Cramer-Rao Lower Bounds for the Synchronization of UWB Signals

We present Cramér-Rao lower bounds (CRLBs) for the synchronization of UWB signals which should be tight lower bounds for the theoretical performance limits of UWB synchronizers. The CRLBs are investigated for both single-pulse systems and time-hopping systems in AWGN and multipath channels. Insights are given into the relationship between CRLBs for different Gaussian monocycles. An approximation method of the CRLBs is discussed when nuisance parameters exist. CRLBs in multipath channels are studied and formulated for three scenarios depending on the way multipath interference is treated. We find that a larger number of multipaths implies higher CRLBs and inferior performance of the synchronizers, and multipath interference on CRLBs cannot be eliminated completely except in very special cases. As every estimate of time delay could not be perfect, the least influence of the synchronization error on the performance of receivers is quantified