E.I. Glushankov1, S.A. Mitianin2

1,2 Saint Petersburg State University of Telecommunications named after prof. M.A. Bonch-Bruevich (St. Petersburg, Russia)

1 glushankov57@gmail.com, 2 s.mityanin@gmail.com

This paper presents a comprehensive sensitivity analysis of filtering algorithms based on stochastic differential equations (SDEs) applied to non-Gaussian fading radio channels. The study focuses on Kalman-type filters synthesized for channels whose attenuation coefficients follow Rayleigh, Gamma, and K distributions. Such models are relevant for wireless systems operating under multipath fading and nonstationary propagation conditions, where the statistical properties of the medium deviate from the Gaussian assumption.

In practical filtering applications, the parameters of the signal and observation models are rarely known precisely. Mismatch between the true system dynamics and their nominal representation in the filter leads to performance degradation and potential instability. Therefore, evaluating the sensitivity of SDE-based filtering algorithms to deviations in model parameters is essential for ensuring reliable operation in real communication systems.

The objective of this research is to analyze the large-sensitivity characteristics of filtering algorithms with respect to variations in the SDE parameters of the state model (ΔF), the observation model (ΔH), their combined effect (ΔF = ΔH), and errors in the estimated noise spectral density (ΔN₀). The analysis aims to determine how parameter mismatches influence the covariance matrices of estimation errors and the overall risk function, thus revealing the robustness of each distribution-based filter.

The study employs numerical modeling in MATLAB. The sensitivity functions were obtained from the covariance matrices of actual and assumed estimation errors for each distribution type. The introduced parameter errors varied from 5% to 95%. The analysis was carried out for three modulation constellations – QAM-128, QAM-256, and QAM-512 – to verify the consistency of the observed effects.

The results show distinct sensitivity patterns for each distribution. For ΔF deviations, the Gamma distribution exhibits the strongest dependence, while Rayleigh and K distributions demonstrate partial insensitivity and asymptotic stability beyond 20% error. The impact of ΔH errors is weaker for all cases, showing monotonically decreasing sensitivity. When ΔF and ΔH errors occur simultaneously, a synergistic effect is observed, producing a stronger sensitivity growth than the sum of individual contributions. Deviations in noise spectral density ΔN₀ lead to a steep drop in sensitivity up to 10…15% error, followed by a gradual decline across the full range. Among the tested models, the Gamma-based filter maintains the most balanced behavior across all perturbations, while Rayleigh and K filters exhibit similar responses with slightly higher robustness to ΔF.

The obtained results confirm that SDE-based filters can remain stable under parameter uncertainty if properly tuned for the underlying distribution type. The proposed sensitivity analysis approach can be used at the design stage of receivers and channel simulators to select optimal SDE parameters, evaluate robustness margins, and ensure consistent performance of filtering algorithms in non-Gaussian environments.

Glushankov E.I., Mitianin S.A. Sensitivity analysis of filtering algorithms in continious radio channels with non-gaussian parameter distributions. Achievements of modern radioelectronics. 2026. V. 80. № 5. P. 43–52. DOI: https://doi.org/10.18127/j20700784-202605-05 [in Russian]

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