Optimal pulse-position modulation order and transmit power in covert communications

Document Type

Journal Article

Publication Title

IEEE Transactions on Vehicular Technology




School of Science




National Key Research and Development Program of China

National Natural Science Foundation of China

Natural Science Foundation of Shandong Province


Li, R., Cui, J., Huang, T., Yang, L., & Yan, S. (2022). Optimal pulse-position modulation order and transmit power in covert communications. IEEE Transactions on Vehicular Technology, 71(5), 5570-5575.



This work tackles the joint optimization of the modulation order L and transmit power P of pulse-position modulation (PPM) in covert communications. Specifically, we consider two scenarios where L used by the PPM at a transmitter Alice for communicating with a receiver Bob is known and unknown to the warden Willie, respectively. In the former scenario, our numerical examination obtained based on our analysis indicates that the optimal L is generally 2 , which is mainly due to the fact that Willie's detection performance increases with L when he knows it. Interestingly, in the latter scenario, we show that the optimal L is 2 when the covertness constraint is strict, while it is 4 when the covertness constraint is relaxed. The main reason is that Willie's detection performance does not depend on L when he does not know it, and the bit error rate for L = 2 is close to that for L = 4 when the signal-to-noise ratio is extremely low caused by the strict covertness constraint, while L = 2 requires less bandwidth and may achieve a higher bandwidth efficiency. Furthermore, we theoretically prove that the covert communication performance is better when Willie does not know L relative to when he knows L.



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