PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 156 > pp. 83-103

FAST, PHASE-ONLY SYNTHESIS OF APERIODIC REFLECTARRAYS USING NUFFTS AND CUDA

By A. Capozzoli, C. Curcio, A. Liseno, and G. Toso

Full Article PDF (3,074 KB)

Abstract:
We deal with one of the computationally most critical steps of the Phase-Only synthesis of aperiodic reflectarrays, namely the fast evaluation of the radiation operator. We present an approach exploiting the use of a fast numerical algorithm using 2D Non-Uniform FFTs (NUFFTs) of NED (Non-Equispaced Data) and NER (non equispaced results) type and of parallel processing on Graphic Processing Units (GPUs). We extend the approach in K. Fourmont, J. Fourier Anal. Appl., vol. 9, n. 5, pp. 431-540, 2013 for implementing NUFFT routines to the 2D case and illustrate the parallel strategies to accelerate the approach. In particular, we show how the two levels of parallelism intrinsic in the interpolation step of the 2D NED-NUFFT can be fruitfully exploited by adopting dynamic parallelism, a feature made available in one of the latest architecture of NVIDIA cards. The presented synthesis results show that the introduction of further degrees of freedom (positions) allows improving the performance with respect to periodic reflectarrays. Also, the possibility of adopting aperiodic reflectarrays of reduced number of elements for fixed performance is demonstrated.

Citation:
A. Capozzoli, 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
http://www.jpier.org/PIER/pier.php?paper=16021904

References:
1. Itoh, T., Numerical Techniques for Microwave and Millimeter-wave Passive Structures, J. Wiley & Sons, New York, 1989.

2. Tao, Y., H. Lin, and H. Bao, "GPU-based shooting and bouncing ray method for fast RCS prediction," IEEE Trans. Antennas Prop., Vol. 58, No. 2, 494-502, Feb. 2010.
doi:10.1109/TAP.2009.2037694

3. Guan, J., S. Yan, and J.-M. Jin, "An OpenMP-CUDA implementation of multilevel fast multipole algorithm for electromagnetic simulation on multi-GPU computing systems," IEEE Trans. Antennas Prop., Vol. 61, No. 7, 3607-3616, Jul. 2013.
doi:10.1109/TAP.2013.2258882

4. Peng, S. and C.-F. Wang, "Precorrected-FFT method on Graphics Processing Units," IEEE Trans. Antennas Prop., Vol. 61, No. 4, 2099-2107, Apr. 2013.
doi:10.1109/TAP.2012.2232892

5. Ricciardi, G. F., J. R. Connelly, H. A. Krichene, and M. T. Ho, "A fast-performing error simulation of wideband radiation patterns for large planar phased arrays with overlapped subarray architecture," IEEE Trans. Antennas Prop., Vol. 62, No. 4, 1779-1788, Apr. 2014.
doi:10.1109/TAP.2013.2255576

6. Meng, H.-T. and J.-M. Jin, "Acceleration of the dual-field domain decomposition algorithm using MPI-CUDA on large-scale computing systems," IEEE Trans. Antennas Prop., Vol. 62, No. 9, 4706-4715, Sep. 2014.
doi:10.1109/TAP.2014.2330608

7. Mu, X., H.-X. Zhou, K. Chen, and W. Hong, "Higher order method of moments with a parallel out-of-core LU solver on GPU/CPU platform," IEEE Trans. Antennas Prop., Vol. 62, No. 11, 5634-5646, Nov. 2014.
doi:10.1109/TAP.2014.2350536

8. Kirk, D. B. and W.-M. W. Hwu, Programming Massively Parallel Processors, 2nd Ed., Moargan Kaufmann, Waltham, Morgan Kaufmann, 2013.

9. Owens, J. D., M. Houston, D. Luebke, S. Green, J. E. Stone, and J. C. Phillips, "GPU computing," Proc. of the IEEE, Vol. 96, No. 5, 879-899, May 2008.
doi:10.1109/JPROC.2008.917757

10. Rossi, F. V., P. P. M. So, N. Fichtner, and P. Russer, "Massively parallel two-dimensional TLM algorithm on Graphics Processing Units," Proc. of the IEEE Microw. Theory Tech. Symp., 153-156, 2008.

11. De Donno, D., A. Esposito, G. Monti, and L. Tarricone, "MPIE/MOM with a general purpose Graphics Processing Unit," IEEE Trans. Microw. Theory Tech., Vol. 60, No. 9, 2693-2701, Sep. 2012.
doi:10.1109/TMTT.2012.2203924

12. Capozzoli, A., C. Curcio, G. D’Elia, A. Liseno, and P. Vinetti, "Fast CPU/GPU pattern evaluation of irregular arrays," Applied Comput. Electromagn. Soc. J., Vol. 25, No. 4, 355-372, Apr. 2010.

