Abstract
MIMO technology can transmit orthogonal waveforms and achieve virtual array aperture gain, providing higher angle measurement accuracy. It has been widely applied in the field of target angle estimation. However, achieving a balance between angle estimation accuracy and computational complexity in complex underwater environments remains challenging, and effective strategies are needed to mitigate the impact of symmetrical noise. This paper proposes the method for bistatic MIMO sonar based on the reduced-order regularized multi-measurement vector Focal Underdetermined System Solver ( RD-MFOCUSS) under Toeplitz symmetric noise. First, the signal covariance matrix is reconstructed by using the imaginary Toeplitz Hermitian transform, and the difference operation is performed with the original covariance matrix to eliminate the influence of noise. Next, according to the structural characteristics of the difference covariance matrix, the direction of departure ( DOD) and the direction of arrival ( DOA) are separated to reduce the search complexity. Finally, the sparse signal is reconstructed using RD-MFOCUSS, thereby achieving the estimation of the target’s DOA and DOD. The proposed approach effectively improves the imbalance between computational complexity and estimation accuracy compared to existing methods. It also performs well with colored noise and target angle estimation under limited measurement data. The effectiveness of the proposed method is validated through numerical simulations.
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References
Tian, Y., Liu, M., Zhang, S., Zhou, T.: Underwater multi-target passive detection based on transient signals using adaptive empirical mode decomposition. Appl. Acoust. 190(108641), 1–3 (2022)
Haimovich, A.M., Blum, R.S., Cimini, L.J.: MIMO radar with widely separated antennas. IEEE Signal Process. Mag. 25, 116–129 (2008)
Andrews, G., et al.: What will 5G be ? IEEE J. Sel. Areas Commun. 32, 1065–1082 (2014)
Gesbert, D., Bolcskei, H., Gore, D.A., Paulraj, A.J.: Outdoor MIMO wireless channels: models and performance prediction. IEEE Trans. Commun. 50, 1926–1934 (2002)
Pailhas, Y., Petillot, Y., Brown, K., Mulgrew, B.: Spatially distributed MIMO sonar systems: principles and capabilities. IEEE J. Ocean. Eng. 42, 738–749 (2017)
Petillot, Y., Chaoran, Du., Thompson, J.S.: Predicted detection performance of mimo radar. IEEE Signal Process. Lett. 15, 83–86 (2008)
Robey, F.C., Coutts, S., Weikle, D., McHarg, J.C., Cuomo, K.: MIMO radar theory and experimental results. IEEE Xplore 1, 300–304 (2004)
Van Veen, B.D., Buckley, K.M.: Beamforming: a versatile approach to spatial filtering. IEEE ASSP Mag. 5, 4–24 (1988)
Schmidt, R.: Multiple emitter location and signal parameter estimation. IEEE Trans. Antennas Propag. 34, 276–280 (1986)
Khan, Z.I., Awang, R.A., Sulaiman, A.A., et al.: Performance analysis for Estimation of signal Parameters via Rotational Invariance Technique (ESPRIT) in estimating Direction of Arrival for linear array antenna, 2008 IEEE International RF and Microwave Conference. Kuala Lumpur, Malaysia (2008)
Yang, Z., Xie, L., Zhang, C.: Off-grid direction of arrival estimation using sparse Bayesian inference. IEEE Trans. Signal Process. 61, 38–43 (2013)
Zhang, D., Zhang, Y., Zheng, G., Feng, C., Tang, J.: Fast super-resolution estimation of DOA and DOD in bistatic MIMO Radar with off-grid targets. Int. J. Electron. 105, 866–881 (2018)
Xenaki, A., Gerstoft, P., Mosegaard, K.: Compressive beamforming. J. Acoust. Soc. Am. 136, 260–271 (2014)
Li, X., Guo, M., Liu, L.: A compressive measurement-based bistatic MIMO radar system for direction finding. IEEE Syst. J. 17, 2237–2246 (2023)
Xia, H., Yang, K., Ma, Y., Wang, Y., Liu, Y.: Noise reduction method for acoustic sensor arrays in underwater noise. IEEE Sens. J. 16, 8972–8981 (2016)
