  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.
