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.
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.
This letter proposes a joint covert and secure transmission scheme in the non-orthogonal multiple access (NOMA) networks against internal eavesdropping and external monitoring. In the network, the strong user wiretaps the signals of the weak user while an external warden monitors the communication behaviors of the strong user. To address the issue, a random artificial noise (AN) based beamforming is adopted, which not only reduces the eavesdropping rate of the strong user but also confuses the warden. We consider the worst case, where the warden can minimize the detection error probability (DEP) by optimizing its detection threshold. Further, we characterize the closed-form expressions of the average minimum DEP of the warden, the connection outage probabilities of the NOMA users and the secrecy outage probability of the weak user under the imperfect successive interference cancellation (SIC). To improve the performance, an effective covert rate maximization problem is formulated, under the constraints of the covertness, reliability and secrecy, which is analytically solved. Numerical results validate the superiority of the proposed scheme.
In this paper, the covert performance of the non-orthogonal multiple access (NOMA) system with random transmit power under hardware impairments over the Nakagami fading channel is investigated, where the stronger user serves as a covert user (Bob) and receives the secure message from the transmitter (Alice) under the cover of the weaker user (Carl). The transmission is monitored by a warden (Willie). To improve the covert performance, we randomize the transmit power of Alice, which is subject to a uniform distribution. Based on this, considering the randomness of covert user’s position, we derive the closed-form expressions of the average detection error probability (ADEP) respectively for the warden with instantaneous and statistical channel information. Then, the optimal detection threshold based on one-dimensional (1D) search method is presented for minimizing the ADEP. To simplify the optimal threshold, the suboptimal threshold with low complexity is also derived. Besides, the outage probability (OP) of the system is deduced for performance analysis and optimization. Under the constraints of covertness and reliability, the power allocation (PA) coefficient is optimized to minimize the OP of the covert user, and the 1D search scheme is proposed to obtain the optimal solution. Also, a suboptimal scheme is presented to reduce the complexity of the optimal scheme. Numerical results are presented to validate our theoretical analysis, and show that randomizing the transmit power can effectively improve the covert performance. Moreover, the system with two optimized thresholds can obtain lower ADEP than that with a fixed threshold, and the system with two optimized PA coefficients has a lower OP than that with a fixed PA.
This paper pioneers the exploitation of power domain superposition to embed covert messages within overt ones in a two-user uplink Non-Orthogonal Multiple Access (NOMA) system. This eliminates the need for a dedicated covert trans-mitter, enhancing practicality. Our method thwarts conventional radiometer detection at Willie, necessitating Likelihood Ratio Testing (LRT), which we evaluate under optimized overt transmission rates and imperfect Successive Interference Cancellation (SIC) scenarios at Willie. We then minimize Willie's detection error probability by optimizing his detection thresholds and subsequently maximize his minimum DEP by exploiting the user's transmit power and overt-covert power allocation. We show that covert communication is safe if the warden, Willie, doesn't decode any overt message and converges to 1 under high transmission power at users.
This letter considers covert communication in downlink NOMA systems, where a public action (communication from Alice to the NOMA-weak user U1) is used to provide a cover for a secret action (communication from Alice to the NOMA-strong user U2). To aid system design, we first derive the detection error probability (DEP) at Willie and the connect outage probabilities (COPs) at U1 and U2. Then, considering the covertness and outage constraints, the optimization of power allocation factor ratio between U1 and U2 is tackled in order to maximize the effective covert rate. The results demonstrate that the minimum DEP is the power allocation factor for U1. In addition, for a given covert constraint, relaxing the outage constraint will effectively increase the maximum effective covert rate within a certain range of the maximum transmit power of U1.
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.
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.