A Compact CRB for the Single Source Conditional Signal Model with Application to Delay-Doppler-Phase Estimation of Band-Limited Signals

Abstract

The derivation of tight estimation lower bounds is a key player to design and assess the performance of new estimators. In this contribution, we derive a new compact Cramér-Rao bound (CRB) for the conditional signal model, where the deterministic parameter's vector includes a real positive amplitude and the signal phase. Then, such CRB is particularized to the delay, Doppler, phase and amplitude estimation with band-limited (narrowband) signals, where transmitter and receiver are in relative uniform radial movement. The latter expression is especially easy to use because it only depends on the signal samples. We provide illustrative results for a representative Global Navigation Satellite System positioning example.