Multiple-input multiple-output (MIMO) radar has superior performance to conventional one. It has been introduced to almost every application field of conventional radar in recent years. In practical application, MIMO radar also faces the problem of congested spectrum assignment, which makes it not possible to have a continuous clear band with large bandwidth. Sparse frequency waveform that contains several individual clear bands is a desirable solution to this problem. In this paper, we propose a method to design sparse frequency waveform set with low sidelobes in autocorrelations and cross-correlations by optimizing an objective function constructed based on Power Spectrum Density requirement and sidelobe performances of waveform set. Thus, besides the property of approximate orthogonality, the designed waveforms obtain the ability of avoiding spectrum interference to/from other users. The waveform is phasecoded and thereby has constant modulus. The effectiveness of the proposed method is illustrated by numerical studies. Practical implementation issues such as quantization effect and Doppler effect are also discussed.
1. Fisher, E., A. Haimovich, R. Blum, L. Cimini, D. Chizhik, and R. Valenzuela, "MIMO radar: An idea whose time has come," Proceedings of IEEE Radar Conference 2004, 71-78, Apr. 2004.
2. Fisher, E., A. Haimovich, R. Blum, L. Cimini, D. Chizhik, and R. Valenzuela, "Spatial diversity in radars --- Models and detection performance," IEEE Transactions on Signal Processing, Vol. 20, No. 3, 823-838, Mar. 2006. doi:10.1109/TSP.2005.862813
3. Bliss, D. W. and K. W. Forsythe, "Multiple-input multiple-output (MIMO) radar and imaging: Degrees of freedom and resolution," Proceedings of 37th Asilomar Conference on Signals, System, and Computers, 54-59, Nov. 2003.
4. Li, J., "MIMO radar: Diversity means superiority," Proceedings of Adaptive Sensor Array Processing-2006, 305-309, Jun. 2006.
5. Li, J., P. Stoica, L. Xu, and W. Roberts, "On parameter identifiability of MIMO radar," IEEE Signal Processing Letters, Vol. 14, No. 12, 968-971, Dec. 2007. doi:10.1109/LSP.2007.905051
6. Sammartino, P. F., C. J. Baker, and H. D. Griffths, "MIMO radar performance in clutter environment," Proceedings of 2006 CIE Radar Conference, 1-4, Shanghai, Oct. 2006.
7. Bekkerman, I. and J. Tabrikian, "Target detection and localization using MIMO radars and sonars," IEEE Transactions on Signal Processing, Vol. 54, No. 10, 3873-3883, Oct. 2006. doi:10.1109/TSP.2006.879267
8. Deng, H., "Polyphase code design for orthogonal netted radar systems," IEEE Transactions on Signal Processing, Vol. 52, No. 11, 3126-3135, Nov. 2004. doi:10.1109/TSP.2004.836530
9. Khan, H. A., Y. Y. Zhang, C. Ji, C. J. Stevens, D. J. Edwards, and D. O'Brien, "Optimizing polyphase sequences for orthogonal netted radar ," IEEE Signal Processing Letters, Vol. 13, No. 10, 589-592, Oct. 2006. doi:10.1109/LSP.2006.877143
10. Li, J., P. Stoica, and X. Zhu, "MIMO radar waveform synthesis," Proceedings of IEEE Radar Conference 2008, 1-6, May 2008. doi:10.1109/RADAR.2008.4721035
11. He, H., P. Stoica, and J. Li, "Designing unimodular sequence sets with good correlations | Including an application to MIMO radar," IEEE Transactions on Signal Processing, Vol. 57, No. 11, 4391-4405, 2009. doi:10.1109/TSP.2009.2025108
12. Frazer, G. J., Y. I. Abramovich, B. A. Johnson, and F. C. Robey, "Recent results in MIMO over-the-horizon radar," Proceedings of IEEE Radar Conference, 1-6, May 2008.
13. Lesturgie, M., "Improvement of high-frequency surface waves radar performances by use of multiple-input multiple-output configurations ," IET Radar Sonar & Navigation, Vol. 3, 49-61, May 2008.
14. Wang, G. H. and Y. L. Lu, "High resolution MIMO-HFSWR using sparse frequency waveforms," Proceedings of ICSP, 1-6, Oct. 2008.
15. Lindenfeld, M. J., "Sparse frequency transmit and receive waveform design," IEEE Trans. on Aerospace and Electronic Systems, Vol. 40, 851-861, Jul. 2004.
16. Liu, W. X., Y. L. Lu, and M. Lesturgie, "Optimal sparse waveform design for HFSWR system," Proc. 2007 International Waveform Diversity and Design conference, 127-130, Pisa, Italy, May 26-30, 2007.
17. Wang, G. H. and Y. L. Lu, "Sparse frequency transmit waveform design with soft-power constraint by using PSO algorithm," Proc. IEEE Radar 2008, 127-130, Roma, Italy, May 2008.
18. Smith, S. T., "Optimum phase-only adaptive nulling," IEEE Transactions on Signal Processing, Vol. 47, No. 2, 1835-1843, Feb. 1999. doi:10.1109/78.771033
19. Kennedy, J. and R. Ebrhart, "Particle swarm optimization," Proc. IEEE Conf. Neural Networks IV, 1942-1948, Nov. 1995.
20. Ebrhart, R. and J. Kennedy, "A new optimizer using particle swarm theory," Proc. Intern. Symp. Micro. Mach. Hum. Sci., 39-43, Apr. 1995. doi:10.1109/MHS.1995.494215
21. Trelea, I. C., "The particle swarm optimization algorithm: Convergence analysis and parameter selection," Information Processing Letters, Vol. 85, 317-325, 2003. doi:10.1016/S0020-0190(02)00447-7
22. Parsopoulos, K. E. and M. N. Vrahatis, "Recent approaches to global optimization problems through particle swarm optimization," Natural Computing, Vol. 1, 235-306, 2002. doi:10.1023/A:1016568309421
23. Abramovich, Y. I., "Bounds on the volume and height distributions for the MIMO radar ambiguity function," IEEE Signal Processing Letters, Vol. 15, 505-508, 2008. doi:10.1109/LSP.2008.922514