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Robust conjugate ambiguity functions and application for strictly noncircular signals in correlated impulsive noise

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Abstract

The assumption of independent and identically distributed noise is often used in basic research, but the correlation between two additive noises cannot be ignored. Based on the characteristic of noncircular signal, the conjugate ambiguity function effectively suppresses correlated Gaussian noise, making it widely applied in signal processing scenarios involving correlated Gaussian noise. However, its performance is severely reduced when non-Gaussian impulsive noise contaminates signal sources. To handle this issue, inspired by the recently developed nonlinear preprocessing method, a new concept called inverse tangent conjugate ambiguity function, which can retain the key information of the signal from being damaged and effectively inhibit the influence of correlated impulsive noise, is defined. Then, the inverse tangent cyclic conjugate ambiguity function is further defined using the cyclostationary property, which can resist both the influence of correlated impulsive noise and co-channel interference. Employing these defined functions, we develop two novel joint time delay of arrival and frequency delay of arrival estimation algorithms. The results of Monte Carlo experiments using different impulsive noise models demonstrate that the performance of the proposed algorithms is better than their competitors, especially under the environment of correlated strong impulsive noise.

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References

  1. Senanayake, R., Smith, P.J., Han, T., Evans, J., Moran, W., Evans, R.: Frequency permutations for joint radar and communications. IEEE Trans. Wirel. Commun. (2022). https://doi.org/10.1109/TWC.2022.3172111

    Article  Google Scholar 

  2. Yan, Y., Wu, G., Dong, Y., Bai, Y.: Floating small target detection in sea clutter using mean spectral radius, IEEE Geosci. Remote Sens. Lett., 19 (2022) 1–5, Art no. 4023405. https://doi.org/10.1109/LGRS.2022.3165163

  3. Zhang, Y., Yu, L., Wei, Y.: Interrupted sampling repeater jamming countermeasure technology based on random interpulse frequency coding LFM signal. Digit. Signal Prog. 131, 103755 (2022). https://doi.org/10.1016/j.dsp.2022.103755

    Article  Google Scholar 

  4. Liu, Z.X., Wang, R., Zhao, Y.J.: Noise-resistant estimation algorithm for TDOA, FDOA and differential doppler rate in passive sensing. Circuits Syst. Signal Process. 39(8), 4155–4173 (2020)

    Article  Google Scholar 

  5. Stein, S.: Algorithms for ambiguity function processing. IEEE Trans. Acoust. Speech Signal Process. 29, 588–599 (1981)

    Article  Google Scholar 

  6. Liu, L., Ji, Y., Zhang, L.: Time-domain and frequency-domain exponential ambiguity functions and their application in joint estimation of delay and Doppler shift. IET Radar Sonar Navig. 16, 437–455 (2022)

    Article  Google Scholar 

  7. Sun, Q., Wu, F.Y., Yang, K., Ma, Y.L.: Estimation of multipath delay-Doppler parameters from moving LFM signals in shallow water. Ocean Eng. 232, 109125 (2021). https://doi.org/10.1016/j.oceaneng.2021.109125

    Article  Google Scholar 

  8. Huang, Z.T., Zhou, Y.Y., Jiang, W.L., Lu, Q.Z.: Joint estimation of Doppler and time difference of arrival exploiting cyclostationary property. IEE Proc. Radar Sonar Navig. 149(4), 161–165 (2002)

    Article  Google Scholar 

  9. Gardner, W.A.: The spectral correlation theory of cyclostationary time-series. Signal Process. 11, 13–36 (1986)

    Article  Google Scholar 

  10. Shin, D.C., Nikias, C.L.: Complex ambiguity functions using nonstationary higher-order cumulant estimates. IEEE Trans. Signal Process. 43, 2649–2664 (1995)

    Article  ADS  Google Scholar 

  11. Li, Z., Pu, R., Xia, Y., Pei, W., Mandic, D.P.: A full second-order analysis of the widely linear mvdr beamformer for noncircular signals. IEEE Trans. Signal Process. 69, 4257–4268 (2021). https://doi.org/10.1109/TSP.2021.3096431

