Array pattern optimization using electromagnetism-like algorithm

doi:10.1016/j.aeue.2008.04.001

AEU - International Journal of Electronics and Communications

Volume 63, Issue 6, June 2009, Pages 491-496

https://doi.org/10.1016/j.aeue.2008.04.001 Get rights and content

Abstract

This paper proposes a design method of array pattern optimization for sidelobe level (SLL) reduction. The element positions and their weights are determined by electromagnetism-like (EM)-like algorithm. Simulation results show that the EM-like algorithm is efficient in SLL reduction for beamwidth restriction. Synthesis of array pattern using EM-like algorithm is very straightforward and efficient. It does not require any gradient operation and is very easy in both formulation and programming. Therefore, the EM-like algorithm can be applied to many other applications in array signal processing.

Introduction

The performance of the communication system depends on the antenna array design. In general, the antenna array design includes beamwidth, sidelobe level (SLL), directivity, etc. The SLL reduction is most useful for array pattern synthesis design via adjusting the positions, weights and phases [1], [2], [3], [4], [5], [6], [7], [8], [9]. In this paper, the element positions and their weights are adjusted for array pattern optimization to achieve maximal SLL reduction. Array pattern synthesis with element positions is generally a nonlinear problem. In the past studies, there are many known analytical optimization methods that have been applied to radiation pattern design. For example, the genetic algorithm (GA) [1], [2] and simulated annealing (SA) algorithm [9] are useful for the solution of this problem. The purpose of this paper is to present a design method of arrays for SLL reduction using electromagnetism-like (EM-like) algorithm. In order to control the width of main beam, we use a method as in [7], [8], [9] to calculate the SLL reduction.

EM-like algorithm [10] is a stochastic evolutionary computation technique based on the EM theory in physics. The convergence property of EM-like algorithm has already been proved in [11]. EM-like algorithm is an intelligent technique different from GA and SA. The way in which the particles of algorithm move is correspondent with particle swarm optimization (PSO) [12] and ant colony optimization (ACO) [13]. The first step of EM-like algorithm is to produce one group random solution from feasible domain, and regard each solution as a charged particle. The charge of each particle is determined with fitness function, and then moves the particle with attraction or repulsion among population. The attraction–repulsion mechanism of EM-like algorithm corresponds to the reproduction, crossover and mutation in GA [14].

EM-like algorithm is via calculating the resultant force in the population to determine moving direction of the current particle by Coulomb's law and superposition principle. The resultant force is decided by the charges and distance among each particle. In this mechanism, the higher charge will produce larger attraction or repulsion. The resultant force is small when the distance between the particles is farther. In latter iteration, the movements of particles will be slow, as those of SA [14]. On the other hand, EM-like algorithm can improve the current optimum solution with local search and advances the feasibility for global search.

The simulated results show that the proposed technique can achieve the array pattern optimization well. In addition, the numerical results calculated by EM-like algorithm are better than those of other existing studies. Unlike the binary system in GA, EM-like algorithm can be treated in decimal system. Furthermore, EM-like algorithm does not need a suitable guess of initial value and has no gradient operation. The proposed optimization technique is easy in programming and can be extensively applied to many other applications.

Section snippets

Array pattern function

Consider a linear array with $2 N - 1$ elements aligned on the x-axis of rectangular coordinate. The array geometry is shown in Fig. 1. If the array elements are isotropic, the array pattern can be expressed as [15] $AP (θ, θ_{o}, \bar{D}, \bar{W}) = |\sum_{i = 1}^{2 N - 1} w_{i} \cos [{kd}_{i} (\sin θ - \sin θ_{o})]|,$ where $θ_{o}$ is the direction of main beam (i.e., the steering angle) and $θ$ is the observation angle. In Eq. (1), $\bar{D}$ is the position vector of array elements given as $\bar{D} = [d_{1}, d_{2}, \dots, d_{2 N - 1}]^{T},$ and $\bar{W}$ is the weight vector of array elements given as $\bar{W} = [w_{1}, w$

EM-like algorithm

In this paper, EM-like algorithm is utilized to optimize the array pattern by adjusting element positions and their weights. EM-like algorithm is a meta-heuristic technique based on the EM theory in physics [10]. It is an intelligent technique that has the concept of the population similar to PSO [12] and ACO [13]. The moving mechanism of the particles is smart and easy to understand. Another advantage of this method is that it can be treated directly in decimal system and is different from GA

Numerical examples

Considering a linear array with array length $L = 50 λ$ . The number of array elements is chosen as 25 so that it is the same as [6], [7], [8], [9]. The positions of starting and ending elements are fixed as $d_{1} = 0$ and $d_{2 N - 1} = 50 λ$ , respectively. Therefore, the position dimension is 23. For symmetric array, the position of central element is further fixed as $d_{N} = 25 λ$ and the dimension is then reduced as 11. In this paper, we assume all positions are constrained to multiples of $0.5 λ$ . In the EM-like

Conclusion

In this study, the array pattern is optimized by EM-like algorithm. The SLL reduction is achieved by using EM-like algorithm to adjust the positions and weights of array elements. Numerical examples show that good performance can be obtained by using EM-like algorithm in such problems. The proposed method is straightforward, easy and efficient. Moreover, the EM-like algorithm contains no gradient operation, and can then achieve global optimization. Unlike the binary system in GA, the EM-like

Acknowledgment

The work in this paper was supported by the National Science Council, Taiwan, under Grant NSC NSC 96-2628-E-006-250-MY3. The authors would like to express their sincere gratitude to it.

Jhen-Yan Jhang was born in Taiwan in 1982. He received the BS degree from the National Taiwan Ocean University in 2005 and currently he is working toward his PhD degree in the Department of Systems and Naval Mechatronic Engineering, National Cheng-Kung University, Tainan, Taiwan. His research interests include theory of wave propagation, array signal processing, wireless communication and underwater communication systems.

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Kun-Chou Lee was born in Chia-yi, Taiwan, in 1966. He received the BS degree in 1989, MS degree in 1991, and PhD degree in 1995, from the National Taiwan University, Taipei, Taiwan, all in Electrical Engineering. From 1995 to 1997, he served in the army of his country. From 1997 to 2003, he served as faculty of the Wu-Feng Institute of Technology, Shu-Te University, and National Kaohsiung University of Applied Sciences all in southern Taiwan. In 2004, he joined the faculty of the Department of Systems and Naval Mechatronic Engineering, National Cheng-Kung University, Tainan, Taiwan, where he is now an associate professor. His research interests include underwater communications and networks.

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Array pattern optimization using electromagnetism-like algorithm

Abstract

Introduction

Section snippets

Array pattern function

EM-like algorithm

Numerical examples

Conclusion

Acknowledgment

AEU-Int J Electron Commun

AEU-Int J Electron Commun

AEU-Int J Electron Commun

AEU-Int J Electron Commun

AEU-Int J Electron Commun

Application of particle swarm algorithm to the optimization of unequally spaced antenna arrays

J Electromagn Waves Appl

Synthesis of unequally spaced arrays by dynamic programming

IEEE Trans Antennas Propag