Skip to main content
SpringerLink
Log in

DOA estimation of LFM signal based on Krylov subspace method

  • Published:
Telecommunication Systems Aims and scope Submit manuscript

Abstract

Direction of arrival estimation of LFM signal is an essential task in radar, sonar, acoustics and biomedical. In this paper, a short time Fourier transform multi-step knowledge aided iterative generalized minimum residual (STFT-MS-KAI-GMRES) approach is presented to amend the angle measurement of this signal. A three stage algorithm is proposed. First, the process is initiated with formulating an estimation algorithm for the carrier frequency and chirp rate, followed by calculation of STFT of the output of array element; this yields a spatial time–frequency distribution matrix. Next, the Krylov subspace-based estimation algorithm is formulated in the presence of MS-KAI-ESPRIT algorithm. If the number of antennas increases, the accuracy of the algorithm will increase, but we will incur more communication costs. Results are presented showing attainment of the CRLB by STFT-MS-KAI-GMRES the for an adequately large signal to noise ratio. An important feature of the method presented in the current study is the low computational complexity that has higher suitability for practical applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Ma, X., Dong, X., & Xie, Y. (2016). An improved spatial differencing method for DOA estimation with the coexistence of uncorrelated and coherent signals. IEEE Sensors Journal, 16(10), 3719–3723.

    Article  Google Scholar 

  2. Poormohammad, S., & Farzaneh, F. (2017). Precision of direction of arrival estimation using novel three dimensional array geometries. International Journal of Electronics and Communications, 75, 35–45.

    Article  Google Scholar 

  3. Middleton, R. J. C. (2012). Dechirp-on-receive linearly frequency modulated radar as a matched-filter detector. IEEE Transactions on Aerospace and Electronic Systems, 48(3), 2716–2718.

    Article  Google Scholar 

  4. Nguyen, V., & Turley, M. (2014). Bandwidth extrapolation of LFM signals for narrowband radar system. International Conference on Adelaide, 51(1), 702–712.

    Google Scholar 

  5. Su, J., Tao, H., Rao, X., Xie, J., & Guo, L. (2015). Coherently integrated cubic phase function for multiple LFM signals analysis. Electronics Letters, 51(5), 411–413.

    Article  Google Scholar 

  6. Gershman, A., & Amin, M. (2000). Wideband direction of arrival estimation of multiple chirp signals using spatial time-frequency distributions. IEEE Signal Processing Letters, 7(6), 152–155.

    Article  Google Scholar 

  7. Yuan, X. (2012). Direction finding wideband linear FM sources with triangular arrays. IEEE Transactions on Aerospace and Electronic Systems, 48(3), 2416–2425.

    Article  Google Scholar 

  8. Sha, Z., Liu, Z., Huang, Z., & Zhou, Y. (2013). Covariance-based direction of arrival estimation of wideband coherent signals via sparse representation. Sensors, 13(9), 11490–11497.

    Article  Google Scholar 

  9. Tang, X., & Li, L. (2016). Time frequency analysis and wavelet transform. Science Press.

    Google Scholar 

  10. Amin, M. (1999). Spatial time frequency distributions for direction finding and blind source separation. In Proceedings of SPIE, International Society for Optical Engineering, Orlando (USA) (pp. 62–70).

  11. Ghofrani, S. (2014). Matching pursuit for direction of arrival estimation in the presence of Gaussian noise and impulsive noise. IET Signal Proceedings, 8(5), 540–551.

    Article  Google Scholar 

  12. Zhang, L., Liu, K., & Yu, X. (2015). Separation and localization of multiple distributed wideband chirps using the fractional Fourier transform. EURASIP Journal of Wireless Communication, 266, 1–8.

    Google Scholar 

  13. Zhang, H., Bi, G., & Cai, Y. (2016). DOA estimation of closely spaced and spectrally overlapped sources using STFT-based MUSIC algorithm. Digital Signal Processing, 52, 25–34.

    Article  Google Scholar 

  14. Caibo, C., Chen, X., & Naichang, Y. (2017). DOA estimation of LFM signals based on STFT and multiple invariance ESPRIT. International Journal of Electronics and Communications, 77(4), 10–17.

    Google Scholar 

  15. Pinto, S. F. B., & Lamare, R. C. (2019). Multi-step knowledge-aided iterative conjugate gradient for direction finding. In Proceedings of IEEE 22nd international conference on digital signal processing (pp. 1–5).

  16. Pinto, S. F. B., & Lamare, R. C. (2017). Multi-step knowledge-aided iterative ESPRIT for direction finding. In Proceedings of IEEE 22nd international conference on digital signal processing (pp. 1–5).

  17. Gabor, D. (1946). Theory of communication (Vol. 93, pp. 429–457).

  18. Saad, Y., & Schultz, M. (1986). GMRES a generalized minimal residual algorithm for solving non-symmetric linear systems. SIAM Journal on Scientific Computing, 7, 856–869.

    Article  Google Scholar 

  19. Pinto, S. F. B., & Lamare, R. C. (2019). Multi-step knowledge-aided iterative conjugate gradient algorithms for DOA estimation. Circuits, Systems, and Signal Processing, 38(8), 3841–3859.

    Article  Google Scholar 

  20. Serbes, A., & Aldimashki, O. (2020). Performance of chirp parameter estimation in the fractional Fourier domains and an algorithm for fast chirp-rate estimation. IEEE Transactions on Aerospace and Electronic Systems, 56(5), 3685–3700.

    Article  Google Scholar 

  21. Pinto, S. F. B., & Lamare, R. C. (2018). Multi-step knowledge-aided iterative ESPRIT: Design and analysis. IEEE Transactions on Aerospace and Electronic Systems, 54, 2189–2201.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Shahed University, Tehran, Iran

    Maedeh FallahReyhani, Hamidreza Bakhshi & Hannan Lohrasbipeyde

Authors
  1. Maedeh FallahReyhani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hamidreza Bakhshi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hannan Lohrasbipeyde
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hamidreza Bakhshi.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

A. Explanation of Eq. (3)

$$ - j2\pi f_{c} \tau + jk\pi \tau^{2} - j\pi k2t\tau = - j\left( {2m + 1} \right)\pi $$
$$ t = \frac{{\left( {2m + 1} \right) - 2f_{c} \tau + k\tau^{2} }}{2k\tau } = \frac{\tau }{2} - \frac{{f_{c} }}{k} - \frac{{\left( {2m + 1} \right)}}{2k\tau } $$

B. Operators and abbreviations

See Tables

Table 3 Description of operators
Full size table

3 and

Table 4 Abbreviations
Full size table

4.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

FallahReyhani, M., Bakhshi, H. & Lohrasbipeyde, H. DOA estimation of LFM signal based on Krylov subspace method. Telecommun Syst 79, 271–278 (2022). https://doi.org/10.1007/s11235-021-00859-x

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11235-021-00859-x

Keywords

Search

Navigation