###### Abstract  
The present work describes a new approach for the design of a Frequency-Selective Surface (PSS) in the context of frequency filters to increase isolation between two vehicle-borne antennas. A compact FSS design based on nested square meandered resonators is optimized for multifrequency operation. Furthermore, a design workflow is proposed. In general, the measurement of low-profile FSS does not correspond to simulation through Floquet modes based on periodic boundary conditions due to the lack of uniformity of mutual coupling among the FSS unit cells. The proposed method demonstrates the agreement between the infinite simulation and the measurement of the finite prototype once a convenient scale factor is applied, which facilitates the design workflow. In this case, an FSS is used as an efficient filter to increase the isolation between antennas by 6 dB in three representative bands (3 GPP, WiFi I and II). In this way, multifrequency antennas can be placed at approximately half their actual distance with the same performance in spatial-constrained vehicular environments. attenuation; frequency selective surface; isolation technology; mutual coupling; multi-frequency antennas; periodic boundary conditions; resonator filters; vehicles +
Footnote †: journal: Applied Sciences  
antennas, which increases costs. Hence, a desirable approach would be to achieve isolation in a non-complex manner, regardless of the type of antenna, which is suitable for both single and multiple-band applications. In this context, decoupling based on a Frequency Selective Surface (FSS) is studied [25; 26; 27]. This method is not antenna-dependent and can be used for several bands. FSSs have been commonly used in radio frequency systems in applications as diverse as microwave ovens, antenna radomes [28], modern metamaterials and radars [4]. An FSS can be added between the antennas to reduce coupling, as shown in Figure 1. It typically consists of a periodic array of printed resonators on a dielectric substrate. FSS acts as a frequency filter between the antennas because it is composed of resonant structures that absorb the energy at certain frequencies. The geometry of the resonator will determine its frequency response, while the array size and the interspace between resonators impact the final attenuation. In the proposed scenario, the FSS is placed perpendicularly to the rooftop of a vehicle (e.g., train) between two multifrequency antennas. A low-profile FSS is convenient for greater clearance and to avoid high impact on the general 3D radiation patterns of the antennas. The actual FSS size will be a trade-off between the aforementioned downsides and the filtering capability, which increases with the FSS cross-section. For a low-profile FSS design, the size of each resonator or the number of them must be reduced. Regarding the size of the resonator, different sizes and designs of compact resonators are studied in [28; 29]. Other investigations deal with reducing the resonator size using discrete components [30]. In terms of the number of elements, simulation methods are often based on infinite array approximation using Floquet modes and reducing the computation domain to a unit cell with periodic boundary conditions. This approach is closer to a filtering problem between the two sides of the FSS than open boundary conditions, as the former provides reflection and transmission parameters. This is no longer possible if a finite FSS is considered because a general transmission coefficient cannot be set. However, unit cell approximation ignores the influence of the edge effect on the isolation due to the actual finite size of the FSS structure. In a finite FSS design, the resonators of the array that are closer to the boundaries are surrounded by air, whereas, in its infinite simulation, they are all equally surrounded by other resonator elements. Then, a discrepancy between infinite (simulated) and finite (measured) FSS is likely to occur unless the resonators are far enough apart to be considered as not influencing one another.