volume | PIER Journals

Abstract

In multi-input multi-output (MIMO) radar transmit beampattern synthesis, most current literature formulates the problems in steradian space. However, since the beampattern and its parameters are both measured and defined in radian space, from the view point of physical meaning, it will be better to reformulate the problems in radian space rather than in steradian space. In this paper, we propose methods in the radian space to synthesize beampatterns based on minimizing sidelobe level for the two main designs in MIMO radar, i.e. minimum sidelobe beampattern design (MSBD) and beampattern matching design (BMD). For MSBD, the design criteria considering both peak sidelobe level and integrated sidelobe level is proposed. By this we can have a good tradeoff between the intensity and power distribution in beampattern synthesis. After a two-step converting, the formulation of the criteria is transformed into a convex programming, where a global optimal solution can be obtained. For BMD, instead of minimizing mean square error directly as in conventional methods, we propose a power-approximation-based method by minimizing integrated sidelobe level. Finally, numerical comparisons with classical methods demonstrate that the proposed MSBD maintains for all range of main lobe width and the proposed BMD has smoother main lobes with maximal power focused in.

1. Li, J., Y. Xie, P. Stoica, X. Zheng, and J. Ward, "Beampattern synthesis via a matrix approach for signal power estimation," IEEE Trans. Signal Process., Vol. 55, No. 12, 5643-5657, Dec. 2007.
doi:10.1109/TSP.2007.899343

2. Qu, Y., G. Liao, S.-Q. Zhu, and X.-Y. Liu, "Pattern synthesis of planar antenna array via convex optimization for airborne forward looking radar," Progress In Electromagnetics Research, Vol. 84, 1-10, 2008.
doi:10.2528/PIER08060301

3. Hu, L., H. Liu, S. Zhou, and S. Wu, "Convex optimization applied to transmit beampattern synthesis and signal waveform design for MIMO radar," 2009 IET International Radar Conference, 1-5, Apr. 2009.

4. Nai, S. E., W. Ser, Z.-L. Yu, and H. Chen, "Beampattern synthesis for linear and planar arrays with antenna selection by convex optimization," IEEE Trans. Antennas Propag., Vol. 58, No. 12, 3923-2930, Dec. 2010.
doi:10.1109/TAP.2010.2078446

5. Zhang, T. and W. Ser, "Robust beampattern synthesis for antenna arrays with mutual coupling effect," IEEE Trans. Antennas Propag., Vol. 59, No. 8, 2889-2895, Feb. 2011.
doi:10.1109/TAP.2011.2152329

6. Fuchs, B., "Synthesis of sparse arrays with focused or shaped beampattern via sequential convex optimizations," IEEE Trans. Antennas Propag., Vol. 60, No. 7, 3499-3503, Jul. 2012.
doi:10.1109/TAP.2012.2196951

7. Fuhrmann, D. and G. San Antonio, "Transmit beamforming for MIMO radar systems using partial signal correlation," Proc. 38th Asilomar Conf. Signals, Syst. Comput., Vol. 1, 295-299, Nov. 2004.

8. Li, J. and P. Stoica, "MIMO radar with colocated antennas," IEEE Signal. Process. Mag., Vol. 24, No. 5, 106-114, Sep. 2007.
doi:10.1109/MSP.2007.904812

9. Qu, Y., G. Liao, S.-Q. Zhu, X.-Y. Liu, and H. Jiang, "Performance analysis of beamforming for MIMO radar," Progress In Electromagnetics Research, Vol. 84, 123-134, 2008.
doi:10.2528/PIER08062306

10. Roberts, W., L. Xu, J. Li, and P. Stoica, "Sparse antenna array design for MIMO active sensing applications," IEEE Trans. Antennas Propag., Vol. 59, No. 3, 846-858, Mar. 2011.
doi:10.1109/TAP.2010.2103550

11. Chen, H., X. Li, and Z. Zhuang, "Antenna geometry conditions for MIMO radar with uncoupled direction estimation," IEEE Trans. Antennas Propag., Vol. 60, No. 7, 3455-3465, Jul. 2012.
doi:10.1109/TAP.2012.2197091

12. Aittomaki, T. and V. Koivunen, "Signal covariance matrix optimization for transmit beamforming in MIMO radars," Proc. 41th Asilomar Conf. Signals, Syst. Comput., 182-186, Nov. 2007.

13. Li, J., P. Stoica, and Y. Xie, "On probing signal design for MIMO radar," Proc. 40th Asilomar Conf. Signals, Syst. Comput., 31-35, Pacific Grove, CA, Oct. 2006.

14. Stoica, P., J. Li, and Y. Xie, "On probing signal design for MIMO radar," IEEE Trans. Signal Process., Vol. 55, No. 8, 4151-4161, Aug. 2007.
doi:10.1109/TSP.2007.894398

15. Aittomaki, T. and V. Koivunen, "Low-complexity method for transmit beamforming in MIMO radars," Proc. IEEE Int. Conf. Acoust., Speech and Signal Processing (ICASSP), 305-308, Apr. 2007.

16. Fuhrmann, D. and G. San Antonio, "Transmit beamforming for MIMO radar systems using signal cross-correlation," IEEE Trans. Aerosp. Electron. Syst., Vol. 44, No. 1, 171-186, Jan. 2008.
doi:10.1109/TAES.2008.4516997

17. Stoica, P., J. Li, and X. Zhu, "Waveform synthesis for diversity-based transmit beampattern design," IEEE Trans. Signal Process., Vol. 56, No. 6, 2593-2598, Jun. 2008.
doi:10.1109/TSP.2007.916139

18. Aittomaki, T. and V. Koivunen, "Beampattern optimization by minimization of quartic polynomial," Proc. 15 IEEE/SP Statist. Signal Process. Workshop, 437-440, Cardiff, UK, Sep. 2009.

19. Ahmed, S., J. Thompson, Y. Petillot, and B. Mulgrew, "Unconstrained synthesis of covariance matrix for MIMO radar transmit beampattern ," IEEE Trans. Signal Process., Vol. 59, No. 8, 3837-3849, Aug. 2011.
doi:10.1109/TSP.2011.2153200

20. Martinezl, A. and J. Marchand, "SAR image quality assessment," Revista de Teledeteccion, Vol. 2, 12-18, Nov. 1993.

21. Liu, Y., Y.-K. Deng, R. Wang, and X. Jia, "Bistatic FMCW SAR raw signal simulator for extended scenes," Progress In Electromagnetics Research, Vol. 128, 479-502, 2012.

22. Boyd, S. and L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, UK, 2004.

Mr. Haisheng Xu

Dr. Jian Wang

Prof. Jian Yuan

Dr. Xiuming Shan