An Upper Bound on PHY-Layer Key Generation for Secure Communications Over a Nakagami-M Fading Channel With Asymmetric Additive Noise

The establishment of convenient and reliable cryptographic keys is not always feasible, especially in low-powered wireless devices where a complex key management infrastructure is unaffordable. Physical layer-based key generation approaches, on the other hand, allow two legitimate users to establish a common secret key by exploiting the parameters of the wireless channel, such as the underlying impulse response. In this paper, a fundamental bound on the maximum achievable key generation rate (KGR) over wireless fading channels with asymmetric additive white Gaussian noise (AWGN) is derived. A Nakagami-m fading channel is considered, and the effect of non-reciprocity on the forward and reverse channels correlation is demonstrated. We validate the theoretical platform through simulations using a key generation protocol based on the level crossing rate (LCR) of the fading process. The proposed LCR protocol models the Nakagami channel by utilizing the sum-of-sinusoids approach, where Doppler shift, fading severity, and number-of-paths are taken into account. The proposed protocol also incorporates a two-level quantizer to extract keys, where the channel estimates between a wireless transmitter and receiver can be used as the basis. Besides providing an upper bound on the KGR, the analytical and simulation results intertwine the effect of channel reciprocity with the key generation process.