Abstract
This chapter analyzes the finite and infinite-precision properties of QR-decomposition recursive least-squares (QRD-RLS) algorithms with emphasis on the conventional QRD-RLS and fast QRD-lattice (FQRD-lattice) formulations. The analysis encompasses deriving mean squared values of internal variables in steady-state and also the mean squared error of the deviations of the same variables assuming fixed-point arithmetic. In particular, analytical expressions for the excess of mean squared error and for the variance of the deviation in the tap coefficients of the QRD-RLS algorithm are derived, and the analysis is extended to the error signal of the FQRD-lattice algorithm. All the analytical results are confirmed to be accurate through computer simulations. Conclusions follow.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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 rotations. IEEE Transactions on Circuits and Systems, vol. 38, no. 6, pp. 625–636 (June 1991)
S. Leung and S. Haykin, Stability of recursive QRD-LS algorithms using finite-precision systolic array implementation. IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 37, no. 5, pp. 760–763 (May 1989)
S. Haykin, Adaptive Filter Theory. Prentice-Hall, Englewood Cliffs, NJ, USA (1991)
J. G. McWhirter, Recursive least-squares minimization using a systolic array. SPIE Real-Time Signal Processing VI, vol. 431, pp. 105–112 (January 1983)
W. H. Gentleman and H. T. Kung, Matrix triangularization by systolic arrays. SPIE Real-Time Signal Processing IV, vol. 298, pp. 19–26 (January 1981)
P. S. R. Diniz and M. G. Siqueira, Finite precision analysis of the QR-recursive least squares algorithm. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 42, pp. 334–348 (May 1995)
A. Papoulis, Probability, Random Variables, and Stochastic Processes. McGraw-Hill Book Company, New York, NY, USA (1965)
C. Caraiscos and B. Liu, A roundoff error analysis of the LMS adaptive algorithm. IEEE Transactions on Acoustics, Speech and Signal Processing, vol. ASSP-32, no, 1, pp. 34–41 (February 1984)
N. Kalouptsidis and S. Theodoridis, Adaptive System Identification and Signal Processing Algorithms, Prentice-Hall, Upper Saddle River, NJ, USA (1993)
M. G. Siqueira and P. S. R. Diniz, Infinite precision analysis of the QR-recursive least squares algorithm. IEEE International Symposium on Circuit and Systems, ISCAS’93, Chicago, USA, pp. 878–881 (May 1993)
C. G. Samson and V. U. Reddy, Fixed point error analysis of the normalized ladder algorithm. IEEE Transactions on Audio, Speech, and Signal Processing, vol. ASSP-31, no. 5, pp. 1177–1191 (October 1983)
M. G. Siqueira, P. S. R. Diniz, and A. Alwan, Infinite precision analysis of the fast QR decomposition RLS algorithm. IEEE International Symposium on Circuits and Systems, ISCAS’94, London, UK, vol. 2, pp. 293–296 (May–June 1994)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Springer-Verlag US
About this chapter
Cite this chapter
Diniz, P.S., Siqueira, M.G. (2009). Finite and Infinite-Precision Properties of QRD-RLS Algorithms. In: QRD-RLS Adaptive Filtering. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09734-3_9
Download citation
DOI: https://doi.org/10.1007/978-0-387-09734-3_9
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-09733-6
Online ISBN: 978-0-387-09734-3
eBook Packages: EngineeringEngineering (R0)