# Pseudo-Fractional Tap-Length Learning Based Applied Soft Computing for Structure Adaptation of LMS in High Noise Environment

## Abstract

The structure of an adaptive time varying linear filter largely depends on its tap-length and the delay units connected to it. The no of taps is one of the most important structural parameters of the liner adaptive filter. Determining the system order or length is not a trivial task. Fixing the tap-length at a fixed value sometimes results in unavoidable issues with the adaptive design like insufficient modeling and adaptation noise. On the other hand a dynamic tap-length adaptation algorithm automatically finds the optimum order of the adaptive filter to have a tradeoff between the convergence and steady state error. It is always difficult to get satisfactory performance in high noise environment employing an adaptive filter for any identification problem. High noise decreases the Signal to noise ratio and sometimes creates wandering issues. In this chapter an improved pseudo-fractional tap-length selection algorithm has been proposed and analyzed to find out the optimum tap-length which best balances the complexity and steady state performance specifically in high noise environment. A steady-state performance analysis has been presented to formulate the steady state tap-length in correspondence with the proposed algorithm. Simulations and results are provided to observe the analysis and to make a comparison with the existing tap-length learning methods.

## Keywords

Adaptive filter Normalized Lease Mean Square (NLMS) algorithm Tap-length Structure adaptation System identification Mean Square Error (MSE) Signal to Noise Ratio (SNR) High noise environment## References

- 1.B. Widrow, S.D. Sterns,
*Adaptive Signal Processing*(Prentice Hall Inc., Englewood Cliffs, 1985)MATHGoogle Scholar - 2.S. Haykin,
*Adaptive Filter Theory*(Prentice Hall Inc, Englewood Cliffs, 1996)Google Scholar - 3.J.J. Shnyk, Frequency domain and multirate adaptive filtering, IEEE Signal Process. Mag.
**9**(1), 14–37 (1992)Google Scholar - 4.Y. Gu, K. Tang, H. Cui, W. Du, Convergence analysis of a deficient-length LMS filter and optimal-length to model exponential decay impulse response. IEEE Signal Process. Lett.
**10**, 4–7 (2003)CrossRefGoogle Scholar - 5.K. Mayyas, Performance analysis of the deficient length LMS adaptive algorithm. IEEE Trans. Signal Process.
**53**(8), 2727–2734 (2005)CrossRefMathSciNetGoogle Scholar - 6.Y. Gong, C.F.N. Cowan, A novel variable tap-length algorithm for linear adaptive fitlers, in
*Proceedings of th IEEE International Conference on Acoustics, Speech, and Signal Processing*, Montreal, QC, Canada, May 2004Google Scholar - 7.Y. Gong, C.F.N. Cowan, An LMS style variable tap-length algorithm for structure adaptation. IEEE Trans. Signal Process.
**53**(7), 2400–2407 (2005)CrossRefMathSciNetGoogle Scholar - 8.Y. Gong, C.F.N. Cowan, Structure adaptation of linear MMSE adaptive filters, Proc. Inst. Elect. Eng. Vis. Image Signal Process.
**151**(4), 271–277 (2004)Google Scholar - 9.C. Schüldt, F. Lindstromb, H. Li, I. Claesson, Adaptive filter length selection for acoustic echo cacellation. Sig. Process.
**89**, 1185–1194 (2009)CrossRefMATHGoogle Scholar - 10.F. Riera-Palou, J.M. Noras, D.G.M. Cruickshank, Linear equalizers with dynamic and automatic length selection, Electron. Lett.
**37**, 1553–1554 (2001)Google Scholar - 11.Z. Pritzker, A. Feuer, Variable length stochastic gradient algorithm. IEEE Trans. Signal Process.
**39**, 997–1001 (1991)CrossRefGoogle Scholar - 12.Y.K. Won, R.H. Park, J.H. Park, B.U. Lee, Variable LMS algorithm using the time constant concept. IEEE Trans. Consum. Electron.
**40**, 655–661 (1994)CrossRefGoogle Scholar - 13.C. Rusu, C.F.N. Cowan, Novel stochastic gradient adaptive algorithm with variable length, in
*Proceedings of the European Conference on Circuit Theory and Design (ECCTD 2001),*Espoo, Finland, pp. 341–344, Aug 2001Google Scholar - 14.T. Aboulnasr, K. Mayyas, A robust variable step-size LMS-type algorithm: analysis and simulations. IEEE Trans. Signal Process.
**45**, 631–639 (1997)CrossRefGoogle Scholar - 15.Y. Gu, K. Tang, H. Cui, W. Du, LMS algorithm with gradient descent filter length. IEEE Signal Process. Lett.
**11**(3), 305–307 (2004)CrossRefGoogle Scholar - 16.A. Kar, R. Nath, A. Barik, A VLMS based pseudo-fractional order estimation algorithm, in
*Proceedings of the ACM Sponsored International Conference on Communication, Computing and Security (ICSSS-11, NIT RKL),*pp. 119–123, Feb 2011Google Scholar - 17.H. Yu, Z. Liu, G. Li, A VSLMS style tap-length learning algorithm for structure adaptation, in
*Proceedings of the IEEE International Conference Communication Systems (ICCS 2008)*, pp. 503–508, 19–21 Nov 2008Google Scholar - 18.H.-C. Huang, J. Lee, A new variable step-size NLMS algorithm and its performance analysis. IEEE Trans. Signal Process.
**60**(4), 2055–2060 (2012)CrossRefMathSciNetGoogle Scholar - 19.A. Kar, A. Barik, R. Nath, An improved order estimation of MSF for stereophonic acoustic echo cancellation, in
*Proceedings of the Springer International Conference on Information System Design and Intelligent Applications (InconINDIA-12)*, Vizag, pp. 319–327, Jan 2011Google Scholar - 20.Y. Gang, N. Li, A. Chambers, Steady-state performance analysis of a variable tap-length LMS algorithm, IEEE Trans. Signal Process.
**56**(2), 839–835 (2008)Google Scholar