# A Physical-Layer Watermarking Scheme Based on 5G NR
## 3 System Performance Simulation
### System Performance in the Gaussian Channel
#### 3.1.1 System Performance under Ideal Carrier Synchronization  
Firstly, it is assumed that the carrier frequency of the transmitter is completely synchronized with the carrier frequency of the receiver. In the Gaussian channel, the performances of three watermarking schemes are compared. The symbol error rates of user data in three watermark schemes are shown in Figure 9.  
In Figure 9, the symbol error rates of user signals in Scheme II and Scheme III are consistent, and both are similar to the theoretical symbol error rate of 16 QAM, lower than that in Scheme I. This is because the watermark signals in Scheme II and Scheme III meet the requirement of symmetry, so when using DMRS to estimate the channel, the results in Scheme II and Scheme III are more accurate and cause less interference with the user signals, so the symbol error rates of user signals are lower. The difference between Scheme II and Scheme III is that the input of hash operation is different, so it has little effect on the user's signal, and there is no difference in the symbol error rate of the user's signal between the two schemes. In Figure 9, compared with the theoretical symbol error rate of 16 QAM, there is still a gap in the user's signal error rates in Scheme II and Scheme III, because channel estimation of the DMRS is not completely accurate. Figure 10 shows the transmission bit error rate of watermark bits. In Figure 10, the bit error rate of the watermark bits in Scheme I is higher than those of Scheme II and Scheme III. This is because channel coding can be used for error detection and correction at the  
Figure 9: Symbol error rates of the user data under ideal synchronization in the Gaussian channel. receiving end. It can be seen that the performance of the watermark in the transmission process is improved by using channel coding, which can not only avoid interference to channel estimation but also correct errors at the receiver. The success rates of user-data transmission and the success rates of watermark authentication in three watermarking schemes are compared in Figure 11. In Figure 11, the success rates of user-data transmission in Scheme II and Scheme III are the same and higher than that in Scheme I, which is due to the symmetry of watermarks in Scheme II and Scheme III. The success rate of watermark authentication in Scheme I is far lower than that of user-data transmission. As the channel coding process is absent in Scheme I, the receiver cannot correct the watermark. Even if the user data are successfully transmitted, the authentication may fail because of the error of watermark-bit transmission. The success rate of watermark authentication in Scheme II is very close to the success rate of user-data transmission because channel coding is added in Scheme II, so the transmission accuracy of the watermark is greatly improved compared with Scheme I. In Scheme III, the success rate of watermark authentication is consistent with the success rate of user-data transmission. Even when the signal-to-noise ratio is low, the authentication rate is higher than the success rate of user-data transmission, because pseudo-user-bits are used instead of user bits as the input of the hash algorithm in Scheme III. Even if some user's signals are demodulated incorrectly, as long as the mapped pseudo-user-bits are correct, the same watermark source bits can still be generated to complete watermark authentication. Therefore, when the success rates of user-data transmission in Scheme II and Scheme III are the same, the authentication success rate in Scheme III is sometimes higher than that in Scheme II. The success rates of watermark-bit transmission and watermark authentication in the three schemes are compared, and the results are shown in Figure 12. In Figure 12, the success rates of watermark bits and watermark authentication in Scheme I are lower than those in Scheme II and Scheme III, which directly illustrates the importance of watermark coding.