Covert Communication in the Presence of an Uninformed Jammer

Abstract

Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to O( √ n) bits in n channel uses. However, this assumes Willie has an accurate statistical characterization of the channel. When Willie has uncertainty about such and his receiver is limited to a threshold test on the received power, Alice can transmit covertly with a power that does not decrease with n, thus conveying O(n) bits covertly and reliably in n uses of an AWGN channel. Here, we consider covert communication of O(n) bits in n channel uses while generalizing the environment and removing any restrictions on Willie's receiver. We assume an uninformed "jammer" is present to help Alice, and we consider AWGN and block fading channels. In some scenarios, Willie's optimal detector is a threshold test on the received power. When the channel between the jammer and Willie has multiple fading blocks per codeword, a threshold test on the received power is not optimal. However, we establish that Alice can remain covert with a transmit power that does not decrease with n even when Willie employs an optimal detector.

Multi-Antenna Jamming in Covert Communication

“…Main Contribution: As mentioned above, in this work we explore the effect of multiple antennas of an uninformed jammer on covert communication. Where we do not consider the problem of whether a strictly positive rate can be achieved or not, since this was already shown, for the case of a single antenna jammer in [8]; thus, the same consequences follow.…”

“…The result in Lemma 1 shows that the addition of multiple antennas at the jammer provides a gain of h † jw VXV † h jw /|h aw | 2 with respect to the case of a single antenna jammer as given in [8].…”

“…This was shown in [8] by using Fisher-Neyman factorization and likelihood ratio ordering techniques. One can realize that, given P j , the average received power P rav w is a Gamma r.v.…”

“…This paper focuses on covert communication with a positive covert rate. Thus, we assume that the jammer assists Alice to create uncertainty at Willie's decoder continuously, regardless of whether or not Alice transmits (Similarly to [8]). We note that the case where the jammer assists Willie is out of this paper's scope, and may be considered as future work.…”

“…Similar to previous works on covert communication ([1], [7], [8], [22]), we assume that Alice and Bob share a codebook which is not revealed to Willie; however, Willie knows its statistics. This codebook is generated by independently drawing symbols from a zero-mean complex Gaussian distribution with variance P a and it is assumed to be used only once.…”