Cheng, X., Wang, Y.: Noise suppression for direction of arrival estimation in co-located MIMO sonar. Sensors 19, 1325–1325 (2019)
Hu, J., Baidoo, E., Tian, Y., Zeng, B.: Hermitian transform-based differencing approach for angle estimation for bistatic mimo radar under unknown colored noise field. IEEE Access 8, 129553–129561 (2020)
Baidoo, E., Hu, J., Zeng, B., Kwakye, B.D.: Joint DOD and DOA estimation using tensor reconstruction based sparse representation approach for bistatic MIMO radar with unknown noise effect. Signal Process. 182, 1–10 (2021)
Bencheikh, M.L., Wang, Y., He, H.: Polynomial root finding technique for joint DOA DOD estimation in bistatic MIMO radar. Signal Process. 90, 2723–2730 (2010)
Chen, P., Cao, Z., Chen, Z., Wang, X.: Off-grid DOA estimation using sparse bayesian learning in MIMO radar with unknown mutual coupling. IEEE Trans. Signal Process. 67, 208–220 (2019)
Liu, Z., Yu, S.: Alternating direction method of multipliers based on ℓ2,0-norm for multiple measurement vector problem. IEEE Trans. Signal Process. 71, 3490–3501 (2023)
Cotter, S.F., Rao, B.D., Engan, K., Kreutz-Delgado, K.: Sparse solutions to linear inverse problems with multiple measurement vectors. IEEE Trans. Signal Process.ans. Signal Process. 53, 2477–2488 (2005)
Acknowledgements
This work was supported in part by the National Key R&D Program of China under Grant 2022YFE0136800, in part by Special Topic on Stable Support for National Defense Basic Research Program Laboratory under Grant JCKYS2023604SSJS009, in part by Marine Defense Technology Innovation Fund of China Shipbuilding Research and Design Center under Grant JJ-2022-719-03, in part by Open Topic of Microsystem Technology National Defense Science and Technology Key Laboratory (6142804230106), in part by Open Fund of Marine Environmental Detection Technology and Application Key Laboratory, Ministry of Natural Resources (MESTA-2022-A006), in part by the new round of "Double First Class" discipline collaborative innovation achievement project in Heilongjiang Province in 2023 under Grant LJGXCG2023-066, in part by Xi’an Science and Technology Plan Project under Grant 2022FWQY16, and in part by Collaborative Detection Technology Based on Multi-Base Passive Sonar Array under Grant KY10800240014.
Funding
The Funding was provided by the National Key R&D Program of China, 2022YFE0136800, Special Topic on Stable Support for National Defense Basic Research Program Laboratory, JCKYS2023604SSJS009, Marine Defense Technology Innovation Fund of China Shipbuilding Research and Design Center, JJ-2022-719-03, Open Topic of Microsystem Technology National Defense Science and Technology Key Laboratory, 6142804230106, Open Fund of Marine Environmental Detection Technology and Application Key Laboratory, Ministry of Natural Resources, MESTA-2022-A006, the new round of "Double First Class" discipline collaborative innovation achievement project in Heilongjiang Province in 2023, LJGXCG2023-066, Collaborative Detection Technology Based on Multi-Base Passive Sonar Array, KY10800240014, Xi’an Science and Technology Plan Project, 2022FWQY16.
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X.M.:Conceptualization, Funding Acquisition,Writing—Original Draft Y.X.:Writing—Original Draft, Software, Formal Analysis H.Z.:Data Curation, Project Administration R.K.:Methodology, Supervision Y.W.:Supervision C.W.:Writing—Review & Editing W.W.:Validation H.W.:Supervision Z.W.:Writing—Review & Editing.
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Ma, X., Xiang, Y., Zhu, H. et al. Joint DOD and DOA estimation for bistatic MIMO sonar based on reduced-order regularized MFOCUSS. SIViP 19, 194 (2025). https://doi.org/10.1007/s11760-024-03802-0
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DOI: https://doi.org/10.1007/s11760-024-03802-0