## 1 Introduction
The other is based on the various working principles, TA could be further categorized into four different types, namely, frequency selective surfaces (FSS) [15; 18; 20; 22; 24], metasurface (MS) [25; 26; 21; 23], the spatial bandpass-filter based structure [27], receive/transmit-mode structure, and so on [16; 28; 29]. Owing to the transmission, amplitude and phase should be taken into consideration at the same time, how to simply the TA while keeping the specific properties of lower SLL as well as greater surface tolerance for the application in 5G communication has become an urgent research hotpot. The method of optimization can be divided into two categories: local and global search algorithms [30]. Literally, the local optimization is worked in a limited space with designed initial values, whereas the global optimization is forced on the entire solution hyperspace and just the random initial values are needed and the best result will be found in the whole search space [31]. As for the optimization of phase distribution, there are always hundreds of elements that need to be optimized and it is difficult to set up suitable initial values for all the elements befittingly, so the global search algorithms are used here for the optimization of phase distribution. Considering the flexible and independent properties of the elements on the array, heuristic method is widely adopted in the optimization of array antenna among which, genetic algorithm (GA) and particle swarm optimization (PSO) show great superiority at the aspect of efficiency and operability [31; 32; 33; 34; 35]. Though PSO and GA both belong to the population-based stochastic optimization, PSO has only two lines of kernel codes compared to the recurrent process of crossover, breeding, and selection in GA. PSO also benefits from less computational bookkeeping with less computational resource [33; 34]. In this paper, we propose a two-layer MS TA antenna feed by the optimized horn antenna to actualize the reduced SLL and high gain at the frequency range around 28 GHz for the 5G communication. This thin TA comprises a single substrate and two circular patches on both sides of the substrate, and four metal was inserted into the substrate at the centrally symmetrical positions for each element, which is based on structure presented in the Ref. [28] working at 20 GHz but with more simple and efficient design. The positions of vias are fixed at the changeless positions on the array in this paper, while the positions of vias changed with the varying patch size to match the requirements of phase distribution in the published paper. Only two sizes of circular patches are used, and the length of slots on the patches will control the transmitted phase. To the author's knowledge, it is the first time when the transmission coefficients are controlled using this structure. Hence, a TA structure with lower cost and easier fabrication is presented in this paper. Then, an optimized Potter horn antenna is exploited as feed structure of the TA, which has good symmetry in principal plane patterns as the corrugated horns, and the smooth wall of the Potter horn greatly reduces the difficulty of manufacturing. The TA and the Potter horn antenna make the whole prototype as a 5G TA antenna, and a 27 dBi maximum gain in the main direction is achieved, while the 3-dB gain bandwidth and aperture efficiency are maintained at 11.8% and 28%, respectively. The SLL is maintained at -20 dB level and after the optimization, the SLL can achieve the level of -30 dB, which can be used as the high-gain array antenna for 5G directional communication. Our contributions are listed as follows: in Section 2, first, a horn antenna is optimized by \(\cos^{\text{q}}\) (\(\theta\))-mode method to get the approximate uniform radiation in azimuthal direction; second, a transmission unit cell with single substrate layer was designed in an easier way without using multisubstrate layer structure or air gaps; and third, particle swarm optimization is used to optimize the SLL of TA antenna radiation pattern.