Steady State Mean Square Analysis of Standard Maximum Versoria Criterion Based Adaptive Algorithm

The Maximum Versoria Criterion (MVC) based adaptive algorithm has recently gained the attention of researchers because of its robustness against impulsive interference and reduced complexity. In this brief, the steady-state Excess Mean Square Error (EMSE) analysis of the standard MVC algorithm is done using the energy conservation relation. For the Gaussian noise case, quadratic equation that can provide the exact value of theoretical steady state EMSE is obtained without any assumptions other than the conventional ones and the Price’s theorem. For the non-Gaussian case, an approximate solution using Taylor’s expansion is derived. Experimental results validate the obtained theoretical findings.

[1]  Tareq Y. Al-Naffouri,et al.  Transient analysis of adaptive filters with error nonlinearities , 2003, IEEE Trans. Signal Process..

[2]  Yi Yu,et al.  Performance Analysis of the Robust Diffusion Normalized Least Mean ${p}$ -Power Algorithm , 2018, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  Sheng Zhang,et al.  Maximum Versoria Criterion-Based Robust Adaptive Filtering Algorithm , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[4]  Badong Chen,et al.  Robust Normalized Least Mean Absolute Third Algorithms , 2019, IEEE Access.

[5]  Tareq Y. Al-Naffouri,et al.  Adaptive Filters with Error Nonlinearities: Mean-Square Analysis and Optimum Design , 2001, EURASIP J. Adv. Signal Process..

[6]  Paulo Sergio Ramirez,et al.  Fundamentals of Adaptive Filtering , 2002 .

[7]  Ali H. Sayed,et al.  A unified approach to the steady-state and tracking analyses of adaptive filters , 2001, IEEE Trans. Signal Process..

[8]  Badong Chen,et al.  A Separable Maximum Correntropy Adaptive Algorithm , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

[9]  Xudong Wang,et al.  The Steady-State Mean-Square Error Analysis for Least Mean p -Order Algorithm , 2009, IEEE Signal Process. Lett..

[10]  Sheng Zhang,et al.  Affine Projection Versoria Algorithm for Robust Adaptive Echo Cancellation in Hands-Free Voice Communications , 2018, IEEE Transactions on Vehicular Technology.

[11]  Robert Price,et al.  A useful theorem for nonlinear devices having Gaussian inputs , 1958, IRE Trans. Inf. Theory.

[12]  Shiyuan Wang,et al.  Robust Multikernel Maximum Correntropy Filters , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

[13]  Yingsong Li,et al.  A Kernel Recursive Maximum Versoria-Like Criterion Algorithm for Nonlinear Channel Equalization , 2019, Symmetry.

[14]  Yanyan Wang,et al.  Noise-Free Maximum Correntropy Criterion Algorithm in Non-Gaussian Environment , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

[15]  Lu Lu,et al.  Recursive Geman–McClure Estimator for Implementing Second-Order Volterra Filter , 2018, IEEE Transactions on Circuits and Systems II: Express Briefs.

[16]  Yi Yu,et al.  Behavior of the LMS algorithm with hyperbolic secant cost , 2020, J. Frankl. Inst..

[17]  Shiyuan Wang,et al.  Robust least mean logarithmic square adaptive filtering algorithms , 2019, J. Frankl. Inst..

[18]  Suleyman Serdar Kozat,et al.  A Novel Family of Adaptive Filtering Algorithms Based on the Logarithmic Cost , 2013, IEEE Transactions on Signal Processing.

[19]  J. Lawrence,et al.  A Catalog of Special Plane Curves , 2013 .

[20]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..