Undetectable Radios: Covert Communication under Spectral Mask Constraints

We consider the problem of covert communication over continuous-time additive white Gaussian noise (AWGN) channels under spectral mask constraints. In addition to requiring the legitimate receiver to reliably decode, covert communication also requires that the warden is unable to estimate whether or not communication is taking place. The spectral mask at the transmitter restricts excessive radiation beyond the bandwidth of interest. We develop a communication scheme with theoretical guarantees for both covertness and reliability, based on pulse amplitude modulation (PAM) with Binary Phase Shift Keying (BPSK) and root raised cosine (RRC) carrier pulses. Given a fixed time T and a spectral mask with bandwidth parameter W, √ we show that one can transmit O( W T ) bits of information covertly and reliably, and our proposed scheme provides a lower bound on the covert capacity.