Generalized CRLB for DA and NDA Synchronization of UWB Signals with Clock Offset

In this paper the Cramer-Rao lower bound (CRLB) of an ultra-wideband (UWB) pulse amplitude modulated (PAM) signal with time hopping (TH) code is derived for the practical case where there is an initial unknown relative clock offset between the transmitter and receiver. However, it is assumed that there is a priori information about the probability density function of clock offset. CRLB expressions are developed for both the data- aided (DA) case with an assumed deterministic pilot for synchronization and for the non data-aided (NDA) case based on blind synchronization. It is shown that the influence of the unknown clock offset on the synchronization performance becomes negligible as the number of multipath components increases emphasizing an advantage in UWB links where the multipath is typically rich. Another observation made is that as the SNR decreases, the difference in the CRLB for the NDA and DA cases increases emphasizing the significance of a pilot. Having a priori information helps to achieve a lower CRLB for the timing or clock offset estimation. This improvement is significant in the case of NDA. Finally at very low SNR CRLB of the clock offset converges to the variance of clock offset based on only a priori information.