13. Capozzoli, A., C. Curcio, and A. Liseno, "GPU-based ω-k tomographic processing by 1D nonuniform FFTs," Progress In Electromagnetics Research M, Vol. 23, 279-298, 2012.
doi:10.2528/PIERM11083003

14. Breglia, A., A. Capozzoli, C. Curcio, and A. Liseno, "CUDA expression templates for electromagnetic applications on GPUs," IEEE Antennas Prop. Mag., Vol. 55, No. 5, Oct. 2013.

15. Lezar, E. and D. B. Davidson, "GPU-accelerated method of moments by example: Monostatic scattering," IEEE Antennas Prop. Mag., Vol. 52, No. 6, 120-135, Dec. 2010.
doi:10.1109/MAP.2010.5723240

16. Topa, T., A. Karwowski, and A. Noga, "Using GPU with CUDA to accelerate MoM-based electromagnetic simulation of wire-grid models," IEEE Antennas Wireless Prop. Lett., Vol. 10, 342-345, 2011.
doi:10.1109/LAWP.2011.2144557

17. Topa, T., A. Noga, and A. Karwowski, "Adapting MoM with RWG basis functions to GPU technology using CUDA," IEEE Antennas Wireless Prop. Lett., Vol. 10, 480-483, 2011.
doi:10.1109/LAWP.2011.2154373

18. Huang, J. and J. A. Encinar, Reflectarray Antennas, J. Wiley & Sons, Hoboken, NJ, 2008.

19. Bialkowski, M. E. and J. A. Encinar, "Reflectarrays: Potentials and challenges," Proc. of the Int. Conf. on Electromagn. in Adv. Appl., 1050-1053, 2007.

20. Encinar, J. A., M. Arrebola, and G. Toso, "A parabolic reflectarray for a bandwidth improved contoured beam coverage," Proc. of the Europ. Conf. on Antennas Prop., 1-5, 2007.

21. Capozzoli, A., C. Curcio, G. D’Elia, A. Liseno, G. Toso, and P. Vinetti, Aperiodic and non-planar array of electromagnetic scatterers, and reflectarray antenna comprising the same, World Patent Nr. WO/2011/033388.

22. Willey, R., "Space tapering of linear and planar arrays," IEEE Trans. on Antennas Prop., Vol. 10, No. 4, 369-377, Jul. 1962.
doi:10.1109/TAP.1962.1137887

23. Skolnik, M. I., "Nonuniform arrays," Antenna Theory, R. E. Colin and F. J. Zucker, Capter 6, McGraw-Hill, New York, 1969.

24. Morabito, A. F., T. Isernia, and L. Di Donato, "Optimal synthesis of Phase-Only reconfigurable linear sparse arrays having uniform-amplitude excitations," Progress In Electromagnetics Research, Vol. 124, 405-423, 2012.
doi:10.2528/PIER11112210

25. Capozzoli, A., C. Curcio, G. D’Elia, A. Liseno, and P. Vinetti, "FFT & aperiodic arrays with phaseonly control and constraints due to super-directivity, mutual coupling and overall size," Proc. of the 30th ESA Antenna Workshop on Antennas for Earth Observ., Science, Telecomm. and Navig. Space Missions, Noordwijk, The Netherlands, CD ROM, May 27-30, 2008.

26. Capozzoli, A., C. Curcio, G. D’Elia, A. Liseno, and P. Vinetti, "FFT & equivalently tapered aperiodic arrays," Proc. of the XXIX General Assembly of the Int. Union of Radio Sci., Chicago, IL, CD ROM, Aug. 7-16, 2008.

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

28. Fourmont, K., "Non-equispaced fast Fourier transforms with applications to tomography," J. Fourier Anal. Appl., Vol. 9, No. 5, 431-450, 2003.
doi:10.1007/s00041-003-0021-1

29. Capozzoli, A. and A. Liseno, "Fast reflectarray antenna analysis and synthesis on GPUs," The GPU Technology Conference, San Jose, California, Mar. 18-21, 2013.

30. Capozzoli, A., C. Curcio, A. Liseno, and G. Toso, "Dynamic parallelism in reflectarray antenna analysis and synthesis on GPU," PIERS Abstracts, 1003, Stockholm, Sweden, Aug. 12-15, 2013.

31. Dynamic Parallelism in CUDA, NVIDIA White Paper, 2012, http://developer.download.nvidia.com/assets/cuda/docs/TechBrief Dynamic Parallelism in CUDA v2.pdf.

32. Bucci, O. M., G. Franceschetti, G. Mazzarella, and G. Panariello, "Intersection approach to array pattern synthesis," IEE Proc. Pt. H, Vol. 137, No. 6, 349-357, Dec. 1990.

