Sequence estimation and synchronization from nonsynchronized samples

The authors study the problem of maximum-likelihood sequence estimation and synchronization from samples of the output of a matched filter taken at integer multiples of the symbol rate, which is assumed perfectly known by the receiver. A general analysis is presented of sampled receivers that handle arbitrary baseband pulse shapes and arbitrary sampling rates. It is observed that the optimal processing of the matched-filter samples consists of digital interpolation, followed by symbol-by-symbol decoding when sampling is at (or above) the Nyquist rate or Viterbi decoding when sampling is below the Nyquist rate. Performance is studied through the Cramer-Rao bound on mean-square estimation error and a lower-bound on error-probability