Optimal Channel Shortening Equalization for MIMO ISI Channels

We consider the problem of channel shortening equalization to perform reduced complexity detection for MIMO channels with intersymbol interference and additive Gaussian noise, the problem is to find a MIMO equalizer and a partial response MIMO target filter such that the combination produces the best detection performance. We show the existence of an infinite family of optimal equalizers and targets that satisfy the a posteriori equivalence condition. Furthermore, these solutions are intimately related to MIMO decision feedback equalizers designed with the "monk determinant" constraint on the feedback filter. These results generalize some recent results on channel shortening based on a posteriori equivalence to the MIMO setting.