Abstract
A novel fast direction-of-arrival (DOA) estimation method of wideband Linear Frequency Modulated (LFM) signals without grid mismatch is proposed. Leveraging the aggregation traits inherent in wideband LFM signals within the Fractional Fourier (FRF) domain, the received model of LFM signals with time-invariant steering vector is drived. To counter the impact of grid mismatch on DOA estimation, this method utilizes atomic norms with continuous space dictionaries as sparse constraints, constructing a sparse recovery optimization problem. By transforming the minimization of atomic norms into a semipositive definite programming problem, the method effectively solves this optimization problem, reconstructing the covariance matrix from limited snapshot data in the FRF domain. Furthermore, addressing the efficiency challenge of solving semi-positive definite programming problems with multiple elements, a fast solution framework considering multiple measurement vectors and partial observation model is derived based on the interior point method theory, Karush-Kuhn-Tucke conditions and Toeplitz matrix characteristics. Compared to existing methods, the proposed method achieves heightened resolution and enhanced accuracy in DOA estimation through gridless sparse reconstruction, notably reducing computational complexity. The effectiveness of this method is robustly validated through simulation results.
Similar content being viewed by others
Data availability
The code and data are available from the corresponding author on reasonable request.
References
Zhang, J., Bao, M., Zhang, X.-P., Chen, Z., Yang, J.: Doa estimation for heterogeneous wideband sources based on adaptive space-frequency joint processing. IEEE Trans. Signal Process. 70, 1657–1672 (2022)
Bekar, M., Baker, C.J., Hoare, E.G., Gashinova, M.: Joint MIMO radar and communication system using a PSK-LFM waveform with TDM and CDM approaches. IEEE Sens. J. 21(5), 6115–6124 (2020)
Lee, D.-H., Shin, J.-W., Do, D.-W., Choi, S.-M., Kim, H.-N.: Robust LFM target detection in wideband sonar systems. IEEE Trans. Aerosp. Electron. Syst. 53(5), 2399–2412 (2017)
Zhao, Y., Yu, H., Wei, G., Ji, F., Chen, F.: Parameter estimation of wideband underwater acoustic multipath channels based on fractional Fourier transform. IEEE Trans. Signal Process. 64(20), 5396–5408 (2016)
Ma, N., Goh, J.T.: Ambiguity-function-based techniques to estimate doa of broadband chirp signals. IEEE Trans. signal Process. 54(5), 1826–1839 (2006)
Qiang, X., Liu, Y., Feng, Q., Zhang, Y., Qiu, T., Jin, M.: Adaptive DOA estimation with low complexity for wideband signals of massive MIMO systems. Signal Process. 176, 107702 (2020)
Su, G., Morf, M.: The signal subspace approach for multiple wide-band emitter location. IEEE Trans. Acoust. Speech Signal Process. 31(6), 1502–1522 (1983)
Wang, H., Kaveh, M.: Coherent signal-subspace processing for the detection and estimation of angles of arrival of multiple wide-band sources. IEEE Trans. Acoust. Speech Signal Process. 33(4), 823–831 (1985)
Valaee, S., Kabal, P.: Wideband array processing using a two-sided correlation transformation. IEEE Trans. Signal Process. 43(1), 160–172 (1995)
Hung, H., Kaveh, M.: Focussing matrices for coherent signal-subspace processing. IEEE Trans. Acoust. Speech Signal Process. 36(8), 1272–1281 (1988)
Valaee, S.: Array processing for detection and localization of narrowband, wideband and distributed sources (1994)
Hung, H., Kaveh, M.: Focussing matrices for coherent signal-subspace processing. IEEE Trans. Acoust. Speech Signal Process. 36(8), 1272–1281 (1988)
Doron, M.A., Weiss, A.J.: On focusing matrices for wide-band array processing. IEEE Trans. Signal Process. 40(6), 1295–1302 (1992)
Sellone, F.: Robust wideband DOA estimation. In: IEEE/SP 13th workshop on statistical signal processing, 2005, pp. 277–282, IEEE (2005)
Ma, F., Zhang, X.: Wideband DOA estimation based on focusing signal subspace. Signal Image Video Process. 13, 675–682 (2019)
Liu, Z., Wang, X., Zhao, G., Shi, G., Lin, J., Gao, Z.: Wideband DOA estimation based on sparse representation-an extension of l 1-SVD in wideband cases. In: 2013 IEEE international conference on signal processing, communication and computing (ICSPCC 2013), pp. 1–4, IEEE (2013)
Luo, J.-A., Zhang, X., Wang, Z.: A novel aliasing-free subband information fusion approach for wideband sparse spectral estimation. EURASIP J. Adv. Signal Process. 2017(1), 1–13 (2017)
Luo, J.A., Zhang, X., Wang, Z.: A new subband information fusion method for wideband DOA estimation using sparse signal representation. In: 2013 IEEE international conference on acoustics, speech and signal processing, pp. 4016–4020, IEEE (2013)
Gerstoft, P., Mecklenbräuker, C.F., Xenaki, A., Nannuru, S.: Multisnapshot sparse Bayesian learning for DOA. IEEE Signal Process. Lett. 23(10), 1469–1473 (2016)
