A Fast Recursive Least Squares Adaptive Second-Order Volterra Filter and Its Performance Analysis

IEEE Transactions on Signal Processing

Volumn 41, Issue 3, 1993, Pages 1087-1102

  Lee, Junghsi ^a   Mathews, V John ^b  

^a INDUSTRIAL TECHNOLOGY RESEARCH INSTITUTE   (Taiwan)

^b UNIVERSITY OF UTAH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE SYSTEMS; LEAST SQUARES APPROXIMATIONS; SIGNAL FILTERING AND PREDICTION;

ADAPTIVE FILTERS; MULTICHANNEL FILTERS; NONLINEAR FILTERS; RLS FILTERS; VOLTERRA FILTERS; VOLTERRA SERIES EXPANSION;

ELECTRIC FILTERS;

EID: 0027555457     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.205715     Document Type: Article

References (48)

1. S. H. Ardalan and L. J. Faber, "A fast ARMA transversal RLS filter algorithm," IEEE Trans. Acoust., Speech, Signal Processing, vol. 36, no. 3, pp. 349–358, Mar. 1988.
2. S. H. Ardalan and S. T. Alexander, "Fixed-point roundoff error analysis of the exponentialy windowed RLS algorithm for time-varying systems," IEEE Trans. Acoust., Speech, Signal Processing, vol.ASSP-35, no. 6, pp. 770–783, June 1987.
3. H. K. Baik and V. J. Mathews, "Adaptive lattice bilinear filters," IEEE Trans. Signal Processing, to be published 1993.
4. M. Bellafemina and S. Benedetto, "Identification and equalization of nonlinear channels for digital transmission," Proc. of the 1985 IEEE Int. Symp. Circuits Syst., Kyoto, Japan, June 1985. pp. 1477-1480.
5. S. Benedetto, E. Biglieri, and V. Castellini, Digital Transmission Theory. Englewood Cliffs, NJ: Prentice-Hall, 1987.
6. J. L. Botto and G. V. Moustakides, "Stabilizing the fast Kalman algorithms," IEEE Trans. Acoust., Speech, Signal Processing, vol.37, no. 9, pp. 1342–1348, Sept. 1989.
7. J. W. Brewer, "Kronecker products and matrix calculus in system theory," IEEE Trans. Circuits Syst., vol. CAS-25, no. 9, pp. 772–781, Sept. 1978.
8. G. Carayannis, D. Manolakis, and N. Kalouptsidis, "A unified view of parametric processing algorithms for prewindowed signals," Signal Processing, vol. 10, pp. 335–368, 1986.
9. J. R. Casar-Corredera, M. Garcia-Otero, and A. R. Figueiras-Vidal, "Data echo nonlinear cancellation," Proc. 1985 IEEE Int. Conf.Acoust., Speech, Signal Processing, Tampa, FL, Mar. 1985, pp. 32.4.1-4.
10. J. M. Cioffi and T. Kailath, "Fast, recursive least squares transversal filters for adaptive filtering," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, no. 2, pp. 304–337, Apr. 1984.
11. J. M. Cioffi, "Limited-precision effects in adaptive filtering," IEEE Trans. Circuits Syst., vol. CAS-34, no. 7, pp. 821–833, July 1987.
12. J. M. Cioffi, "The fast adaptive ROTOR's RLS algorithm," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, no. 4, pp. 631–653, Apr. 1990.
13. M. J. Coker and D. N. Simkins, "A nonlinear adaptive noise canceller," Proc. 1980 IEEE Int. Conf. Acoust., Speech, Signal Processing, 1980, pp. 470-473.
14. C. F. N. Cowan and P. F. Adams, "Nonlinear system modeling:Concept and application," Proc. 1984 IEEE Int. Conf. Acoust., Speech, Signal Processing, San Diego, CA, Apr. 1984. pp. 45.6.14.
15. C. E. Davila, A. J. Welch, and H. G. Rylander, III, "A second-order adaptive Volterra filter with rapid convergence," IEEE Trans.Acoust., Speech, Signal Processing, vol. ASSP-35, no. 9, pp. 1259–1263, Sept. 1987.
16. E. Eleftheriou and D. D. Falconer, "Tracking properties and steady-state performance of RLS adaptive filter algorithms," IEEE Trans.Acoust., Speech, Signal Processing, vol. ASSP-34, no. 5, pp. 1097–1109, Oct. 1986.
17. G. O. Glentis and N. Kalouptsidis, "Fast adaptive algorithms for multichannel LS filtering," Proc. 1990 IEEE Int. Symp. Circuits Syst., New Orleans, LA, May 1990. pp. 801-804.
18. S. Haykin, Adaptive Filter Theory, second ed. Englewood Cliffs, NJ: Prentice-Hall, 1991.
19. I. W. Hunter and M. J. Korenberg, "The identification of nonlinear biological systems: Wiener and Hammerstein cascade models," Biolog. Cybern., vol. 55, pp. 135–144, 1986.
20. S. C. Jacobsen, S. G. Meek, and R. R. Fullmer, "An adaptive myoelectric filter," presented at the 6th IEEE Conf. Eng. Medicine Biology Soc, 1984.
21. A. Javed, B. A. Syrett, and P. A. Goud, "Intermodulation distortion analysis of reflection-type IMPATT amplifiers using Volterra series representation," IEEE Trans. Microwave Theory Techniques, vol.MTT-25, no. 9, pp. 729–733, Sept. 1977.
22. R. J. Kenefic and D. D. Weiner. "Application of the Volterra functional expansion in the detection of nonlinear functions of Gaussian processes," IEEE Trans. Commun., vol. COM-33, no. 3, pp. 276–279, Mar. 1985.
