# Disguised Full-Duplex Covert Communications
## 5 Numerical Results  
We evaluate the proposed solutions for covert communications with the disguised FD node through numerical results. The effects of various system parameters such as the source transmit power, disguised FD destination transmit power budget, noise uncertainty bound, and minimum DEP threshold on the achievable covert rate \(r_{\text{\tiny{C}\text{,R}}}\) in (5) with the derived optimal destination transmit power \(P_{D}^{\star}\) in (20) are examined in the upcoming figures. We also focus on verification that \(P_{D}^{\star}\) fulfills the DEP requirements for any desired threshold \(\varepsilon\) in (17e) and compare with baseline schemes to stress the significance of \(P_{D}^{\star}\). The distance-dependent channel model is adopted for \(h_{\text{\tiny{XV}}}\)[43]. Concretely, we let \(\left|h_{\text{\tiny{XV}}}\right|^{2}=L_{\text{\tiny{XV}}}\!\left|\tilde{h}_{ \text{\tiny{XV}}}\right|^{2}\), where \(L_{\text{\tiny{XV}}}\triangleq L_{0}(d_{\text{\tiny{XV}}}/d_{0})^{-\beta}\) indicates the path loss between X and Y. Here, \(L_{0}\) stands for the path loss at a reference distance \(d_{0}=1\) m, \(\beta\) represents the path loss exponent, and \(d_{\text{\tiny{XV}}}\) indicates the distance between X and Y. Also, the small-scale channel variable \(\tilde{h}_{\text{\tiny{XV}}}\) follows \(CN(0,1)\). The four nodes are placed with certain distances from the origin \(O=(0,0)\) in a Cartesian coordinate system such that the coordinates of \(S\), \(D\), \(R\), \(W\) are \((-d_{OS},0)\), \((d_{OD},0)\), \((0,d_{OR})\), \((0,-d_{OW})\), respectively (Figure 2). The overall system parameters are fixed as follows unless otherwise stated: the bandwidth \(B=20\) MHz, \(d_{\text{\tiny{OX}}}=100\) m, source transmit power \(P_{S}=23\) dBm, destination transmit power budget \(\bar{P}_{D}=23\) dBm, public message quality of service \(\bar{r}_{P,D}=0.1\) bps/Hz, mean noise power at the warden node \(\sigma_{W}^{2}=-160\) dBm/Hz, noise uncertainty bound \(\zeta=5\) dB, noise power at the destination node and hidden receiver \(\sigma_{D}^{2}=\sigma_{R}^{2}=-160\) dBm/Hz, residual self-interference \(\sigma_{\text{\tiny{SI}}}^{2}=-100\) dB, minimum DEP threshold \(\varepsilon=0.45\), and pathloss exponent \(\beta=3.5\). Figure 3 shows the average covert rate \(r_{\text{\tiny{C}\text{,R}}}\) as the source transmit power \(P_{S}\) varies. Motivated by the fact that the destination transmit power \(P_{D}\) should be much lower than \(P_{S}\) for successful covert transmissions, we compare the optimal scheme with \"\(\alpha\%\)\(P_{S}\)\" in which \(P_{D}\) is fixed as \(\min(\alpha\%\) of \(P_{S}\), \(\bar{P}_{D})\). We notice that the proposed public data rate in (18) and destination transmit power in (20) result in the highest covert rate for every \(P_{S}\) value, indicating the importance of optimizing \(r_{P}\) and \(P_{D}\). We also observe from the \"\(\alpha\%\)\(P_{S}\)\" schemes that applying more \(P_{D}\) to a covert transmission induces a higher covert rate when \(P_{S}\) is low, while less \(P_{D}\) is preferred when \(P_{S}\) is high. First, when \(P_{S}\) is low, the public data rate constraints in (17b) and (17c) dominate determining \(P_{D}^{\star}\) from (20). If \(\
u\triangleq\min(\mathrm{E}[\left|h_{\text{\tiny{S}\text{N}}}\right|^{2}/( \left|h_{\text{\tiny{D}\text{N}}}\right|^{2}(2^{\bar{r}_{P}}-1))],\mathrm{E}[ \left|h_{\text{\tiny{SD}}}\right|^{2}/(\left|\tilde{h}_{\text{\tiny{DD}}} \right|^{2}(2^{\bar{r}_{P}}-1))])\), then any \"\(\alpha\%\)\(P_{S}\)\" schemes with \(\alpha\%>\
u\) are likely to be infeasible on average. It can be inferred from Figure 3 that that \(\
u\geq 5\%\) for our system setup since \"\(5\%\)\(P_{S}\)\" performs the best among the other fixed \(P_{D}\) schemes. On the other hand, when \(P_{S}\) is high, the DEP constraint in (17e) and the power budget \(\bar{P}_{D}\) dominate deciding \(P_{D}^{*}\). Hence, only the \"a% \(P_{S}\)\" schemes with sufficiently low \(\alpha\)% can meet these requirements and be feasible on average.