## 1 Introduction  
The retrodirective array (RDA), which has the unique ability to transmit a received signal back toward the source direction without any prior information about the source location, has been the competitive choice for possible wireless communication scenarios in which high-speed target tracking and high link gain levels are desired [1]. Applications that could benefit from the use of an RDA include solar power satellites [2; 3], vehicle radars [4], and wireless power transmission systems [5].  
The well-known techniques for realizing an RDA consist of a corner reflector, the Van Atta array [6], and a heterodyne RDA integrated with an RF circuit for phase conjugation [7]. Because compact and planar topologies are highly desired in modern wireless communications, most of the reported RDAs were based on Van Atta arrays and on heterodyne RDA arrays [8; 9; 10; 11; 12]. In these RDAs, radiating elements were designed with a linear polarization operation. Therefore, when the incident waves are also linearly polarized (LP) waves, the reflected or scattering waves retain the same polarization. Consequently, the scattering and retrodirective signals are mixed, making it difficult to extract the retrodirective signal from the total bistatic radar cross-section (BRCS) response. In order to overcome this problem, an RDA capable of polarization rotation was introduced [13]. However, with this technique, the transmitting and receiving antennas must be designed with different polarizations, thus increasing the cost and size of the overall system. Therefore, the RDA with circular polarization becomes a promising solution for use in an RDA system. In a circularly polarized (CP) RDA system, the reflected or scattering waves are orthogonal to the incident waves, while the polarization state of the retrodirective waves is identical to that of the incident waves. Consequently,the same antenna can be used as the transmitting and receiving antennas, hence improving the compactness and reducing the cost of the overall system. However, there are very limited works on the design of RDAs with circular polarization in the literature [14; 15; 16].  
In this paper, we investigate a technique to enhance the performance of a CP RDA. The CP RDA is designed using an array of CP Koch-shaped patch antennas [17]. To achieve a compact size array, the inter-element spacing is decreased to 0.4\(\lambda\) (\(\lambda\) is the wavelength in free space at the designed frequency of 5.2 GHz). Because the inter-element spacing is small, the mutual coupling effects become critical and considerably affect the CP behavior of the RDA. EBG structures are then implemented between the antenna elements to reduce the mutual coupling. The performance of the CP RDA with the EBGs is verified through wireless power transmission scenarios. As a result, when the power receiver is at the broadside direction, a received power improvement of about 12.45% is achieved using the 10 \(\times\) 10 CP RDA with the EBGs as a transmitter compared to the use of a CP RDA without the EBGs. The paper is arranged as follows. Section 2 introduces the design of the proposed CP RDA with the EBGs and its performance improvement. The performance of the CP RDA with the EBGs during a wireless power transmission assessment is presented in Section 3. Finally, the conclusion is given in Section 4.