Performance analysis of the selective coefficient update NLMS algorithm in an undermodeling situation

The selective coefficient update normalized least mean-square (SCU-NLMS) algorithm was proposed to reduce computational complexity while preserving close performance to the full-update NLMS algorithm, which brought it a lot of attention. In practical applications, the length of the unknown system impulse response is not known and, therefore, the length of the adaptive filter can be less than that of the unknown system particularly in situations when the unknown system impulse response is long. In all existing analysis of the SCU-NLMS algorithm, exact modeling of the unknown system is assumed, i.e., the length of the adaptive filter is equal to that of the unknown system impulse response. In this paper, we present mean-square performance analysis for the SCU-NLMS algorithm in an undermodeling situation and assuming independent and identically distributed (i.i.d.) input signals. The analysis model takes into account order statistics employed in the SCU-NLMS algorithm leading to accurate transient and steady state theoretical results. Analysis extends easily to the exact modeling case where expressions quantifying the algorithm mean-square performance are presented and shown to be more accurate than the ones reported in the literature. Simulation experiments validate the accuracy of the theoretical results in predicting the actual behavior of the algorithm.

[1]  Kutluyil Dogancay,et al.  Adaptive filtering algorithms with selective partial updates , 2001 .

[2]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[3]  Khaled A. Mayyas,et al.  Performance analysis of the deficient length LMS adaptive algorithm , 2005, IEEE Transactions on Signal Processing.

[4]  B. Arnold,et al.  A first course in order statistics , 1994 .

[5]  S.C. Douglas,et al.  Analysis and implementation of the max-NLMS adaptive filter , 1995, Conference Record of The Twenty-Ninth Asilomar Conference on Signals, Systems and Computers.

[6]  Ehud Weinstein,et al.  Convergence analysis of LMS filters with uncorrelated Gaussian data , 1985, IEEE Trans. Acoust. Speech Signal Process..

[7]  Patrick A. Naylor,et al.  Selective-Tap Adaptive Filtering With Performance Analysis for Identification of Time-Varying Systems , 2007, IEEE Transactions on Audio, Speech, and Language Processing.

[8]  Tyseer Aboulnasr,et al.  Selective coefficient update of gradient-based adaptive algorithms , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[9]  S. C. Douglas.  Analysis and implementation of the max-NLMS adaptive filterAdaptive discrete cosine transform for feedback active noise control , 1995 .

[10]  Khaled A. Mayyas,et al.  A variable step-size selective partial update LMS algorithm , 2013, Digit. Signal Process..

[11]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[12]  Arie Feuer,et al.  Convergence and performance analysis of the normalized LMS algorithm with uncorrelated Gaussian data , 1988, IEEE Trans. Inf. Theory.

[13]  Stefan Werner,et al.  Partial-update NLMS algorithms with data-selective updating , 2004, IEEE Trans. Signal Process..

[14]  Scott C. Douglas,et al.  Analysis of the multiple-error and block least-mean-square adaptive algorithms , 1995 .

[15]  Saralees Nadarajah,et al.  A Comment on “Partial-Update NLMS Algorithms With Data-Selective Updating” , 2007, IEEE Transactions on Signal Processing.

[16]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[17]  Tyseer Aboulnasr,et al.  Complexity reduction of the NLMS algorithm via selective coefficient update , 1999, IEEE Trans. Signal Process..

[18]  Zakkula Govindarajulu.  Exact Lower Moments of Order Statistics in Samples from the Chi- Distribution (1 d.f.) , 1962 .

[19]  B. Arnold,et al.  A first course in order statistics , 2008 .

[20]  Woo-Jin Song,et al.  An Affine Projection Adaptive Filtering Algorithm With Selective Regressors , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[21]  Woon-Seng Gan,et al.  A lowcomplexity fast converging partial update adaptive algorithm employing variable step-size for acoustic echo cancellation , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.