Nonparametric method for signal detection using SG statistics
DOI:
https://doi.org/10.3103/S0735272724090061Keywords:
SG statistics, chi2-statistics, ATS algorithm, signal detection, singular decompositionAbstract
The paper proposes a new nonparametric method for signal detection based on Savit and Green (SG) statistics and signal observation processing using the surrogate data technology, namely Attractor Trajectory Surrogates (ATS) algorithm. The proposed detection method does not depend on a priori information about the interference probability distribution density and does not consider the model of the observed signal. Using the ATS algorithm allows us to reduce the noise in signal observation. The noise observation estimate has been obtained from the observation itself using the singular spectral analysis for the first time. A comparative analysis of the proposed nonparametric and classical signal detection methods using an energy receiver based on χ2-statistics has been performed. The simulation results showed an increase in the probability of signal detection using the SG statistics-based method for different signal-to-noise ratios compared to using an energy detector. It is also demonstrated that the proposed nonparametric detection method does not depend on the density of the interference probability distribution, using an example of interference with a logistic distribution. Recommendations are given for selecting the parameters of the proposed nonparametric detection method.
References
- H. V. Poor, An Introduction to Signal Detection and Estimation. Springer Science & Business Media, 1998.
- F. E. Nathanson, J. P. Reilly, M. N. Cohen, Radar Design Principles: Signal Processing and the Environment, 2nd ed. New York: Scitech Pub Inc, 1999.
- S. E. Falkovich, Signal parameter evaluation, [in Russian]. Moscow: Sov. Radio, 1970.
- Y. D. Shirman, Theoretical foundations of radiolocation. Moscow: Sov. Radio, 1970.
- Y. Wang, Y. Cao, T.-S. Yeo, Y. Cheng, Y. Zhang, “Sparse reconstruction-based joint signal processing for MIMO-OFDM-IM integrated radar and communication systems,” Remote Sens., vol. 16, no. 10, p. 1773, 2024, doi: https://doi.org/10.3390/rs16101773.
- J. Xu, “Design of high-speed radar signal processor based on FPGA,” J. Comb. Math. Comb. Comput., vol. 125, pp. 93–107, 2025, doi: https://doi.org/10.61091/jcmcc125-07.
- A. El-Awamry, F. Zheng, T. Kaiser, M. Khaliel, “Harmonic FMCW radar system: Passive tag detection and precise ranging estimation,” Sensors, vol. 24, no. 8, p. 2541, 2024, doi: https://doi.org/10.3390/s24082541.
- P. Y. Kostenko, S. Y. Falkovich, Foundations of Statistical Theory of Information-Measuring Radio-Engineering Systems. Kharkiv: KhNUPS, 2021.
- D. Lai, “Asymptotic distributions of the correlation integral based statistics,” J. Nonparametric Stat., vol. 10, no. 2, pp. 127–135, 1999, doi: https://doi.org/10.1080/10485259908832757.
- P. Y. Kostenko, K. S. Vasiuta, S. N. Symonenko, A. N. Barsukov, “Nonparametric BDS detector of chaotic signals against the background of white noise,” Radioelectron. Commun. Syst., vol. 54, no. 1, pp. 19–25, 2011, doi: https://doi.org/10.3103/S0735272711010031.
- H. Kantz, T. Schreiber, Nonlinear Time Series Analysis. Cambridge: Cambridge University Press, 2004.
- M. Small, “Attractor trajectory surrogates: hypothesis testing and prediction,” in International Symposium on Nonlinear Theory and its Applications, 2004, pp. 123–126.
- R. Savit, M. Green, “Time series and dependent variables,” Phys. D Nonlinear Phenom., vol. 50, no. 1, pp. 95–116, 1991, doi: https://doi.org/10.1016/0167-2789(91)90083-L.
- P. Kostenko, K. Vasiuta, V. Slobodyanuk, V. Chystov, M. Alonkin, “Application of predictability index for process classification in information and communication systems,” Radioelectron. Commun. Syst., vol. 67, no. 5, pp. 225–237, 2024, doi: https://doi.org/10.3103/S0735272724060013.
- F. Centofanti, M. Hubert, B. Palumbo, P. J. Rousseeuw, “Multivariate singular spectrum analysis by robust diagonalwise low-rank approximation,” J. Comput. Graph. Stat., vol. 34, no. 1, pp. 360–373, 2025, doi: https://doi.org/10.1080/10618600.2024.2362222.
