Optimum Radar Signal-Filter Pairs in a Cluttered Environment

In a recent paper on radar detection in clutter, the authors stated that the signal-to-interference ratio
\rho_{cf} (u)
obtained with the signal
u
and its optimum filter can have stationary points which are not stationary points of
\rho_{mf} (u)
, the signal-to-interference ratio obtained with
u
and its matched filter, even when the clutter distribution in range and Doppler is symmetric. This letter strengthens this statement and exhibits an example to support it. The stronger statement is the following: Even for symmetric clutter distributions, the global maximum of
\rho_{cf}
can exceed the global maximum of
\rho_{mf}
.