Cramer-Rao Lower Bound for Non-coherent TOA Estimation with Impulse Signal

The non-coherent time-of-arrival (TOA) estimations are applied in impulse location for its simplicity. However, the multipath propagation of the narrow pulse results in complicated performance analysis. By fitting the output envelope of energy detection into a exponential decay, we approximately deduce the closed-form Cramer-Rao low bound (CRLB) of TOA estimation. Simulations with non-coherent TOA algorithms, such as threshold crossing (TC) and maximum energy selection (MES), validate the analysis. Furthermore, the integration window and multipath delay spread in ultra-wideband channel are considered to obtain a referable bound.