Lower bound on the achievable DSP performance for localizing step-like continuous signals in noise

Estimating the time of arrival (TOA) of step-like signals (e.g., a rectangular pulse), which are, theoretically, of infinite bandwidth, is essential for many applications. In modern signal processing, the TOA estimator is implemented by digital signal processing (DSP) techniques. Existing tools for studying the TOA estimation performance do not take into consideration the estimation error caused by the finite sampling rate of the system. In this paper, we present a new Cramér-Rao type lower bound that is used to evaluate the achievable performance of TOA estimation in a given processing sampling rate. We use it to refer to the important question of what processing sampling rate to use when localizing a step-like signal. We show that for a given signal-to-noise ratio (SNR), there exists a certain sampling rate threshold beyond which performance does not improve by increasing the sampling rate, and we show how to find it.