# 基于EMD的物理层生成密钥方案在车辆通信中的研究Research on EMD-Based Physical Layer Key Generation Scheme in Vehicle Communication

Abstract: It is an effective method to use the inherent randomness and reciprocity of the channel to generate the shared key needed to realize the secure communication of the vehicle. However, due to some factors, there are some discrepancies between the channel measurement sequences obtained after the two communication parties complete the mutual detection of channels. In addition, when these measured values are directly used to generate the key sequence, it will lead to a high bit mismatch rate and add a certain load to the information reconciliation stage. In this article, we use Empirical Mode Decomposition (EMD) to preprocess these measurements, and the resulting sequence undergoes quantification and coding, information reconciliation and privacy amplification steps to generate the final shared key. Moreover, we have done some experiments to evaluate the scheme. The results demonstrate that after the preprocessing of the EMD scheme, the difference between the channel detection sequences of the communicating parties is significantly reduced, and the generated shared key has passed the randomness test.

1. 引言

1) 提出一种生成共享密钥方案，该方案可以应用于环境复杂的车辆通信中。

3) 这种数据处理方法在一定程度上能改善其他技术，如傅里叶变换、小波变换等，处理非线性、非平稳的数据不够良好的效果，并将其引入到车辆通信中。

2. 理论知识

$y\left(t\right)=\underset{0}{\overset{{\tau }_{\mathrm{max}}}{\int }}h\left(\tau ,t\right)x\left(t-\tau \right)\text{d}\tau +n\left(t\right),$ (1)

2.2. 数据预处理技术

EMD往往被称为是一个“筛选”过程。这个筛选过程依据信号特点自适应地把任意一个复杂信号分解为若干固有模态函数(IMFs)。这些IMF是满足一定条件的分量：1) 信号极值点的数量与零点数相等或相差是一，2) 信号的由极大值定义的上包络和由极小值定义的下包络的局部均值为零。因此，给定任意一维离散信号，EMD最终可以编写成

$\xi \left(t\right)=\underset{i=1}{\overset{K}{\sum }}IM{F}_{i}\left(t\right)+{r}_{K}\left(t\right),$ (2)

1) 首先，必须识别局部极限的数据，即信号 的最小值和最大值。

2) 最大值与插值连接，创建信号的顶部包络。

3) 最小值与插值相连，产生信号的下包络。

4) 计算上下包络的平均值。

5) 从原始信号中减去局部平均值。

6) 剩下的数据被认为是相同的数据，重复以上步骤相同的过程。

${r}_{K}$ 的极大值或极小值点数目有一个为零，或者 ${r}_{K}$ 已经是单调时，表示 ${r}_{K}$ 无法分离出IMF，此时EMD这一步就彻底结束了 [15] [16]。

3. 提出的方案

3.1. 信道探测

3.2. 预处理

3.3. 量化及编码

${q}_{n}=\mu +{\alpha }_{k}\sigma ,$ (3)

$Q\left(r\right)=\left\{\begin{array}{c}\begin{array}{cc}00& 若r\le {q}_{1}\\ 01& 若{q}_{1}{q}_{4}\end{array}\end{array}\right\},$ (4)

3.4. 信息协商和保密增强

4. 仿真结果与分析

Figure 1. BMR comparison of different methods under different data sets.

4.1. 比特不匹配率BMR

4.2. 密钥序列随机性

Table 1. Randomness test of key sequence obtained by applying our scheme

5. 结论

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