International Journal of Antennas and Propagation

Volume 2018, Article ID 8075318, 8 pages

https://doi.org/10.1155/2018/8075318

## Synthesis of the Sparse Uniform-Amplitude Concentric Ring Transmitting Array for Optimal Microwave Power Transmission

Shanghai Institute of Advanced Communication and Data Science, Key laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai University, Shanghai 200444, China

Correspondence should be addressed to Xue-Xia Yang; nc.ude.uhs@xx.gnay

Received 8 March 2018; Revised 16 May 2018; Accepted 6 June 2018; Published 8 July 2018

Academic Editor: Ikmo Park

Copyright © 2018 Hua-Wei Zhou 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

Beam capture efficiency (*BCE*) is one key factor of the overall efficiency for a microwave power transmission (MPT) system, while sparsification of a large-scale transmitting array has a practical significance. If all elements of the transmitting array are excited uniformly, the fabrication, maintenance, and feed network design would be greatly simplified. This paper describes the synthesis method of the sparse uniform-amplitude transmitting array with concentric ring layout using particle swarm optimization (PSO) algorithm while keeping a higher *BCE*. Based on this method, uniform exciting strategy, reduced number of elements, and a higher *BCE* are achieved simultaneously for optimal MPT. The numerical results of the sparse uniform-amplitude concentric ring arrays (SUACRAs) optimized by the proposed method are compared with those of the random-located uniform-amplitude array (RLUAA) and the stepped-amplitude array (SAA), both being reported in the literatures for the maximum *BCE*. Compared to the RLUAA, the SUACRA saves 32% elements with a 1.1% higher *BCE*. While compared to the SAA, the SUACRA saves 29.1% elements with a bit higher *BCE*. The proposed SUACRAs have higher *BCE*s, simple array arrangement and feed network, and could be used as the transmitting array for a large-scale MPT system.

#### 1. Introduction

Microwave power transmission (MPT) technology transfers power from one location to another by the microwave beam, which could be applied in supplying power to the space power satellites, unmanned aerial vehicles, the far-reached areas, and so on [1]. For a large-scale MPT system, the most important parameter is the beam capture efficiency (*BCE*), which is the ratio of the captured microwave power by the receiving antenna array to the transmitted power by the transmitting antenna array [2].

In 1974, Dr. Brown performed an MPT experiment with a distance of 1.7 m in the laboratory. The overall efficiency up to 54% and the *BCE* is 95% [3]. However, the MPT experiment carried out next year only obtained an overall efficiency of 7% and *BCE* of 11.3% when the range was 1.54 km [4]. Until now, the overall efficiency of a MPT system is not higher than 10% because of a low *BCE* [2].

The transmitting aperture illuminated by the Gaussian amplitude distribution can obtain a maximum beam capture efficiency *BCE*^{max} higher than 99% because of the broad beam width and low side lobe level in the far field [5]. Discrete transmitting aperture, namely, antenna array, is more practical for expanding the MPT system to a large scale. The optimized excitation amplitudes of a planar array for the *BCE*^{max} can be achieved by solving generalized eigenvalue problem [6]. Nevertheless, owing to the continuous amplitude distribution, many different amplifiers would be required for every distinct element, which results in a complex transmitting array. To reduce the kinds of amplifiers, Baki et al. and Li et al. [7, 8] proposed the isosceles trapezoidal distribution (ITD) and stepped-amplitude arrays (SAAs), respectively. The design and implementation of transmitting array could be greatly simplified if all elements are uniformly excited [9]. The random-located uniform-amplitude array (RLUAA) comprising of 100 elements was optimized by particle swarm optimization (PSO) algorithm with a *BCE* of 89.96% being obtained [10]. However, the computation amount would grow up rapidly as the element number increases, which could not be applied in a large-scale transmitting array design.

Besides the exciting strategy, the sparsification of a large-scale transmitting array has a practical significance. Sparse arrays can not only reduce the complexity of the feed networks but also can decrease the weight. Most studies on sparse antenna arrays [11–13] are focused on reducing the number of elements, the peak side lobe level, the computational effort, and so on but not considering the power transmission efficiency. In the MPT scenario, the element numbers of antenna arrays were reduced to 65% and 64% of the original one through compressive sensing (CS) and convex programming (CP) methods, respectively, in [14, 15]. By combining these two methods, the element number was reduced to 54% of the original one and the *BCE* was improved about 3.16% [16]. Unfortunately, arrays in [14–16] were not uniformly illuminated. Moreover, CS and CP would not be efficient for the large-scale array design due to strong nonlinear relationship between the array factor and the element positions [17]. The Bessel-approximation array factor of a concentric ring array (CRA) is only related to the radius and excitation of each ring, which would reduce the computation amount and could be used in optimizing a large-scale array.

PSO algorithm was firstly introduced by Kennedy and Eberhart in 1995 [18]. Due to its high search efficiency, PSO has been widely used in enhancing antenna gain [19] and beam pattern synthesis [20] and improving *BCE* of a MPT system [10]. In this work, the synthesis of the sparse uniform-amplitude transmitting array is discussed for the optimal MPT. The exciting strategy, element number, and *BCE* are considered simultaneously for the MPT system. The outline of this paper is organized as follows. Section 2 describes the calculation equations of *BCE* of the sparse uniform-amplitude CRA (SUACRA). Section 3 introduces the optimization model for the SUACRA, and Section 4 presents the numerical results of SUACRAs, which have been compared with those of RLUAA discussed in [10] and SAA proposed in [8].

#### 2. Theoretical Foundation

As shown in Figure 1, the transmitting array is a CRA located in the XOY plane with an element in the center, and the radial space between the (*m* − 1)th and the *m*th rings is denoted by . All elements are excited by the identical phase and amplitude.