A Class of Square Root and Division Free Algorithms and Architectures for QRD-Based Adaptive Signal Processing

IEEE Transactions on Signal Processing

Volumn 42, Issue 9, 1994, Pages 2455-2469

  Frantzeskakis, E N ^a   Liu, K J R ^a  

^a UNIVERSITY OF MARYLAND   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE CONTROL SYSTEMS; ALGORITHMS; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; PARAMETER ESTIMATION; SIGNAL FILTERING AND PREDICTION; VECTORS;

ADAPTIVE SIGNAL PROCESSING; LEAST SQUARES MINIMIZATION PROBLEM; SQUARE ROOT AND DIVISION FREE ALGORITHMS;

SIGNAL PROCESSING;

EID: 0028495758     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.317867     Document Type: Article

References (19)

1. J. L. Barlow and I. C. F. Ipsen, “Scaled Givens rotations for the solution of linear least squares problems on systolic arrays,” SIAM J. Sci., Statist. Comput., vol. 8, no. 5, pp. 716–733, Sept. 1987.
2. W. M. Gentleman, “Least squares computations by Givens transformations without square roots,” J. Inst. Math. Applicat., vol. 12, pp. 329–336, 1973.
3. W. M. Gentleman and H. T. Kung, “Matrix triangularization by systolic arrays,” in Proc. SPIE 298, Real-Time Signal Processing IV, pp. 19–26, 1981.
4. J. Gotze and U. Schwiegelshohn, “A square root and division free Givens rotation for solving least squares problems on systolic arrays,” SIAM J. Sci., Statist. Comput., vol. 12, no. 4, pp. 800–807, July 1991.
5. S. Hammarling, “A note on modifications to the Givens plane rotation,” J. Inst. Math. Applicat., vol. 13, pp. 215–218, 1974.
6. S. Haykin, Adaptive Filter Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 1991.
7. S. F. Hsieh, K. J. R. Liu, and K. Yao, “Dual-state systolic architectures for up/downdating RLS adaptive filtering,” IEEE Trans. Circuits, Syst. II, vol. 39, no. 6, pp. 382–385, June 1992.
8. S. F. Hsieh, “A unified approach for QRD-based recursive least-squares estimation without square roots,” IEEE Trans. Signal Processing, vol. 41, no. 3, pp. 1405–1409, March 1993.
9. S. Kalson and K. Yao, “Systolic array processing for order and time recursive generalized least-squares estimation,” in Proc. SPIE 564, Real-Time Signal Processing VIII, 1985, pp. 28–38.
10. F. Ling, “Efficient least squares lattice algorithm based on Givens rotations with systolic array implementation,” IEEE Trans. Signal Processing, vol. 39, pp. 1541–1551, July 1991.
11. F. Ling, D. Manolakis, and J. G. Proakis, “A recursive modified Gram-Schmidt algorithm for least-squares estimation, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, no. 4, pp. 829–836, Aug. 1986.
12. K. J. R. Liu, S. F. Hsieh, and K. Yao, “Systolic block Housholder transformation for RLS algorithm with two-level pipelined implementation,” IEEE Trans. Signal Processing, vol. 40, no. 4, pp. 946–958, Apr. 1992.
13. K. J. R. Liu, S. F. Hsieh, K. Yao, and C. T. chiu, “Dynamic range, stability and fault-tolerant capability of finite precision RLS systolic array based on Givens rotation,” IEEE Trans. Circuits, Syst., vol. 38, no. 6, pp. 625–636, June 1991.
14. J. G. McWhirter, “Recursive least-squares minimization using a systolic array,” in Proc. SPIE, Real Time Signal Processing VI, vol. 431, 1983, pp. 105–112.
15. J. G. McWhirter and T. J. Shepherd, “Systolic array processor for MVDR beamforming,” in IEE Proc., pt. F, vol. 136, no. 2, Apr. 1989, pp. 75–80.
16. I. K. Proulder, J. G. McWhirter, and T. J. Shepherd, “The QRD-based least squares lattice algorithm: Some computer simulations using finite wordlength,” in Proc. IEEE ISCAS (New Orleans, LA), May 1990, pp. 258–261
17. T. J. Shepherd, J. G. McWirter, and J. E. Hudson, “Parallel weight extraction from a systolic adaptive beamforming,” Math. Signal Processing II, 1990.
18. R. W. Stewart, R. Chapman, and T. S. Durrani, “Arithmetic implementation of the Givens QR tiarray,” in Proc. IEEE/ICASSP, 1989, pp. V-2405-2408.
19. C. F. T. Tang, K. J. R. Liu, and S. Tretter, “Optimal weight extraction for adaptive beamforming using systolic arrays,” IEEE Trans. Aerosp., Electron. Syst., vol. 30, no. 2, pp. 367–385, Apr. 1994.