Feasibility of LMS adaptation of an all-pass equalizer

In a magnetic recording channel with a two-sided transition response, a low-order all-pass filter can be used to equalize the channel for decision feedback equalization so that its overall transfer function is minimum-phase. A form of the least-mean square (LMS) algorithm is proposed for adapting the poles of an arbitrary-order all-pass filter. An estimate of the gradient of the mean-squared error with respect to the locations of the poles only requires the knowledge of the filter output, and not its internal states. This gradient is characterized numerically, and is shown to yield optimal filter design.