Physical-Layer Secret Key Generation with Colluding Untrusted Relays

In this paper, we propose a physical-layer secret key generation scheme for multiantenna legitimate nodes with the help of multiple untrusted relays, equipped with multiple antennas. The untrusted relays conform to the relaying transmission protocol of legitimate nodes, but they also eavesdrop the confidential information of an legitimate transmitter. The key generation scheme is designed with zero forcing (ZF) and minimum mean square error (MMSE) channel estimators for non-, partially, and fully colluding modes of untrusted relays. Furthermore, we propose a scheme adaptive to channel coherence time. Specifically, to achieve a higher secret key rate (SKR) within the channel coherence time, the number of relay and legitimate nodes' antennas are optimally determined and the most suitable antennas are selected for the key generation. Our results show that the proposed scheme achieves a higher SKR than a prior work, and non- and partially colluding modes provide a higher SKR than the fully colluding mode through the proposed scheme. We also verify that exploiting more antennas of untrusted relays does not always enhance the SKR by showing the existence of the optimal number of antennas of the relays participating in the scheme.