A.A. Galiev1, A.I. Sulimov2, A.V. Karpov3

1–3 Kazan Federal University (Kazan, Russia)

1 ggalievv@mail.ru; 2 asulimo@gmail.com; 3 arkadi.karpov@kpfu.ru

Variations in channel characteristics within mobile radio communication systems serve as a natural source of randomness for generating two identical copies of binary random sequences between a pair of communication devices. These identical binary sequences are essential for securing the information channel between users A and B, and they are created by digitizing phase measurements of the fading signal transmitted through a multipath radio channel in opposite directions. However, phase-based methods face a challenge due to the strict requirement for frequency synchronization between communication devices at points A and B, making the technical implementation of the system more complex. To address the instability issue with reference generators, an alternative approach based on differential phase was proposed. Simulation modeling of the multipath propagation of a dual-frequency probing signal in urban conditions demonstrated an immunity of the differential phase method to frequency instability of the reference clocks.

This article aims to experimentally investigate probabilistic properties of the differential phase of a dual-frequency probing signal and evaluate its applicability to generating binary random sequences. Achieving this objective necessitated the development of new equipment capable of bidirectional dual-frequency probing of the multipath environment and capturing the differential phase of the multipath response. The designed experimental setup is based on software-defined transceivers. An original solution is the use of two separate transceivers for each harmonic of the probing signal, which mitigated the dependency of the required computational resources on the frequency spacing. The control software for the transceivers was developed using the GNU Radio programming environment and comprised three main modules: 1) the probing signal generation module, 2) the reception and processing module for response analyzing of the environment, and 3) the probing protocol implementation module. To test the immunity of the differential phase method against mutual discrepancies of the reference clocks at points A and B, deliberate frequency offsets were introduced at the side B by manipulating the feedback loop in the phase-locked loop (PLL) system of its reference clock. The experimental results obtained by dual-frequency probing of the multipath channel within a frequency spacing range of 20 to 80 MHz confirmed the immunity of the differential phase measurements against frequency instabilities of reference clocks. The achieved immunity allows for the utilization of this method in the generation of binary random sequences in multipath scenarios. Furthermore, it was experimentally demonstrated that a minimum frequency spacing of 80 MHz is required to achieve satisfactory probabilistic properties of the differential phase in the dual-frequency probing signal. A high mutual correlation (not less than 0.95) of differential phase measurements at both ends of the radio link was achieved. Additionally, a probabilistic model for the differential phase of the multipath radio signal was presented, and the experimental data correspond well to the proposed theoretical model.

Galiev A.A., Sulimov A.I., Karpov A.V. Experimental study of probabilistic properties of differential phase response of multipath environment. Radiotekhnika. 2023. V. 87. № 12. P. 88−98. DOI: https://doi.org/10.18127/j00338486-202312-10 (In Russian)

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