A pattern synthesis approach based on a modified alternating projection method in an affine coordinate system is proposed in this paper. The approach is suitable for large planar arrays with periodic parallelogram element layout. According to the affine transformation theory, the radiation pattern of the array with a periodic parallelogram element layout could be written down immediately from that of a conventional one with rectangle cells when a pattern invariant group is defined. Just as known, the conventional alternating projection method is sensitive to the starting point and easy to fall into local optimum; in this paper we introduce a modified alternating projection method with a variable projection operator. To verify the rationality of the proposed method, several examples have been performed on our personal computer. Results show that the method could quickly synthesize the array patterns to the required with high accuracy. In addition, if the array has a triangle or parallelogram element layout, the required antennas to fill up the aperture is reduced when compared with the conventional one with antennas arranged along a rectangle grid. In our examples, the maximum reduction is about 18.09%, which is quite beneficial to reduce the weight and cost of the array.
1. Sharp, E. D., "A triangular arrangement of planar-array elements that reduces the number needed," IRE Transactions on Antennas and Propagation, Vol. 9, No. 2, 126-129, 1961. doi:10.1109/TAP.1961.1144967
2. Lo, Y. T. and S. W. Lee, "A±ffie transformation and its application to antenna arrays," IEEE Transactions on Antennas and Propagation, Vol. 13, No. 6, 890-896, 1965. doi:10.1109/TAP.1965.1138541
3. Han, J. H., S. H. Lim, and N. H. Myung, "Array antenna TRM failure compensation using adaptively weighted beam pattern mask based on genetic algorithm," IEEE Antennas and Wireless Propagation Letters, Vol. 11, 18-21, 2012. doi:10.1109/LAWP.2011.2181475
4. Cen, L., et al., "Linear aperiodic array synthesis using an improved genetic algorithm," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 2, 895-902, 2012. doi:10.1109/TAP.2011.2173111
5. Ismail, T. H. and Z. M. Hamici, "Array pattern synthesis using digital phase control by quantized particle swarm optimization," IEEE Transactions on Antennas and Propagation, Vol. 58, No. 6, 2142-2145, 2010. doi:10.1109/TAP.2010.2046853
6. Wang, W. B., Q. Y. Feng, and D. Liu, "Synthesis of thinned linear and planar antenna arrays using binary PSO algorithm," Progress In Electromagnetics Research, Vol. 127, 371-387, 2012. doi:10.2528/PIER12020301
7. Bai, Y. Y., et al., "A hybrid IWO/PSO algorithm for pattern synthesis of conformal phased arrays," IEEE Transactions on Antennas and Propagation, Vol. 61, No. 4, 2328-2332, 2013. doi:10.1109/TAP.2012.2231936
8. Yang, J., et al., "A hybrid ABC-DE algorithm and its application for time-modulated arrays pattern synthesis," IEEE Transactions on Antennas and Propagation, Vol. 61, No. 11, 5485-5495, 2013. doi:10.1109/TAP.2013.2279093
9. Keizer, W. P. M. N., "Fast low-sidelobe synthesis for large planar array antennas utilizing successive fast Fourier transforms of the array factor," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 3, 715-722, 2007. doi:10.1109/TAP.2007.891511
10. Keizer, W. P. M. N., "Element failure correction for a large monopulse phased array antenna with active amplitude weighting," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 8, 2211-2218, 2007. doi:10.1109/TAP.2007.902008
11. Keizer, W. P. M. N., "Large planar array thinning using iterative FFT techniques," IEEE Transactions on Antennas and Propagation, Vol. 57, 3359-3362, 2009. doi:10.1109/TAP.2009.2029382
12. Wang, X. K., Y. C. Jiao, and Y. Y. Tan, "Synthesis of large thinned planar arrays using a modified iterative Fourier technique," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 4, 1564-1571, 2014. doi:10.1109/TAP.2014.2302836
13. Bucci, O. M., et al., "Intersection approach to array pattern synthesis," IEE Proceedings H, on Microwaves, Antennas and Propagation, Vol. 137, No. 6, 349-357, 1990. doi:10.1049/ip-h-2.1990.0064
14. Bucci, O. M., et al., "Antenna pattern synthesis: A new general approach," Proceedings of the IEEE, Vol. 82, No. 3, 358-371, 1994. doi:10.1109/5.272140
15. Trincia, D., et al., "Modified projection method for array pattern synthesis," IEEE 34th European Microwave Conference, 1397-1400, Amsterdam, Netherlands, Oct. 2004.
16. Quijano, J. L. A. and G. Vecchi, "Alternating adaptive projections in antenna synthesis," IEEE Transactions on Antennas and Propagation, Vol. 58, No. 3, 727-737, 2010. doi:10.1109/TAP.2009.2039307
17. Han, D. D., W. Wu, and B. Du, "Perturbation alternating projections method for pattern synthesis of phased array antenna," IEEE Global Symposium on Millimeter Waves (GSMM), 385-388, Harbin, China, May 2012.
18. Franceschetti, G., G. Mazzarella, and G. Panariello, "Array synthesis with excitation constraints," IEEE Antennas and Propagation Society International Symposium, 1192-1195, Jun. 1988.