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arXiv:1901.04914 · IEEE Transactions on Vehicular Technology

Robust Power Allocation in Covert Communication: Imperfect CDI

Moslem Forouzesh, Paeiz Azmi, Nader Mokari, Dennis Goeckel

Published Apr 29, 2021• 25 citations
arXivHTMLPDF

Abstract

The study of the fundamental limits of covert communications, where a transmitter Alice wants to send information to a desired recipient Bob without detection of that transmission by an attentive and capable warden Willie, has emerged recently as a topic of great research interest. Previous work has assumed that the distribution of the multipath fading on the channel, which we term the channel distribution information (CDI), is known to Alice, hence facilitating her characterization of Willie's capabilities to detect the signal. However, in practice, Willie tends to be passive and the environment heterogeneous, implying a lack of signaling interchange between the transmitter and Willie makes it difficult if not impossible for Alice to estimate the CDI exactly and provide covertness guarantees. In this paper, we address this issue by developing covert communication schemes for various assumptions on Alice's imperfect CDI: 1) when the transmitter knows the channel distribution is within some distance of a nominal distribution; 2) when only the mean and variance of the channel distribution are available; 3) when Alice knows the channel distribution is complex Gaussian but the variance is unknown. In each case, we formulate new optimization problems to find the power allocations that maximize covert rate subject to a covertness requirement under uncertain CDI. Moreover, Willie may be able to estimate CDI exactly or be faced with an error in estimation, and we investigate two these issues. Numerical results are presented to compare the proposed schemes from various aspects, for attaining desirable covert system performance.

DOI
10.1109/tvt.2021.3076709

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The study of the fundamental limits of covert communications, where a transmitter Alice wants to send information to a desired recipient Bob without detection of that transmission by an attentive and capable warden Willie, has emerged recently as a topic of great research interest. Previous work has assumed that the distribution of the multipath fading on the channel, which we term the channel distribution information (CDI), is known to Alice, hence facilitating her characterization of Willie's capabilities to detect the signal. However, in practice, Willie tends to be passive and the environment heterogeneous, implying a lack of signaling interchange between the transmitter and Willie makes it difficult if not impossible for Alice to estimate the CDI exactly and provide covertness guarantees. In this paper, we address this issue by developing covert communication schemes for various assumptions on Alice's imperfect CDI: 1) when the transmitter knows the channel distribution is within some distance of a nominal distribution; 2) when only the mean and variance of the channel distribution are available; 3) when Alice knows the channel distribution is complex Gaussian but the variance is unknown. In each case, we formulate new optimization problems to find the power allocations that maximize covert rate subject to a covertness requirement under uncertain CDI. Moreover, Willie may be able to estimate CDI exactly or be faced with an error in estimation, and we investigate two these issues. Numerical results are presented to compare the proposed schemes from various aspects, for attaining desirable covert system performance.
It is challenging to covert communication under channel distribution information (CDI) uncertainty caused by limited feedback and rapid-changing channels. This letter investigates covert communication in uplink non-orthogonal multiple access (NOMA) systems under CDI uncertainty, where a covert user (CU) and reliable user (RU) transmit messages to a legitimate receiver (Bob) threatened by a warden (Willie). RU not only transmits its public messages but also helps CU to send private messages against Willie’s detection. To protect CU’s transmission with imperfect CDI, we first study the worst case for NOMA users and obtain a lower bound of the worst-case detection error probability (DEP). In addition, both closed-form expressions for RU and CU’s connection outage probabilities are derived. Constrained by the DEP and connection outage probability, we maximize the expected covert rate (ECR) and derive the optimal power settings for RU and CU under imperfect CDI. Numerical results show that the proposed robust power setting scheme achieves a positive maximum ECR despite CDI uncertainty causing the reduction of covertness performance.
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)\mathcal{O}(\sqrt{n})O(n​) bits in nnn 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 nnn, thus conveying O(n)\mathcal{O}(n)O(n) bits covertly and reliably in nnn uses of an AWGN channel. Here, we consider covert communication of O(n)\mathcal{O}(n)O(n) bits in nnn 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 nnn even when Willie employs an optimal detector.
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.
This dissertation studies covert wireless communications where a transmitter (Alice) intends to transmit messages to a legitimate receiver (Bob) such that the presence of the message is hidden from an attentive warden (Willie). Here we consider pertinent aspects of covert communications that focus on moving such systems closer to implementation. For example, previous studies use the standard discrete-time communication model when analyzing covert communications, since this is commonly assumed without loss of generality in standard communication theory. However, it is not clear that such a model captures the salient aspects of the continuous-time covert communications problem. A power detector that is optimal for the warden in a discrete-time covert communications scenario may not be optimal on a continuous- time model. Thus, it is of interest to consider this more realistic model for physical channels. After analyzing a power optimization problem using the standard discrete-time model, we move to the key part of system implementation: the instantiation in true continuous-time systems of the discrete-time models studied to this point in the literature. A key goal is to examine Willie’s detection capability on a continuous-time model and study how the limits of covert communications change from the discrete-time case. In particular, we show that detectors for Willie can benefit from the continuous-time setting and outperform detectors based on the discrete-time model; not surprisingly, this has a significant impact on the true covert throughput of the system. Nevertheless, we establish constructions such that efficient covert communications can still be achieved in a continuous-time model, and prove the fundamental limit on the covert communication rate. After considering the continuous-time problem in detail, we then turn to addressing another limitation of previous work - the requirement for an intentional jammer to facilitate efficient covert communication. Instead, we consider how to exploit a pre-existing interference source – a radar - to achieve covert communication. We establish a covert communication scheme in such an environment, and analyze the corresponding covert rate. Finally, we consider the use of a detection technique similar to that in the covert communications problem, in the area of quantized signal detection.
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.
In this work, we consider a system of covert communication with the aid of a full-duplex (FD) receiver to enhance the performance in a more realistic scenario, i.e., only the channel distribution information (CDI) rather than channel state information (CSI) is known to a warden. Our work shows that transmitting random AN can improve the covert communication with the infinite blocklength. Specifically, we jointly design the optimal transmit power and AN power by minimizing the outage probability at Bob, and we find that the outage probability decreases and then increases as the maximum allowable AN power increases. Intuitively, once AN exceeds an optimal value, the performance will become worse because of the self-interference. The simulation results also show that the performance behaviors of CDI and CSI are different. When Willie only knows CDI, there is an optimal AN power that minimizes Bob's outage probability. However, when Willie knows CSI, the outage probability monotonically decreases with AN power.