## 4 Numerical Results
### 5G Antenna Design  
With the advent of fifth-generation (5G) and its forthcoming operation in millimeter-wave frequency bands of mobile communication networks, certain requirements, such as wide and ultra-wide spectrum, multi-band operation, and data rates in the order of Gigabits-per second (Gbps), will change drastically the specifications in antenna design. The use of microstrip patch antennas in millimeter-wave frequency bands is a candidate solution to provide efficacious and robust designs. In the literature, there are several efforts in designing antennas for millimeter-wave frequency bands of 5G mobile communication systems [94,95]. E-shaped patch antennas can extend the operation and functionality of patch antennas in dual- or multi-frequency bands [31, 32, 33]. Their design is subjected to the following constraints [31,90]  
\[ \begin{split} L_{slot1}&<L_{antenna}\\ L_{slot2}&<L_{antenna}\\ \frac{D_{slot}}{2}+W_{slot}&<\frac{W_{antenna}}{2} \end{split}  \tag{15}\]  
where \(L_{slot1}\) is the length of the first slot in the E-shaped antenna, \(L_{slot2}\) is the length of the second slot, \(L_{antenna}\) is the length of the E-shaped antenna, \(W_{slot}\) is the width of the slot, \(W_{antenna}\) is the width of the E-shaped antenna, and \(D_{slot}\) is the distance of the slot from the center of the E-shaped antenna. One of the challenging tasks in antenna design is the choice of the feeding technique. Besides classical feeding techniques, such as coaxial or microstrip feeding, shaped aperture-coupled feeding has gained noticeable interest due to the comparative characteristics that can provide, i.e., dual- or multi-band operation, wide and ultra-wide bandwidth, dual-polarization mode, and high gain values [96, 97, 98, 99]. Shaped aperture-coupled feeding can be also applied in millimeter-wave frequency band antennas [100]. However, for the patch antenna to achieve a dual-band operation when using aperture-coupled feeding, the shape of the aperture should be modified. A representative example of aperture shape modification to achieve dual-band operation in patch antenna design has been presented in [33]. Design methods for aperture-coupled patch antennae have been presented in [101]. These guidelines are applied for evaluation to design two different cases of an aperture-coupled patch antenna in the millimeter-wave frequency bands. The selected frequencies of the evaluation fall into the n258 (center frequency: 26.4 GHz) and n260 (center frequency: 38.5 GHz) 5G NR frequency bands. Table 6 lists the extracted parameter values as they obtained from the design method described in [101]. Moreover, Figure 7 displays the perspective views (Figure 7a,b) and the computed results of the reflection coefficient as a function of frequency (Figure 7c) for the two different use cases of an aperture-coupled patch antenna in the millimeter-wave frequency bands. From the presented results, it is evident that the design method that was introduced in [101] cannot be applied in the millimeter-wave frequency bands. Both of the use cases (Figure 7a,b) do not resonate at the desired frequencies of the 5G NR bands. Moreover, the method in [101] cannot provide an efficient way of designing a patch antenna that performs in a dual-frequency band mode. Finally, taking into consideration the antenna complexity and the requirements of 5G NR frequency bands in antenna design, it seems that an optimization method is a straightforward process to obtain feasible solutions of antenna design in the aforementioned frequency bands if we recast this problem as an optimization one. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**WOA vs.** & **GWO** & **SSA** & **PSO** & **ABC** & **FA** \\ \hline \(p\)-value & 6.93 \(\times\) 10\({}^{-02}\) & **4.88 \(\times\) 10\({}^{-04}\)** & **1.95 \(\times\) 10\({}^{-03}\)** & **7.32 \(\times\) 10\({}^{-03}\)** & **4.88 \(\times\) 10\({}^{-04}\)** \\ \hline \hline \end{tabular}
\end{table}