Skip to main content
SpringerLink
Log in

PESO: Probabilistic evaluation of subspaces orthogonality for wideband DOA estimation

  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

This paper introduces a novel direction-of-arrival (DOA) estimation method for the closely related wideband sources. The new method estimates the DOAs accurately by evaluating the probability relation between the signal and the noise subspaces of multiple frequency components of the sources using supervised singular value decomposition (SupSVD) and likelihood mean shift (LMS) methods. Also, the introduced method uses the selective criteria of the reference frequency in minimum noisy subband-TOPS (MNS-TOPS) which is an improved version of test of orthogonality of projected subspaces (TOPS) method. This reference frequency is used as the primary set of interest and other sub-bands are used as supervised set to accurately extract the DOAs from a very noisy reception of the signals. The performance of the introduced method compared with well-known methods such as incoherent signal subspace method (ISSM), TOPS, weighted squared-TOPS (WS-TOPS), and MNS-TOPS. The simulations show that the new method outclasses all other methods in all ranges of SNR values. The newly introduced method tested with the lowest ever used number of snapshots (12) and very low SNR values (\(<-\)10 dB). The new method estimates the exact DOAs at the lowest computational cost while the conventional methods can not produce accurate results.

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
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25

Similar content being viewed by others

References

  • Abdelbari, A. (2018). Direction of arrival estimation of wideband RF sources. Master’s thesis, Near East University

  • Asadzadeh, A., Alavi, S., Karimi, M., & Amiri, H. (2020). Coherent wide-band signals DOA estimation by the new CTOPS algorithm. Multidimensional Systems and Signal Processing, 31, 1–15.

    Article  MathSciNet  Google Scholar 

  • Athley, F. (1999). Asymptotically decoupled angle-frequency estimation with sensor arrays. In: Conference Record of the Thirty-Third Asilomar Conference on Signals, Systems, and Computers (Cat. No.CH37020), vol. 2, pp 1098–1102

  • Bilgehan, B., & Abdelbari, A. (2019). Fast detection and DOA estimation of the unknown wideband signal sources. International Journal of Communication Systems, 32(11), e3968.

    Article  Google Scholar 

  • Cadzow, J. A. (1988). A high resolution direction-of-arrival algorithm for narrow-band coherent and incoherent sources. IEEE Transactions on Acoustics, Speech, and Signal Processing, 36(7), 965–979.

    Article  Google Scholar 

  • Chen, H., & Zhao, J. (2005). Coherent signal-subspace processing of acoustic vector sensor array for DOA estimation of wideband sources. Signal Processing, 85(4), 837–847.

    Article  Google Scholar 

  • Chen, W., Zhang, X., Xu, L., & Cheng, Q. (2019). Successive DSPE-based coherently distributed sources parameters estimation for unmanned aerial vehicle equipped with antennas array. Physical Communication, 32, 96–103.

    Article  Google Scholar 

  • Chen, Z., Gokeda, G., & Yu, Y. (2010). Introduction to direction-of-arrival estimation. Artech House signal processing library. Norwood: Artech House.

    Google Scholar 

  • Chung, H., Park, Y., & Kim, S. (2020). Wideband DOA estimation on co-prime array via atomic norm minimization. Energies, 13, 3235.

    Article  Google Scholar 

  • Chung, P. J., Viberg, M., & Yu, J. (2014). Chapter 14-DOA estimation methods and algorithms. In A. M. Zoubir, M. Viberg, R. Chellappa, & S. Theodoridis (Eds.), Library in signal processing (Vol. 3, pp. 599–650). New York: Elsevier.

    Google Scholar 

  • Ciuonzo, D. (2017). On time-reversal imaging by statistical testing. IEEE Signal Processing Letters, 24(7), 1024–1028.

    Article  Google Scholar 

  • Ciuonzo, D., Romano, G., & Solimene, R. (2015). Performance analysis of time-reversal MUSIC. IEEE Transactions on Signal Processing, 63(10), 2650–2662.

    Article  MathSciNet  Google Scholar 

  • Comaniciu, D., & Meer, P. (2002). Mean shift: a robust approach toward feature space analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(5), 603–619.

    Article  Google Scholar 

  • Dassios, I., & Baleanu, D. (2020). Optimal solutions for singular linear systems of caputo fractional differential equations. Mathematical Methods in the Applied Sciences,. https://doi.org/10.1002/mma.5410.

