volume | PIER Journals

Abstract

In this work, a novel use of the Non-Uniform Fast Fourier Transform (NUFFT) in reflectarray antenna analysis is proposed to greatly accelerate the computation of radiation patterns using a nonuniform, reduced and adaptive grid in the spectral domain. The proposed methodology is very useful for very large reflectarrays, which have very narrow beamwidths due to their large directivity, and shaped-beam reflectarrays for satellite applications such as Direct Broadcast Satellite (DBS), which might require a compliance analysis in very small angular regions. In those cases, high resolution in the radiation pattern is required, while a low resolution could be enough elsewhere to account for side lobes. However, current analysis techniques for such reflectarrays present limitations regarding large memory footprints or slow computations. The methodology presented in this work allows to overcome those limitations by performing computations in a non-uniform, reduced and adaptive grid in the transformed UV domain, achieving faster computations using considerably less memory. Numerical examples for current applications of interest are provided to assess the capabilities of the technique. In particular, the use of the NUFFT allows to compute efciently the radiation pattern in any principal plane with improved resolution for multibeam applications. Also, compliance analyses for DBS applications may be improved with the use of a reduced, multiresolution grid and the NUFFT. The proposed technique is thus suitable to greatly accelerate optimization algorithms.

1. Capozzoli, A., C. Curcio, A. Liseno, and G. Toso, "Phase-only synthesis of at aperiodic reflectarrays," Progress In Electromagnetics Research, Vol. 133, 53-89, 2013.
doi:10.2528/PIER12080109

2. Prado, D. R., M. Arrebola, M. R. Pino, and F. Las-Heras, "Application of the NUFFT to the analysis and synthesis of aperiodic arrays," 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA), 708-711, Verona, Italy, Sep. 11–15, 2017.

3. Haupt, R. L., "Thinned arrays using genetic algorithms," IEEE Trans. Antennas Propag., Vol. 42, No. 7, 993-999, Jul. 1994.
doi:10.1109/8.299602

4. Mahanti, G. K., N. N. Pathak, and P. K. Mahanti, "Synthesis of thinned linear antenna arrays with fixed sidelobe level using real-coded genetic algorithm," Progress In Electromagnetics Research, Vol. 75, 319-328, 2007.
doi:10.2528/PIER07061304

5. Panduro, M. A., C. A. Brizuela, D. Covarrubias, and C. Lopez, "A trade-off curve computation for linear antenna arrays using an evolutionary multi-objective approach," Soft Comput., Vol. 10, No. 2, 125-131, Jan. 2006.
doi:10.1007/s00500-004-0434-z

6. Gabrielli, L. H. and H. E. Hernandez-Figueroa, "Aperiodic antenna array for secondary lobe suppression," IEEE Photon. Technol. Lett., Vol. 28, No. 2, 209-212, Jan. 2016.
doi:10.1109/LPT.2015.2492419

7. Suárez, S., G. León, M. Arrebola, L. F. Herrán, and F. Las-Heras, "Experimental validation of linear aperiodic array for grating lobe suppression," Progress In Electromagnetics Research C, Vol. 26, 193-203, 2012.
doi:10.2528/PIERC11110706

8. Panduro, M. A., "Design of non-uniform linear phased arrays using genetic algorithms to provide maximum interference reduction capability in a wireless communication system," J. Chin. Inst. Eng., Vol. 29, No. 7, 1195-1201, 2006.
doi:10.1080/02533839.2006.9671221

9. Li, J., Q. Chen, K. Sawaya, and Q. Yuan, "Amplitude controlled reflectarray using non-uniform FSS reflection plane," IEEE International Symposium on Antennas and Propagation (APSURSI), 2180-2183, Spokane, Washington, USA, Jul. 3–8, 2011.

10. Panduro, M. A., C. A. Brizuela, and D. H. Covarrubias, "Design of electronically steerable linear arrays with evolutionary algorithms," Appl. Soft. Comput., Vol. 8, No. 1, 46-54, Jan. 2008.
doi:10.1016/j.asoc.2006.10.011

11. Martínez-de-Rioja, E., J. A. Encinar, A. Pino, B. González-Valdés, S. V. Hum, and C. Tienda, "Bifocal design procedure for dual reflectarray antennas in offset configurations," IEEE Antennas Wireless Propag. Lett., Vol. 17, No. 8, 1421-1425, Aug. 2018.
doi:10.1109/LAWP.2018.2848719

12. Rengarajan, S. R., "Reflectarrays of rectangular microstrip patches for dual-polarization dual-beam radar interferometers," Progress In Electromagnetics Research, Vol. 133, 1-15, 2013.
doi:10.2528/PIER12091615

13. Tienda, C., M. Younis, P. López-Dekker, and P. Laskowski, "Ka-band reflectarray antenna system for SAR applications," The 8th European Conference on Antennas and Propagation (EUCAP), 1603-1606, The Hague, The Netherlands, Apr. 6–11, 2014.

