Mathematical Problems in Engineering

Volume 2015, Article ID 365280, 8 pages

http://dx.doi.org/10.1155/2015/365280

## Thinning of Concentric Circular Antenna Arrays Using Improved Binary Invasive Weed Optimization Algorithm

Department of Electronic Engineering, Naval University of Engineering, Wuhan 430033, China

Received 23 May 2014; Accepted 6 November 2014

Academic Editor: Hsuan-Ling Kao

Copyright © 2015 Huaning Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This study presents a novel optimization algorithm based on invasive weed optimization (IWO) for reduction of the maximum side lobe level (SLL) with specific half power beam width (HPBW) of thinned large multiple concentric circular arrays of uniformly excited isotropic elements. IWO is a powerful optimization technique for many continuous problems. But, for discrete problems, it does not work well. In this paper, the authors propose an improved binary IWO (IBIWO) for pattern synthesis of thinned circular array. The thinning percentage of the array is kept equal to or more than 50% and the HPBW is attempted to be equal to or less than that of a fully populated, uniformly excited, and half wavelength spaced concentric circular array of the same number of elements and rings. Simulation results are compared with previous published results of DE, MPSO, and BBO to verify the effectiveness of the proposed method for concentric circular arrays.

#### 1. Introduction

Circular antenna arrays have considerable interest in a variety of applications including radar, sonar, and mobile and commercial satellite communication systems [1]. It consists of a number of elements which are usually omnidirectional and arranged on a circle and can be employed for beamforming in the azimuth plane, for example, at the base stations of the mobile radio communications systems [2–4]. As very popular type of antenna array is the circular array that has several advantages over other array geometries such as all-azimuth scan capability (it can perform 360-degree scan around its center) and the beam pattern can be kept invariant [5]. Moreover, circular arrays are less sensitive to mutual coupling as compared with linear and rectangular arrays since these do not have edge elements [1]. Concentric circular antenna array (CCAA) that contains many concentric circular rings of different radii and number of elements have several advantages including flexibility in array pattern synthesis and design both in narrowband and broadband beamforming applications [2–4]. CCAA is also used in direction-of-arrival applications since it provides almost invariant azimuth angle converge.

Uniform concentric circular antenna array (UCCA) is one of the most important types of the CCA where the interelement spacing in individual ring is kept almost half of the wavelength and all the elements in the array are uniformly excited. Uniform antenna arrays exhibit high directivity; however, they usually suffer from high side lobe level [1]. To reduce the SLL, the array is made aperiodic by altering the positions of the antenna elements with uniform amplitude excitations. The other method to reduce SLL is to use an equally spaced array with radically tapered amplitude distribution [3, 4]. However, uniform excitation is desired to reduce the complexity in designing a feed network.

The process is known as array thinning and is widely employed to reduce the SLL of antenna array with large number of elements. Array thinning is related to the removal of some elements from a uniformly spaced or periodic array to achieve a desired radiation pattern. Thinning not only reduces SLL but also brings down the cost, weight, and power consumption by decreasing the number of radiating elements. However, synthesis of antenna array is a tough challenge, and it cannot be solved by analytical methods. But there are various global optimization algorithms for thinning such as genetic algorithms (GA) [6], particle swarm optimization [7], differential evolution (DE) [8], and biogeography-based optimization (BBO) [9]. Haupt has used GA for thinning of linear arrays and a center element fed concentric ring array antenna to reduce the SLL [10, 11]. Orthogonal GA has been proposed by Zhang et al. for pattern synthesis of thinned linear array [12]. Ghosh and Das utilized DE with global and local neighborhood (DEGL) for thinning planar circular array [13]. Thinning of a planar concentric circular array to SLL reduction using modified PSO (MPSO) algorithm is proposed by Pathak et al. [14]. Chatterjee et al. have compared the performance of MPSO and gravitational search algorithm for thinning of a scanned concentric ring array [15]. BBO has been utilized by Singh and Kamal for thinning large multiple concentric circular ring arrays [16]. Wang et al. proposed a chaotic binary PSO (CBPSO) algorithm to synthesis of thinned linear and planar antenna array [17]. Basu and Mahanti introduced the fire fly algorithm (FFA) to thinning of concentric two-ring circular array antenna [18]. Chatterjee et al. have compared the performance of binary FFA and binary PSO to thin planar concentric ring antenna array to minimize SLL in a number of predefined -planes [19].

In this paper, we present the method of optimization of uniformly spaced concentric circular array using an improved binary variant of recently proposed metaheuristic algorithm called invasive weed optimization. The IWO algorithm has found successful application in many electromagnetic problems like design of printed Yagi antenna [20], E-shaped MIMO antenna [21], multifeed reflector antennas [22], broadband patch antenna [23], conformal phased arrays [24], circular antenna arrays [25], and so forth. Results obtained using IWO for these problems are encouraging. However, the nature of reproduction operators in classical IWO limits its application, such as discrete optimization problems. In this paper, an improved binary version of IWO algorithm (IBIWO) has been proposed for large multiple concentric ring arrays of isotropic elements for SLL reduction and at the same time keeping the half power beam width (HPBW). The thinning percentage of the array is kept to more than 50% and the HPBW is kept equal to or less than that of the array with the same number of elements and rings. The same problem has been dealt by DEGL, MPSO, and BBO, respectively. To the best of our knowledge, IWO has not been utilized for the thinning of concentric circular array before. Simulation results obtained are compared with the above algorithm.

The rest of the paper is organized in follows. A formulation of the thinned CCAA pattern synthesis as an optimization task has been discussed in Section 2. Section 3 gives a comprehensive overview of the proposed IBIWO algorithm. Section 4 presents the simulation results and in Section 5 conclusions are presented.

#### 2. Thinned Planar Circular Array

Thinning an array means turning off some radiating elements in a uniformly spaced or periodic array in order to generate a pattern with low side lobe levels. Typical applications for thinned array include satellite-receiving antennas that operate against a jamming environment, ground-based high frequency radars, and design of interferometer array of radio astronomy. In this work, we assumed that the positions of elements are fixed and the elements can have only two states: either “on” or “off.” An antenna in an “on” state only contributes to the total array pattern. On the other hand, an antenna is in “off” state if the element is either passively terminated to a matched load or is open circuited and hence it does not contribute to the total array pattern. Thinning an array to produce low side lobes is much simpler than the more general problem of nonuniform spacing of the elements. Nonuniform spacing has an infinite number of possibilities for placement of the elements.

In CCAA, the elements are arranged in such a manner that all antenna elements are positioned in multiple concentric circular rings, which vary in radii and in number of elements. Figure 1 shows the general configuration of CCAA with concentric circular rings, where the th () ring has a radius and the corresponding number of elements is . Assuming that all the elements are isotropic sources, the far-field pattern of this array can be written as