Designing training sequences for carrier frequency estimation in frequency-selective channels

Abstract

A procedure for selecting a training sequence (TS) is developed for frequency estimation in frequency-selective channels. An expression for the unconditional Cramer-Rao bound (UCRB) is obtained by averaging the CRB for frequency estimation over the probability density function of Gaussian random channels. In addition, a necessary and sufficient condition for minimizing the UCRB is derived. Based on these results, a procedure for selecting a TS is developed. Through a computer search, binary TSs up to length 24 are found and tabulated. It is observed that periodic TSs tend to be selected when the TS length is twice the channel duration. Simulation results demonstrate that the proposed TSs can enhance the performance of the maximum likelihood (ML) frequency estimate.