E.I. Glushankov1, V.Ya. Kontorovich2, S.A. Mityanin3, Z.K. Kondrashov4

1 St. Petersburg State University of Telecommunications named after prof. M.A. Bonch-Bruevich (St. Petersburg, Russia)

3 SMA-RT LLC (St. Petersburg, Russia)

4 JSC NIIMA Progress (Moscow, Russia)

1 glushankov57@gmail.com; 3 s.mityanin@gmail.com; 4 info@i-progress.tech

The article deals with the development of mathematical models for continuous communication channels, a cornerstone of modern radio communication system design. Such models play a pivotal role in evaluating advanced signal processing and reception techniques without necessitating costly and time-intensive field trials. By simulating the impact of environmental factors and interference, these models enable the development of channel simulators that accurately mimic real-world conditions, aiding in the refinement of system performance during the design phase.

The research highlights the inherently stochastic nature of radio wave propagation in real-world scenarios, where variations in signal characteristics depend on time, frequency, and spatial coordinates. These variations are effectively modeled as random processes, with the communication channel described mathematically through stochastic differential equations (SDEs).

The study focuses on prominent probability distributions, including the Rayleigh, Gamma, and K-distributions, which are widely used to characterize different propagation scenarios. Each distribution is associated with specific SDEs, tailored to represent the random processes underlying the corresponding propagation conditions. A novel contribution is the synthesis of a first-order SDE for the K-distribution, which simplifies computational requirements while preserving accuracy in the simulation of these stochastic processes.

Finite-difference methods, particularly the Euler scheme, are employed to simulate processes described by the derived SDEs. Simulations conducted in MATLAB validate the alignment between the simulated outputs and theoretical probability distributions, assessed using the Kolmogorov-Smirnov test. Results demonstrate that the proposed models are most effective within certain parameter ranges, depending on the distribution type. The K-distribution SDE, in particular, shows remarkable accuracy and a broad range of applicability, even under resource-constrained computational conditions.

The scientific novelty of the work lies in the development of a software package that enables the evaluation of the actual applicability domains of finite-difference schemes for first-order SDEs of the specified distributions, as well as the first-ever synthesis of a first-order SDE for the K-distribution.

This research underscores the significance of parameter-specific evaluations when applying SDEs to model communication channels. It lays a robust foundation for developing efficient and accurate tools for simulating propagation environments, ultimately contributing to the advancement of radio communication system design and optimization.

Glushankov E.I., Kontorovich V.Ya., Mityanin S.A., Kondrashov Z.K. Analysis of features of application of stochastic differential equations in modeling random processes with rayleigh-, gamma- and K-distributions. Radiotekhnika. 2025. V. 89. № 6. P. 14−23. DOI: https://doi.org/10.18127/j00338486-202506-02 (In Russian)

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