# A Physical-Layer Watermarking Scheme Based on 5G NR
## 3 System Performance Simulation
### System Performance in the Fading Channel
#### 3.2.2 System Performance in the Presence of Carrier Frequency Offset  
In an actual system, it is difficult to achieve accurate synchronization of the carrier frequency. Similarly to the Gaussian channel, this section analyzes the system's performance when the carrier frequency offset is 90 Hz. The authentication threshold is set to 0.7, as in the case of ideal carrier synchronization.  
The success rates of user-data transmission and watermark authentication are shown in Figure 20. The success rates of user-data transmission and watermark authentication in Scheme III under ideal synchronization are also given. The success rate of watermark authentication in Scheme I is lower than that of user-data transmission because the watermark in Scheme I is not encoded. The success rate of watermark authentication in Scheme II is almost the same as the success rate of user-data transmission, because the watermark is encoded in Scheme II, and the success rate of watermark authentication depends on the success rate of user-data transmission. The success rate of watermark authentication in Scheme III is much higher than the success rate of user-data transmission because pseudo-user-bits are used instead of user bits as the input of hash operation in Scheme III. Even if the user's signal makes a wrong decision due to frequency offset, the mapped pseudo-user-bits may still be correct, thus ensuring the accuracy of watermark  
Figure 18: Success rates of user-data transmission and watermark authentication under ideal synchronization in the fading channel.  
authentication. Therefore, in the presence of frequency offset, the success rates of user's signal transmission in Scheme II and Scheme III are the same, far lower than that in ideal synchronization, but the success rate of watermark authentication in Scheme III can be consistent with that in ideal synchronization, far higher than that in Scheme II. Figure 19 directly shows the anti-noise and anti-frequency-offset effects of Scheme III in the fading channel.  
Finally, the success rates of watermark-bit transmission and watermark authentication in three schemes are compared in Figure 21. Under the condition of frequency offset, the transmission success rates of watermark bits in Scheme II and Scheme III can reach the transmission success rate of watermark bits in ideal synchronization, and are much higher than that in Scheme I. However, because the symbol error rate of user data is increased due to the existence of the frequency offset, the receiver in Scheme II may not be able to generate the same watermark as the sender, so the authentication success rate in Scheme II is lower than that in Scheme III. Figure 20 intuitively shows that when a frequency offset  
Figure 19: Success rates of watermark-bit transmission and watermark authentication under ideal synchronization in the fading channel.  
Figure 20: Success rates of user-data transmission and watermark authentication with frequency offset in the fading channel.  
exists, the transmission success rate and authentication success rate of watermark source bits in Scheme III can reach the same level as in the case of ideal synchronization; that is, Watermark Scheme III has good anti-frequency-offset performance.  
According to the above simulation results, Watermarking Scheme III, which was proposed in this paper, is also feasible for fading channels and has good anti-noise and anti-frequency-offset performance.