On the Secret-Key Capacity Over Multipath Fading Channel

Secret-key generation (SKG) at physical layer is considered as a promising solution for lightweight key distribution. On the analysis of the secret-key capacity over multipath fading channels, existing studies generally neglect the channel observation method, which has a direct impact on the secret-key capacity. Moreover, there is a lack of concise and interpretable expressions for the secret-key capacity based on the channel state information. Motivated by the above, we analyze the performance of SKG based on MMSE estimation of channel impulse response over multipath fading channels. The general expression of secret-key capacity is derived. We find that the secret-key capacity depends on the estimation signal-to-noise ratios (SNRs) of channel-tap gains. Then, the condensed-parameter expressions of exact secret-key capacity and the expressions of asymptotic secret-key capacity at high SNR are derived in two specific PDP cases. We show that the bandwidth and the transmission SNR determine the upper bound of secret-key capacity over channels with different degrees of freedom for the flat PDP case. In addition, we find that the asymptotic secret-key capacities under these two PDPs follow a uniform form, which is a linear function of the channel estimation SNR (in dB). Finally, we simulate the channel probing process under different transmission and channel parameters and exploit the simulated channel estimates to estimate the secret-key capacity through numerical methods. The simulation results demonstrate the theoretical analysis and conclusions.