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2011-04-07
Flexible Array Beampattern Synthesis Using Hypergeometric Functions
By
Progress In Electromagnetics Research M, Vol. 18, 1-15, 2011
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.
Citation
Lei Tu Boon Ng , "Flexible Array Beampattern Synthesis Using Hypergeometric Functions," Progress In Electromagnetics Research M, Vol. 18, 1-15, 2011.
doi:10.2528/PIERM10120803
http://www.jpier.org/PIERM/pier.php?paper=10120803
References

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

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.

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.

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

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.

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.

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.

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

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

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.

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

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.

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

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

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, New York, 1997.

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

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

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.