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Theoretical Limits and a Practical Estimator for Joint Estimation of Respiration and Heartbeat Rates Using UWB Impulse Radio

In this paper, Cramer-Rao lower bounds are derived for joint estimation of respiration and heartbeat rates via impulse radio ultra-wideband signals. Generic models are employed for displacement functions due to respiration and heartbeat, and the bounds are obtained for the cases of known and unknown channel coefficients. In addition, a two-step suboptimal estimator is proposed, which is based on joint time-delay estimation followed by a least-squares approach. It is shown that the proposed estimator is asymptotically optimal under mild conditions. Simulation studies are performed to evaluate the lower bounds and performance of the proposed estimator for realistic system parameters.