# Ultra-Wideband Antenna Design for 5G NR Using the Bezier Search Differential Evolution Algorithm
## 3 Optimization Results and Discussion
* Size Control Value of Pre-Pattern Matrix, L: 2.5, to assure balance between exploration and exploitation mechanisms. * Number of Iterations: 100. * Size of Pattern Matrix, N (Size of Population): 40. * Problem Dimensions, D (Variables): 3. * Structure Scaling Factor: \([0.5,1.5]\). - Stub Width: \([1,10]\) (mm). - Stub Length: \([10,35]\) (mm). The calculated number of antenna design simulations and cost functions, which corresponded to the stopping criteria of the optimization process, was 4000, and an acceptable solution was any design with the reflection coefficient \(S_{11}\leq-10\) dB across the target operation band. As the main frequency, that of the center of the n78 band was selected, at \(f_{c}=3.55\) GHz, for the optimizer algorithm to focus on minimizing the \(S_{11}\) value in this frequency band, to include 5G NR in the operational bandwidth. Then, as depicted in detail in the graph (\(S_{11}\), Figure 4), the optimal antenna result operates efficiently from 1.4 GHz to 3.9 GHz, as \(S_{11}<-10\) dB is satisfied across this band,  
Figure 4: The frequency response of the best antenna found: black solid line (with the stub) and red dashed line (without the stub). while two minima are also demonstrated in the graph, which represent resonances in the frequencies \(f_{1}=1.72\) GHz with \(S_{11}=-20\) dB and \(f_{2}=3.8\) GHz with \(S_{11}=-38\) dB. This frequency band includes all the technologies that the original design was capable of harvesting from, namely GSM at 1.8 GHz, UMTS at 2.1 GHz, Wi-Fi at 2.4 GHz, and LTE at 2.6 GHz, but also includes 5G NR technologies at 3.5 GHz. As a result of the bandwidth broadening in the optimal antenna, not only 5G NR is included in it, but other technologies that were not the initial target of the optimization also are, as the bandwidth of the original antenna was 1 GHz (from 1.7 to 2.7 GHz), and that of the optimal antenna is 2.5 GHz (from 1.4 to 3.9 GHz). Moving forward, the rest of the graphs that describe the behavior of the optimal antenna should also be examined. Apart from the \(S_{11}\) graph, the impedance graph of the antenna is also significant, as its values should represent good impedance matching between the patch and the line, in order for the energy to be transferred without major losses to the following component of the system. Ideally, the value of the antenna impedance response should be as close to \(50+0j\)\(\Omega\) as possible across the operation bandwidth. As depicted in Figure 5, from 1.4 to 3.9 GHz, the reactance value has a mean value below \(30j\)\(\Omega\), and the resistance is \(50\pm 10\)\(\Omega\) across the whole band. These values are vastly acceptable, as perfect matching cannot be realistically achieved in a bandwidth as large as 2.5 GHz, but the small reactance and resistance close to 50 \(\Omega\) prove that the antenna indeed has ultra-wideband characteristics from to 1.4 to 3.9 GHz, including all the aforementioned technologies (GSM, UMTS, Wi-Fi, LTE, 5G NR). In the following, since the impedance and \(S_{11}\) response graphs confirm the wideband properties of the antenna across the target frequency band, the efficiency of it is examined. These three metrics are codependent, but convenient values in one of them do not guarantee that the rest of them are as expected, i.e., in cases where the search produces structural results that contain design violations. As depicted in Table 5, the optimal antenna can successfully harvest energy from the ambient environment, with values greater than 84% for all technologies of interest, across the entire frequency band, and up to 96% for some frequency points. The efficiency in Table 5 proves that the optimal antenna is capable of harvesting energy from all target technologies, from GSM 1.8 GHz, UMTS 2.1 GHz, Wi-Fi 2.4 GHz, LTE 2.6 GHz, and 5G NR 3.5 GHz, which is also solidified by the impedance and \(S_{11}\) response graphs. Figure 5: The impedance response of the optimal antenna. Last but not least, another key attribute of antennas for rectenna applications is their omnidirectionality.