    Article  Google Scholar 

  • Dassios, I., Fountoulakis, K., & Gondzio, J. (2015). A preconditioner for a primal-dual newton conjugate gradient method for compressed sensing problems. SIAM Journal on Scientific Computing, 37(6), A2783–A2812.

    Article  MathSciNet  Google Scholar 

  • Dassios, I., Tzounas, G., & Milano, F. (2020). Participation factors for singular systems of differential equations. Circuits Systems and Signal Processing, 39, 83–110.

    Article  Google Scholar 

  • Dehghani, M., & Aghababaiyan, K. (2018). FOMP algorithm for direction of arrival estimation. Physical Communication, 26, 170–174.

    Article  Google Scholar 

  • Demmel, F. (2009). Chapter 2—practical aspects of design and application of direction-finding systems. In T. E. Tuncer & B. Friedlander (Eds.), Classical and Modern Direction-of-Arrival Estimation (pp. 53–92). Boston: Academic Press.

    Chapter  Google Scholar 

  • di Claudio, E. D., & Parisi, R. (2001). WAVES: weighted average of signal subspaces for robust wideband direction finding. IEEE Transactions on Signal Processing, 49(10), 2179–2191.

    Article  Google Scholar 

  • Grenier, D., Elahian, B., & Blanchard-Lapierre, A. (2016). Joint delay and direction of arrivals estimation in mobile communications. Signal, Image and Video Processing, 10(1), 45–54.

    Article  Google Scholar 

  • Gruber, F. K., Marengo, E. A., & Devaney, A. J. (2004). Time-reversal imaging with multiple signal classification considering multiple scattering between the targets. The Journal of the Acoustical Society of America, 115(6), 3042–3047.

    Article  Google Scholar 

  • Hayashi, H. (2016). DOA estimation for wideband signals based on weighted squared TOPS. EURASIP Journal on Wireless Communications and Networking, 1, 243.

    Article  Google Scholar 

  • Hu, N., Wang, T., Wei, Q., & Hu, J. (2020). Underdetermined wideband DOA estimation utilizing noncircular complex gaussian distribution. IEEE Sensors Letters, 4(5), 1–4.

    Article  Google Scholar 

  • Jolliffe, I. T., & Cadima, J. (2016). Principal component analysis: A review and recent developments. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 374(2065), 20150202.

    Article  MathSciNet  Google Scholar 

  • Kanungo, T., Mount, D. M., Netanyahu, N. S., Piatko, C. D., Silverman, R., & Wu, A. Y. (2002). An efficient k-means clustering algorithm: Analysis and implementation. IEEE Transactions on Pattern Analysis & Machine Intelligence, 24(07), 881–892.

    Article  Google Scholar 

  • Lee, H. B., & Wengrovitz, M. S. (1991). Statistical characterization of the MUSIC null spectrum. IEEE Transactions on Signal Processing, 39(6), 1333–1347.

    Article  Google Scholar 

  • Li, G., Yang, D., Nobel, A. B., & Shen, H. (2016). Supervised singular value decomposition and its asymptotic properties. Journal of Multivariate Analysis, 146, 7–17. (Special Issue on Statistical Models and Methods for High or Infinite Dimensional Spaces).

    Article  MathSciNet  Google Scholar 

  • Little, M. A., & Jones, N. S. (2011). Generalized methods and solvers for noise removal from piecewise constant signals background theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 467(2135), 3088–3114.

    Article  Google Scholar 

  • Ma, F., & Zhang, X. (2019). Wideband DOA estimation based on focusing signal subspace. Signal, Image and Video Processing, 13(4), 675–682.

    Article  Google Scholar 

  • Ning, Y., Ma, S., Meng, F., & Wu, Q. (2020). DOA estimation based on ESPRIT algorithm method for frequency scanning LWA. IEEE Communications Letters, 24(7), 1441–1445.

    Article  Google Scholar 

  • Ottersten, B., & Kailath, T. (1990). Direction-of-arrival estimation for wide-band signals using the ESPRIT algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing, 38(2), 317–327.

    Article  Google Scholar 

  • Qiang, X., Liu, Y., Feng, Q., Zhang, Y., Qiu, T., & Jin, M. (2020). Adaptive DOA estimation with low complexity for wideband signals of massive MIMO systems. Signal Processing, 176, 107702.

    Article  Google Scholar 

  • Schmidt, R. (1986). Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation, 34(3), 276–280.

    Article  Google Scholar 

  • Sellone, F. (2006). Robust auto-focusing wideband DOA estimation. Signal Processing, 86(1), 17–37.

