一种无线信道密钥容量求解方法

A Solution of the Secret Key Capacity for Wireless Channel

为了准确求解合法通信双方利用无线信道生成共享密钥的容量,借助于瑞利衰落统计模型和互易性对无线信道进行建模,得到合法双方接收信号的统计分布;通过对统计分布进行雅克比变换分别推导出双方包络的联合分布和相位的联合分布,进而通过互信息公式求解出相应的两个密钥容量表达式。利用窄带信道的互易性,提出了一种发送信号为非相干载波的密钥生成协议,合法双方在相干时间内以时分双工(TDD)方式对无线信道进行多载波探测,双方分别利用接收信号包络、相位信息生成密钥,将两密钥去除相关性后拼接起来作为最终的密钥以用于安全通信。该协议能够同时利用接收信号的包络和相位信息,且密钥容量与非相干载波的个数成正比。仿真结果表明:分别基于信号包络、相位信息生成的密钥存在相关性;仅由包络和相位信息生成密钥并未充分利用信道特性信息,当信噪比为10dB时,利用接收信号包络、相位的密钥容量的数值求和比利用接收信号的密钥容量低0.3b/s。

A model for wireless channel is established to evaluate accurately the capacity of the shared secret key generated by legitimate users in the channel.The building of the model is based on statistical models of Rayleigh fading and reciprocity from the statistical distribution of the received signals.The joint probability density functions of both the envelope and the phase at the legitimate users are respectively derived by using a Jacobi transform.The corresponding expressions of the two secret key capacities are then deduced by using the formula of mutual information.Then a protocol of secret key generation in which the transmitted signals are multicarriers is presented by utilizing the reciprocity of the narrowband channel.The legitimate users implement the multi-carrier channel sounding in TDD mode within the coherence time,and exploit the information of envelope and phase in the received signals to generate secret keys.The keys are spliced together to realize secure communication by removing the correlation between them.The proposed protocol can use information of the envelope and the phase simultaneously,and the capacity of the secret key is proportional to the number of carriers.Simulation results show that correlation exists between the secret keys generated based on information of the envelope and the phase,and that the numerical sum of key capacity that exploits information of the envelope and the phase is lower than that of received signals by 0.3 bit/s when the SNR is 10 dB.It can be concluded that legitimate users can utilize more information in the received signals to generate shared secret key.