Intelligent Reflecting Surface-induced Randomness for mmWave Key Generation

Secret key generation in physical layer security exploits the unpredictable random nature of wireless channels. However, the millimeter wave (mmWave) channels have limited multipath and may not be Gaussian distributed. In this paper, for mmWave secret key generation of physical layer security, we use intelligent reflecting surface (IRS) to produce randomness and induce artificial Rayleigh fading directly in the wireless environments. We first formulate the model of IRS-assisted key generation in mmWave environments. The IRS-assisted reflection channel varies according to the IRS weights' variation and induces randomness. When considering the IRS weights are continuous and discrete uniformly distributed, we find that the reflection channel variance is equal to the number of IRS elements. Besides, we prove that the magnitude and phase are Rayleigh and uniformly distributed when the weights are continuously and discretely distributed with more than one quantization bit. With the simulation results verifying the analytical results, this work explains the mathematical principles behind the IRS-assisted physical layer security secret key generation and lays a foundation for future mmWave key generation evaluation and optimization of channel randomness.