block identity \(I_2\) matrix and block Hadamard \(H_2\) matrix. In this paper, a block fading channel model is used, where the channel is constant during a transmission block and varies independently between transmission blocks. The proposed block-circulant Jacket matrices can also achieve about 3db gain in high SNR regime with MIMO channel. This algorithm for realizing these transforms can be applied to the Kronecker MIMO channel.

Keywords

Circulant Hadamard conjecture Center-weighted Hadamard matrix Reciprocal transpose Block-circulant Jacket transform DFT matrix Toeplitz matrix Kronecker MIMO channel 

Notes

Acknowledgements

The second author visited Concordia University from July 4 to July 25, 2008, in Canada, and talked about Jacket Matrix many times, thanks to Professor M. Omair Ahmad and Professor M.N.S. Swamy.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Information Science and TechnologyDonghua UniversityShanghaiPeople’s Republic of China
  2. 2.Engineering Research Center of Digitized Textile & Apparel TechnologyMinistry of EducationShanghaiPeople’s Republic of China
  3. 3.Division of Electronic Engineering, IT Convergence Research CenterChonbuk National UniversityJeonjuKorea
  4. 4.School of Mathematical Sciences, MOE-LSCShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China

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