On the Ungerboeck and Forney Observation Models for Offset QPSK

The Ungerboeck and Forney observation models for offset QPSK are derived for three different representations for OQPSK. The representations and their corresponding Ungerboeck observation models are different, but the trellises used by the maximum likelihood sequence estimators possess the same complexity. The Forney observation models are obtained in straight-forward way for the bit-based representations for OQPSK, but there is no Forney observation model in the traditional sense for the symbol-based OQPSK representation. In the case of the symbol-based OQPSK representation, a method for whitening the resulting non-linear system is described.