Refer to Problem 9.49 and answer the following questions. a. Determine the maximum...

Refer to Problem 9.49 and answer the following questions.

a. Determine the maximum value of that can be used to ensure that the equalizer coefficients converge during operation in the adaptive mode.

b. What is the variance of the self-noise generated by the three-tap equalizer when operating in an adaptive mode, as a function of would you select?

c. If the optimum coefficients of the equalizer are computed recursively by the method of steepest descent, the recursive equation can be expressed in the form

where I is the identity matrix. The above represents a set of three coupled first order difference equations. They can be decoupled by a linear transformation that diagonalizes the matrix Γ. That is, Γ = UΛUt where Λ is the diagonal matrix having the eigenvalues of Γ as its diagonal elements and U is the (normalized) modal matrix that can be obtained from your answer to Problem 9.49(b). Let C ‘ = UtC and determine the steady-state solution for C ‘. From this, evaluate C = (Ut )−1C ‘ = UC ‘ and, thus, show that your answer agrees with the result obtained in Problem 9.49(a).