A Simple Physical-Layer Key Generation for Frequency-Division Duplexing (FDD)

Common randomness of channels offers the possibility to create cryptographic keys without the need for a key exchange procedure. Channel reciprocity for TDD (time-division duplexing) systems has been used for this purpose many times. FDD (frequency-division duplexing) systems, however, were long considered to not provide any usable symmetry. However, since the scattering transmission parameters S12 and S21 would ideally be the same due to reciprocity, when using neighboring frequency ranges for both directions, they would just follow a continuous curve when putting them next to each other. To not rely on absolute phase, we use phase differences between antennas and apply a polynomial curve fitting, thereafter, quantize the midpoint between the two frequency ranges with the two measurement directions. This is shown to work even with some spacing between the two bands. For key reconciliation, we force the measurement point from one direction to be in the midpoint of the quantization interval by a grid shift (or likewise measurement data shift). Since the histogram over the quantization intervals does not follow a uniform distribution, some source coding / hashing will be necessary. The key disagreement rate toward an eavesdropper was found to be close to 0.5. Additionally, when using an antenna array, a random permutation of antenna measurements can even further improve the protection against eavesdropping.