Reciprocity and Secret Key Generation for FDD Systems using Non-Linear Quantization

Abstract

Secret key generation based on wireless channel reciprocity has received quite some attention, recently. Channel reciprocity as an inherent feature of time division duplexing (TDD) systems leads to creating cryptographic keys without the need for a key exchange procedure. Using different carrier frequencies for the uplink and the downlink, however, means that there is no such symmetry in the frequency response of frequency division duplex (FDD) systems and it makes the key generation for these systems challenging. In this paper, we use the phase differences between neighboring antennas as a frequency-independent channel parameter that provides the required reciprocity in FDD systems. For our studies, we consider neighboring frequency ranges for both directions, which should result in a continuous curve through the two frequency ranges in the two directions. For denoising we use a polynomial curve fitting procedure on the phase differences between antennas. Moreover, we propose a non-linear scheme to quantize the midpoint between the two frequency ranges with the two measurement directions. As a consequence, in contrast to using a linear scheme, the proposed framework would be highly desirable for secret key applications as it gives rise to a more uniform distribution for the resulting histogram over the quantization intervals. Numerical simulation results are shown to verify the effectiveness of the proposed method.