Sequence estimation and synchronization from nonsynchronized samples

Recent advances in digital signal processing chips have motivated the study of algorithms for data detection and timing extraction that are easily digitally implemented. These algorithms operate on samples of the output of a matched-filter obtained asynchronously with the actual symbol timing in order to extract their timing and data estimates. 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 (sequence) 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