# Phased Antenna-Array Synthesis Using Taylor-Series Expansion and Neural Networks
## 4 Validation Using CST Microwave Studio for 5G Antenna Arrays
### 16-Element MIMO Antenna Array  
The MIMO system under investigation comprises 16 antennas aligned in the same direction and arranged parallel to each other, with an inter-element spacing of \(\lambda/2\), as shown in Figure 12. This configuration has been carefully designed to maximize network directivity while minimizing mutual coupling between radiating elements, ensuring efficient signal transmission in millimeter-wave frequency bands. Each patch element has a width of \(W=2.6\) mm and a length of \(L=2.6\) mm and is designed on a substrate with a thickness of \(h=0.41\) mm. The elements are uniformly spaced by \(\lambda/2\), resulting in a total array length of approximately 89.4 mm. The results presented in Figure 13 highlight the stability of mutual coupling across the entire operational frequency band. Specifically, the electromagnetic performance assessment shows that the maximum mutual coupling between antennas remains below \(-15\) dB, indicating excellent isolation among the array elements. Such a high degree of isolation is essential for preserving radiation efficiency, as it reduces interference and mitigates losses caused by unwanted electromagnetic interactions. This characteristic is crucial for optimiz  
The Figure 13 shows the S-parameters of the antenna, which are crucial for assessing its reflection and transmission characteristics. S\({}_{11}\) represents the reflection coefficient, indicating how much signal is reflected back into the antenna; lower values (typically below \(-10\) dB) suggest good impedance matching and minimal reflection losses. S\({}_{21}\) indicates the forward transmission efficiency, with higher values reflecting better signal transmission. S\({}_{12}\), the reverse transmission coefficient, should ideally be low to minimize back reflections, while S\({}_{22}\), the reflection coefficient at the output port, provides insight into the matching at the output. Overall, low reflection coefficients (S\({}_{11}\) and S\({}_{22}\)) and high transmission coefficients (S\({}_{21}\)) indicate optimal antenna performance, ensuring efficient signal transmission with minimal losses across the operating frequencies.  
Figures 14-25 show the radiation patterns of the antenna at various angles, ranging from 25\({}^{\circ}\) to 135\({}^{\circ}\). At lower angles such as 25\({}^{\circ}\) and 35\({}^{\circ}\), the radiation pattern is more concentrated, with the main lobe pointing in a specific direction, indicating a narrower beamwidth. As the angle increases to 45\({}^{\circ}\) and 55\({}^{\circ}\), the main lobe begins to widen, indicating an expansion of the radiation coverage. This trend continues through angles of 65\({}^{\circ}\), 75\({}^{\circ}\), and 85\({}^{\circ}\). The radiation patterns of the antenna at various angles are shown in Figure 15.  
Figure 11: Three-dimensional radiation pattern of the antenna. (**a**) At 28.14 GHz; (**b**) at 37.88 GHz.  
Figure 12: Design of a 16-element MIMO antenna array.  
Figure 13: S-parameters of the antenna.  
and 85\({}^{\circ}\), when the antenna starts to radiate more broadly, providing wider coverage. At higher angles, such as 95\({}^{\circ}\) to 135\({}^{\circ}\), the radiation pattern continues to spread, and the energy is directed over a larger area. The main lobe shifts progressively, and the side lobes also change in intensity, reflecting how the antenna adapts its radiation characteristics across different angular orientations. This behavior illustrates the antenna's ability to provide directional or omnidirectional radiation, depending on the required application, and it emphasizes the flexibility of the antenna design in accommodating a wide range of angular orientations for optimal signal distribution. Figure 26 presents the radiation pattern of 16 antennas synthesized using the Taylor method with different amplitude synthesis levels of \(-20\) dB, \(-30\) dB, \(-40\) dB, and \(-50\) dB, along with uniform excitation.