On Time-Delay Estimation Accuracy Limit Under Phase Uncertainty
Résumé
Accurately determining signal time-delay is crucial across various domains, such as localization and communication systems. Understanding the achievable optimal estimation performance of such technologies, especially during design phases, is essential for benchmarking purposes. One common approach is to derive bounds like the Cramér-Rao Bound (CRB), which directly reflects the minimum achievable estimation error for unbiased estimators. Different studies vary in their approach to deal with the degree of misalignment in the global phase originating from both the transmitter and the receiver in a single input, single output (SISO) link during time-delay estimation assessment. While some treat this phase term as unknown, others assume ideal calibration and compensation. As an alternative to these two opposing approaches, this study adopts a more balanced approach by considering that such a phase can be estimated with a defined uncertainty, a measure that could be implemented in many practical applications. The primary contribution provided lies in the derivation of a closed-form CRB expression for this alternative signal model, which, as observed, exhibits an asymptotic behavior transitioning between the results observed in previous studies, influenced by the uncertainty assumed for the mentioned phase term.
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