On the Impact of Unknown Signals in Passive Radar with Direct Path and Reflected Path Observations

TL;DR

This paper derives the Cramer-Rao bound for joint estimation of time delay and Doppler shift in passive radar systems with unknown signals, considering various practical scenarios and signal conditions.

Contribution

It generalizes existing CRB results to unknown signals in passive radar, providing insights into the number of observations needed for accurate parameter estimation.

Findings

Derived closed-form CRB expressions for unknown signals.

Analyzed the impact of different signal-to-clutter ratios on estimation accuracy.

Extended results to various practical signal and noise conditions.

Abstract

We derive the closed form Cramer-Rao bound (CRB) expressions for joint estimation of time delay and Doppler shift with unknown signals with possibly known structure. The results are especially useful for passive radar where direct path and reflected path signals are present. Time delay and Doppler shift estimation is an important fundamental tool in signal processing which has received extensive study for cases with known transmitted signals, but little study for unknown transmitted signals. The presented results generalize previous results for known transmitted signals and show how many looks from the direct path and the reflected path we need to derive an accurate joint estimation of time delay and Doppler shift. After analysis under a simple common signal-to-clutter-plus-noise ratio (SCNR) model with separated direct and reflected path signals, white clutter-plus-noise and line of sight propagation, extensions to cases with different direct and reflected path SCNRs, correlated clutter-plus-noise, nonseparated direct and reflected path signals and multipath propagation are discussed to support the utility of the CRB with unknown signals.