# Wireless Covert Communication with Polarization Dirty Constellation
## 5 Performance Evaluations
### Experiment Results
#### 5.2.2 Undetectability  
Undetectability is an important measure of wireless covert communication. It is typically assessed using measures such as 'KL divergence' and 'KS Test'. The undetectability of \(I\) vectors, \(Q\) vectors, amplitude, and phases are detected with constellation errors. In Figure 10a,b, we investigate the impact of the distance between Alice and Willie on undetectability. The \(SNR\) of the received signal at Bob is kept at 20 dB, and the \(CSR\) of the signal is set at 10 dB. As shown in Figure 10a, the KL divergence decreases with increasing distance between Alice and Willie. When the distance between Alice and Willie is greater than 5 m, the KL divergence of phase reaches a threshold and no longer changes, while the KL divergence of \(I\) vector, \(Q\) vector, and amplitude decrease with increasing distance. It can be observed that WCC-PDC can achieve better undetectability than WCC-DC, and our proposed WCC-PDC strategy can significantly improve the undetectability of covert communication. In Figure 10b, the KL divergence decreases rapidly with increasing distance. It is important to note that the value of the KS test is generally higher than that of KL divergence at the same distance, which indicates that the KS test has better detection performance when the environmental noise is stable. However, when the noise power is uncertain, the KS test may have a high probability of detection error and may no longer be accurate, as we will confirm in the following simulation section. In order to evaluate the undetectability of wireless covert communication, we analyzed the impact of [PERSON]'s \(SNR\) on undetectability using KL divergence and KS distance measures. Specifically, we conducted experiments shown in Figure 11a,b, where we investigated the case when the \(CSR\) is set to 10 dB. Our findings suggest that when the \(SNR\) of the secret carrier signal is 20 dB, the KL divergence reaches a critical value, beyond which higher values will be deemed as covert communication. However, when the \(SNR\) is less than 20 dB, the KL divergence detection method cannot reliably detect the existence of covert communication. In this case, the results of the KS test are even worse than the KL divergence test, and a higher \(SNR\) of 23 dB is required to detect the presence of covert communication. These observations indicate that the KL divergence test results are superior to the KS test when the ambient noise power is high. Figure 10: Detection values versus detection distance. Furthermore, our experiments revealed that the wireless covert channel WCC-PDC, which we proposed, can achieve better undetectability compared to the wireless covert channel WCC-DC. This implies that under the same environment, WCC-PDC can utilize higher power than WCC-DC for covert communication without being detected. In summary, the results of our experiments suggest that WCC-PDC can provide better undetectability than WCC-DC, and the KL divergence test is a suitable method for detecting covert communication when the ambient noise power is high. To evaluate the concealment performance of our proposed covert channel WCC-PDC at low power, we conducted experiments with a \(CSR\) of 15 dB, which is the same as the experimental environment in Figure (a)a. In Figure (a)a, we observed that the KL divergence values at \(CSR=15\) dB are smaller than those at \(CSR=10\) dB, indicating better undetectability at low power. Additionally, the WCC-PDC cannot be detected when [PERSON]'s \(SNR\) is below 25 dB. This threshold is difficult to achieve in conventional communication and demonstrates that our proposed covert channel can achieve excellent concealment performance even at low power levels. In Figure (b)b, we also observed that both wireless covert channels are virtually undetectable under KS test when [PERSON]'s \(SNR\) is below 25 dB. Furthermore, the WCC-PDC outperforms the WCC-DC in terms of undetectability, making covert communication nearly impossible to detect.