The tap-leaky LMS algorithm in Problem 13.8 may be obtained by minimizing the cost funct...

The tap-leaky LMS algorithm in Problem 13.8 may be obtained by minimizing the cost function

where c is a constant and e(n) is the error between the desired filter output and the actual filter output. Show that the minimization of with respect to the filter coefficient vector leads to the following tap-leaky LMS algorithm.

Reference of Problem 13.8

The tap-leaky LMS algorithm proposed by Gitlin, Meadors, and Weinstein (1982) may be expressed as

where is the step size, and is the data vector at time n. Determine the condition for the convergence of the mean value of