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Modified Gram-Schmidt Algorithm Using Equivalent Wiener-Hopf Equation  

Ahn, Bong-Man (전북대학교 Next 사업단)
Hwang, Jee-Won (전북대학교 응용시스템공학부)
Cho, Ju-Phil (군산대학교 전자정보공학부)
Publication Information
The Journal of Korean Institute of Communications and Information Sciences / v.33, no.7C, 2008 , pp. 562-568 More about this Journal
Abstract
This paper proposes the scheme which obtain the coefficients of TDL filter and two normalization algorithms among methods which get solution of equivalent Wiener-Hopf Equation in Gram-Schmidt algorithm. Compared to the conventional NLMS algorithm, normalizes with sum of power of inputs, the presented algorithms normalize using sums of eigenvalues. Using computer simulation, we perform an system identification in an unstable environment where two poles are located in near position outside unit circle. Consequently, the proposed algorithms get the coefficients of TDL filter in Gram-Schmidt algorithm recursively and show better convergence performance than conventional NLMS algorithm.
Keywords
Wiener-Hopf; LMS; TDL; Gram-Schmidt; Regression coefficient; Weight vector extraction;
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1 J. R. Rice, 'Experiments on Gram-Schmidt orthogonalization,' Math. Comp., Vol.20, pp.325-328   DOI
2 Y. Gong, T. J. Lim, B. Farhang-Boroujeny, 'Adaptive least mean square CDMA detection with Gram-Schmidt pre-processing,' Communications, IEE Proceedings, Vol.148, Issue 4, pp.249 - 254, Aug. 2001
3 김규남, 이원로, 오성세, 김영수, 안인우, 및 하헌범, 'CDMA무선중계기 잡음제거 탐색기 개발-정보통신 산업기술개발사업 최종연구개발 결과보고서', 2003
4 S. M. Kuo and D. R. Morgan, 'Active Noise Control: A Tutorial Review,' Proceedings of the IEEE, Vol.87, NO.6, pp.943-973, June 1999
5 S. Haykin, Adaptive filter Theory-fourth edition, Prentice-Hall, Inc. 2002, chapter 6
6 S. Haykin, Adaptive filter Theory-third edition, Prentice-Hall, Inc. 1991, chpter 6
7 D. Manolakis, L. Fuyun, J. G. Proakis, 'Efficient time-recursive least-squares algorithms for finite-memory adaptive filtering.' IEEE Trans. on Circuits and Systems, Vol.34, Issue 4, pp.400-408, Apr., 1987   DOI
8 J. M. Kates,'Feedback Cancellation in Hearing Aids: Results from a Computer Simulation,' IEEE Trans. on Signal Processing, Vol.39, No.3, pp.553-562, March 1991   DOI
9 H. Sakai, 'Recursive least-squares algorithms of modified Gram-Schmidt type for parallel weight extraction,' IEEE Trans. on Signal Processing, Vol.42, No.2, Feb., 1994
10 안봉만 , 황지원 , 조주필, '등가의 Wiener-Hopf 방정식을 이용한 LMS 알고리즘에 관한 연구,' 한국통신학회 제 33권, vol.5, 2008
11 X. Huang, M. Caron, D. Hindson, 'A recursive Gram-Schmidt orthonormalization procedure and its application to communications,' Wireless Communications, 2001. (SPAWC '01). 2001 IEEE Third Workshop on Signal Processing Advances in 20-23, pp.340 - 343, March 2001
12 J. G. Proakis, C. M. Rader, and C. L. Nikias, Advanced Digital Signal Processing. Macmillan Publishing Company, 1992., chap. 7
13 C. K. Singh, S. H. Prasad; P. T. Balsara, 'VLSI Architecture for Matrix Inversion using Modified Gram-Schmidt based QR Decomposition,' VLSI Design, 2007. Held jointly with 6th International Conference on Embedded Systems., 20th International Conference on, pp.836 - 841, Jan. 2007
14 L. Fuyun, D. Manolakis, J. G. Proakis, 'A recursive modified Gram-Schmidt algorithm for least- squares estimation.' IEEE Trans. on Acoustics, Speech and Signal Processing, Vol.34, Issue 4, pp.829-836, Aug. 1986   DOI