We address the issue of detecting transmitted symbols when there is a timing error in the sampled waveform, along with intersymbol interference (ISI) and additive channel noise. We built a special trellis to jointly characterize the liming uncertainty and the channel. The method derived here provides the joint maximum a posteriori probability detection for each input symbol and the quantized phase offset of each sample. It also generates 'soft' decisions, which are essential for soft-decision iterative decoding algorithms.
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