Covert Communications in Multi-Channel Slotted ALOHA Systems

Abstract

The fundamental limits of covert communication, where a message is sent from transmitter Alice to intended recipient Bob without detection by an attentive adversary warden Willie, has been considered extensively in recent years at the physical layer. The covert throughput depends critically on the warden's understanding of the characteristics of the radio environment and the type of receiver that he employs, and, as expected, the throughput increases when the warden has some uncertainty about the environment or some non-idealities in his receiver. In this paper, we consider the covert throughput when the adversary is only able to observe the medium access control (MAC) layer in a wireless communication system. In particular, given that the system has a rate of <inline-formula><tex-math notation="LaTeX">$\lambda$</tex-math></inline-formula> packets per slot transmitted over <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> channels by allowable system users, we study the allowable rate <inline-formula><tex-math notation="LaTeX">$\lambda _a$</tex-math></inline-formula> by covert users while maintaining covertness from an attentive warden observing the channel status in a slotted ALOHA system. We characterize performance for wardens with different abilities to discern the number of packets on a given channel, ranging from simple receivers that detect only whether there was a packet present to complicated receivers that can determine the number of packets involved in any collision, and also consider intended recipients Bob with varying abilities to perform multi-packet reception. In contrast to prior work in covert communications, the application considered motivates the consideration of results for finite (often small) observation vector lengths <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> at the adversary. Numerical results are provided both to illustrate the tightness of our achievability regions for the packet transmission rate of the covert transmitters and to demonstrate the covert throughput of the system as a function of <inline-formula><tex-math notation="LaTeX">$\lambda$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> .