An algorithm of step-size factor adjustment in the adaptive filter

In this paper a model of transversal filter is presented to study the adaptive match of the time-variant channel. A least mean square error filtering method is used to obtain the weighting coefficients of the filter.
The factor of step size μ is always in need when using the steepst desent method as well as the LMS algorithm to solve the adaptive iteration equation. In the past, only a limit as 0<μ<1/λmax was given to the iterative step size μ, where λmax is a maximum eigenvalue of the data correlation matrix and μ remains as a constant during the iteration. However, it is very difficult to find an optimal value of μ. In case of small μ, the convergence speed of the adaptive iteration equation is rather slow. On the contrary, the function of error energy will oscilate or diverge if the μ is too big. With the purpose to speed the convergence of the iteration equation of the adaptive filtering,in this paper an adaptive adjustment of iterative step size is deduced. The result of the computer simulation shows that, in the case of using the adaptive μ. the convergence speed of the iteration equation is increased about 2 times in comparison with constant μ. The study suggests that the adaptive filter with adaptive μ will be able to follow the time-variant characteristics of the channel.