On MAP symbol detection for ISI channels using the Ungerboeck observation model

In this letter, the well-known problem of a transmission over an additive white Gaussian noise channel affected by known intersymbol interference is considered. We show that the maximum a posteriori (MAP) symbol detection strategy, usually implemented by using the Forney observation model, can be equivalently implemented based on the samples at the output of a filter matched to the received pulse, i.e., based on the Ungerboeck observation model. Although interesting from a conceptual viewpoint, the derived algorithm has a practical relevance in turbo equalization schemes for partial response signalling, where the implementation of a whitening filter can be avoided.