14. Patyuchenko, A., C. Tienda, M. Younis, S. Bertl, P. López-Dekker, and G. Krieger, "Concept of a multi-beam reflectarray digital-beam forming synthetic aperture radar," IEEE International Symposium on Phased Array Systems and Technology, 346-351, Waltham, Massachusetts, USA, Oct. 15–18, 2013.

15. Encinar, J. A., M. Arrebola, L. F. de la Fuente, and G. Toso, "A transmit-receive reflectarray antenna for direct broadcast satellite applications," IEEE Trans. Antennas Propag., Vol. 59, No. 9, 3255-3264, Sep. 2011.
doi:10.1109/TAP.2011.2161449

16. Zornoza, J. A. and M. E. Bialkowski, "Australia and New Zealand satellite coverage using a microstrip patch reflectarray," Microw. Opt. Technol. Lett., Vol. 37, No. 5, 321-325, Jun. 2003.
doi:10.1002/mop.10907

17. Legay, H., D. Bresciani, E. Labiole, R. Chiniard, and R. Gillard, "A multi facets composite panel reflectarray antenna for a space contoured beam antenna in Ku band," Progress In Electromagnetics Research B, Vol. 54, 1-26, Aug. 2013.
doi:10.2528/PIERB13061407

18. Cooley, J. W. and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Comp., Vol. 19, No. 90, 297-301, Apr. 1965.
doi:10.1090/S0025-5718-1965-0178586-1

19. Huang, J. and J. A. Encinar, Reflectarray Antennas, John Wiley & Sons, 2008.

20. Prado, D. R., M. Arrebola, M. R. Pino, and F. Las-Heras, "An efficient calculation of the far field radiated by non-uniformly sampled planar fields complying Nyquist theorem," IEEE Trans. Antennas Propag., Vol. 63, No. 2, 862-865, Feb. 2015.
doi:10.1109/TAP.2014.2384033

21. Prado, D. R., M. Arrebola, M. R. Pino, F. Las-Heras, and J. A. Encinar, "Efficient computation of the reflectarray far fields in adaptive grids for speed improvement," IEEE International Symposium on Antennas and Propagation (APSURSI), 1181-1182, San Diego, California, USA, Jul. 9–14, 2017.

22. Lee, J.-Y. and L. Greengard, "The type 3 nonuniform FFT and its applications," J. Comput. Phys., Vol. 206, No. 1, 1-5, Jun. 2005.
doi:10.1016/j.jcp.2004.12.004

23. Bucci, O. M. and M. D. Migliore, "A novel Non Uniform Fast Fourier Transform algorithm and its application to aperiodic arrays," IEEE Antennas Wireless Propag. Lett., 1472-1475, 2017.
doi:10.1109/LAWP.2016.2646401

24. Dutt, A., "Fast Fourier transforms for nonequispaced data,", Ph.D. dissertation, Yale University, Aug. 1993.

25. Greengard, L. and J.-Y. Lee, "Accelerating the nonuniform fast fourier transform," SIAM Rev., Vol. 46, No. 3, 443-454, Jul. 2004.
doi:10.1137/S003614450343200X

26. Fessler, J. A. and B. P. Sutton, "Nonuniform fast Fourier transforms using min-max interpolation," IEEE Trans. Signal Process., Vol. 51, No. 2, 560-574, Feb. 2003.
doi:10.1109/TSP.2002.807005

27. Liu, Q. H. and N. Nguyen, "An accurate algorithm for nonuniform fast Fourier transforms (NUFFT’s)," IEEE Microw. Guided Wave Lett., Vol. 8, No. 1, 18-20, Jan. 1998.
doi:10.1109/75.650975

28. Dutt, A. and V. Rokhlin, "Fast fourier transforms for nonequispaced data," SIAM J. Sci. Comput., Vol. 14, No. 6, 1368-1393, Nov. 1993.
doi:10.1137/0914081

29. Zornoza, J. A. and J. A. Encinar, "Efficient phase-only synthesis of contoured-beam patterns for very large reflectarrays," Int. J. RF Microw. Comput. Eng., Vol. 14, No. 5, 415-423, Sep. 2004.
doi:10.1002/mmce.20028

Dr. Daniel Rodríguez Prado

Dr. Manuel Arrebola

Dr. Marcos R. Pino

Dr. Jose Antonio Encinar Garcinuno

Dr. Fernando Las-Heras