In this work, we investigate the feasibility of applying deep learning to phase synthesis of reflectarray antenna. A deep convolutional neural network (ConvNet) based on the architecture of AlexNet is built to predict the continuous phase distribution on reflectarray elements given the beam pattern. The proposed ConvNet is sufficiently trained with data set generated by array-theory method. With radiation pattern and beam direction arrays as input, the ConvNet can make real-time and fairly accurate predictions in milliseconds with the average relative error below 0.7%. This paper shows that deep convolutional neural networks can ``learn'' the principle of reflectarray phase synthesis due to their inherent powerful learning capacity. The proposed approach may provide us a potential scheme for real-time phase synthesis of antenna arrays in electromagnetic engineering.
2. Mao, Y., S. Xu, F. Yang, and A. Z. Elsherbeni, "A novel phase synthesis approach for wideband reflectarray design," IEEE Transactions on Antennas and Propagation, Vol. 63, No. 9, 4189-4193, 2015. doi:10.1109/TAP.2015.2447004
3. Yang, H., F. Yang, X. Cao, S. Xu, J. Gao, X. Chen, M. Li, and T. Li, "A 1600-element dual-frequency electronically reconfigurable reflectarray at X/Ku-band," IEEE Transactions on Antennas and Propagation, Vol. 65, No. 6, 3024-3032, 2017. doi:10.1109/TAP.2017.2694703
4. Barbiere, D., "A method for calculating the current distribution of Tschebyscheff arrays," Proceedings of the IRE, Vol. 40, No. 1, 78-82, 1952. doi:10.1109/JRPROC.1952.273938
5. Chakraborty, A., B. Das, and G. Sanyal, "Beam shaping using nonlinear phase distribution in a uniformly spaced array," IEEE Transactions on Antennas and Propagation, Vol. 30, No. 5, 1031-1034, 1982. doi:10.1109/TAP.1982.1142917
6. Nayeri, P., F. Yang, and A. Z. Elsherbeni, Reflectarray Antennas: Theory, Designs, and Applications, Wiley-IEEE Press, 2018. doi:10.1002/9781118846728
7. Johnson, J. M. and Y. Rahmat-Samii, "Genetic algorithm optimization and its application to antenna design," Proceedings of IEEE Antennas and Propagation Society International Symposium and URSI National Radio Science Meeting, Vol. 1, 326-329, IEEE, 1994. doi:10.1109/APS.1994.407746
8. Lommi, A., A. Massa, E. Storti, and A. Trucco, "Sidelobe reduction in sparse linear arrays by genetic algorithms," Microwave and Optical Technology Letters, Vol. 32, No. 3, 194-196, 2002. doi:10.1002/mop.10128
9. Robinson, J. and Y. Rahmat-Samii, "Particle swarm optimization in electromagnetics," IEEE Transactions on Antennas and Propagation, Vol. 52, No. 2, 397-407, 2004. doi:10.1109/TAP.2004.823969
10. Ferreira, J. A. and F. Ares, "Pattern synthesis of conformal arrays by the simulated annealing technique," Electronics Letters, Vol. 33, No. 14, 1187-1189, 1997. doi:10.1049/el:19970838
11. Prado, D. R., A. F. Vaquero, M. Arrebola, M. R. Pino, and F. Las-Heras, "Acceleration of gradient-based algorithms for array antenna synthesis with far-field or near-field constraints," IEEE Transactions on Antennas and Propagation, Vol. 66, No. 10, 5239-5248, 2018. doi:10.1109/TAP.2018.2859915
12. Mahanti, G., A. Chakraborty, and S. Das, "Phase-only and amplitude-phase only synthesis of dual-beam pattern linear antenna arrays using oating-point genetic algorithms," Progress In Electromagnetics Research, Vol. 68, 247-259, 2007. doi:10.2528/PIER06072301
13. Capozzoli, A., C. Curcio, A. Liseno, and G. Toso, "Fast, phase-only synthesis of aperiodic reflectarrays using NUFFTs and CUDA," Progress In Electromagnetics Research, Vol. 156, 83-103, 2016. doi:10.2528/PIER16021904
14. Robustillo, P., J. Zapata, J. A. Encinar, and J. Rubio, "Ann characterization of multi-layer reflectarray elements for contoured-beam space antennas in the Ku-band," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 7, 3205-3214, 2012. doi:10.1109/TAP.2012.2196941
15. El Zooghby, A. H., C. G. Christodoulou, and M. Georgiopoulos, "A neural network-based smart antenna for multiple source tracking," IEEE Transactions on Antennas and Propagation, Vol. 48, No. 5, 768-776, 2000. doi:10.1109/8.855496
17. Prado, D. R., J. A. Lopez-Fernandez, G. Barquero, M. Arrebola, and F. Las-Heras, "Fast and accurate modeling of dual-polarized reflectarray unit cells using support vector machines," IEEE Transactions on Antennas and Propagation, Vol. 66, No. 3, 1258-1270, 2018. doi:10.1109/TAP.2018.2790044
18. Prado, D. R., J. A. López-Fernández, M. Arrebola, and G. Goussetis, "Support vector regression to accelerate design and crosspolar optimization of shaped-beam reflectarray antennas for space applications," IEEE Transactions on Antennas and Propagation, Vol. 67, No. 3, 1659-1668, 2018. doi:10.1109/TAP.2018.2889029
19. Collobert, R. and J. Weston, "A unified architecture for natural language processing: Deep neural networks with multitask learning," Proceedings of the 25th International Conference on Machine Learning, 160-167, 2008.
