A Variable Step Size LMS Algorithm

A Variable Step Size LMS Algorithm - A Variable Step Size...

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A Variable Step Size LMS Algorithm w,= W. Y. Chen Bell Communications Research Morristown, New Jersey Wl w2 ' wn k R. A. Haddad Polytechnic University Brooklyn, New York x,= ABSTRACT The LMS algorithm has been used in many adaptive signal processing systems. The LMS algorithm is robust and it needs the least computation power. The adjustment of step size in the LMS algorithm affects both the convergence speed a.nd the residual error level. To improve the performance of an adaptive signal processing system, fast Kalman algorithms have been developed. However, these fast algorithms need at least four times more computation power than the conventional LMS algorithm. Besides, many of these fast algorithms could become numerically unstable if they are implemented with limited precision computational hardware. In this paper, a variable step size LMS algorithm is proposed. The variable step size LMS algorithm has a big step size at the beginning, for a maximum convergence speed, and a much smaller step size after the convergence, for a minimum residual error. The variable step size algorithm is derived according to the shortest distance norm between the Kalman gain and the LMS gain vectors. The exponential window is included in the derivation for maintaining a non-zero stable step size. Both the convergence speed and the stable value of the step size can be adjusted. Little additional multiplication is required to implement this variable step size LMS algorithm. z@) z(k-I) . s(k-'n+l) 1. Introduction The LMS algorithm['] has been used in many channel equalization and echo cancellation applications. The LMS algorithm is robust and it needs the least computation power. However, the adjustment of step size in the LMS algorithm affects both the convergence speed and the residual error level. If the step size of the LMS algorithm can be adjusted in a proper way, the performance of the LMS algorithm can be enhanced. We would like to see a big step size at the beginning of the convergence process to have the fastest convergence speed and a smaller step size after the convergence to have the smallest residual error level. The algorithm for the application of Kalman filtering['] to channel equalization has a similar structure to the LMS algorithm except for the gain vectors and related calculations. The LMS algorithm has a fixed gain coming from the data vector multiplied by a fixed step size. The Kalman algorithm has a variable gain coming from the data vector multiplied by a time variable matrix. In general the norm of the time variable matrix varies from large values to almost zero in a decaying fashion. Hence, the information in the norm can be used to control the step size of a variable step size LMS algorithm. In this paper, a variable step size LMS algorithm is proposed.
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This note was uploaded on 04/24/2010 for the course COMUNICATI 1 taught by Professor 1 during the Spring '10 term at Xiamen University.

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A Variable Step Size LMS Algorithm - A Variable Step Size...

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