Gerstoft, P., Mecklenbräuker, C.F.: Wideband sparse bayesian learning for doa estimation from multiple snapshots. In: 2016 IEEE sensor array and multichannel signal processing workshop (SAM), pp. 1–5, IEEE (2016)
Gershman, A.B., Amin, M.G.: Wideband direction-of-arrival estimation of multiple chirp signals using spatial time-frequency distributions. IEEE Signal Process. Lett. 7(6), 152–155 (2000)
Cui, K., Wu, W., Huang, J., Chen, X., Yuan, N.: Doa estimation of lfm signals based on stft and multiple invariance esprit. AEU-International Journal of Electronics and Communications 77, 10–17 (2017)
Cui, K., Wu, W., Huang, J., Chen, X., Yuan, N.-C.: 2-d DOA estimation of LFM signals for UCA based on time-frequency multiple invariance esprit. Prog. Electromag. Res. M 53, 153–165 (2017)
Almeida, L.B.: The fractional Fourier transform and time-frequency representations. IEEE Trans. Signal Process. 42(11), 3084–3091 (1994)
Tao, R., Zhou, Y.: A novel method for the direction of arrival estimation of wideband linear frequency modulated sources based on fractional fourier transform. Trans. Beijing Inst. Technol. 25(10), 895–899 (2005)
Leong, P.H., Abhayapala, T.D., Lamahewa, T.A.: Multiple target localization using wideband echo chirp signals. IEEE Trans. Signal Process. 61(16), 4077–4089 (2013)
Chong, H., Xiaomin, Z.: Doa estimation of multi-component LFM in complex environment using esprit based on FRFT. In: 2011 IEEE international conference on signal processing, communications and computing (ICSPCC), pp. 1–4, IEEE (2011)
Li, B., Wang, X.: Sparse representation-based doa estimation of coherent wideband lfm signals in frft domain. EURASIP J. Wirel. Commun. Netwk. 2017(1), 1–9 (2017)
Zhong, J., Chen, Z., Peng, F., Bi, X., Chen, T.: Direction-of-arrival estimation for wideband linear frequency modulated signals with weighted l1-norm in the fractional fourier domain. IET Radar Sonar Navig. 17(9), 1420–1429 (2023)
Tang, G., Bhaskar, B.N., Shah, P., Recht, B.: Compressed sensing off the grid. IEEE Trans. Inform. Theory 59(11), 7465–7490 (2013)
Yang, Z., Xie, L.: Exact joint sparse frequency recovery via optimization methods. IEEE Trans. Signal Process. 64(19), 5145–5157 (2016)
Li, Y., Chi, Y.: Off-the-grid line spectrum denoising and estimation with multiple measurement vectors. IEEE Trans. Signal Process. 64(5), 1257–1269 (2015)
Yang, Z., Xie, L.: Enhancing sparsity and resolution via reweighted atomic norm minimization. IEEE Trans. Signal Process. 64(4), 995–1006 (2015)
Yang, Z., Xie, L.: Achieving high resolution for super-resolution via reweighted atomic norm minimization. In: 2015 IEEE international conference on acoustics, speech and signal processing (ICASSP), pp. 3646–3650, IEEE, (2015)
Ozaktas, H.M., Arikan, O., Kutay, M.A., Bozdagt, G.: Digital computation of the fractional Fourier transform. IEEE Trans. Signal Process. 44(9), 2141–2150 (1996)
Bhaskar, B.N., Tang, G., Recht, B.: Atomic norm denoising with applications to line spectral estimation. IEEE Trans. Signal Process. 61(23), 5987–5999 (2013)
Hansen, T.L., Jensen, T.L.: A fast interior-point method for atomic norm soft thresholding. Signal Process. 165, 7–19 (2019)
Toh, K.-C., Todd, M.J., Tütüncü, R.H.: Sdpt3-a MATLAB software package for semidefinite programming, version 1.3. Optim. Methods Softw. 11(1–4), 545–581 (1999)
Malioutov, D., Cetin, M., Willsky, A.S.: A sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Trans. Signal Process. 53(8), 3010–3022 (2005)
Funding
This work was supported in part by the autonomously deployed “Frontier Exploration” type project (QYTS202013) from the Institute of Acoustics, Chinese Academy of Sciences.
Author information
Authors and Affiliations
Contributions
Wei Zhao: Conceptualization, methodology, software, writing—original draft and writing—review and editing. Xuan Li: Methodology, writing— review and editing. Yiding Gao: Software, investigation. Chengpeng Hao: Supervision, writing—review and editing.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no Conflict of interest regarding this work.
Ethics approval
The authors confirm that they have complied with the publication ethics and state that this work is original and has not been used for publication anywhere before.
Consent to participate
The authors are willing to participate in journal promotions and updates.
Consent for publication
The authors give consent to the journal regarding the publication of this work.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zhao, W., Li, X., Gao, Y. et al. Fast gridless direction-of-arrival estimation for wideband linear frequency modulated signals Based on fractional Fourier transform. SIViP 19, 57 (2025). https://doi.org/10.1007/s11760-024-03627-x
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11760-024-03627-x