  The visibilities measured by radio astronomical interferometers include
non-astronomical correlated signals that arise from the local environment of
the array. These correlated signals are especially important in compact arrays
such as those under development for 21\,cm intensity mapping. The amplitudes of
the contaminated visibilities can exceed the expected 21\,cm signal and
represent a significant systematic effect. We study the receiver noise radiated
by antennas in compact arrays and develop a model for how it couples to other
antennas. We apply the model to the Tianlai Dish Pathfinder Array (TDPA), a
compact array of 16, 6-m dish antennas. The coupling model includes
electromagnetic simulations, measurements with a network analyzer, and
measurements of the noise of the receivers. We compare the model to drift-scan
observations with the array and set requirements on the level of antenna
cross-coupling for 21\,cm intensity mapping instruments. We find that for the
TDPA, cross-coupling would have to be reduced by TBD orders of magnitude in
order to contribute negligibly to the visibilities.
