Achievable Rates for Physical-Layer Cooperative Key Generation with Correlated Eavesdropping Channels

This paper investigates the cooperative jamming based key generation scheme in a cooperative wireless network, where Alice and Bob aim to generate a secret key (SK) that is secret from Eve and a private key (PK) that is secret from both the relay and Eve, with the assistance of a relay. The correlation between legitimate channels and eavesdropping channels is considered. The SK and PK rates are evaluated based on minimum mean square error (MMSE) and zero forcing (ZF) estimation methods, respectively. The analytical expressions are further simplified with asymptotic forms in the high signal-to-noise ratio (SNR) regime. We demonstrate that the MMSE method is optimal to estimate channels, and the ZF method is asymptotically optimal in the high SNR regime. Moreover, we prove that the double-hop key generation strategy cannot achieve a higher rate than the single-hop strategy. Finally, numerical results validate the analysis and demonstrate that the cooperative jamming based key generation scheme significantly outperforms the traditional pairwise key generation scheme.