volume | PIER Journals

Abstract

For array beampattern synthesis, it is possible to simplify the model and reduce the computational load by formulating it to be a Quadratic Programming (QP) problem. The QP method is conceptually simple and imposes no restriction on array geometry. In the QP method, a key component is the template function which describes the desired beampattern as a deterministic function of direction. In this paper, the template functions in the form of Hypergeometric Function corresponding to Legendre arrays and Dolph-Chebyshev arrays, namely Legendre Hypergeometric Function (LHF) and Dolph-Chebyshev Hypergeometric Function (DCHF), are derived and the synthesis procedures are also presented. The simulation results show that the DCHF and LHF work in the QP method and provide the exactly synthesized beampattern. Moreover, another synthesis method using a Gegenbauer polynomial to synthesize the beampattern of a Uniform Linear Array, is proposed. This method gives rise to the Gegenbauer arrays. Gegenbauer arrays are very generalized and Legendre arrays and Dolph-Chebyshev arrays are considered as its special cases. Using the Gegenbauer array synthesis method, one is able to further adjust the beam efficiency and the directivity when the Side-Lobe Level and the element number are specified. As well as Dolph-Chebyshev arrays and Legendre arrays, its template function for the QP method, Gegenbauer Hypergeometric Function, is also derived.

1. Dolph, C. L., "A current distribution for broadside arrays which optimizes the relationship between beamwidth and side-lobe level," Proc. IRE, Vol. 34, 335-348, Jun. 1946.
doi:10.1109/JRPROC.1946.225956 Google Scholar

2. Qu, L., W. Ser, and Z. H. Shao, "An efficient adaptive beamforming technique with pattern control ability," IEEE 64th Vehicular Technology Conference, 479-483, 2006. Google Scholar

3. Qu, L., W. Ser, and Z. H. Shao, "Beam pattern synthesis in the presence of interference and multipath," International Symposium International Symposium, 267-271, 2006. Google Scholar

4. Keizer, W. P. M. N., "Fast low-sidelobe synthesis for large planar array antennas utilizing successive fast Fourier transforms of the array factor," IEEE Trans. Antennas Propagat., Vol. 55, 715-722, 2007.
doi:10.1109/TAP.2007.891511 Google Scholar

5. Wang, F., V. Balakrishnan, and P. Y. Zhou, "Optimal array pattern synthesis using semidefinite programming," IEEE Trans. Antennas Propagat., Vol. 51, 1172-1183, 2003. Google Scholar

6. Corcoles, J., M. A. Gonzalez, and J. Rubio, "Mutual coupling compensation in arrays using a spherical wave expansion of the radiated field," IEEE Trans. Antennas Propagat., Vol. 8, 108-111, 2009. Google Scholar

7. Corcoles, J., M. A. Gonzalez, and J. Rubio, "Array design for different SLL and null directions with an interior-point optimization method from the generalized-scattering-matrix and spherical modes," 3rd European Conference on Antannas and Propagation, 1319-1323, 2009. Google Scholar

8. Bucci, O. M., D. D'Elia, G. Mazzarella, and G. Panatiello, "Antenna pattern synthesis: A new general approach," Proc. IEEE, Vol. 82, 358-371, Mar. 1994.
doi:10.1109/5.272140 Google Scholar

9. Lebret, H. and S. Boyd, "Antenna array pattern synthesis via convex optimization," IEEE Trans. on Signal Processing, Vol. 45, No. 3, 526-532, Mar. 1997.
doi:10.1109/78.558465 Google Scholar

10. Bucci, O. M., M. D'Urso, and T. Isernia, "Exploiting convexity in array antenna synthesis problems," Radar Conference 2008, Roma, Italy, Proceedings of the Conference, May 26-30, 2008. Google Scholar

11. Rocca, P., L. Manica, R. Azaro, and A. Massa, "A Hybrid approach to the synthesis of subarrayed monopulse linear arrays," IEEE Trans. Antennas Propagat., Vol. 57, No. 1, 280-283, Jan. 2009.
doi:10.1109/TAP.2008.2009776 Google Scholar

12. Ng, , B. P., M. H. Er, C. Kot, "A flexible array synthesis method using quadratic programming," IEEE Trans. Antennas Propagat.,, Vol. 41, 1541-1550, Nov. 1993. Google Scholar

13. Phongcharoenpanich, C., M. Krairiksh, K. Meksamoot, and T. Wakabayashi, "Legendre array," Proc. TJSAP, 197-201, May 1997. Google Scholar

14. Goto, N., "A synthesis of array antennas for high directivity and low sidelobes," IEEE Trans. Antennas Propagat., Vol. 20, No. 4, 427-431, Jul. 1972.
doi:10.1109/TAP.1972.1140239 Google Scholar

15. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, , Dover, New York, 1965.

16. Bailey, W. N., Generalised Hypergeometric Series, University Press, Cambridge, England, 1935.

17. Balanis, C. A., Antenna Theory Analysis and Design, John Wiley and Sons, 1997.

18. Suetin, P. K., "Encyclopaedia of Mathematics," Springer, 2001. Google Scholar

19. Er, M. H. and A. Cantoni, "A new set of linear constraints for broadband time domain element space processors," IEEE Trans. Antennas Propagat., Vol. 34, No. 3, 320-329, Mar. 1986.
doi:10.1109/TAP.1986.1143834 Google Scholar

20. Ng, B. P., "Generalised approach to the design of narrowband antenna array processors with broadband capability," IEE Proc. F, Vol. 137, No. 1, 41-47, Feb. 1990. Google Scholar

Mr. Lei Tu

Dr. Boon Ng