Cramer-Rao lower bound for frequency estimation for coherent pulse train with unknown pulse

Previous results for the Cramer-Rao lower bound (CRLB) of the frequency of a coherent pulse train make severely simplifying assumptions not always valid in real-world applications. Here, the CRLB is derived for the case that the pulse is arbitrary but unknown. This paper poses and answers the important question: Does a priori knowledge of the pulse shape confer a fundamental advantage (i.e., lower CRLB) as compared to the case of known pulse shape? The surprising answer is that such prior knowledge provides very little advantage in any expected real-world scenarios.