volume | PIER Journals

Abstract

Element failure distorts the main-lobe pattern and increases side-lobe power level, which is almost impossible to be corrected artificially for space-borne array. It might be solved by redistributing the excitations of the left functional elements; however, this is a nonlinear, non-convex, and NP-hard problem. In this paper, two effective approaches are proposed for failure correction, which is performed for space-borne hexagonal array using digital beamforming (DBF). One method, a modified real-code genetic algorithm (RCGA), is employed that uses reinsertion and worst-elimination schemes, but it pays the high computation complexity. The other approach based on convex optimization chooses the excitations synthesized by RCGA as the initial points, and skillfully transforms the non-convex problem into a sequence of second-order cone programming (SOCP) problem, which is solved iteratively by efficient optimization tool. Numerical results confirm that after the correction based on iterative convex optimization, the average root-mean-square error (RMSE) is reduced by 36%, and the relative side-lobe level (RSLL) is improved by 6.7 dB, with respect to the RCGA-based correction pattern.

1. Rohwer, A. B., D. H. Desrosiers, W. Bach, et al. "Iridium main mission antennas: A phased array success story and mission update," IEEE International Symposium on Phased Array Systems and Technology, 504-511, 2010. Google Scholar

2. Croq, F., E. Vourch, M. Reynaud, et al. "The Globalstar 2 antenna sub-system," 3rd European Conference on Antennas and Propagation, 598-602, 2009. Google Scholar

3. Liang, G., W. Gong, H. Liu, et al. "Development of 61-channel digital beam-forming (DBF) transmitter array for mobile satellite communication," Progress In Electromagnetics Research, Vol. 97, 175-195, 2009. Google Scholar

4. Mailloux, R. J., "Array failure correction with a digital beamformed array," IEEE Transactions on Antennas and Propagation, Vol. 44, No. 12, 1543-1550, 1996.
doi:10.1109/8.546240 Google Scholar

5. Levitas, M., D. A. Horton, and T. C. Cheston, "Practical failure compensation in active phased arrays," IEEE Transactions on Antennas and Propagation, Vol. 47, No. 3, 524-535, 1999.
doi:10.1109/8.768788 Google Scholar

6. Peters, T. J., "A conjugate gradient-based algorithm to minimize the sidelobe level of planar arrays with element failures," IEEE Transactions on Antennas and Propagation, Vol. 39, No. 10, 1497-1504, 1991.
doi:10.1109/8.97381 Google Scholar

7. Mitilineos, S. A. and C. N. Capsalis, "On array failure mitigation using genetic algorithms and a priori joint optimization," IEEE Transactions on Antennas and Propagation, Vol. 47, No. 5, 227-232, 2005.
doi:10.1109/MAP.2005.1599213 Google Scholar

8. Yeo, B. K. and Y. Lu, "Fast array failure correction using improved particle swarm optimization," Apmc: 2009 Asia Pacific Microwave Conference, Vol. 1, 1537-1540, 2009.
doi:10.1109/APMC.2009.5384420 Google Scholar

9. Acharya, O. P., A. Patnaik, and B. Choudhury, "Fault finding in antenna arrays using bacteria foraging optimization technique," National Conference on Communications (NCC), 1-5, 2011. Google Scholar

10. Zhao, H., Y. Zhang, E. Li, et al. "Diagnosis of array failure in impulsive noise environment using unsupervised support vector regression method," IEEE Transactions on Antennas and Propagation, Vol. 61, No. 11, 5508-5516, 2013.
doi:10.1109/TAP.2013.2275750 Google Scholar

11. Lebret, H. and S. Boyd, "Antenna array pattern synthesis via convex optimization," IEEE Transactions on Signal Processing, Vol. 45, No. 3, 526-532, 1997.
doi:10.1109/78.558465 Google Scholar

12., Microwave Vision Group, Antenna Measurement and Radome Test System, MVG-EBOOK, 2013.

13. Song, H., G. Liang, W. Gong, et al. "Performance analysis of a seven-beam CDMA-based LEO satellite system," IEEE Asia-Paci¯c Conference on Antennas and Propagation, 174-175, 2012. Google Scholar

14. Kenneth, A., J. De, A. D. Kenneth, et al. "Generation gaps revisited," Foundations of Genetic Algorithms, 1992. Google Scholar

15. Wang, F., V. Balakrishnan, P. Y. Zhou, et al. "Optimal array pattern synthesis using semidefinite programming," IEEE Transactions on Signal Processing, Vol. 51, No. 5, 1172-1183, 2003.
doi:10.1109/TSP.2003.810308 Google Scholar

16. Fuchs, B., A. Skrivervik, and J. R. Mosig, "Shaped beam synthesis of arrays via sequential convex optimizations," IEEE Antennas and Wireless Propagation Letters, Vol. 12, 1049-1052, 2013.
doi:10.1109/LAWP.2013.2280043 Google Scholar

17. Sturm, J. F., "Using SeDuMi 1.02, A matlab toolbox for optimization over symmetric cones," Optimization Methods and Software, Vol. 11, No. 12, 625-653, 1999.
doi:10.1080/10556789908805766 Google Scholar

Dr. Haiwei Song

Professor Guang Liang

Dr. Wenbin Gong

Dr. Jinpei Yu