M. Rupp:

"Asymptotic equivalent analysis of the LMS algorithm under linearly filtered processes";

EURASIP Journal on Advances in Signal Processing,2016:18(2016), 18; 1 - 16.

While the least mean square (LMS) algorithm has been widely explored for some specific statistics of the driving

process, an understanding of its behavior under general statistics has not been fully achieved. In this paper, the mean

square convergence of the LMS algorithm is investigated for the large class of linearly filtered random driving

processes. In particular, the paper contains the following contributions: (i) The parameter error vector covariance

matrix can be decomposed into two parts, a first part that exists in the modal space of the driving process of the LMS

filter and a second part, existing in its orthogonal complement space, which does not contribute to the performance

measures (misadjustment, mismatch) of the algorithm. (ii) The impact of additive noise is shown to contribute only to

the modal space of the driving process independently from the noise statistic and thus defines the steady state of the

filter. (iii) While the previous results have been derived with some approximation, an exact solution for very long filters

is presented based on a matrix equivalence property, resulting in a new conservative stability bound that is more

relaxed than previous ones. (iv) In particular, it will be shown that the joint fourth-order moment of the decorrelated

driving process is a more relevant parameter for the step-size bound rather than, as is often believed, the second-order

moment. (v) We furthermore introduce a new correction factor accounting for the influence of the filter length as well

as the driving process statistic, making our approach quite suitable even for short filters. (vi) All statements are

validated by Monte Carlo simulations, demonstrating the strength of this novel approach to independently assess the

influence of filter length, as well as correlation and probability density function of the driving process

While the least mean square (LMS) algorithm has been widely explored for some specific statistics of the driving

process, an understanding of its behavior under general statistics has not been fully achieved. In this paper, the mean

square convergence of the LMS algorithm is investigated for the large class of linearly filtered random driving

processes. In particular, the paper contains the following contributions: (i) The parameter error vector covariance

matrix can be decomposed into two parts, a first part that exists in the modal space of the driving process of the LMS

filter and a second part, existing in its orthogonal complement space, which does not contribute to the performance

measures (misadjustment, mismatch) of the algorithm. (ii) The impact of additive noise is shown to contribute only to

the modal space of the driving process independently from the noise statistic and thus defines the steady state of the

filter. (iii) While the previous results have been derived with some approximation, an exact solution for very long filters

is presented based on a matrix equivalence property, resulting in a new conservative stability bound that is more

relaxed than previous ones. (iv) In particular, it will be shown that the joint fourth-order moment of the decorrelated

driving process is a more relevant parameter for the step-size bound rather than, as is often believed, the second-order

moment. (v) We furthermore introduce a new correction factor accounting for the influence of the filter length as well

as the driving process statistic, making our approach quite suitable even for short filters. (vi) All statements are

validated by Monte Carlo simulations, demonstrating the strength of this novel approach to independently assess the

influence of filter length, as well as correlation and probability density function of the driving process

Adaptive gradient-type filters, Mismatch, Misadjustment

http://dx.doi.org/10.1186/s13634-015-0291-1

http://publik.tuwien.ac.at/files/PubDat_248333.pdf

Created from the Publication Database of the Vienna University of Technology.