Abstract
A family of systolic array architectures for adaptive multichannel least squares lattice (MLSL) filters is presented. These architectures are based on a recently developed algorithm that provides an efficient, numerically sound, and well-structured set of recursions for realizing MLSL filters. The algorithm is based on the recursive QR decomposition of the forward and backward error correlation matrices. Form input channels andp filter taps,O(pm 2) computations are required per time step. Numerous space-time tradeoffs are available in mapping the algorithm's recursions to systolic architectures, leading to the architectural family presented here.
Similar content being viewed by others
References
B. Friedlander, “Lattice Filters for Adaptive Processing,”Proc. IEEE, 70, 1982, pp. 829–867.
L.J. Griffiths and C.W. Jim, “An Alternate Approach to Linearly Constrained Adaptive Beamforming,”IEEE Trans. Antennas and Propagation, AP-30, 1982, pp. 27–34.
T. Kawase, H. Sakai, and H. Tokumaru, “Recursive Least Squares Circular Lattice and Escalator Estimation Algorithms,”IEEE Trans. Acoustics, Speech, and Signal Processing, ASSP- 31, 1983, pp. 228–231.
F. Ling and J.G. Proakis, “A Generalized Multichannel Least Squares Lattice Algorithm Based on Sequential Processing Stages,”IEEE Trans. Acoustics, Speech, and Signal Processing, ASSP-32, 1984, pp. 381–389.
H. Lev-Ari, “Modular Architectures for Adaptive Multichannel Lattice Algorithms,”IEEE Trans. Acoustics, Speech, and Signal Processing, ASSP-35, 1987, pp. 543–552.
P.S. Lewis, “QR-based Algorithms for Multichannel Adaptive Least Squares Lattice Filters,”IEEE Trans. Acoustics, Speech, and Signal Processing, ASSP-38, 1990, pp. 421–432.
P.S. Lewis, “Algorithms and Architectures for Adaptive Least Squares Signal Processing, with Applications in Magnetoencephalography,” Ph.D. thesis, University of Southern California, Dept. Electrical Engineering—Systems, Los Angeles, CA, August 1988. Los Alamos National Laboratory report LA-11409-T, October 1988.
P.S. Lewis, “QR Algorithm and Array Architectures for Multichannel Adaptive Least Squares Lattice Filters,” InProc. 1988 Int. Conf. Acoustics, Speech, and Signal Processing, April 1988, pp. 2041–2044.
B. Yang, and J.F. Böhme, “On a Parallel Implementation of the Adaptive Multichannel Least-Squares Lattice Filter,” InProc. Int. Symp. Signals, Systems, and Electronics (ISSSE), September 1989.
P.S. Lewis, “Multichannel Adaptive Least Squares—Relating the “Kalman” Recursive Least Squares (RLS) and Least Squares Lattice (LSL) Adaptive Algorithms,” InProc. 1988 Int. Conf. Acoustics, Speech, and Signal Processing, April 1988, pp. 1926–1929.
G.H. Golub and C.F. Van Loan,Matrix Computations, Baltimore, MD, The Johns Hopkins University Press, 1983.
P.S. Lewis, “Systolic Architectures for Adaptive Multichannel Least Squares Lattice Filters,” In J. McCanny, J. McWhirter, and E. Swartzlander, eds.,Systolic Array Processors, Englewood Cliffs, NJ: Prentice Hall, pp. 237–246.
S.Y. Kung,VLSI Array Processors, Englewood Cliffs, NJ: Prentice-Hall, 1988.
S.Y. Kung, S.N. Jean, S.C. Lo, and P.S. Lewis, “Design Methodologies for Systolic Arrays: Mapping Algorithms to Architecture,” In chapter 6, Chen, ed.Signal Processing Handbook, New York: Marcel Dekker, Inc., 1988, pp. 145–191.
J.G. McWhirter, “Recursive Least-Squares Minimization Using a Systolic Array,”Real Time Signal Processing VI, vol. 431, 1983, p. 105.
S. Haykin,Adaptive Filter Theory, Englewood Cliffs, NJ, Prentice-Hall, 1986.
W.M. Gentleman and H.T. Kung, “Matrix Triangularization by Systolic Arrays,” InProc. Real-Time Signal Processing IV, vol. 298, August 1981, pp. 19–26.
Author information
Authors and Affiliations
Additional information
Los Alamos National Laboratory is operated by the University of California for the United States Department of Energy under contract W-7405-ENG-36.
Rights and permissions
About this article
Cite this article
Lewis, P.S. Systolic architectures for adaptive multichannel least squares lattice filters. J VLSI Sign Process Syst Sign Image Video Technol 2, 29–36 (1990). https://doi.org/10.1007/BF00931034
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00931034