  Coherent electron cooling is a promising technique to cool high-intensity
hadron bunches by imprinting the noise in the hadron beam on a beam of
electrons, amplifying the electron density modulations, and using them to apply
cooling kicks to the hadrons. The typical size for these perturbations can be
on the $\mu$m scale, allowing us to extend the reach of classical stochastic
cooling by several orders of magnitude. However, it is crucial to ensure that
the electron and hadron beams are longitudinally aligned within this same
$\mu$m scale. In order to provide fast feedback for this process, we discuss
the extension of signal suppression to coherent electron cooling, and show in
both theory and simulation that certain components of the spectral noise in the
hadron beam will be predictably modified at the several percent level, which
may be detected by observations of the radiation of the hadron beam.
