# A Physical-Layer Watermarking Scheme Based on 5G NR
## 2 Watermark System Model on 5G NR
### Improved Watermarking Scheme
#### 2.2.1 Improved Watermark Generation Scheme  
The basic watermark generation scheme has the prerequisite for successful authentication: that the demodulated user symbols and watermark bits are both completely right. For the receiver, in addition to extracting the watermark bits embedded by the sender from the received signal, the receiver's key should be hashed with the user bits demodulated by the receiver to regenerate the watermark. If the watermark generated by the receiver is the same as the extracted watermark, the authentication is successful. Otherwise, the authentication fails. Therefore, when one of the demodulated user symbols is wrong, even if the sender's watermark is correctly transmitted to the receiver, the receiver cannot generate a consistent watermark, resulting in authentication failure. When there are errors in user data, even if there is only one symbol error, the hashed results will be completely inconsistent, which directly leads to the failure of identity authentication. Therefore, the premise that authentication is successful only when demodulation is completely correct is not very reasonable in practical applications. How to correctly design a watermark generation scheme which can implement different watermarks for different data frames without depending on the correct demodulation of the user's signal is an important aspect of improving watermark generation schemes. How to reduce the bit error rate of watermark bits during transmission is another aspect of improving watermark generation schemes. To solve the above problems, in this paper, channel coding is added to the watermark generation scheme, and the receiver can increase the accuracy of watermark extraction through channel decoding. In this paper, (7, 4) cyclic code is used as the channel coding method of the watermark signal [22]. In addition, when the modulation scheme adopted by the user's signal is 16 QAM, there are three different amplitudes, so the user bits can be replaced by the modulus of the user's symbol as the input of hash encryption, as shown in Figure 6. In Figure 6, blue represents the user bits as the input of the hash, and red circles represent the moduli of the user symbols as the input of hash encryption. When the user bits are used as the input of hash encryption, it must be ensured that every point on the constellation can be correctly judged. When the modulus of the user's signal is used as the input of hash, one only needs to ensure that the judged modulus is equal to the real modulus. Obviously, by using the modulus of the user's signal instead of the user bits as the input of the hash algorithm, the authentication error caused by the transmission error of user bits can be reduced. It is worth noting that the three moduli in 16 QAM are not uniformly distributed. In Figure 6, the three moduli  
Figure 6: Two input forms of hash encryption. Blue circles represent the user symbols as the input of hash (each points represents four user bits), and red circles represent the modulus of user symbols as the input of hash encryption. 1.3416 in turn, which are denoted as \(a_{1}\), \(a_{2}\) and \(a_{3}\), and their differences are 0.5528 and 0.3416. It can be seen that the difference between the larger two moduli is small, which may confuse one when judging the modulus. The ultimate goal of the watermark generation scheme is to generate different watermarks for different data frames, so it does not emphasize the accurate judgment of modulus, and only needs the changing of the modulus in different data frames. To improve the accuracy of the judging modulus, two larger moduli can be regarded as the same situation and then distinguished from the smallest modulus. In this paper, the distinguishing modulus is defined as the pseudo-user-bit, and the formula is as follows:  
\[b^{\prime}= \begin{cases}1&|s|>(a_{1}+a_{2})/2\\ 0&|s|\leq(a_{1}+a_{2})/2\end{cases}