On the performance of bit-synchronizers in an ISI channel and a related lower bound

  • Authors:

  • Amin Emad;Norman C. Beaulieu

  • Affiliations:

  • Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada;Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada

  • Venue:
  • GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
  • Year:
  • 2009

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Abstract

The maximum likelihood (ML) criterion for symbol timing estimation is derived for a sequence of pulse amplitude modulated pulses in the presence of intersymbol interference (ISI) and Gaussian noise. The performance of this synchronizer is used as a benchmark to evaluate the performance of other synchronizers in a practical scenario. It is shown that a previous lower bound based on the ISI-free ML synchronizer cannot be used to lower bound the mean square error (MSE) of bit-synchronizers. A detection theory bound (DTB) is applied to the symbol timing recovery problem in an ISI channel and it is shown that this bound is a tight lower bound on the MSE of the ML synchronizer. A simple lower bound on this DTB is derived and it is shown that the simple bound is almost as tight as the well known modified Cramer-Rao bound (MCRB) at moderate values of SNR while it does not suffer from the shortcomings of the MCRB at small values of SNR.