An Introduction to Numerical Methods with MATLAB
An Introduction to Numerical Methods with MATLAB
Convergence Analysis of Adaptive Filters Using Normalized Sign-Sign Algorithm
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Improved analysis and design of efficient adaptive transversal filtering algorithms with particular emphasis on noise, input and channel modeling
Journal of Signal Processing Systems
Adaptive threshold nonlinear algorithm for adaptive filters withrobustness against impulse noise
IEEE Transactions on Signal Processing
A unified approach to the steady-state and tracking analyses ofadaptive filters
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Transient analysis of data-normalized adaptive filters
IEEE Transactions on Signal Processing
Hi-index | 0.00 |
This paper studies the convergence analysis of the least mean M-estimate (LMM) and normalized least mean M-estimate (NLMM) algorithms with Gaussian inputs and additive Gaussian and contaminated Gaussian noises. These algorithms are based on the M-estimate cost function and employ error nonlinearity to achieve improved robustness in impulsive noise environment over their conventional LMS and NLMS counterparts. Using the Price's theorem and an extension of the method proposed in Bershad (IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP-34(4), 793---806, 1986; IEEE Transactions on Acoustics, Speech, and Signal Processing, 35(5), 636---644, 1987), we first derive new expressions of the decoupled difference equations which describe the mean and mean square convergence behaviors of these algorithms for Gaussian inputs and additive Gaussian noise. These new expressions, which are expressed in terms of the generalized Abelian integral functions, closely resemble those for the LMS algorithm and allow us to interpret the convergence performance and determine the step size stability bound of the studied algorithms. Next, using an extension of the Price's theorem for Gaussian mixture, similar results are obtained for additive contaminated Gaussian noise case. The theoretical analysis and the practical advantages of the LMM/NLMM algorithms are verified through computer simulations.