## 2 Transmitarray Antenna Design
### Optimization Result  
As the simulation of TA antenna established before, it has a gain of 27 dB with the SLL of \(-\)20 dB at 28 GHz, and this result is based on the optimized _f/D_ of 0.65, but the position of feed is not the only part that can be optimized in a system of TA antenna. In order to reduce SLL or form multibeams in the desired direction, the phase and magnitude distribution of array can also be optimized [36]. In the Refs. [38; 39], various parameters and conditions about the PSO were discussed and compared. In this paper, a 660-dimensional hyperspace is chosen as one possible solution to this phase optimization with 660 elements on the array. In this hyperspace, there are 15 particles with 5000 iterations flying around to find the best position separately (\(p_{best}\)), and meanwhile, they share the information with others dynamically (\(g_{best}\)), hence they have the tendency to be in the best position, which is the best one for all the particles. This swarm behavior is based on the Equations (4) and (5) of velocity updating and position updating:  
\[v_{n+1}=\omega\times v_{n}+c_{1}\times rand()\times(P_{best,n}-x_{n}) \tag{4}\] \[+c_{2}\times rand()\times(g_{best,n}-x_{n})\]  
\[x_{n+1}=x_{n}+v_{n}\times t \tag{5}\]  
where \(v_{n}\) and \(x_{n}\) are the particle's velocity and the coordinate in the nth dimension, respective; \(\omega\) is the inertial factor that relates to the previous direction of velocity, and it decreases from 0.9 to 0.4 linearly, which means that it has weaker and weaker relationship with the previous position and turns to the local best position at that moment. \(C_{1}\) and \(C_{2}\) are the leaning factor in which \(C_{1}\) is the self-learning factor and \(C_{2}\) is the global learning factors, and they are set as the same value of 2.0 to balance autonomy and group learning ability [38; 39]. The function of random number rand (1) give a stochastic value between 0.0 and 1.0 in every iteration so that the particle can explore as largest possible hyperspace. Equation (5) shows how the particle move to the next position with the common time step  
Figure 10: Simulated far-field radiation pattern of feed source and TA antenna in two cut planes at 28 GHz: (**a**) E-plane comparison and (**b**) H-plane comparison. Figure 9: Electric field (Ex) amplitude distribution: (**a**) E-plane and (**b**) H-plane. one radial row. The optical parameters for two kinds of unit cells of first line along horizontal direction from center to edge are \(L_{11}\) = 1.27 mm, \(L_{12}\) = 1.29 mm, \(L_{13}\) = 1.26 mm, \(L_{14}\) = 1.27 mm, \(L_{15}\) = 1.16 mm, \(L_{16}\) = 1.02 mm, \(L_{21}\) = 1.81 mm, \(L_{22}\) = 1.70 mm, \(L_{23}\) = 1.36 mm, \(L_{17}\) = 1.27 mm, \(L_{18}\) = 0.95 mm, \(L_{24}\) = 1.80 mm, \(L_{25}\) = 1.47 mm, \(L_{26}\) = 1.27 mm, and \(L_{19}\) = 1.12 mm, and \(L_{i}\)(\(i=1,2\)) refers to Unit Cell A and Unit Cell B, respectively. The reflection coefficient of the proposed antenna is shown in Figure 13. The feed antenna has wide passband, and the Gain the whole antenna is limited by TA. Figure 14 indicates the compared radiation pattern of measured results with the simulated results before the optimization in two cut planes, and it is easy to find that the SLL in E plane changes from \(-\)19.6 to \(-\)30 dB and in H plane from \(-\)21.7 to \(-\)30 dB, and all the side lobes, except the first side lobe, are kept below \(-\)35 dB. In summary, the SLL of this TA antenna achieves the level of \(-\)30 dB from the level of \(-\)20 dB by using the PSO. Figure 15 illuminates the measured gains within the operating frequency band. The PSO is good for the design of directional array antenna, which has great potentials in the design of beam steering antenna and MIMO (Multi Input Multi Output, MIMO) array antennas. Besides the analysis of gain and SLL, the property of aperture efficiency is also an aspect to evaluate the performance of TA antenna.