The measurement of far-field radiation patterns is time consuming and expensive. Therefore, a novel technique that reduces the samples required to measure radiation patterns is proposed where random far-field samples are measured to reconstruct two-dimensional (2D) or three-dimensional (3D) far-field radiation patterns. The proposed technique uses a compressive sensing algorithm to reconstruct radiation patterns. The discrete Fourier transform (DFT) or the discrete cosine transform (DCT) are used as the sparsity transforms. The algorithm was evaluated by using 3 antennas modeled with the High-Frequency Structural Simulator (HFSS) --- a half-wave dipole, a Vivaldi, and a pyramidal horn. The root mean square error (RMSE) and the number of measurements required to reconstruct the antenna pattern were used to evaluate the performance of the algorithm. An empirical test case was performed that validates the use of compressive sensing in 2D and 3D radiation pattern reconstruction. Numerical simulations and empirical tests verify that the compressive sensing algorithm can be used to reconstruct radiation patterns, reducing the time and number of measurements required for good antenna pattern measurements.
1. Hansen, J. E., Spherical Near-field Antenna Measurement, The Institution of Engineering and Technology, United Kingdom, 1988. doi:10.1049/PBEW026E
2. D’Agostino, F., F. Ferrara, C. Gennarelli, R. Guerriero, and M. Migliozzi, "Far-field reconstruction from a minimum number of spherical spiral data using effective antenna modelings," Progress In Electromagnetics Research B, Vol. 37, 43-58, 2012. doi:10.2528/PIERB11072707
3. Farouq, M., M. Serhir, and D. Picard, "Matrix method for far-field calculation using irregular near-field samples for cylindrical and spherical scanning surfaces," Progress In Electromagnetics Research B, Vol. 63, 35-48, 2015. doi:10.2528/PIERB15040905
5. Trzasko, J., A. Manduca, and E. Borisch, "Highly under sampled magnetic resonance image reconstruction via homotopic ell-0-minimization," IEEE Trans. Med. Imag., Vol. 28, No. 1, 106-121, 2009. doi:10.1109/TMI.2008.927346
6. Baraniuk, R. and P. Steeghs, "Compressive radar imaging," IEEE Radar Conf., Waltham, Massachusetts, 2007.
7. Carin, L., D. Liu, and B. Gua, "In situ compressive sensing," IEEE Science Inverse Problems, Vol. 24, 2008.
8. Giordanengo, G., M. Righero, F. Vipiana, G. Vecchi, and M. Sabbadini, "Fast antenna testing with reduced near field sampling," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 5, 2501-2513, 2014. doi:10.1109/TAP.2014.2309338
9. Verdin, B. and P. Debroux, "Reconstruction of missing sections of radiation patterns using compressive sensing," IEEE International Symposium, 780-781, 2015.
11. Candes, E. J., T. Tao, and J. Romberg, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. on Inf. Theory, Vol. 52, No. 2, 489-509, 2006. doi:10.1109/TIT.2005.862083
12. Candes, E. J. and T. Tao, "Near optimal signal recovery from random projections: Universal encoding strategies?," IEEE Trans. on Inf. Theory, Vol. 52, No. 12, 5406-5425, 2006. doi:10.1109/TIT.2006.885507
13. Fornasier, M. and H. Rauhut, "Compressive sensing," Handbook of Mathematical Methods in Imaging, 187-228, 2010.
14. Rauhut, H., "Compressive sensing and structural random matrices," Theoretical Foundations and Numerical Methods for Sparse Recovery, 1-91, 2010.
15. Fang, H., S. S. Vorobyov, H. Jiang, and O. Taheri, "Permutation meets parallel compressed sensing: How to relax restricted isometry property for 2D sparse signals," Proc. Inst. Elect. Eng. 12th Int. Conf. Antennas Propagation ICAP, 751-744, 2003.