Detection in magnetic recording with cross-track interference

The authors analyze the simple case of an isolated pulse with a single interfering pulse to get insight into the cross-track interference problem. They treat the problem in signal space to gain an intuitive geometric interpretation. The maximum likelihood (ML) detector, the linear minimum mean squared error (LMMSE) detector, and the minimum probability of error (MPE) linear detector are derived. The MPE detector was found to closely approach the performance of the optimal ML nonlinear detector, and to significantly improve on the performance of the LMMSE detector as well as a detector naively designed to match a channel without cross-track interference