An Adaptive IIR Equaliser

While the IIR Wiener filter exhibits a distinct performance advantage over a FIR filter of the same order when used to equalise a known channel, significant problems are encountered with the former when the channel is unknown or time-varying and an adaptive filter structure is required. An initial approach to the problem might be to postulate an adaptive algorithm such as those suggested in [101] that would recursively estimate the coefficients of the IIR Wiener filter in the same manner as the LMS algorithm [31] is used to estimate the coefficients of the FIR Wiener filter. However, in the process of adaptation, there is a finite probability that the poles of the filter will move outside the unit circle in the z-plane. This can lead to instability if the poles remain outside the unit circle for an extended period [101]. As discussed in chapter 5, adaptive IIR filter algorithms do exist whose convergence in a mean sense is assured but few theoretical results are available with which to predict the MSE convergence properties ot these algorithms.