Covert Communication Gains From Adversary’s Ignorance of Transmission Time

Abstract

The recent square root law (SRL) for covert communication demonstrates that Alice can reliably transmit O( √ n) bits to Bob in n uses of an additive white Gaussian noise (AWGN) channel while keeping ineffective any detector employed by the adversary; conversely, exceeding this limit either results in detection by the adversary with high probability or non-zero decoding error probability atBob. This SRL is under the assumption that the adversary knows when Alice transmits (if she transmits); however, in many operational scenarios he does not know this. Hence, here we study the impact of the adversary's ignorance of the time of the communication attempt. We employ a slotted AWGN channel model with T (n) slots each containing n symbol periods, where Alice may use a single slot out of B. A. Bash is with Raytheon BBN Technologies,

Gaussian Signalling for Covert Communications

“…As such, in the rest of this proof we use p 1 (y) to represent p(z). Following (12) and noting that x is independent of n b , we have…”

“…Considering additive white Gaussian noise (AWGN) channels, a square root law was established in [3], which states that Alice can transmit no more than O( √ n) bits in n channel uses covertly and reliably to Bob. Besides, some works in the literature focused on the design and performance analysis of covert communications in practical application scenarios, for example, by considering unknown background noise power [11], ignorance of transmission time [12], noise uncertainty [13], delay constraints [14], [15], channel uncertainty [16], practical modulation [17], uninformed jamming [18], relay networks [19], [20], broadcast channels [21], key generation [22], and artificial noise [23], [24]. In covert communications, for an optimal detector at Willie, we have ξ * = 1 − V T (p 0 , p 1 ), where ξ * is the minimum detection error probability and V T (p 0 , p 1 ) is the total variation between the likelihood function p 0 (y) of the observation y under the null hypothesis (when Alice does transmit to Bob) and the likelihood function p 0 (y) under the alternative hypothesis (when Alice transmits to Bob).…”

Covert Capacity of Non-Coherent Rayleigh-Fading Channels

“…In other words, encoding information in the phase of modulation symbols together with a diffuse power is crucial for optimality. Gaussian signaling has therefore been used to further study covertness over Gaussian and wireless channels, as in [11], [12] to show the benefits of uninformed jammers, in [13] to analyze the role of randomized timing, in [14] to study the effect of randomized power allocation, and in [15] to analyze covert relaying strategies. We note that all aforementioned works exploit random Gaussian codebooks, which simplifies the covertness analysis by reducing the optimal attack to a radiometer.…”

Covert Millimeter-Wave Communication via a Dual-Beam Transmitter

“…For instance, it is shown in [9], [10] that Willie's uncertainty about his noise power helps in achieving positive covert rates. Moreover, by considering slotted AWGN channels, it is proved in [11] that positive covert rates are achievable if the warden does not know when the transmission is taking place. The possibility of achieving positive-rate covert communication is further demonstrated for amplify-and-forward (AF) relaying networks with a greedy relay attempting to transmit its own information to the destination on top of forwarding the source's information [12], dual-hop relaying systems with channel uncertainty [13], a downlink scenario under channel uncertainty and with a legitimate user as cover [14], and a single-hop setup with a full-duplex receiver acting as a jammer [15].…”

“…The expected value of P * e,w form Alice's perspective can be characterized as(11) shown at the top of the next page where P aw (L) = P LOS (d aw ), P aw (N) = 1 − P LOS (d aw ), Γ(·) is the gamma function[22, Eq. (8.310.1)], and g(a,s) k and b (a,s) k are defined above for k ∈ {1, 2}.…”