### I. Introduction

*real-coded GA*(RGA), was used because of its simplicity and its direct operation on the parameters. Therefore, in this paper, an unusual single-layer, wide-bandwidth, high-performance FSS structure designed with a GA and its effect on the antenna radiation pattern characteristics (antenna gain, directivity, and front-to-back ratio) are presented. The proposed FSS, which uses the RGA-based symmetric inserting selection strategy, responds to the design requirements, diminishes the design time, and avoids the regular structure design limits of human intellectuals. After the FSS was implanted, the antenna impedance bandwidth improved from 96.1% to 98.07% with the center frequency of 5.2 GHz. Moreover, the antenna gain showed a maximum enhancement of 7.8 dBi for a peak gain of 10.1 dBi, and the gain was sustained at higher than 9 dBi, unlike as reported studies.

### II. FSS Unit Cell Design

*ɛ*

*=4.4, a loss tangent of δ = 0.02, and a thickness of 0.8 mm, as it is low-cost and easy to manufacture. Then, we set up the properties of the chosen substrate with an assumption dimension of 13 mm, the fundamental requirements, and the design specification targets of the GA program. The GA process was simplified as shown in Fig. 1. In other words, the top surface of the FSS structure unit cell was subdivided into*

_{r}*N × N*specific cells. At this time, to improve the insertion selection speed of a cell and the angular stability of the unit cell, the symmetric criterion was chosen. The non-conducting or conducting property of each cell was described using binary encoding. As shown in Fig. 2, in the case of the conducting cell, the corresponding gene was nominated as 1; and in the case of the non-conducting cell, the assigned gene was 0.

Generate a random string of binary numbers.

Generate the shape of the FSS reflector from the binary matrix.

Create the models of the symmetric condition unit cell with the chosen substrate and solve the models using the High-Frequency Structure Simulator (HFSS) software.

Export the S-parameter (

*S*_{1},*S*_{21}) results of the models to a data file.-
The fitness function is the link between the physical shape and the optimization produces.

The fitness function is given by: -
Generate the next generation by applying the GA operators.

*Lp*=

*Wp*= 12.7 mm and a thickness of 0.8 mm, as shown in Fig. 3, respectively.

*N*

*), the population size (*

_{par}*N*

*), the crossover probability (*

_{pop}*P*

*), and the mutation probability (*

_{cross}*P*

*) are very important. These values will determine the convergence performance and the efficiency of the attainment of the optimum solution. In the RGA adopted in this study,*

_{mut}*N*

*= 6 and*

_{par}*N*

*= 50. The convergence criterion was set as small as possible [the value computed in equation (1)].*

_{pop}*P*

*= 0.9 and*

_{cross}*P*

*= 0.1, respectively. The considered frequency range from 1 GHz to 10 GHz with the total number frequency points was 1,000. At this time, the optimization was terminated after 100 generations.*

_{mut}_{21}).

*θ*= 0

^{0}). On average, each generation in the RGA simulation took about 3 min and 5 sec. The CPU time of the entire simulation process was 7 h and 35 min. It must be noted that the RGA used in this study was able to obtain the true profiles with a lower number of generations. Table 1 compares the performance of this study to that of earlier studies. Fig. 6 plots the transmission coefficient of the FSS unit cell versus the frequency, with the elevation angle as a parameter for the TE and TM polarizations, respectively. In the figure, it is clearly visible that the designed FSS has a relatively stable frequency response with respect to the oblique incidence angles.

*Lg*=

*Wg*= 12.9 mm, 13.2 mm, and 13.7 mm corresponded to the spacing parameters between the adjacent cells of 0.2 mm, 0.5 mm, and 1 mm, respectively. From the figure, it can be seen that with a large spacing value, the resonant frequency and the reflection phase increased, and the bandwidth of the FSS stopband gradually became narrower. Therefore, the optimal design for the FSS reflector was chosen as that with

*Lg*=

*Wg*= 12.9 mm. Fig. 7 shows the surface current distribution of the FSS unit cell at the frequencies of 3.5 GHz, 5.2 GHz, and 5.8 GHz, respectively. The results exhibited a transmission coefficient (S

_{21}) of −48.5 dB and a stopband bandwidth (when S

_{21}

*<*−10 dB and the reflection phase was± 90

^{0}) of 5.5 GHz from 2.6 GHz to 8.1 GHz, which produced 105% of impedance bandwidth with respect to the central frequency of 5.2 GHz. The results prominently show that the proposed FSS can be used to improve the antenna performance.

### III. Application of FSS on Antenna Performance

*ɛ*

*=4.4 and a loss tangent of 0.02, and the other side had a partial T-shaped ground plane.*

_{r}*ε*

*) and the reflected back-radiated waves from the antenna toward the FSS (*

_{S}*ε*

*)] were added in the phase, which triggered a rise in the constructive interference [19]. The evaluation of the phase at the reference T-plane is depicted by the following equation:*

_{R}*ε*

*should be equal to zero or an integral multiple 2π at all frequencies. As shown in (3), the antenna-back-radiated*

_{T}*ε*

*will increase with the augmentation of the frequency and be controlled by the spacing Z. In this study, the spacing between the antenna and the FSS layer was analyzed to obtain the excellent radiation characteristics.*

_{R}^{0}, whereas the maximum was along the broadside 0

^{0}in the case of the antenna loaded with an FSS reflector. As a consequence, the radiation pattern and the directivity of the antenna significantly improved after the FSS application. Finally, Table 3 shows a summarized performance comparison of this study with the most relevant studies reported in literature.

_{21}) value of −48.5 dB (105%) and offered an effective phase that exhibited constructive interference with the antenna back-radiated wave. Those qualities that could not be found with the fundamental design method make the designed FSS a candidate for applications that require a high-performance, high-gain, low-profile, and broadband antenna.