Enhancing Covert Communication in OOK Schemes by Phase Deflection

This work proposes an On-Off Keying (OOK) coding scheme for covert communication over complex Gaussian channels. In particular, a transmitter Alice employs phase deflection to covertly transmit information to a receiver Bob, simultaneously ensuring that the communication intent is concealed from a warden Willie. The utilization of phase deflection allows Alice to improve the transmission rate by leveraging Willie’s uncertainty about the received phase, without changing the codebook construction. Considering the asymmetry of the OOK codebook’s input distribution and shape constellation, we first analyze the relationship between the input distribution and the signal amplitude, and then propose a scheme that can achieve covert transmission with the input distribution of the “on” symbol $a_{n}=\mathcal {O}\left ({{\frac {1}{\sqrt {n}}}}\right)$ and an average transmission power $\beta ^{2}=\mathcal {O}({1})$ . We quantify the improvement brought from the phase resource as phase deflection gain and derive its closed-form expression by approximating the Kullback-Leibler (KL) divergence and mutual information through Taylor expansion. Numerical results show that our scheme achieves significant phase deflection gain, and the maximum gain can be achieved by fully utilizing the phase resources through three stages.