    Article  Google Scholar 

  • Sharman, K., Durrani, T., Wax, M., & Kailath, T. (1984). Asymptotic performance of eigenstructure spectral analysis methods. In: ICASSP ’84. IEEE international conference on acoustics, speech, and signal processing (vol. 9, pp. 440–443)

  • Stoica, P., & Nehorai, A. (1989). MUSIC, maximum likelihood, and cramer-rao bound. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37(5), 720–741.

    Article  MathSciNet  Google Scholar 

  • Strang, G. (2009). Introduction to Linear Algebra (4th ed.). Wellesley, MA: Wellesley-Cambridge Press.

    MATH  Google Scholar 

  • Valaee, S., & Kabal, P. (1995). Wideband array processing using a two-sided correlation transformation. IEEE Transactions on Signal Processing, 43(1), 160–172.

    Article  Google Scholar 

  • Wajid, M., Kumar, B., Goel, A., Kumar, A., & Bahl, R. (2019). Direction of arrival estimation with uniform linear array based on recurrent neural network. In: 2019 5th international conference on signal processing, computing and control (ISPCC) (pp. 361–365)

  • Wang, H., & Kaveh, M. (1985). Coherent signal-subspace processing for the detection and estimation of angles of arrival of multiple wide-band sources. IEEE Transactions on Acoustics, Speech, and Signal Processing, 33(4), 823–831.

    Article  Google Scholar 

  • Wang, J., Zhao, Y., & Wang, Z. (2008). Low complexity subspace fitting method for wideband signal location. In: 2008 5th IFIP international conference on wireless and optical communications networks (WOCN ’08) (pp. 1–4)

  • Wang, X., Wan, L., Huang, M., Shen, C., Han, Z., & Zhu, T. (2020). Low-complexity channel estimation for circular and noncircular signals in virtual MIMO vehicle communication systems. IEEE Transactions on Vehicular Technology, 69(4), 3916–3928.

    Article  Google Scholar 

  • Wax, M., Shan, T. J., & Kailath, T. (1984). Spatio-temporal spectral analysis by eigenstructure methods. IEEE Transactions on Acoustics, Speech, and Signal Processing, 32(4), 817–827.

    Article  Google Scholar 

  • Wu, H., Shen, Q., Liu, W., & Cui, W. (2020). Underdetermined low-complexity wideband DOA estimation with uniform linear arrays. In: 2020 IEEE 11th sensor array and multichannel signal processing workshop (SAM) (pp. 1–5)

  • Xu, X., & Buckley, K. M. (1992). Bias analysis of the MUSIC location estimator. IEEE Transactions on Signal Processing, 40(10), 2559–2569.

    Article  Google Scholar 

  • Yoon, YS., Kaplan, L., & McClellan, H. J. (2006a). DOA estimation of wideband signals. Advances in Direction-of-Arrival Estimation

  • Yoon, Y. S., Kaplan, L. M., & McClellan, J. H. (2006b). TOPS: New DOA estimator for wideband signals. IEEE Transactions on Signal Processing, 54(6), 1977–1989.

    Article  Google Scholar 

  • Yu, H., Liu, J., Huang, Z., Zhou, Y., & Xu, X. (2007). A new method for wideband DOA estimation. In: 2007 international conference on wireless communications, networking and mobile computing (pp. 598–601)

  • Zhang, J., Dai, J., & Ye, Z. (2010). An extended TOPS algorithm based on incoherent signal subspace method. Signal Processing, 90(12), 3317–3324. https://doi.org/10.1016/j.sigpro.2010.05.031.

    Article  MATH  Google Scholar 

  • Zhang, Q. T. (1995). Probability of resolution of the MUSIC algorithm. IEEE Transactions on Signal Processing, 43(4), 978–987.

    Article  Google Scholar 

  • Zou, H., Hastie, T., & Tibshirani, R. (2006). Sparse principal component analysis. Journal of Computational and Graphical Statistics, 15(2), 265–286.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, Near East University, Nicosia, TRNC, Mersin 10, Turkey

    Amr Abdelbari & Bülent Bilgehan

Authors
  1. Amr Abdelbari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bülent Bilgehan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amr Abdelbari.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abdelbari, A., Bilgehan, B. PESO: Probabilistic evaluation of subspaces orthogonality for wideband DOA estimation. Multidim Syst Sign Process 32, 715–746 (2021). https://doi.org/10.1007/s11045-020-00757-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11045-020-00757-6

Keywords

Search

Navigation