EURASIP Journal on Applied Signal Processing
Volume 2005 (2005), Issue 3, Pages 426-438
doi:10.1155/ASP.2005.426

Cramér-Rao Lower Bounds for the Synchronization of UWB Signals

Jian Zhang, Rodney A. Kennedy, and Thushara D. Abhayapala

National ICT Australia (NICTA) and the Department of Telecommunications Engineering, Research School of Information Sciences and Engineering, The Australian National University, Canberra ACT 0200, Australia

Received 30 September 2003; Revised 10 February 2004

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.