## 5 Simulation Results  
In this section, the performance of our proposed scheme is verified through Monte Carlo simulations. The experiment is repeated \(10^{6}\) times in each simulation. We use a single antenna for [PERSON], [PERSON], and [PERSON]. The wireless channel is modeled as a Rayleigh fading channel. In addition, the transmitted bits are modulated by BPSK. When simulating the BER of the coding channel and the secure transmission rate, we assume that the power allocation for the pilot and data signals is the same, i.e., \(\alpha=0.5\). The BER performance of the coding channel with different quantization precisions \(q\) in the two schemes is illustrated in Figure 6. It is obvious that the BER of our proposed scheme is lower than that of the NRK-SC scheme in [15; 16; 17; 18] at the same quantization precision, which verifies the correctness of the theoretical derivation. The reason for this is that our proposed scheme makes full use of channel correlation, and there are similar error probabilities between keys and transmitted bits. Thus, the errors that occur in both keys and transmitted bits can be corrected via an XOR operation, which is conducive to reducing the BER of the coding channel. In addition, note that the BER between [PERSON] and [PERSON] is always kept at 0.5 as the SNR increases, which indicates that [PERSON] cannot obtain any private information from the key, regardless of the computing power. This is due to the fact that the generated keys are firmly bound to the channel characteristics. Furthermore, the eavesdropping channel and the legitimate channels are independent of each other. Therefore, the generated keys between [PERSON] and [PERSON] are not correlated. Figure 6: Comparison of the BERs of the coding channels [15; 16; 17; 18]. In order to verify the superiority of our proposed adaptive coding algorithm, a comparison between adaptive coding and the single-code-rate coding method in different channel environments is given in Table 1. We take a low SNR of 0 dB and a high SNR of 20 dB as examples for analysis. We compare the code rate and the BER after decoding using BCH code with code length \(n=127\). When the BER is lower than \(10^{-6}\), we consider that reliable transmission can be achieved. That is, the BER is equal to 0 in Table 1. It is observed that the BER using adaptive coding and coding with 1/4 code rate can satisfy the BER requirements at 0 dB and 20 dB. However, it is noted that the code rate of adaptive coding is higher than 1/4, and therefore a higher secure transmission efficiency can be achieved. In addition, when the SNR is 0 dB, The BER using the error correction for the 1/2 code rate is \(10^{-4}\), which cannot realize the reliability of communication systems. At 20 dB SNR, although using the 1/2 code rate to correct errors can meet the BER requirements, the code rate is lower than that of adaptive coding. Meanwhile, adding more redundant code bits will lead to lower secure transmission efficiency. The upper bound of the secure transmission rate versus SNR is plotted in Figure 7. The secure transmission rate of our proposed scheme is higher than that of the existing NRK-SC scheme in [15; 16; 17; 18] at the same quantization precision. This is because the BER is obviously decreased in our scheme, and fewer redundant code bits are required to correct errors. Therefore, a higher secure transmission rate can be achieved. Reasonable power allocation can minimize the BER of communication systems, which has an important impact on improving the reliability of communication systems, especially in resource-limited communication systems. In order to achieve optimal power allocation, the BER of the coding channel versus the power allocation parameter is given in Figure 8. Note that the minimum values of the BER at different SNRs are obtained at \(\alpha>0.5\). This is due to the fact that the errors of communication systems include inconsistent keys and transmitted error bits, and most of the errors originate from inconsistent keys.