## 3 Results
### IFA Design Using DH-BPSO  
An application of the proposed DH-BPSO to an antenna design is demonstrated in this section. Although any antenna can be chosen to demonstrate an application of DH-BPSO, we select a planar IFA, one of the common antenna geometries in mobile devices. The IFA is modelled with an electromagnetic simulator, ANSYS HFSS 2019 R2. The design parameters of the IFA geometry are shown in Figure 3.  
The resonant frequency of the IFA is mainly determined by _arm_z_ which is approximately a quarter-wave long at the resonant frequency. The width of the conducting IFA arm is denoted as _arm_w_ and is fixed to be 1 mm. The input impedance is controlled by adjusting _feed_gap_ and _feed_z_. The _slot_w_ is the spacing between the parasitic patches and set to be 0.25 mm. A 1 mm thick FR4 substrate with standard double-sided copper cladding is used. The permittivity and loss tangent of the FR4 substrate are 4.4 and 0.02, respectively. The size of the substrate is fixed for all IFAs and defined with _sub_z_ and _sub_x_ which is 85 \(\times\) 140 mm\({}^{2}\). The width of the parasitic patches (_patch_z_2) is fixed to be 7.05 mm, whereas the width of the patches closest to the feed and grounding strip (_patch_z_1) varies depending on feed position for impedance matching. The _feed_z_ is set to be 2.5 mm. The ground clearance _GND_clr_ is the distance between the IFA arm and ground plane. The ground clearance region is divided into 24 sections that represent either activated or deactivated parasitic patches. The yellow squares represent patches that are activated to be conductive and the grey squares represent the deactivated patches to be non-conductive. The state (active or inactive) of a particular parasitic patch maps to the state of a bit (1 or 0) in the integer that represents the position of a particle. Hence there are 16,777,216 (224) possible patch configurations, and the particles of the DH-BPSO algorithm traverse a discrete 24-dimensional space. The conductive elements are modelled as copper sheets with a thickness of 35 \(\upmu\)m and a conductivity of 5.8 \(\times\) 10\({}^{8}\) S/m. A unique antenna design is created for a range of values of ground clearance (_GND_clr_) from 9 to 14 mm. For each clearance length, the reference base design (i.e., no active parasitic elements) is optimized to resonate at 720 MHz by adjusting the _feed_gap_ and _arm_z_ parameters. The exact value of these and other parameters are given in Table 3. The parasitic patch design is then optimized by applying the DH-BPSO algorithm with 10 particles, a maximum velocity of 10, and a minimum velocity of 1. The goal of the optimization is to improve the \(-\)10 dB bandwidth of the reflection coefficient of the IFAs, which is simulated from 500 MHz to 1 GHz. Because DH-BPSO searches for the global minima of a cost function, the negative of the \(-\)10 dB bandwidth is used as the cost function. The minima of this cost function correspond to wider bandwidths. Figure 3: Design parameters of the inverted-F antenna (IFA) antenna with parasitic patches. The IFA element is in orange and FR4 substrate is in blue. To show a fair comparison, three different antenna patch configurations were simulated: (1) a base IFA design with no parasitic patches as a reference, (2) a base IFA with all parasitic patches activated, and (3) the optimized IFA. The reflection coefficient versus frequency plot for the 14 mm ground clearance IFA is shown in Figure 4. The simulation results indicate that the DH-BPSO algorithm improves the bandwidth from the conventional IFA without the parasitic patches by 74.3%. The base IFA with all patches activated shows poor input impedance mismatch and shift of resonant frequency to the lower frequency. Regarding the radiation pattern of the three different IFAs shown in Figure 5, the optimized IFA shows similar omnidirectional pattern on \(\varphi=90^{\circ}\) plane and figure \"8\" shape on \(\varphi=0^{\circ}\) plane relative to the base IFA.