Commenced in January 2007
Paper Count: 30184
Mean-Square Performance of Adaptive Filter Algorithms in Nonstationary Environments
Abstract:Employing a recently introduced unified adaptive filter theory, we show how the performance of a large number of important adaptive filter algorithms can be predicted within a general framework in nonstationary environment. This approach is based on energy conservation arguments and does not need to assume a Gaussian or white distribution for the regressors. This general performance analysis can be used to evaluate the mean square performance of the Least Mean Square (LMS) algorithm, its normalized version (NLMS), the family of Affine Projection Algorithms (APA), the Recursive Least Squares (RLS), the Data-Reusing LMS (DR-LMS), its normalized version (NDR-LMS), the Block Least Mean Squares (BLMS), the Block Normalized LMS (BNLMS), the Transform Domain Adaptive Filters (TDAF) and the Subband Adaptive Filters (SAF) in nonstationary environment. Also, we establish the general expressions for the steady-state excess mean square in this environment for all these adaptive algorithms. Finally, we demonstrate through simulations that these results are useful in predicting the adaptive filter performance.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1072333Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1748
 B. Widrow and S. D. Stearns, Adaptive Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1985.
 S. Haykin, Adaptive Filter Theory. NJ: Prentice-Hall, 4th edition, 2002.
 A. H. Sayed, Fundamentals of Adaptive Filtering. Wiley, 2003.
 B. Widrow, J. M. McCool, M. Larimore, and C. R. Johnson, "Stationary and nonstationry learning characteristics of the LMS adaptive filter," in Proc. IEEE, 1976, pp. 1151-1162.
 N. J. Bershad, P. Feintuch, A. Reed, and B. Fisher, "Tracking charcteristics of the LMS adaptive line enhancer: Response to a linear chrip signal in noise," IEEE Trans. Acoust., Speech, Signal Processing, vol. 28, pp. 504-516, 1980.
 S. Marcos and O. Macchi, "Tracking capability of the least mean square algorithm: Application to an asynchronous echo canceller," IEEE Trans. Acoust., Speech, Signal Processing, vol. 35, pp. 1570-1578, 1987.
 E. Eweda, "Analysis and design of a signed regressor LMS algorithm for stationary and nonstationary adaptive filtering with correlated Gaussian data," IEEE Trans. Circuits, Syst., vol. 37, pp. 1367-1374, Nov. 1990.
 ÔÇöÔÇö, "Optimum step size of the sign algorithm for nonstationary adaptive filtering," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1897-1901, 1990.
 ÔÇöÔÇö, "Comparsion of RLS and LMS, and sign algorithms for tracking randomly time-varying channels," IEEE Trans. Signal Processing, vol. 42, pp. 2937-2944, 1994.
 N. R. Yousef and A. H. Sayed, "Steady-state and tracking analyses of the sign algorithm without the explicit use of the independence assumption," IEEE Signal Processing Letters, vol. 7, pp. 307-309, 2000.
 ÔÇöÔÇö, "A unified approach to the steady-state and tracking analyses of adaptive filters," IEEE Trans. Signal Processing, vol. 49, pp. 314-324, 2001.
 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.
 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, 1996.
 M. S. E. Abadi and A. M. Far, "A unified approach to steady-state performance analysis of adaptive filters without using the independence assumptions," Signal Processing, vol. 87, pp. 1642-1654, 2007.
 H.-C. Shin and A. H. Sayed, "Mean-square performance of a family of affine projection algorithms," IEEE Trans. Signal Processing, vol. 52, pp. 90-102, Jan. 2004.
 H.-C. Shin, W. J. Song, and A. H. Sayed, "Mean-square performance of data-reusing adaptive algorithms," IEEE Signal Processing Letters, vol. 12, pp. 851-854, Dec. 2005.
 J. H. Hus├©y and M. S. E. Abadi, "A common framework for transient analysis of adaptive filters," in Proc. 12th IEEE Mediterranean Electrotechnical Conference, Dubrovnik, Croatia, May 2004, pp. 265-268.
 ÔÇöÔÇö, "Transient analysis of adaptive filters using a general framework," Automatika, Journal for Control, Measurement, Electronics, Computing and Communications, vol. 45, pp. 121-127, 2004.
 J. H. Hus├©y, "A streamlined approach to adaptive filters," in Proc. EUSIPCO, Firenze, Italy, Sept. 2006, published online by EURASIP at http://www.arehna.di.uoa.gr/Eusipco2006/papers/1568981236.pdf.
 P. S. R. Diniz, Adaptive Filtering: Algorithms and practical implementation, 2nd ed. Kluwer, 2002.
 S. S. Pradhan and V. E. Reddy, "A new approach to subband adaptive filtering," IEEE Trans. Signal Processing, vol. 47, pp. 655-664, 1999.
 M. de Courville and P. Duhamel, "Adaptive filtering in subbands using a weighted criterion," IEEE Trans. Signal Processing, vol. 46, pp. 2359- 2371, 1998.
 K. A. Lee and W. S. Gan, "Improving convergence of the NLMS algorithm using constrained subband updates," IEEE Signal Processing Letters, vol. 11, pp. 736-739, 2004.
 J. Apolinario, M. L. Campos, and P. S. R. Diniz, "Convergence analysis of the binormalized data-reusing LMS algorithm," IEEE Trans. Signal Processing, vol. 48, pp. 3235-3242, Nov. 2000.
 S. G. Sankaran and A. A. L. Beex, "Normalized LMS algorithm with orthogonal correction factors," in Proc. Asilomar Conf. on Signals, Systems, and Computers, 1997, pp. 1670-1673.
 B. A. Schnaufer and W. K. Jenkins, "New data-reusing LMS algorithms for improved convergence," in Proc. Asimolar Conf.,, Pacific Groves, CA, May 1993, pp. 1584-1588.
 R. A. Soni, W. K. Jenkins, and K. A. Gallivan, "Acceleration of normalized adaptive filtering data-reusing methods using the Tchebyshev and conjugate gradient methods," in Proc. Int. Symp. Circuits Systems, 1998, pp. 309-312.
 S. L. Gay and J. Benesty, Acoustic Signal Processing for Telecommunication. Boston, MA: Kluwer, 2000.
 T. K. Moon and W. C. Sterling, Mathematical Methods and Algorithms for Signal Processing. Upper Saddle River: Prentice Hall, 2000.
 H. Malvar, Signal Processing with Lapped Transforms. Artech House, 1992.