The least square method has been widely applied in many fields. However, while the approach is used for antenna array pattern synthesis, it is not excellent. In this paper, the least square is used to synthesize antenna array pattern and its performance is reviewed. Then contraposing to the shortcoming of the least square method, a new steerable least square(SLS) method is put forward. For an antenna array whose manifold matrix has been determined, the projection matrix equation can be derived from array manifold matrix easily. In order to get premium solution of array element excitation, a novel projection matrix equation with adjustable matrices is adopted. The results of simulations show that the pattern synthesized by the traditional least square method fits the targeted pattern badly and is worse in the key performance indicators of main-lobe width, peak level of side-lobe and null beam level than the targeted pattern; however, the pattern synthesized by the new SLS method fits the targeted pattern well in zero point and local peak distribution and is better in the key performance indicators of main-lobe width, peak level of side-lobe and null beam level than the targeted pattern.
"A Steerable Least Square Approach for Pattern Synthesis," Progress In Electromagnetics Research M,
Vol. 59, 181-191, 2017. doi:10.2528/PIERM17052404
1. Ohira, T., "Adaptive array antenna beamforming architectures as viewed by a microwave circuit designer," Proc. Asia-Pacific Microw. Conf., 828-833, Sydney, Australia, Dec. 2000.
2. Denno, S. and T. Ohiro, "Modified constant modulus algorithm for digital signal processing adaptive antennas with microwave analog beam-forming," IEEE Trans. Antennas Propag., Vol. 50, No. 6, 850-857, Jun. 2002. doi:10.1109/TAP.2002.1017667
3. Sarkar, T. K., J. Koh, R. Adve, et al. "A pragmatic approach to adaptive antennas," IEEE Acoust., Speech, and Signal Processing Mag., Vol. 42, No. 2, 39-55, Feb. 2000.
4. Chen, Y., S. Yang, and Z. Nie, "The application of a modified differential evolution strategy to some array pattern synthesis problems," IEEE Trans. Antennas Propag., Vol. 56, No. 7, 1919-1927, Jul. 2008. doi:10.1109/TAP.2008.924713
5. Manica, L., P. Rocca, M. Benedetti, and A. Massa, "A fast graph-searching algorithm enabling the efficient synthesis of sub-arrayed planar monopulse antennas," IEEE Trans. Antennas Propag., Vol. 57, No. 3, 652-663, Mar. 2009. doi:10.1109/TAP.2009.2013423
6. He, H., P. Stoica, and J. Li, "Wideband MIMO systems: Signal design for transmit beampattern synthesis," IEEE Transactions on Signal Processing, Vol. 59, No. 2, 618-628, 2011. doi:10.1109/TSP.2010.2091410
7. Oliveri, G., M. Carlin, and A. Massa, "Complex-weight sparse linear array synthesis by Bayesian compressive sampling," IEEE Trans. Antennas Propag., Vol. 60, No. 5, 2039-2026, May 2012. doi:10.1109/TAP.2012.2189742
8. Chen, H., Q. Wang, and R. Fan, "Beampattern synthesis using reweighted l1-norm minimization and array orientation diversity," Radioengineering, Vol. 22, No. 2, 602-609, Jun. 2013.
9. Choi, W., T. K. Sarkar, H. Wang, and E. L. Mokole, "Adaptive processing using real weights based on a direct data domain least squares approach," IEEE Trans. Antennas Propag., Vol. 54, No. 1, 182-191, Jan. 2006. doi:10.1109/TAP.2005.859753
10. Zhang, X., Modern Signal Processing, Tsinghua University Press, Beijing, 2012.
11. Caorsi, S., F. De Natale, M. Donelli, D. Franceschini, and A. Massa, "A versatile enhanced genetic algorithm for planar array design," Journal of Electromagnetic Waves and Applications, Vol. 18, No. 11, 1533-1548, 2004. doi:10.1163/1569393042954893
12. Massa, A., M. Donelli, F. De Natale, S. Caorsi, and A. Lommi, "Planar antenna array control with genetic algorithms and adaptive array theory," IEEE Trans. Antennas Propag., Vol. 52, No. 11, 2919-2924, 2004. doi:10.1109/TAP.2004.837523
13. Donelli, M. and P. Febvre, "An inexpensive reconfigurable planar array for Wi-Fi applications," Progress In Electromagnetics Research C, Vol. 28, 71-81, 2012. doi:10.2528/PIERC12012304
14. Wang, B.-H. and Y. Guo, "Frequency-invariant and low cross-polarization pattern synthesis for conformal array antenna," IEEE Radar Conf., 1-6, May 26-30, 2008.
15. Comisso, M. and R. Vescovo, "Fast co-polar and cross-polar 3D pattern synthesis with dynamic range ratio reduction for conformal antenna arrays," IEEE Trans. Antennas Propag., Vol. 61, No. 2, 614-626, Feb. 2013. doi:10.1109/TAP.2012.2224834
16. Mautz, J. R. and R. F. Harrington, "Computational methods for antenna pattern synthesis," IEEE Trans. Antennas Propag., Vol. 23, 507-512, Jul. 1975.
17. Khzmalyan, A. D. and A. S. Kondrat Yev, "Phase-only synthesis of antenna array amplitude pattern," Int. J. Electron., Vol. 81, No. 5, 585-589, 1996. doi:10.1080/002072196136490
18. Vaskelainen, L. I., "Constrained least-square optimization in conformal array antenna synthesis," IEEE Trans. Antennas Propag., Vol. 55, 859-867, Mar. 2007. doi:10.1109/TAP.2007.891860
19. Ares-Pena, F. J., J. A. Rodriguez-Gonzalez, E. Villanueva-Lopez, and S. R. Rengarajan, "Genetic algorithms in the design and optimization of antenna array patterns," IEEE Trans. Antennas Propag., Vol. 47, No. 3, 506-510, 1999. doi:10.1109/8.768786