Cramer-Rao lower bound for data-aided and non-data-aided synchronisation of ultra-wideband signals with clock offset

The Cramer-Rao lower bound (CRLB) for the data-aided (DA) and non-data-aided (NDA) estimation of ultra-wideband (UWB) multipath channel parameters has been previously derived in the literature based on the assumption of a perfectly synchronised clock frequency between the transmitter and the receiver. These results are extended by considering the practical case where there is an initial unknown clock frequency offset that needs to be jointly estimated as part of a successful acquisition of the UWB signal. Intuitively, the additional uncertainty of the clock offset should inflate the CRLB for the estimation of the UWB channel parameters. However, as shown here, this is only valid for a small number of multipath components. As the number of multipath components is increased, the inflation of the CRLB of the channel parameter estimation because of the unknown clock offset becomes negligible. This is of practical significance for UWB propagation channels as they are typically characterised by a large number of multipath components.