  This paper investigates the capacity of a communications channel that, in
addition to additive white Gaussian noise, also suffers from interference
caused by a co-existing radar transmission. The radar interference (of short
duty-cycle and of much wider bandwidth than the intended communication signal)
is modeled as an additive term whose amplitude is known and constant, but whose
phase is independent and identically uniformly distributed at each channel use.
The capacity achieving input distribution, under the standard average power
constraint, is shown to have independent modulo and phase. The phase is
uniformly distributed in $[0,2\pi]$. The modulo is discrete with countably
infinitly many mass points, but only finitely many in any bounded interval.
From numerical evaluations, a proper-complex Gaussian input is seen to perform
quite well for weak radar interference. We also show that for very large radar
interference, capacity is equal to $1/2\log (1 + S)$ and a proper-complex
Gaussian input achieves it. It is concluded that the presence of the radar
interference results in a loss of half of the degrees of freedom compared to an
AWGN channel without radar interference.