    Article  ADS  MathSciNet  Google Scholar 

  12. Qi, X.: TDOA-FDOA estimation with conjugate ambiguity function. Aerosp. Electron. Warf. 25, 58–61 (2009)

    Google Scholar 

  13. Nikias, C.L., Shao, M.: Signal Processing With Alpha-Stable Distributions and Applications. Wiley, New York (1995)

    Google Scholar 

  14. Kozick, R.J., Sadler, B.M.: Maximum-likelihood array processing in non-Gaussian noise with Gaussian mixtures. IEEE Trans. Signal Process. 48, 3520–3535 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  15. Long, J., Wang, H., Li, P., Fan, H.: Applications of fractional lower order time-frequency representation to machine bearing fault diagnosis. IEEE-CAA J. Autom. Sin. 4, 734–751 (2017)

    Article  Google Scholar 

  16. Ma, X., Nikias, C.L.: Joint estimation of time delay and frequency delay in impulsive noise using fractional lower order statistics. IEEE Trans. Signal Process. 44(11), 2669–2687 (1996). https://doi.org/10.1109/78.542175

    Article  ADS  Google Scholar 

  17. Liu, Y., Qiu, T.S.: A robust method for joint time delay and doppler estimation based on multi-cycle frequencies. Acta Electron. Sin. 39(10), 2311–2316 (2011)

    Google Scholar 

  18. Luan, S., Zhao, M., Gao, Y., Zhang, Z., Qiu, T.: Generalized covariance for non-gaussian signal processing and GC-MUSIC under alpha-stable distributed noise. Digit. Signal Process. 110, 102923 (2021)

    Article  Google Scholar 

  19. Liu, T., Qiu, T., Zhang, J., Luan, S.: Hyperbolic tangent cyclic correlation and its application to the joint estimation of time delay and doppler shift. Signal Process. (2021). https://doi.org/10.1016/j.sigpro.2020.107863

    Article  Google Scholar 

  20. Dou, Y.Z., Abdelrhman, O.M., Li, S.: Time delay estimation method based on generalized logarithmic hyperbolic secant function in impulsive noise. EURASIP J. Adv. Signal Process. (2022). https://doi.org/10.1186/s13634-022-00945-5

    Article  Google Scholar 

  21. Jiang, X., Zeng, W.-J., So, H.C., Rajan, S., Kirubarajan, T.: Robust matched filtering in lp-space. IEEE Trans. Signal Process. 63(23), 6184–6199 (2015). https://doi.org/10.1109/TSP.2015.2464179

    Article  ADS  MathSciNet  Google Scholar 

  22. Li, S., He, R., Lin, B., Sun, F.: DOA estimation based on sparse representation of the fractional lower order statistics in impulsive noise. IEEE/CAA J. Autom. Sin. 5(4), 860–868 (2018). https://doi.org/10.1109/JAS.2016.7510187

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to thank anyone who supported the publication of this paper.

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant (61971083), and in part by the fundamental research funds for the central university under Grants (3132019341). This work was supported in part by the National Natural Science Foundation of China under Grant,and in part by the fundamental research funds for the central university under Grants,61971083 and 3132019341,61971083 and 3132019341,61971083 and 3132019341,61971083 and 3132019341

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Authors and Affiliations

  1. Information Science and Technology College, Dalian Maritime University, Dalian, China

    Yuzi Dou, Omer M. Abdelrhman, Yabo Ding & Sen Li

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  1. Yuzi Dou
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  2. Omer M. Abdelrhman
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  3. Yabo Ding
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  4. Sen Li
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Contributions

S.L. and Y.D. contributed to the research idea, methods, and simulations and drafted the manuscript. O.M. and Y.D. further examined the manuscript. All authors reviewed the final manuscript.

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Correspondence to Sen Li.

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Dou, Y., Abdelrhman, O.M., Ding, Y. et al. Robust conjugate ambiguity functions and application for strictly noncircular signals in correlated impulsive noise. SIViP 18, 2355–2365 (2024). https://doi.org/10.1007/s11760-023-02912-5

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