Abstract
In this paper, we investigate the problem of joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation for bistatic multiple-input multiple-output radar with unknown spatially colored noise. By exploiting the sparse structure of the noise covariance matrix, a new de-noising scheme is designed. The signal covariance matrix is recast as a low-rank matrix with missing entries, which can be approximately tackled via solving an optimization problem. Thereafter, DODs and DOAs are obtained with the traditional subspace techniques. The proposed method does not bring any virtual aperture loss; thus, it achieves more accurate estimation performance than several state-of-the-art de-noising methods. Finally, the stochastic Cramer–Rao bound for joint direction finding is derived. Numerical computer simulations verify the effectiveness of the proposed algorithm.
Similar content being viewed by others
References
J.F. Cai, E.J. Candes, Z. Shen, A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20(4), 1956–1982 (2008)
E.J. Candes, B. Recht, Exact matrix completion via convex optimization. Found. Comput. Math. 9(6), 717 (2009)
J. Chen, H. Gu, W. Su, A new method for joint DOD and DOA estimation in bistatic MIMO radar. Signal Process. 90(2), 714–718 (2010). https://doi.org/10.1016/j.sigpro.2009.08.003
C. Duofang, C. Baixiao, Q. Guodong, Angle estimation using esprit in MIMO radar. Electron. Lett. 44(12), 770–771 (2008). https://doi.org/10.1049/el:20080276
M. Fazel, H. Hindi, S.P. Boyd, A rank minimization heuristic with application to minimum order system approximation, in Proceedings of the American Control Conference, vol. 6, pp. 4734–4739 (2001)
E. Fishler, A. Haimovich, R. Blum, D. Chizhik, L. Cimini, R. Valenzuela, Mimo radar: an idea whose time has come, in Proceedings of the IEEE Radar Conference, pp. 71–78 (2004). https://doi.org/10.1109/NRC.2004.1316398
A.B. Gershman, P. Stoica, M. Pesavento, E.G. Larsson, Stochastic Cramer–Rao bound for direction estimation in unknown noise fields. IET Radar Sonar Navig. 149(1), 2–8 (2002)
A. Haimovich, R. Blum, L. Cimini, MIMO radar with widely separated antennas. IEEE Signal Process. Mag. 25(1), 116–129 (2008). https://doi.org/10.1109/MSP.2008.4408448
K. Han, A. Nehorai, Nested vector-sensor array processing via tensor modeling. IEEE Trans. Signal Process. 62(10), 2542–2553 (2014). https://doi.org/10.1109/TSP.2014.2314437
S. Hong, X. Wan, F. Cheng, H. Ke, Covariance differencing-based matrix decomposition for coherent sources localisation in bi-static multiple-input Cmultiple-output radar. IET Radar Sonar Navig. 9(5), 540–549 (2015). https://doi.org/10.1049/iet-rsn.2014.0193
H. Jiang, J.K. Zhang, K.M. Wong, Joint DOD and DOA estimation for bistatic MIMO radar in unknown correlated noise. IEEE Trans. Veh. Technol. 64(11), 5113–5125 (2015). https://doi.org/10.1109/TVT.2014.2384495
M. Jin, G. Liao, J. Li, Joint dod and doa estimation for bistatic MIMO radar. Signal Process. 89(2), 244–251 (2009). https://doi.org/10.1016/j.sigpro.2008.08.003
J. Li, P. Stoica, Mimo radar with colocated antennas. IEEE Signal Process. Mag. 24(5), 106–114 (2007). https://doi.org/10.1109/MSP.2007.904812
J. Li, P. Stoica, L. Xu, W. Roberts, On parameter identifiability of MIMO radar. IEEE Signal Process. Lett. 14(12), 968–971 (2007). https://doi.org/10.1109/LSP.2007.905051
