Joint synchronization and detection from samples taken through integrate-and-dump

The problem of sequence and timing error estimation for arbitrary baseband pulse shapes and arbitrary sampling rates in integrate-and-dump optical communications is studied. It is shown that the error probability due to timing error reduces to the same as that with perfect synchronization as the sampling rate goes to infinity, and a lower bound on the error probability is also derived. The general results are then applied to the popular cases of OOK and BPPM. The same problem is also studied for the Gaussian channel with samples taken by an integrate-and-dump filter. A lower bound on the error probability is also derived, and it is shown to be the same as the one with samples taken from the matched filter for NRZ signaling