Transient analysis of adaptive filters with error nonlinearities

IEEE Transactions on Signal Processing

Volumn 51, Issue 3, 2003, Pages 653-663

  Al Naffouri, Tareq Y ^a   Sayed, Ali H ^b  

^a Stanford University   (United States)

^b University of California   (United States)

Author keywords

Adaptive filter; Energy conservation; Error nonlinearity; Feedback analysis; Mean square error error; Steady state analysis; Transient analysis

Indexed keywords

DATA REDUCTION; ENERGY CONSERVATION; GAUSSIAN NOISE (ELECTRONIC); LINEARIZATION; MATHEMATICAL MODELS; THEOREM PROVING; VECTORS;

LEAST-MEAN FOURTH (LMF) ALGORITHM;

ADAPTIVE FILTERING;

EID: 0037333299     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2002.808108     Document Type: Article

References (41)

1. S. Haykin, Adaptive Filter Theory. Englewood Cliffs, NJ: Prentice-Hall, 1996.
2. B. Widrow and S. D. Stearns, Adaptive Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1985.
3. O. Macchi, Adaptive Processing: The LMS Approach with Applications in Transmission. New York: Wiley, 1995.
4. D. L. Duttweiler, "Adaptive filter performance with nonlinearities in the correlation multiplier," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-30, pp. 578-586, Aug. 1982.
5. E. Walach and B. Widrow, "The least-mean fourth (LMF) adaptive algorithm and its family," IEEE Trans. Inform. Theory, vol. IT-30, pp. 275-283, Apr. 1984.
6. J. Gibson and S. Gray, "MVSE adaptive filtering subject to a constraint on MSE," IEEE Trans. Circuits Syst., vol. 35, pp. 603-608, May 1988.
7. W. Sethares, "Adaptive algorithms with nonlinear data and error functions," IEEE Trans. Signal Processing, vol. 40, pp. 2199-2206, Sept. 1992.
8. V. Mathews and S. Cho, "Improved convergence analysis of stochastic gradient adaptive filters using the sign algorithm," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, pp. 450-454, Apr 1987.
9. N. J. Bershad, "On error saturation nonlinearities in LMS adaptation," IEEE Trans. Acoust., Speech, Signal Processing, vol. 36, pp. 440-452, Apr. 1988.
10. N. J. Bershad and M. Bonnet, "Saturation effects in LMS adaptive echo cancellation for binary data," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1687-1696, Oct. 1990.
11. E. Eweda, "Comparison of RLS, LMS, and sign algorithms for tracking randomly time-varying channels," IEEE Trans. Signal Processing, vol. 42, pp. 2937-2944, Nov. 1994.
12. T. Claasen and W. Mecklenbräuker, "Comparison of the convergence of two algorithms for adaptive FIR digital filters," IEEE Trans. Circuits Syst., vol. CAS-28, pp. 510-518, June 1981.
13. O. Tanrikulu and J. A. Chambers, "Convergence and steady-state properties of the least-mean mixed-norm (LMMN) adaptive algorithm," Proc. Inst. Elect. Eng.-Vision, Image Signal Process., vol. 143, no. 3, pp. 137-142, June 1996.
14. J. A. Chambers, O. Tanrikulu, and A. G. Constantindes, "Least mean mixed-norm adaptive filtering," Electron. Lett., vol. 30, no. 19, pp. 1574-1575, Sept. 1994.
15. S. Koike, "Convergence analysis of a data echo canceler with a stochastic gradient adaptive FIR filter using the sign algorithm," IEEE Trans. Signal Processing, vol. 43, pp. 2852-2861, Dec. 1995.
16. R. Sharma, W. Sethares, and J. Bucklew, "Asymptotic analysis of stochastic gradient-based adaptive filtering algorithms with general cost functions," IEEE Trans. Signal Processing, vol. 44, pp. 2186-2194, Sept. 1996.
17. S. Florian and A. Feuer, "Performance analysis of the LMS algorithm with a tapped delay line (two-dimensional case)," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 1542-1549, Dec 1986.
18. S. C. Douglas and W. Pan, "Exact expectation analysis of the LMS adaptive filter," IEEE Trans. Signal Processing, vol. 43, pp. 2863-2871, Dec. 1995.
