Development of a unified spectral-correlation phase mathematical model for single-pass joint estimation of time delay and direction of arrival in noisy wideband signals

Authors

DOI:

https://doi.org/10.15587/1729-4061.2026.352271

Keywords:

spectral-correlation analysis, mathematical modeling, one-pass estimation, time delay and direction of arrival, wideband signals

Abstract

The object of this study is the delay and direction of arrival (DOA) of wideband signals in additive noise observed by a synchronized two-channel receiving system. The problem is that most wideband delay and DOA estimation methods rely on multi-stage or iterative procedures – such as peak search, covariance and eigen-decomposition, angular scanning, or sparse recovery – which increase computational load and restrict real-time applicability.

The essence of the obtained results is a unified spectral-correlation model that enables joint estimation of delay and DOA directly from the phase of the complex cross-spectrum. The delay is determined from the linear phase slope with respect to frequency, while the DOA is obtained from a deterministic phase offset defined by the known antenna baseline. This formulation eliminates iterative refinement and angular scanning and reduces computational complexity to O(Nlog2N).

Numerical experiments with linear frequency-modulated signals in Gaussian noise demonstrate predictable accuracy behavior: with increasing signal-to-noise ratio, the DOA root-mean-square error decreases from 0.15–0.18° to 0.03–0.04°, while the delay error decreases from tens of nanoseconds to a few nanoseconds.

These results are explained by the deterministic relationship between time shifts, spatial delays, and phase behavior in the frequency domain under stationary noise conditions. The proposed model can be applied in practice for synchronized two-channel wideband reception with known geometry and fixed antenna baseline in real-time passive monitoring and direction-finding systems.

Author Biographies

Anar Khabay, Satbayev University; Almaty Technological University

PhD, Associate Professor

Department of Electronics, Telecommunications and Space Technologies

Department of Automation and Robotics

Nurzhigit Smailov, Institute of Mechanics and Mechanical Engineering named after Academician U. A. Dzholdasbekov; Satbayev University

PhD, Professor

Department of Radio Engineering, Electronics and Space Technologies

Gulbakhar Yussupova, ALT University

PhD

Department of Radio Engineering and Telecommunications

Amandyk Tuleshov, Institute of Mechanics and Mechanical Engineering named after Academician U. A. Dzholdasbekov

Doctor of Technical Sciences, Professor

Valentyn Tsyporenko, Zhytomyr Polytechnic State University

PhD

Department of Biomedical Engineering and Telecommunications

Vitaliy Tsyporenko, Zhytomyr Polytechnic State University

PhD

Department of Biomedical Engineering and Telecommunications

Zhandos Dosbayev, Institute of Mechanics and Machine Engineering named after Academician U. A. Joldasbekov; Satbayev University

PhD

Department of Radio Engineering, Electronics and Space Technologies

Gulden Khairusheva, Kazakhstan University Innovation and Telecommunications Systems

Master, Senior Lecturer

Department of Technical Disciplines

Akezhan Sabibolda, Institute of Mechanics and Mechanical Engineering named after Academician U. A. Dzholdasbekov; Almaty Academy of Ministry of Internal Affairs

PhD

Department of Cyber Security and Information Technology

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Development of a unified spectral-correlation phase mathematical model for single-pass joint estimation of time delay and direction of arrival in noisy wideband signals

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Published

2026-02-27

How to Cite

Khabay, A., Smailov, N., Yussupova, G., Tuleshov, A., Tsyporenko, V., Tsyporenko, V., Dosbayev, Z., Khairusheva, G., & Sabibolda, A. (2026). Development of a unified spectral-correlation phase mathematical model for single-pass joint estimation of time delay and direction of arrival in noisy wideband signals. Eastern-European Journal of Enterprise Technologies, 1(4 (139), 19–35. https://doi.org/10.15587/1729-4061.2026.352271

Issue

Vol. 1 No. 4 (139) (2026): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

License

Copyright (c) 2026 Anar Khabay, Nurzhigit Smailov, Gulbakhar Yussupova, Amandyk Tuleshov, Valentyn Tsyporenko, Vitaliy Tsyporenko, Zhandos Dosbayev, Gulden Khairusheva, Akezhan Sabibolda

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