volume | PIER Journals

Abstract

In this paper, an algorithm based on penalty cost function for synthesizing at-top patterns is proposed. A descent algorithm (DA) as its optimizing approach is proposed in this paper as well. Apparently, whole algorithm efficiency totally depends on the DA. Unlike traditional descent method, the DA defines step length by solving a inequality, instead of Wolf or Armijo-type search rule, stimulation results indicate that it can improve the computational efficiency. Under mild conditions, we prove that the DA has strong convergence properties. Several numerical examples are presented to illustrate the effectiveness of the proposed algorithm. The results indicate that the approach is effective in the pattern shape precisely in both mainlobe and sidelobe region for arbitrary linear arrays.

1. Li, R., L. Xu, X.-W. Shi, N. Zhang, and Z.-Q. Lv, "Improved differential evolution strategy for antenna array pattern synthesis problems," Progress In Electromagnetics Research, Vol. 113, 429-441, 2011. Google Scholar

2. Lin, C., A.-Y. Qing, and Q.-Y. Feng, "Synthesis of unequally spaced antenna arrays by using differential evolution," IEEE Transactions on Antennas and Propagation, Vol. 58, 2553-2561, 2010.
doi:10.1109/TAP.2010.2048864 Google Scholar

3. Wang, W.-B., Q.-Y. Feng, and D. Liu, "Application of chaotic particle swarm optimization algorithm to pattern synthesis of antenna arrays," Progress In Electromagnetics Research, Vol. 115, 173-189, 2011. Google Scholar

4. Liu, D., Q.-Y. Feng, W.-B. Wang, and X. Yu, "Synthesis of unequally spaced antenna arrays by using inheritance learning particle swarm optimization," Progress In Electromagnetics Research, Vol. 118, 205-221, 2011.
doi:10.2528/PIER11050502 Google Scholar

5. Li, W.-T., Y.-Q. Hei, and X.-W. Shi, "Pattern synthesis of conformal arrays by a modified particle swarm optimization," Progress In Electromagnetics Research, Vol. 117, 237-252, 2011. Google Scholar

6. Mahanti, , G., K., N. Pathak, and P. Mahanti, "Synthesis of thinned linear antenna arrays with fixed sidelob elevel using real-coded genetic algorithm," Progress In Electromagnetics Research, Vol. 75, 319-328, 2007.
doi:10.2528/PIER07061304 Google Scholar

7. Xu, Z., et al. "Pattern synthesis of conformal antenna array by the hybrid genetic algorithm," Progress In Electromagnetics Research, Vol. 79, 75-90, 2008.
doi:10.2528/PIER07091901 Google Scholar

8. Chen, K., Z. He, and C. Han, "A modified real GA for the sparse linear array synthesis with multiple constraints," IEEE Trans. Antennas Propag., Vol. 54, No. 7, 2169-2173, 2006.
doi:10.1109/TAP.2006.877211 Google Scholar

9. Yuan, W., et al. "Nonlinear least-square solution to flat-top pattern synthesis using arbitrary linear array," Signal Processing,, Vol. 85, 1869-1874, Sept. 2005. Google Scholar

10. Li, M. and H. Feng, "A sufficient descent LS conjugate gradient method for unconstrained optimization problems," Applied Mathematics and Computation, Vol. 218, 1577-1586, Nov. 1, 2011. Google Scholar

11. Nocedal, J. and S. J. Wright, Numerical optimization, Springer Verlag, 1999.
doi:10.1007/b98874

12. Zhang, X.-D., Matrix Analysis and Application, Springer, 2004.

Dr. Tiao Jun Zeng

Prof. Quanyuan Feng