volume | PIER Journals

Abstract

Antenna arrays with shaped power patterns have many applications in communications and radars. Many antenna array synthesis techniques for shaped patterns have been developed in the past years, and most of them deal only with uniformly spaced arrays. In this paper, a new method is proposed for the synthesis of nonuniform linear antenna arrays with shaped power patterns. The proposed synthesis method consists of three steps. First, we find a satisfactory power pattern for the required radiation characteristics by solving a constrained least-squares problem which is obtained with the help of non-redundant representation of squared magnitude of a linear array factor. Then, we factorize the polynomial associated with the power pattern by using polynomial rooting, and consequently obtain the corresponding field patterns. Finally, the forward-backward matrix pencil method is used to obtain a nonuniform linear array with optimized excitation magnitudes, phases and locations for a specific choice of field patterns. The synthesized array has a smaller number of elements than the one with uniformly spaced elements for the same pattern performance. Several synthesis experiments are conducted to validate the effectiveness and advantages of the proposed synthesis method.

1. Woodward, P. M., "A method of calculating the field over a plane aperture required to produce a given polar diagram," J. Inst. Elect. Eng., Vol. 93, 1554-1558, 1947.

2. Stutzman, W. L., "Synthesis of shaped-beam radiation patterns using the iterative sampling method," IEEE Trans. Antennas Propagat., Vol. 19, No. 1, 36-41, 1971.

3. Elliott, R. S. and G. J. Stern, "A new technique for shaped beam synthesis of equispaced arrays," IEEE Trans. Antennas Propagat., Vol. 32, No. 10, 1129-1133, 1984.

4. Milne, K., "Synthesis of power radiation patterns for linear array antennas ," IEE Proceedings H, Vol. 134, No. 3, 285-296, 1987.

5. Zhang, W.-X. and Y.-M. Bo, "Pattern synthesis for linear equalspaced antenna array using an iterative eigenmodes method," IEE Proceedings H, Vol. 135, No. 3, 167-170, 1988.

6. Werner, D. H. and A. J. Ferraro, "Cosine patterns synthesis for single and multiple main beam uniformly spaced linear arrays," IEEE Trans. Antennas Propagat., Vol. 37, No. 11, 1480-1484, 1989.

7. Isernia, T., O. M. Bucci, and N. Fiorentino, "Shaped beam antenna synthesis problems: Feasibility criteria and new strategies," Journal of Electromagnetic Waves and Applications, Vol. 12, No. 1, 103-138, 1998.

8. Cid, J. M., J. A. Rodriguez, and F. Ares, "Shaped power patterns produced by equispaced linear arrays: Optimized synthesis using orthogonal sin(Nx)/sin(x) beams," Journal of Electromagnetic Waves and Applications, Vol. 13, No. 7, 985-992, 1999.

9. Azevedo, J. A. R., "Shaped beam pattern synthesis with nonuniform sample phases ," Progress In Electromagnetics Research B, Vol. 5, 77-90, 2008.

10. Akdagli, A. and K. Guney, "Shaped-beam pattern synthesis of equally and unequally spaced linear antenna arrays using a modified tabu search algorithm," Microwave Opt. Technol. Lett., Vol. 36, No. 1, 16-20, 2003.

11. Kazemi, S., H. R. Hassani, G. R. Dadashzadeh, and F. Geran, "Performance improvement in amplitude synthesis of unequally spaced array using least mean square method," Progress In Electromagnetics Research B, Vol. 1, 135-145, 2008.

12. Marcano, D. and F. Duran, "Synthesis of antenna arrays using genetic algorithms," IEEE Antennas Propag. Mag., Vol. 42, No. 3, 12-22, 2000.

13. Dritschel, M. A., "On factorization of trigonometric polynomials," Integr. Equ. Oper. Theory, Vol. 49, No. 1, 11-42, 2004.

14. Liu, Y.-H., Z.-P. Nie, and Q. H. Liu, "Reducing the number of elements in a linear antenna array by the matrix pencil method," IEEE Trans. Antennas Propagat., Vol. 56, No. 9, 2955-2962, 2008.

15. Liu, Y.-H., Q. H. Liu, and Z.-P. Nie, "Reducing the number of elements in the synthesis of shaped-beam patterns by the forward-backward matrix pencil method," IEEE Trans. Antennas Propagat., Vol. 58, No. 2, 604-608, 2010.

16. Miller, E. K. and D. M. Goodman, "A pole-zero modeling approach to linear array synthesis I: The unconstrained solution," Radio Sci., Vol. 18, 57-69, 1983.

17. Oppenheim, A. V. and R. W. Schafer, Digital Signal Processing, Prentice-Hall, Englewood Ciffs, 1975.

18. Hua, Y. and T. K. Sarkar, "Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise," IEEE Trans. Acoust., Speech, Signal Processing, Vol. 38, No. 5, 814-824, 1990.

Dr. Yanhui Liu

Professor Zai-Ping Nie

Prof. Qing Huo Liu