19. V. H. Nascimento and A. H. Sayed, "Stability of the lms adaptive filter by means of a state equation," in Proc. 36th Annu. Allerton Conf. Commun., Contr., Comput., 1998, pp. 242-251.
20. W. A. Gardner, "Learning characteristic of stochastic-descent algorithms: A general study, analysis, and critique," Signal Process., vol. 6, no. 2, pp. 113-133, Apr. 1984.
21. A. Feuer and E. Weinstein, "Convergence analysis of LMS filters with uncorrelated Gaussian data," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, Jan. 1985.
22. M. Rupp, "The behavior of LMS and NLMS algorithms in the presence of spherically invariant processes," IEEE Trans. Signal Processing, vol. 41, pp. 1149-1160, Mar. 1993.
23. J. E. Mazo, "On the independence theory of equalizer convergence," Bell Syst. Tech. J., vol. 58, pp. 963-993, May/June 1979.
24. J. Bermudez and N. J. Bershad, "A nonlinear analytical model for the quantized LMS algorithm- The arbitrary step size case," IEEE Trans. Signal Processing, vol. 44, pp. 1175-1183, May 1996.
25. J. Mai and A. H. Sayed, "A feedback approach to the steady-state performance of fractionally-spaced blind adaptive equalizers," IEEE Trans. Signal Processing, vol. 48, pp. 80-91, Jan. 2000.
26. N. R. Yousef and A. H. Sayed, "A unified approach to the steady-state and tracking analyzes of adaptive filters," IEEE Trans. Signal Processing, vol. 49, pp. 314-324, Feb. 2001.
27. _, "Ability of adaptive filters to track carrier offsets and random channel nonstationarities," IEEE Trans. Signal Processing, vol. 50, pp. 1533-1544, July 2002.
28. _, "A feedback analysis of the tracking performance of blind adaptive equalization algorithms," in Proc. CD Conf., vol. 1, 1999, pp. 174-179.
29. A. H. Sayed and M. Rupp, "A time-domain feedback analysis of adaptive algorithms via the small gain theorem," in Proc. SPIE, vol. 2563, 1995, pp. 458-469.
30. M. Rupp and A. H. Sayed, "A time-domain feedback analysis of filtered-error adaptive gradient algorithms," IEEE Trans. Signal Processing, vol. 44, pp. 1428-1439, June 1996.
31. A. H. Sayed and M. Rupp, "Robustness issues in adaptive filtering," in DSP Handbook. Boca Raton, FL: CRC, 1998, ch. 20.
32. M. Rupp and A. H. Sayed, "On the convergence of blind adaptive equalizers for constant-modulus signals," IEEE Trans. Commun., vol. 48, pp. 795-803, May 2000.
33. T. Y. Al-Naffouri and A. H. Sayed, "Transient analysis of data-normalized adaptive filters," IEEE Trans. Signal Processing, vol. 51, pp. 639-652, Mar. 2003.
34. R. Price, "A useful theorem for nonlinear devices having gaussian inputs," IEEE Trans. Inform. Theory, vol. IT-4, pp. 69-72, June 1958.
35. P. Billingsley, Probability and Measure, 3rd ed. New York: Wiley, 1995.
36. S. C. Douglas and T. H. -Y. Meng, "Stochastic gradient adaptation under general error criterion," IEEE Trans. Signal Processing, vol. 42, pp. 1335-1351, June 1994.
37. T. Birkel, "Laws of large numbers under dependence assumptions," Statist. Probab. Lett., vol. 14, no. 4, pp. 355-362.
38. T. Y. Al-Naffouri, A. Zerguine, and M. Bettayeb, "Convergence analysis of the LMS algorithm with a general error nonlinearity and an iid input," in Proc. Asilomar Conf. Signals, Syst., Comput., vol. 1, 1998, pp. 556-559.
39. N. R. Yousef and A. H. Sayed, "Tracking analysis of the LMF and LMMN adaptive algorithms," in Proc. Asilomar Conf. Signals, Syst., Comput., vol. 1, 1999, pp. 786-790.
40. M. K. Simon and M. -S. Alouini, "A unified approach to the probability of error for noncoherent and differentially coherent modulations over generalized fading channels," IEEE Trans. Commun., vol. 46, pp. 1625-1638, Dec. 1998.
41. E. Masry and F. Bullo, "Convergenece analysis of the sign algorithm for adaptive filtering," IEEE Trans. Inform. Theory, vol. 41, pp. 489-495, Mar. 1995.