  We consider the problem of covert communication over continuous-time additive
white Gaussian noise (AWGN) channels under spectral mask constraints, wherein
two legitimate parties attempt to communicate reliably in the presence of an
eavesdropper that should be unable to estimate if communication takes place.
The spectral mask constraint is imposed to restrict excessive radiation beyond
the bandwidth of interest. We develop a communication scheme with theoretical
reliability and covertness guarantees based on pulse amplitude modulation (PAM)
with Binary Phase Shift Keying (BPSK) and root raised cosine (RRC) carrier
pulses. Given a fixed transmission duration T and a spectral mask with
bandwidth parameter W, we show that one can reliably and covertly transmit
$O(\sqrt{WT})$ bits of information. We characterize the constant behind the $O$
and show that it is tight under some conditions.
