Journal of the Institute of Electronics and Information Engineers (전자공학회논문지)

The Institute of Electronics and Information Engineers (대한전자공학회)
권호 표지
DOI QR코드

DOI QR Code

The New Block Circulant Hadamard Matrices

새로운 블록순환 Hadamard 행렬

  • Park, Ju Yong (Department of Internet, Information & Communication, Shyngyeong University) ;
  • Lee, Moon Ho (Division of Electronic Engineering, Chonbuk National University) ;
  • Duan, Wei (Division of Electronic Engineering, Chonbuk National University)
  • 박주용 (신경대학교 인터넷정보통신학과) ;
  • 이문호 (전북대학교 전자공학부) ;
  • 단위 (전북대학교 전자공학부)
  • Received : 2013.11.08
  • Accepted : 2014.03.01
  • Published : 2014.05.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we review the typical Toeplitz matrices and block circulant matrices, and propose the a circulant Hadamard matrix which is consisted of +1 and -1, but its structure is different from typical Hadamard matrix. The proposed circulant Hadamard matrix decreases computational complexities to $Nlog_2N$ additions through high speed algorithm compare to original one. This matrix is able to be applied to Massive MIMO channel estimation, FIR filter design, amd signal processing.

본 논문에서는 기존 Toeplitz행렬(matrix)과 블록 순환(block circulant)행렬에 대해 검토하고, 새로운 순환 Hadamard 행렬을 제안했다. 제안한 순환 Hadamard 행렬은 +1과 -1로 구성되나 구조가 기존 Hadamard 행렬과는 다르다. 고속 알고리즘을 통해 원래의 계산량을 $Nlog_2N$개의 덧셈으로 줄일 수 있다. 이 행렬은 Massive MIMO 채널 추정 및 FIR 필터 설계, 신호처리 등에 응용이 가능하다.

Keywords

References

  1. J. D. Haupt, G. M. Raz, S. J. Wright, R. D. Nowak, "Toeplitz-Structured Compressed Sensing Matrices," Workshop on Statistical Signal Processing, pp.294-298, 2007.
  2. R. M. Gray, "Toeplitz and Circulant Matrices: A review," Foundations and Trends in communications and Information Theory, Vol 2, Issue 3, pp.155-39, 2006.
  3. T. M. Apostol, Mathematical Analysis, Addison-Wesly, 1974.
  4. D. S. Bernstein, Matrix Mathematics: Theory, Facts, and Formulas, Princeton University Press, 2009.
  5. A. Bottcher, J. Gutierrez-Gutierrez, and P. M. Crespo, "Mass Concentration in Quasicommutators of Toeplitz Matrices," Journal of Computational and Applied Mathematics, Vol. 205, pp. 129-148, 2007. https://doi.org/10.1016/j.cam.2006.04.046
  6. W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, Wily, 2005.
  7. P. M. Crespo and J. Gutierrez-Gutierrez, "On the Elementwise Convergence of Continuous Functions of Hermitian Banded Toeplitz Matrices," IEEE Transactions on Information Theory, vol.53, no.3, pp.1168-1176, March 2007. https://doi.org/10.1109/TIT.2006.890697
  8. J. Gutierrez-Gutierrez, I. Iglesias and A. Podhorski, "Geometric MMSE for One-Sided and Two-Sided Vector Linear Predictors: From the Finite-Length Case to the Infinite-Length Case," Signal Processing, vol.91, pp.2237-2245, 2011. https://doi.org/10.1016/j.sigpro.2011.04.001
  9. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1994.
  10. T. Kailath, Linear Systems, Prentice-Hall, 1980.
  11. M. H. Lee, Jacket Matrices: Construction and Its Applications for Fast Cooperative Wireless signal Processing, LAP LAMBERT, Germany, 2012.
  12. M. H. Lee, M. M. Matalgah and W. Song, "Fast method for precoding and decoding of distributive multi-input multi-output channels in relay-based decode-and-forward cooperative wireless networks," IET Communications, vol. 4, Issue 2, 22, pp. 144-153, January 2010. https://doi.org/10.1049/iet-com.2008.0712