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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. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of joint covert communication and secure transmission in untrusted relaying networks when multiple wardens exist in the network. We first consider a system model consisting of one source, one untrusted amplify-and-forward relay, one destination, and one warden. For covert communications, our aim is to prevent the warden from detecting the presence of communications via the source-relay-destination link. For secure transmission, our aim is to prevent the untrusted relay from decoding the source signal. To satisfy these requirements, we propose that the destination and the source inject jamming signals during the source-to-relay and relay-to-destination transmission phases, respectively. For the considered system model, we propose a power allocation strategy to maximize the secrecy rate and satisfy the covert requirements in both of the phases. Given that the proposed optimization problem is non-convex, we employ the successive convex approximation (SCA) approach to derive a tractable solution. To obtain further insights, we generalize our analytical results to consider multiple untrusted relays and multiple wardens. We focus on two scenarios of non-colluding and colluding wardens. Our results highlight that as the number of relays increases, the achievable secrecy rate increases while the average detection error probability decreases. This is a novel observation of a fundamental trade-off between covert requirement and secrecy performance. [ABSTRACT FROM AUTHOR]