**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30184

##### Mean-Square Performance of Adaptive Filter Algorithms in Nonstationary Environments

**Authors:**
Mohammad Shams Esfand Abadi,
John Hakon Husøy

**Abstract:**

**Keywords:**
Adaptive filter,
general framework,
energy conservation,
mean-square performance,
nonstationary environment.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1072333

**References:**

[1] B. Widrow and S. D. Stearns, Adaptive Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1985.

[2] S. Haykin, Adaptive Filter Theory. NJ: Prentice-Hall, 4th edition, 2002.

[3] A. H. Sayed, Fundamentals of Adaptive Filtering. Wiley, 2003.

[4] 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.

[5] 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.

[6] 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.

[7] 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.

[8] ÔÇöÔÇö, "Optimum step size of the sign algorithm for nonstationary adaptive filtering," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1897-1901, 1990.

[9] 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.

[10] 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.

[11] ÔÇöÔÇö, "A unified approach to the steady-state and tracking analyses of adaptive filters," IEEE Trans. Signal Processing, vol. 49, pp. 314-324, 2001.

[12] 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.

[13] 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.

[14] 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.

[15] 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.

[16] 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.

[17] 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.

[18] 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.

[19] 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.

[20] P. S. R. Diniz, Adaptive Filtering: Algorithms and practical implementation, 2nd ed. Kluwer, 2002.

[21] S. S. Pradhan and V. E. Reddy, "A new approach to subband adaptive filtering," IEEE Trans. Signal Processing, vol. 47, pp. 655-664, 1999.

[22] M. de Courville and P. Duhamel, "Adaptive filtering in subbands using a weighted criterion," IEEE Trans. Signal Processing, vol. 46, pp. 2359- 2371, 1998.

[23] 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.

[24] 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.

[25] 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.

[26] 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.

[27] 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.

[28] S. L. Gay and J. Benesty, Acoustic Signal Processing for Telecommunication. Boston, MA: Kluwer, 2000.

[29] T. K. Moon and W. C. Sterling, Mathematical Methods and Algorithms for Signal Processing. Upper Saddle River: Prentice Hall, 2000.

[30] H. Malvar, Signal Processing with Lapped Transforms. Artech House, 1992.