20. Krizhevsky, A., I. Sutskever, and G. E. Hinton, "Imagenet classification with deep convolutional neural networks," Advances in Neural Information Processing Systems, Vol. 25, 1097-1105, 2012.
21. Ng, J. Y.-H., M. Hausknecht, S. Vijayanarasimhan, O. Vinyals, R. Monga, and G. Toderici, "Beyond short snippets: Deep networks for video classification," Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 4694-4702, 2015.
22. Guo, X., W. Li, and F. Iorio, "Convolutional neural networks for steady flow approximation," Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 481-490, 2016. doi:10.1145/2939672.2939738
23. Massa, A., D. Marcantonio, X. Chen, M. Li, and M. Salucci, "DNNs as applied to electromagnetics, antennas, and propagation - A review," IEEE Antennas and Wireless Propagation Letters, Vol. 18, No. 11, 2225-2229, 2019. doi:10.1109/LAWP.2019.2916369
24. Chen, X., Z. Wei, M. Li, and P. Rocca, "A review of deep learning approaches for inverse scattering problems (invited review)," Progress In Electromagnetics Research, Vol. 167, 67-81, 2020. doi:10.2528/PIER20030705
25. Wei, Z. and X. Chen, "Deep-learning schemes for full-wave nonlinear inverse scattering problems," IEEE Transactions on Geoscience and Remote Sensing, Vol. 57, No. 4, 1849-1860, 2018. doi:10.1109/TGRS.2018.2869221
26. Li, M., R. Guo, K. Zhang, Z. Lin, F. Yang, S. Xu, X. Chen, A. Massa, and A. Abubakar, "Machine learning in electromagnetics with applications to biomedical imaging: A review," IEEE Antennas and Propagation Magazine, 2021.
27. Shan, T., W. Tang, X. Dang, M. Li, F. Yang, S. Xu, and J. Wu, "Study on a fast solver for poisson's equation based on deep learning technique," IEEE Transactions on Antennas and Propagation, Vol. 68, No. 9, 6725-6733, 2020. doi:10.1109/TAP.2020.2985172
28. Shan, T., X. Pan, M. Li, S. Xu, and F. Yang, "Coding programmable metasurfaces based on deep learning techniques," IEEE Journal on Emerging and Selected Topics in Circuits and Systems, Vol. 10, No. 1, 114-125, 2020. doi:10.1109/JETCAS.2020.2972764
29. Shan, T., M. Li, S. Xu, and F. Yang, "Synthesis of reflectarray based on deep learning technique," 2018 Cross Strait Quad-Regional Radio Science and Wireless Technology Conference (CSQRWC), 1-2, IEEE, 2018.
30. Hinton, G. E., N. Srivastava, A. Krizhevsky, I. Sutskever, and R. R. Salakhutdinov, "Improving neural networks by preventing co-adaptation of feature detectors,", arXiv preprint arXiv:1207.0580, 2012.
31. Kingma, D. P. and J. Ba, "Adam: A method for stochastic optimization,", arXiv preprint arXiv:1412.6980, 2014.