Impact of symbol transition density on timing estimation

The symbol transition density in a digitally modulated signal affects the performance of practical synchronization schemes designed for timing estimation. This work focuses on the derivation of a simple performance limit for the estimation of the time delay of a noisy linearly modulated signal in the presence of various degrees of symbol correlation produced by the various transition densities in the symbol streams. The approach relies on the (Gaussian) unconditional Cramer-Rao bound (UCRB), well known in the array signal processing literature. The derived bound is valid only for the class of quadratic, nondata-aided (NDA) timing recovery schemes, but it becomes asymptotically the true CRB for low-SNR. To illustrate the validity of the derive bound, it is compared with the actual performance achieved by some well-known quadratic NDA timing recovery schemes.