Search search
Publication Date
to
Vol. 18
Latest Volume
All Volumes
PIERM 139 PIERM 138 PIERM 137 PIERM 136 PIERM 135 PIERM 134 PIERM 133 PIERM 132 PIERM 131 PIERM 130 PIERM 129 PIERM 128 PIERM 127 PIERM 126 PIERM 125 PIERM 124 PIERM 123 PIERM 122 PIERM 121 PIERM 120 PIERM 119 PIERM 118 PIERM 117 PIERM 116 PIERM 115 PIERM 114 PIERM 113 PIERM 112 PIERM 111 PIERM 110 PIERM 109 PIERM 108 PIERM 107 PIERM 106 PIERM 105 PIERM 104 PIERM 103 PIERM 102 PIERM 101 PIERM 100 PIERM 99 PIERM 98 PIERM 97 PIERM 96 PIERM 95 PIERM 94 PIERM 93 PIERM 92 PIERM 91 PIERM 90 PIERM 89 PIERM 88 PIERM 87 PIERM 86 PIERM 85 PIERM 84 PIERM 83 PIERM 82 PIERM 81 PIERM 80 PIERM 79 PIERM 78 PIERM 77 PIERM 76 PIERM 75 PIERM 74 PIERM 73 PIERM 72 PIERM 71 PIERM 70 PIERM 69 PIERM 68 PIERM 67 PIERM 66 PIERM 65 PIERM 64 PIERM 63 PIERM 62 PIERM 61 PIERM 60 PIERM 59 PIERM 58 PIERM 57 PIERM 56 PIERM 55 PIERM 54 PIERM 53 PIERM 52 PIERM 51 PIERM 50 PIERM 49 PIERM 48 PIERM 47 PIERM 46 PIERM 45 PIERM 44 PIERM 43 PIERM 42 PIERM 41 PIERM 40 PIERM 39 PIERM 38 PIERM 37 PIERM 36 PIERM 35 PIERM 34 PIERM 33 PIERM 32 PIERM 31 PIERM 30 PIERM 29 PIERM 28 PIERM 27 PIERM 26 PIERM 25 PIERM 24 PIERM 23 PIERM 22 PIERM 21 PIERM 20 PIERM 19 PIERM 18 PIERM 17 PIERM 16 PIERM 14 PIERM 13 PIERM 12 PIERM 11 PIERM 10 PIERM 9 PIERM 8 PIERM 7 PIERM 6 PIERM 5 PIERM 4 PIERM 3 PIERM 2 PIERM 1
All Journals
PIER PIER B PIER C PIER M PIER Letters PIER Photonics
2011-04-07
Flexible Array Beampattern Synthesis Using Hypergeometric Functions
By
Lei Tu,

    Mr. Lei Tu

    Nanyang Technological University

    Singapore

    Homepage

Boon Ng

    Dr. Boon Ng

    School of Electrical and Electronic Engineering

    Nanyang Technological University

    Singapore

    Homepage

Progress In Electromagnetics Research M, Vol. 18, 1-15, 2011
doi:10.2528/PIERM10120803 | Google Scholar

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.
Download Full Article (975) View Full Article volume
Citation
Lei Tu, and Boon Ng, "Flexible Array Beampattern Synthesis Using Hypergeometric Functions," Progress In Electromagnetics Research M, Vol. 18, 1-15, 2011.
doi:10.2528/PIERM10120803
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        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

Download Full Article (975) View Full Article volume


The EM Academy piers.org jpier.org Who's Who in EM
Copyright © 2022 The Electromagnetics Academy. All Rights Reserved.