J. Li, X. Zhang, R. Cao, M. Zhou, Reduced-dimension MUSIC for angle and array gain-phase error estimation in bistatic MIMO radar. IEEE Commun. Lett. 17(3), 443–446 (2013). https://doi.org/10.1109/LCOMM.2013.012313.122113
B. Liao, Fast angle estimation for MIMO radar with nonorthogonal waveforms. IEEE Trans. Aerosp. Electron. Syst. 54(4), 2091–2096 (2018). https://doi.org/10.1109/TAES.2018.2847958
J. Liu, X. Wang, W. Zhou, Covariance vector sparsity-aware DOA estimation for monostatic MIMO radar with unknown mutual coupling. Signal Process. 119, 21–27 (2016a). https://doi.org/10.1016/j.sigpro.2015.07.012
J. Liu, W. Zhou, X. Wang, Fourth-order cumulants-based sparse representation approach for doa estimation in MIMO radar with unknown mutual coupling. Signal Process. 128, 123–130 (2016). https://doi.org/10.1016/j.sigpro.2016.03.019
P. Stoica, J. Li, Y. Xie, On probing signal design for MIMO radar. IEEE Trans. Signal Process. 55(8), 4151–4161 (2007). https://doi.org/10.1109/TSP.2007.894398
X. Wang, W. Wang, X. Li, J. Wang, A tensor-based subspace approach for bistatic MIMO radar in spatial colored noise. Sensors 14(3), 3897–3907 (2014a). https://doi.org/10.3390/s140303897
X. Wang, W. Wang, J. Liu, X. Li, J. Wang, A sparse representation scheme for angle estimation in monostatic MIMO radar. Signal Process. 104(6), 258–263 (2014). https://doi.org/10.1016/j.sigpro.2014.04.007
X. Wang, W. Wang, J. Liu, Q. Liu, B. Wang, Tensor-based real-valued subspace approach for angle estimation in bistatic MIMO radar with unknown mutual coupling. Signal Process. 116, 152–158 (2015). https://doi.org/10.1016/j.sigpro.2015.03.020
F. Wen, X. Xiong, J. Su, Z. Zhang, Angle estimation for bistatic MIMO radar in the presence of spatial colored noise. Signal Process. 134, 261–267 (2017a). https://doi.org/10.1016/j.sigpro.2016.12.017
F. Wen, Z. Zhang, G. Zhang, Y. Zhang, X. Wang, X. Zhang, A tensor-based covariance differencing method for direction estimation in bistatic MIMO radar with unknown spatial colored noise. IEEE Access 5, 18451–18458 (2017). https://doi.org/10.1109/ACCESS.2017.2749404
F. Wen, Z. Zhang, X. Zhang, CRBs for direction-of-departure and direction-of-arrival estimation in collocated MIMO radar in the presence of unknown spatially coloured noise. IET Radar Sonar Navig. 13(4), 530–537 (2019). https://doi.org/10.1049/iet-rsn.2018.5386
F. Wen, Computationally efficient DOA estimation algorithm for MIMO radar with imperfect waveforms. IEEE Commun. Lett. 23(6), 1037–1040 (2019). https://doi.org/10.1109/LCOMM.2019.2911285
F. Wen, C. Mao, G. Zhang, Direction finding in MIMO radar with large antenna arrays and nonorthogonal waveforms. Digital Signal Process. 94, 75–83 (2019). https://doi.org/10.1016/j.dsp.2019.06.008
H. Yan, J. Li, G. Liao, Multitarget identification and localization using bistatic MIMO radar systems. EURASIP J. Adv. Signal Process. 2008, 48 (2008). https://doi.org/10.1155/2008/283483
Z.D. Zheng, J.Y. Zhang, Fast method for multi-target localisation in bistatic MIMO radar. Electron. Lett. 47(2), 138–139 (2011). https://doi.org/10.1049/el.2010.2577
Acknowledgements
This work was supported by National Natural Science Foundation of China (61701046, 61601504 and 61571349).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wen, F., Shi, J. & Zhang, Z. Direction Finding for Bistatic MIMO Radar with Unknown Spatially Colored Noise. Circuits Syst Signal Process 39, 2412–2424 (2020). https://doi.org/10.1007/s00034-019-01260-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-019-01260-5