33. Fatica, M. and W.-K. Jeong, "Accelerating Matlab with CUDA," Proc. of the High Performance Embedded Comput. Workshop, Lexington, MA, Sep. 18-20, 2007.

34. Suh, J. W. and Y. Kim, Accelerating Matlab with GPU Computing: A Primer with Examples, Waltham, MA, Morgan Kaufmann, 2014.

35. Advanced reflectarray antennas, ESA LET-SME 2009 Project, Technical Report Nr. 1, Jul. 2010(Available on Request to the European Space Agency).

36. Advanced reflectarray antennas, ESA LET-SME 2009 Project,, Technical Report Nr. 2, Mar. 2011(Available on Request to the European Space Agency).

37. Capozzoli, A., C. Curcio, A. Liseno, M. Migliorelli, and G. Toso, "Power pattern synthesis of advanced flat aperiodic reflectarrays," Proc. of the 33rd ESA Workshop on Challenges for Space Antenna Systems, 2011.

38. Blaser, M., "Lower bounds for the multiplicative complexity of matrix multiplication," Comput. Complex., Vol. 8, No. 3, 203-226, Dec. 1999.
doi:10.1007/s000370050028

39. Atkinson, K. and D. D. K. Chien, "A fast matrix-vector multiplication method for solving the radiosity equation," Adv. in Comput. Math., Vol. 12, No. 2–3, 151-174, Feb. 2000.
doi:10.1023/A:1018961001209

40. Blair, J. M., "Rational Chebyshev approximations for the modified Bessel functions I0 and I1," Math. Comp., Vol. 28, No. 126, 581-583, Apr. 1974.

41. Frigo, M. and S. G. Johson, "The design and implementation of FFTW3," Proc. of the IEEE, Vol. 93, No. 2, 216-231, Feb. 2005.
doi:10.1109/JPROC.2004.840301

42. Bulatsyk, O. O., B. Z. Katsenelenbaum, Y. P. Topolyuk, and N. N. Voitovich, Phase Optimization Problems, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2010.

43. Capozzoli, A., C. Curcio, E. Iavazzo, A. Liseno, M. Migliorelli, and G. Toso, "Phase-only synthesis of a-periodic reflectarrays," Proc. of the Europ. Conf. on Antennas Prop., 1031-1035, Rome, Italy, Apr. 11-15, 2011.

44. Bucci, O. M., G. D’Elia, G. Mazzarella, and G. Panariello, "Antenna pattern synthesis: A new general approach," Proc. of the IEEE, Vol. 82, No. 3, 358-371, Mar. 1994.
doi:10.1109/5.272140

45. Capozzoli, A. and G. D’Elia, "Global optimization and antennas synthesis and diagnosis, Part I: Concepts, tools, strategies and performances," Progress In Electromagnetics Research, Vol. 56, 195-232, 2006.
doi:10.2528/PIER04123001

46. Capozzoli, A. and G. D’Elia, "Global optimization and antennas synthesis and diagnosis, Part II: Applications to advanced reflector antenna synthesis and diagnosis techniques," Progress In Electromagnetics Research, Vol. 56, 233-261, 2006.
doi:10.2528/PIER05032503

47. Wolpert, D. H. and W. G. Macready, "No free lunch theorems for optimization," IEEE Trans. Evolutionary Comput., Vol. 1, No. 1, 67-82, Apr. 1997.
doi:10.1109/4235.585893

48. Rinnooy Kan, A. G. H. and G. T. Timmer, "Stochastic global optimization methods, Part I: Clustering methods," Math. Progr., Vol. 39, No. 1, 27-56, Sep. 1987.
doi:10.1007/BF02592070

49. Rinnooy Kan, A. G. H. and G. T. Timmer, "Stochastic global optimization methods, Part II: Multi level methods," Math. Progr., Vol. 39, No. 1, 57-78, Sep. 1987.
doi:10.1007/BF02592071

50. Capozzoli, A., C. Curcio, and A. Liseno, "Fast GPU-based interpolation for SAR backprojection," Progress In Electromagnetics Research, Vol. 133, 259-283, 2013.
doi:10.2528/PIER12071909

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

52. Capozzoli, A., C. Curcio, A. Liseno, M. Migliorelli, and G. Toso, "Aperiodic conformal reflectarrays," Proc. of the Antennas Prop. Soc. Int. Symp., 361-364, Spokane, WA, Jul. 3-8, 2011.

53. Capozzoli, A., C. Curcio, A. Liseno, and A. Riccardi, "Parameter selection and accuracy in type-3 non-uniform FFTs based on Gaussian gridding," Progress In Electromagnetics Research, Vol. 142, 743-770, 2013.
doi:10.2528/PIER13072402


© Copyright 2014 EMW Publishing. All Rights Reserved