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

Authors
  • Hai, Han1, 2
  • Lee, Moon Ho3
  • Zhang, Xiao-Dong4
  • 1 Donghua University, College of Information Science and Technology, Shanghai, People’s Republic of China , Shanghai (China)
  • 2 Ministry of Education, Engineering Research Center of Digitized Textile & Apparel Technology, Shanghai, 201620, People’s Republic of China , Shanghai (China)
  • 3 Chonbuk National University, Division of Electronic Engineering, IT Convergence Research Center, Jeonju, 561-756, Korea , Jeonju (South Korea)
  • 4 Shanghai Jiao Tong University, School of Mathematical Sciences, MOE-LSC, No. 800 Dongchuan Road, Shanghai, 200240, People’s Republic of China , Shanghai (China)
Type
Published Article
Journal
Circuits, Systems, and Signal Processing
Publisher
Springer US
Publication Date
Dec 19, 2018
Volume
38
Issue
4
Pages
1847–1875
Identifiers
DOI: 10.1007/s00034-018-0995-1
Source
Springer Nature
Keywords
License
Yellow

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,4kp,np\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N=2p, 4p, 4^kp, np$$\end{document}, 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 I2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_2$$\end{document} matrix and block Hadamard H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_2$$\end{document} 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.

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