  We derive a detector that optimizes the target detection performance of any
single-input single-output noise radar satisfying the following properties: it
transmits Gaussian noise, it retains an internal reference signal for matched
filtering, all external noise is additive white Gaussian noise, and all signals
are measured using heterodyne receivers. This class of radars, which we call
noise-type radars, includes not only many types of standard noise radars, but
also a type of quantum radar known as quantum two-mode squeezing radar. The
detector, which we derive using the Neyman-Pearson lemma, is not practical
because it requires foreknowledge of a target-dependent correlation coefficient
that cannot be known beforehand. (It is, however, a natural standard of
comparison for other detectors.) This motivates us to study the family of
Neyman-Pearson-based detectors that result when the correlation coefficient is
treated as a parameter. We derive the probability distribution of the
Neyman-Pearson-based detectors when there is a mismatch between the pre-chosen
parameter value and the true correlation coefficient. We then use this result
to generate receiver operating characteristic curves. Finally, we apply our
results to the case where the correlation coefficient is small. It turns out
that the resulting detector is not only a good one, but that it has appeared
previously in the quantum radar literature.
