Characterization measurements of wideband antennas can be a time intensive and an expensive process as many data points are required in both the angular and frequency dimensions. Parallel compressive sensing is proposed to reconstruct the radiation-frequency patterns (RFP) of antennas from a sparse and random set of measurements. The modeled RFP of the dual-ridge horn, bicone, and Vivaldi antennas are used to analyze the minimum number of measurements needed for reconstruction, the difference in uniform versus non-uniform reconstruction, and the sparsity transform function used in the compressive sensing algorithm. The effect of additive white Gaussian noise (AWGN) on the minimum number of data points required for reconstruction is also studied. In a noise-free environment, the RFP of the antennas were adequately reconstructed using as little as 33% of the original data points. It was found that the RFPs were adequately reconstructed with less data points when the discrete cosine transforms (DCT), rather than discrete Fourier transforms (DFT) was used in the compressive sensing algorithm. The presence of noise increases the number of data points required to reconstruct an RFP to a specified error tolerance, but the antenna RFPs can be reconstructed to within 1% root-mean-square-error of the original with a signal to noise ratio as high as -15 dB. The use of compressive sensing can thus lead to a new measurement methodology whereby a small subset of the total angular and frequency measurements is taken at random, and a full reconstruction of radiation and frequency behavior of the antenna is achieved during post-processing.
1. Miller, E. K., "Using adaptive estimation to minimize the number of samples needed to develop a radiation or scattering pattern to a specified uncertainty," ACES Journal, Vol. 17, No. 3, 176-185, 2002.
2. Werner, D. H. and R. J. Allard, "The simultaneous interpolation of antenna radiation patterns in both the spatial and frequency domains using model-based parameter estimation," IEEE Transactions on Antennas and Propagation, Vol. 48, No. 3, 383-392, March 2000. doi:10.1109/8.841899
3. Martı-Canales, J. and L. P. Lighart, "Reconstruction of measured antenna patterns and related time-varying aperture fields," IEEE Transactions on Antennas and Propagation, Vol. 52, No. 11, 3143-3147, November 2004. doi:10.1109/TAP.2004.835235
4. Tkadlec, R. and Z. Novacek, "Radiation pattern reconstruction from the near-field amplitude measurement on two planes using PSO," Radioengineering, Vol. 14, No. 4, 63-67, December 2005.
5. Rammal, R., M. Lalande, M. Jouvet, N. Feix, J. Andrieu, and B. Jecko, "Far-field reconstruction from transient near-field measurements using cylindrical modal development," International Journal of Antennas and Propagation, Article ID 798473, 2009.
6. Koh, J., A. De, T. K. Sarkar, H. Moon, W. Zhao, and M. Salazar-Palma, "Free space radiation pattern reconstruction from non-anechoic measurements using an impulse response of the environment," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 2, 821-831, February 2012. doi:10.1109/TAP.2011.2173117
7. Wei, S.-J., X.-L. Zhang, J. Shi, and K.-F. Liao, "Sparse array microwave 3-D imaging: Compressed sensing recovery and experimental study," Progress In Electromagnetic Research, Vol. 135, 161-181, 2013. doi:10.2528/PIER12082305
8. Verdin, B. and P. Debroux, "2D and 3D far-field radiation patterns reconstruction based on compressive sensing," Progress In Electromagnetic Research M, Vol. 46, 47-56, 2016. doi:10.2528/PIERM15110306
9. Baraniuk, R. G., "Compressive sensing," IEEE Signal Processing Magazine, 118, July 2007.
10. Fornasier, M. and H. Rauhut, Handbook of Mathematical Methods in Imaging, Chapter 6, 187-228, Springer, 2011.
11. Fornasier, M. and H. Rauhut, Handbook of Mathematical Methods in Imaging, Vol. 1, Springer, 2010.
12. Candes, E., J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Transactions on Information Theory, Vol. 52, No. 2, 489-509, February 2006. doi:10.1109/TIT.2005.862083
13. Romberg, J., , L1qc logbarrier.m.statweb.stanford.edu/˜candes/l1magic/, October 2005, accessed: 2016-11-15.
14. ANSYS, HFSS for Antenna Design Training Manual, 1st Ed., ANSYS, May 2016.
15. Fang, H., S. A. Vorobyov, H. Jiang, and O. Taheri, "Permutation meets parallel compressed sensing: How to relax restricted isometry property for 2D sparse signals," IEEE Transactions on Signal Processing, Vol. 62, No. 1, 196-210, January 2014. doi:10.1109/TSP.2013.2284762
16. Boufonos, P., M. F. Duarte, and R. G. Baraniuk, "Sparse signal reconstruction from noisy compressive measurement using cross validation," 2007 IEEE/SP 14th Workshop on Statistical Signal Processing, IEEE Signal Processing Society, IEEE, August 2007.