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 that 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 that 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.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 that 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 that 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.

IEEE Transactions on Wireless CommunicationsJun 30, 2017451 citations

Covert Communication in the Presence of an Uninformed Jammer

Tamara V. Sobers, Boulat A. Bash, Saikat Guha +2 more

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 $\mathcal{O}(\sqrt{n})$ 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 $\mathcal{O}(n)$ bits covertly and reliably in $n$ uses of an AWGN channel. Here, we consider covert communication of $\mathcal{O}(n)$ 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.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 $\mathcal{O}(\sqrt{n})$ 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 $\mathcal{O}(n)$ bits covertly and reliably in $n$ uses of an AWGN channel. Here, we consider covert communication of $\mathcal{O}(n)$ 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.

arXiv:1608.00698Aug 2, 20162 citations

Covert Communication in Continuous-Time Systems

Ke Li, Don Towsley, Dennis Goeckel

Recent works have considered the ability of transmitter Alice to communicate reliably to receiver Bob without being detected by warden Willie. These works generally assume a standard discrete-time model. But the assumption of a discrete-time model in standard communication scenarios is often predicated on its equivalence to a continuous-time model, which has not been established for the covert communications problem. Here, we consider the continuous-time channel directly and study if efficient covert communication can still be achieved. We assume that an uninformed jammer is present to assist Alice, and we consider additive white Gaussian noise (AWGN) channels between all parties. For a channel with approximate bandwidth W, we establish constructions such that O(WT) information bits can be transmitted covertly and reliably from Alice to Bob in T seconds for two separate scenarios: 1) when the path-loss between Alice and Willie is known; and 2) when the path-loss between Alice and Willie is unknown.Recent works have considered the ability of transmitter Alice to communicate reliably to receiver Bob without being detected by warden Willie. These works generally assume a standard discrete-time model. But the assumption of a discrete-time model in standard communication scenarios is often predicated on its equivalence to a continuous-time model, which has not been established for the covert communications problem. Here, we consider the continuous-time channel directly and study if efficient covert communication can still be achieved. We assume that an uninformed jammer is present to assist Alice, and we consider additive white Gaussian noise (AWGN) channels between all parties. For a channel with approximate bandwidth W, we establish constructions such that O(WT) information bits can be transmitted covertly and reliably from Alice to Bob in T seconds for two separate scenarios: 1) when the path-loss between Alice and Willie is known; and 2) when the path-loss between Alice and Willie is unknown.

arXiv:2001.06932Jan 20, 20201 citation

Covert Communication in Continuous-Time Systems in the Presence of a Jammer

Ke Li, Tamara V. Sobers, Don Towsley +1 more

Covert communication considers the ability of transmitter Alice to communicate reliably to receiver Bob without being detected by warden Willie. Previous work has generally considered a discrete-time model, and, in the standard Alice-Bob-Willie scenario, it has been shown that a discrete-time model captures the salient aspects of the underlying continuous-time covert communications system. However, in the presence of a jammer assisting Alice, where it has been shown in previous work that Alice can achieve a positive covert rate on a discrete-time model, we demonstrate here that a straightforward extension of the discrete-time construction to the continuous-time system does not guarantee a positive covert rate, hence indicating that the discrete-time model does not capture the salient aspects of the continuous-time system in such a scenario. This is because Willie is able to exploit excess bandwidth for co-channel interference suppression, as we demonstrate with an interference cancellation receiver. Hence, for the case when Alice is assisted by an uninformed jammer, we consider the continuous-time channel directly and study whether efficient covert communication can still be achieved against any possible receiver that Willie might employ. By presenting and characterizing an approach much different than that suggested by previous work for discrete-time systems in such a scenario, we establish that $\mathcal {O}(WT)$ information bits can be transmitted covertly and reliably on a continuous-time channel of asymptotic bandwidth $W$ in $T$ seconds, regardless of the receiver that Willie employs. This is done for two separate scenarios: 1) when there is perfect frame synchronization between Alice and the jammer’s signals; 2) when there is no frame synchronization between Alice and the jammer’s signals. Numerical results are provided to validate the theory.Covert communication considers the ability of transmitter Alice to communicate reliably to receiver Bob without being detected by warden Willie. Previous work has generally considered a discrete-time model, and, in the standard Alice-Bob-Willie scenario, it has been shown that a discrete-time model captures the salient aspects of the underlying continuous-time covert communications system. However, in the presence of a jammer assisting Alice, where it has been shown in previous work that Alice can achieve a positive covert rate on a discrete-time model, we demonstrate here that a straightforward extension of the discrete-time construction to the continuous-time system does not guarantee a positive covert rate, hence indicating that the discrete-time model does not capture the salient aspects of the continuous-time system in such a scenario. This is because Willie is able to exploit excess bandwidth for co-channel interference suppression, as we demonstrate with an interference cancellation receiver. Hence, for the case when Alice is assisted by an uninformed jammer, we consider the continuous-time channel directly and study whether efficient covert communication can still be achieved against any possible receiver that Willie might employ. By presenting and characterizing an approach much different than that suggested by previous work for discrete-time systems in such a scenario, we establish that$\mathcal {O}(WT)$information bits can be transmitted covertly and reliably on a continuous-time channel of asymptotic bandwidth$W$in$T$seconds, regardless of the receiver that Willie employs. This is done for two separate scenarios: 1) when there is perfect frame synchronization between Alice and the jammer’s signals; 2) when there is no frame synchronization between Alice and the jammer’s signals. Numerical results are provided to validate the theory.

