# On IRS-Assisted Covert Communication with a Friendly UAV
## 2 System Model  
Figure 1 demonstrates an IRS-assisted CCS with a transmitter and receiver for covert messages and a monitor. The transmitter of covert messages, which generally is a base station, is denoted as [PERSON] in a typical CCS, while the receiver is denoted as [PERSON]. The monitor, denoted as [PERSON], observes communications between [PERSON] and [PERSON] to determine whether there is a covert communication channel between them. Because a large volume of barriers exists in the surroundings, such as in a city with large buildings, the links between [PERSON] and [PERSON] and between [PERSON] and [PERSON] are not line-of-sight (LoS). In this case, we propose deploying IRS on the surfaces of buildings to relay messages from [PERSON] to [PERSON]. However, if [PERSON] is located close to [PERSON], the received signal power of [PERSON] increases with that of [PERSON] when adopting the IRS, which enlarges the probability of [PERSON] detecting covert communication between [PERSON] and [PERSON]. Thus, we adopt a UAV as a friendly node used by [PERSON] to interfere with [PERSON]'s attempts to detect covert communication between [PERSON] and [PERSON]. In the proposed system, [PERSON] acts as the coordinator who controls the UAV and IRS by delivering the control command and collecting the running parameters. The covert communication system works as both a hacking tool and as an important mechanism for transmitting secret information such as private keys. Therefore, such covert communication systems have become a novel solution for network authentication, copyright protection, and cybercrime evidence-gathering.  
The fades of the channels are respectively denoted as \(h_{AI}\) ([PERSON] and IRS), \(h_{IB}\) (IRS and [PERSON]), and \(h_{IV}\) (IRS and [PERSON]). Let all nodes be in a three-dimensional Cartesian coordinate system, and let [PERSON], the IRS, [PERSON], and [PERSON] be in the ground plane with a height of 0. Thus, their coordinates can be expressed as \(\omega_{A}=[x_{A},y_{A}]^{T}\), \(\omega_{I}=[x_{I},y_{I}]^{T}\), \(\omega_{B}=[x_{B},y_{B}]^{T}\), and \(\omega_{W}=[x_{W},y_{W}]^{T}\), respectively. Moreover, we assume here that the respective positions of [PERSON], the IRS, the UAV, [PERSON], and [PERSON] are all known to each other. Because [PERSON] knows the location of [PERSON], [PERSON]'s location close to [PERSON] leads to a significant increase in the detection rate of covert communication. Let the start and end coordinates of the UAV be \(c_{A}\) and \(c_{F}\), respectively; the UAV flies from the start coordinate to the coordinate in finite time \(N\), where \(N=TL\) and \(L\) is the length of a single time slot, allowing \(N\) to be divided into \(T\) intervals. Let \(H\) be the altitude of the UAV and \(M\) the number of IRS units. Changes in the flying altitude of the UAV change the power of the received jamming signals at [PERSON]'s location, leading to different detection rates of covert communication. Here, \(V_{max}\) denotesthe maximum speed of the UAV, which may influence the covert rate of the system, and \(P\) denotes the transmission power of the base station.  
We define \(C=[c[1],c[2],\ldots,c[T]]^{T}\) as the set of UAV coordinates; thus, letting \(c[T]=c_{F},c[1]=c_{A}\), we have  
\[\|c[t+1]-c[t]\|^{2}\leq D^{2}, \tag{1}\]  
where \(c[t]=[x[t],y[t]]^{T}\) represents the position of the UAV in the \(t\)-th time slot, \(V_{max}\) is the maximum speed of the UAV, and \(D=V_{max}L\).  
In addition, the IRS consists of \(M\) reflecting elements. The phase shift and amplitude of the IRS in the \(t\)-th time slot are defined as a matrix \(\Theta[t]=diag\{\alpha_{1}e^{i\alpha_{1}[t]},\ldots,\alpha_{M}e^{i\beta_{M}[t]}\}\), where \(\alpha_{m}[t]\in[0,1]\). When the optimal amplitude is obtained, \(\alpha\) can be set as \(1\), allowing the diagonal matrix to be rewritten as \(\Theta[t]=diag\{e^{i\theta_{1}[t]},\ldots,e^{i\beta_{M}[t]}\}\).