Abstract
We propose an approach to design waveform sets with good auto- and cross-correlation properties. The designed waveform sets can be used for multiple-input multiple-output radars to minimize the cross-interference, and consequently improve the radar performance. Firstly, we transform the original correlation optimization problem into a spectral approximation problem. Secondly, we define the objective function based on the square error between the designed waveform matrix and the ideal one. Finally, the problem is solved by using an algorithm based on alternating projection and phase retrieval. We further improve the proposed method, and derive an extended version to design waveforms with sparse spectrum and good correlation property for combating electronic jamming. The algorithms are computationally efficient because their main steps are based on fast Fourier transform. The effectiveness of the proposed approach is demonstrated by numerical simulations.
Similar content being viewed by others
References
Bekkerman, I., & Tabrikian, (2006). Target detection and localization using MIMO radars and sonars. IEEE Transactions on Signal Processing, 54(10), 3873–3883.
Daniel, J. R., & Peter, P. (2004). Ubiquitous MIMO multifunction digital array radar. IEEE Asilomar conference on signals, systems and computers, pp. 1057–1064.
Deng, H. (2004). Polyphase code design for orthogonal netted radar systems. IEEE Transactions on Signal Processing, 52(11), 3126–3135.
Eran, F., Alexander, H., & Rick, S. B. (2006). Spatial diversity in radars-models and detection performance. IEEE Transactions on Signal Processing, 54(3), 823–838.
Guang, H., & Saman, S. A. (2013). Receiver design for range and doppler sidelobe suppression using MIMO and phased-array radar. IEEE Transactions on Signal Processing, 61(6), 1315–1326.
He, H., Stoica, P., & Li, J. (2009a). Designing unimodular sequences sets with good correlations-including an application to MIMO radar. IEEE Transactions on Signal Processing, 57(11), 4391–4405.
He, H., Stoica, P., & Li, J. (2009b) . Unimodular sequence sets with good correlations for MIMO radar. IEEE radar conference, pp. 1–6.
He, H., Stoica, P., & Li, J. (2010a). On aperiodic-correlation bounds. IEEE Signal Processing Letters, 17(3), 253–256.
He, H., Stoica, P., & Li, J. (2010b). Waveform design with stopband and correlation constraints for congnitive radar. IEEE international workshop on congnitive, information processing(CIP), pp. 344–349.
Karl, G., Michael, R. F., & Michael, J. S. (2011). Spectral nulling on transmit via nonlinear fm radar waveforms. IEEE Transactions on Aerospace and Electronic Systems, 47(2), 1507–1515.
Lee, K.P., Christine, A.B., & Braham, H. (2012). Radar-centric design of waveforms with disjoint spectral support. IEEE radar conference, pp. 0269–0274.
Leong, H. W. H., & Dawe, B. (2001). Channel availability for east coast high frequency surface wave radar systems. Technical report, DREO TR 2001-104, Defence R&D Canada.
Li, F. C., Zhao, Y. N., & Qiao, X. L. (2014). A waveform design method for suppressing range sidelobes in desired intervals. Signal Processing, 96, 203–211.
Li, J., & Stoica, P. (2007). MIMO radar with colocated antennas. IEEE Signal Processing Magazine, 24(5), 106–114.
Li, J., Stoica, P., & Xu, L. Z. (2007). On parameter identifiability of MIMO radar. IEEE Signal Processing Letters, 14(12), 968–971.
Li, J., Stoica, P., & Zheng, X. Y. (2008a). Signal synthesis and receiver design for MIMO radar imaging. IEEE Transactions on Signal Processing, 56(8), 3959–3968.
Li, J., Xu, L. Z., & Stoica, P. (2008b). Range compression and waveform optimization for MIMO radar: a cramer-rao bound based study. IEEE Transactions on Signal Processing, 56(1), 218–232.
Li, J. F., & Zhang, X. F. (2013). Sparse representation-based joint angle and doppler frequency estimation for MIMO radar. Multidimensional Systems and Signal Processing. doi:10.1007/s11045-013-0248-1.
Lindenfeld, M. J. (2004). Sparse frequency transmit and receive waveform design. IEEE Transaction on Aerospace and Electronic Systems, 40(3), 851–861.
Ma, C. Z., Tat, S. Y., & Chee, S. T. (2010). Receiver design for MIMO radar range sidelobes suppression. IEEE Transactions on Signal Processing, 58(10), 5469–5474.
Patton, L. K., & Rigling, B. D. (2012). Phase retrieval for radar waveform optimization. IEEE Transaction on Aerospace and Electronic Systems, 48(4), 3287–3302.
Patton, L. K., Frost, S. W., & Rigling, B. D. (2011). Efficient design of radar waveforms for optimised detection in coloured noise. IET Radar, Sonar & Navigation, 6(1), 21–29.
Soltanalian, P., & Stoica, P. (2012). Computational design of sequences with good correlation properties. IEEE Transactions on Signal Processing, 60(5), 2180–2193.
Steven, M. K. (1993). Fundamentals of statistical signal processing: Estimation theory. New Jersey: Prentice Hall PTR.
Stoica, P., He, H., & Li, J. (2009). New algorithms for designing unimodular sequences with good correlation properties. IEEE Transactions on Signal Processing, 57(4), 1415–1425.
Tropp, J. A., Dhillon, I. S., & Health, R. W. (2012). Designing structured tight frames via an alternating projection method. IEEE Transaction on Information Theory, 51(1), 188–209.
Wang, G. H., & Lu, Y. (2011). Designing single/multiple sparse frequency waveforms with sidelobe constraint. IET Radar, Sonar & Navigation, 5(1), 32–38.
Wang, Y. C., Dong, L., & Xue, X. (2012a). On the design of constant modulus probing signals for MIMO radars. IEEE Transactions on Signal Processing, 60(8), 4432–4438.
Wang, Y. C., Dong, L., & Xue, X. (2012b). On the design of constant modulus sequences with low correlation sidelobes levels. IEEE Communications Letters, 16(4), 462–465.
Yang, Y., Blum, R. S., & He, Z. S. (2009). Waveform design for MIMO radar using an alternating projection. IEEE Asilomar conference on signals, systems and computers, pp. 1201–1205.
Zheng, G. M., & Chen, B. X. (2013). Unitary dual-resolution ESPRIT for joint DOD and DOA estimation in bistatic MIMO radar. Multidimensional Systems and Signal Processing. doi:10.1007/s11045-013-0244-5.
Zhuang, S. N., & Zhu, X. H. (2013). Improved design of unimodular waveforms for MIMO radar. Multidimensional Systems and Signal Processing, 24(3), 447–456.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (61371181).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhao, Yn., Li, Fc., Zhang, T. et al. Computational design of optimal waveforms for MIMO radar via multi-dimensional iterative spectral approximation. Multidim Syst Sign Process 27, 43–60 (2016). https://doi.org/10.1007/s11045-014-0288-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11045-014-0288-1