23. T. Koh and E. J. Powers, "An adaptive nonlinear digital filter with lattice orthogonalization," Proc. 1983 IEEE Int. Conf. Acoust., Speech, Signal Processing, Boston, MA, Apr. 1983, pp. 37-40.
24. T. Koh and E. J. Powers, "Second-order Volterra filtering and its application to nonlinear system identification," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, no. 6, pp. 1445-1455 Dec. 1985.
25. D. W. Lin, "On digital implementation of the fast Kalman algorithm," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, no. 5, pp. 998–1005, Oct. 1984.
26. L. Ljung, M. Morf, and D. D. Falconer. "Fast calculation of gain matrices for recursive estimation schemes," Int. J. Conlr., vol. 27, pp. 1–19, Jan. 1978.
27. S. Ljung and L. Ljung, "Error propagation properties of recursive least-squares adaptation algorithms." Automatica, vol. 21. no. 2. pp. 157–167, 1985.
28. Y. Lou, C. L. Nikias, and A. N. Venetsanopoulos, "Efficient VLSI array processing structures for adaptive quadratic digital filters," Circuits, Syst. Signal Processing, vol. 7. no. 2, pp. 253–273, 1988.
29. R. W. Lucky, "Modulation and detection for data transmission on the telephone channel," New Directions in Signal Processing in Communication and Control, J. K. Skwirzynski, Ed. Leiden, Holland: Noordhoff, 1975.
30. O. M. Macchi and N. J. Bershad, "Adaptive recovery of a chirped sinusoid in noise, Part 1: Performance of the RLS algorithm," IEEE Trans. Signal Processing, vol. 39, no. 3, pp. 583–594, Mar. 1991.
31. M. Maqusi, "Performance of baseband digital data transmission in nonlinear channels with memory," IEEE Trans. Commun., vol.COM-33, no. 7, pp. 715–719, July 1985.
32. V. Z. Marmarelis, "Practicable identification of nonstationary nonlinear systems," Proc. Inst. Elec. Eng., vol. 128, Pt. D, no. 5, pp. 211–214, Sept. 1981.
33. V. J. Mathews, "A fast recursive least-squares adaptive nonlinear filter," Proc. 21st Ann. Asilomar Conf. Syst. Signals, Comput., Pacific Grove, CA, Nov. 1987, pp. 156-160.
34. J. E. Mazo, "On the independence theory of equalizer convergence," Bell Syst. Tech. J., vol. 58, no. 5, pp. 963–993, May-June, 1979.
35. S. Narayanan, "Transistor distortion analysis using Volterra series representation," Bell Syst. Tech. J., vol. 46, pp. 991–1024, May-June 1967.
36. A. Prochazka and R. Neumann, "High-frequency distortion analysis of a semi-conductor diode for CATV applications," IEEE Trans. Consumer Electron., vol. CE-21, no. 2, pp. 120–129, May 1975.
37. G. Ramponi and G. L. Sicuranza, "Decision-directed nonlinear filters for image processing," Electron. Lett., vol. 23, no. 23, pp. 1218–1219, Nov. 5, 1987.
38. I. S. Reed, "On a moment theorem for complex Gaussian processes," IRE Trans. Inform. Theory, vol. IT-8, no. 3, pp. 194-195 Apr. 1962.
39. W. J. Rugh. Nonlinear System Theory, The Volterra-Wiener Approach. Baltimore, MD: Johns Hopkins University Press, 1981.
40. I. W. Sandberg, "On Volterra expansions for time-varying nonlinear systems," IEEE Trans. Circuits Syst., vol. CAS-30, no. 2, pp. 61-67. Feb. 1983.
41. M. Schetzen, The Volterra and Wiener Theory of the Nonlinear Systems. New York: Wiley, 1980.
42. M. Schetzen, "Nonlinear system modeling based on the Wiener theory," Proc. IEEE, vol. 69, no. 12, pp. 1557–1573, Dec. 1981.
43. G. L. Sicuranza, A. Bucconi, and P. Mitri, "Adaptive echo cancellation with nonlinear digital filters," Proc. 1984 IEEE Int. Conf.Acoust., Speech, Signal Processing, San Diego, CA, pp. 3.10.1-4, Mar. 1984.
44. G. L. Sicuranza and G. Ramponi, "Adaptive nonlinear digital filters using distributed arithmetic," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, no. 3, pp. 518–526, June 1986.
45. D. T. M. Slock and T. Kailath, "Numerically stable fast transversal filters for recursive least-squares adaptive filtering," IEEE Trans. Signal Processing, vol. 39, no. 1, pp. 92–114, Jan. 1991.
46. M. j. Smith, C. F. N. Cowan, and P. F. Adams, "Nonlinear echo cancellers based on transpose distributed arithmetic," IEEE Trans. Circuits Syst., vol. CAS-35, no. 1, pp. 6–18, Jan. 1988.
47. M. A. Syed and V. J. Mathews, "Lattice and QR decomposition-based algorithms for recursive least squares adaptive nonlinear filters." Proc. 1990 IEEE Int. Symp. Circuits Syst., New Orleans, LA, May 1990, pp. 262-265.
48. D. H. Youn, K. K. Yu, and V. J. Mathews, "Adaptive nonlinear digital filter with sequential regression algorithm," Proc. 22nd Annu. Allerton Conf. Contr. Commun. Computing, Urbana-Champaign, IL, Oct. 3-5. 1984, pp. 152-161.