IEEE Transactions on Wireless CommunicationsDec 16, 202122 citations

Optimal Power Adaptation in Covert Communication With an Uninformed Jammer

Ke Li, Patrick A. Kelly, Dennis Goeckel

Covert communication is achieved if a transmitter (Alice) sends a message to a legitimate receiver (Bob) without being detected by an attentive warden (Willie). Recent work has taken an outage approach that considers an infinite blocklength and analyzes the probability that channel conditions are such that communication is reliable and/or covert. Power adaptation via truncated channel inversion (TCI) has been examined in previous work in an attempt to minimize outage under the covertness constraint. However, the optimality of TCI was not established, and the associated parameters in the TCI scheme were only found numerically. We provide the exact optimal power adaptation schemes under different covertness constraints and with different channel models: 1) when the channel between Willie and an uninformed jammer is AWGN; and 2) when the channel is a Rayleigh fading channel. We also examine the performance improvement of these schemes over standard approaches. This establishes that TCI is optimal in some, but not all, scenarios of interest.Covert communication is achieved if a transmitter (Alice) sends a message to a legitimate receiver (Bob) without being detected by an attentive warden (Willie). Recent work has taken an outage approach that considers an infinite blocklength and analyzes the probability that channel conditions are such that communication is reliable and/or covert. Power adaptation via truncated channel inversion (TCI) has been examined in previous work in an attempt to minimize outage under the covertness constraint. However, the optimality of TCI was not established, and the associated parameters in the TCI scheme were only found numerically. We provide the exact optimal power adaptation schemes under different covertness constraints and with different channel models: 1) when the channel between Willie and an uninformed jammer is AWGN; and 2) when the channel is a Rayleigh fading channel. We also examine the performance improvement of these schemes over standard approaches. This establishes that TCI is optimal in some, but not all, scenarios of interest.

IEEE Transactions on Wireless CommunicationsFeb 21, 202071 citations

Covert Communications When the Warden Does Not Know the Background Noise Power

Dennis Goeckel, Boulat A. Bash, Saikat Guha +1 more

If the warden Willie attempting to detect the transmission knows the statistics of his receiver noise, Alice can transmit no more than O(√n) covert bits reliably to Bob in n channel uses of an AWGN channel. However, if Willie does not know his noise statistics exactly, Alice can covertly transmit O(n) bits. In this letter, Willie lacks knowledge of his channel statistics but observes T(n) length-n codeword slots, where some number may be used by Alice to attempt covert transmission. We show that Willie can often limit Alice to the same performance scaling as when he knows his channel statistics.If the warden Willie attempting to detect the transmission knows the statistics of his receiver noise, Alice can transmit no more than O(√n) covert bits reliably to Bob in n channel uses of an AWGN channel. However, if Willie does not know his noise statistics exactly, Alice can covertly transmit O(n) bits. In this letter, Willie lacks knowledge of his channel statistics but observes T(n) length-n codeword slots, where some number may be used by Alice to attempt covert transmission. We show that Willie can often limit Alice to the same performance scaling as when he knows his channel statistics.

IEEE Communications LettersDec 10, 2015150 citations

\mathcal{O}(\sqrt{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

\mathcal{O}(n)

bits covertly and reliably in

n

uses of an AWGN channel. Here, we consider covert communication of

\mathcal{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.

\mathcal {O}(WT)

information bits can be transmitted covertly and reliably on a continuous-time channel of asymptotic bandwidth

W

T

seconds, regardless of the receiver that Willie employs. This is done for two separate scenarios: 1) when there is perfect frame synchronization between Alice and the jammer’s signals; 2) when there is no frame synchronization between Alice and the jammer’s signals. Numerical results are provided to validate the theory.