Theoretical Limits for Estimation of Periodic Movements in Pulse-Based UWB Systems

In this paper, Cramer-Rao lower bounds (CRLBs) for estimation of signal parameters related to periodically moving objects in pulse-based ultra-wideband (UWB) systems are presented. The results also apply to estimation of vital parameters, such as respiration rate, using UWB signals. In addition to obtaining the CRLBs, suboptimal estimation algorithms are also presented. First, a single-path channel with additive white Gaussian noise is considered, and closed-form CRLB expressions are obtained for sinusoidal object movements. Also, a two-step suboptimal algorithm is proposed, which is based on time delay estimation via matched filtering followed by least-squares estimation, and its asymptotic optimality property is shown in the limit of certain system parameters. Then, a multipath environment is considered, and exact and approximate CRLB expressions are derived. Moreover, suboptimal schemes for parameter estimation are studied. Simulation studies are performed for the estimation of respiration rates in order to evaluate the lower bounds and performance of the suboptimal algorithms for realistic system parameters.