Adaptation of an all-pass equalizer for decision feedback equalization

Recording channels using decision feedback equalization require a minimum phase response and white noise at the detector to achieve maximum signal-to-noise ratio. A low-order all-pass filter can equalize the feedforward path so that it approximately achieves a minimum phase response. In this paper, we describe an adaptive algorithm for iteratively determining the optimal transfer function of the all-pass filter. Adaptation is based on estimating the gradient of the mean-square error with respect to the poles of the filter. This estimate is then used to update the positions of the poles. One simplifying feature of this technique is that these gradients are determined by applying the output of the all-pass to low-order finite impulse response (FIR) filters. We do not require values from the internal states of the filter, The proposed adaptation algorithm is characterized for first- and second-order all-pass filters over a range of storage densities. The optimality of the resulting equalizer is evaluated as a function of the order of the FIR filters used in estimating the gradients.