## 4 Simulation and Optimization  
The design process sought to optimize the key performance parameters of impedance matching, gain, and the ECC. The design techniques were tailored for each antenna. Radiation gain was enhanced, and signal interference and inter-element coupling minimized. Figure 3 illustrates the mechanical configuration and integration of the multi-port antenna. Metal-frame coupling enables compact integration within a commercial smartphone platform. The design supports four sub-6 GHz MIMO ports but minimizes interference with critical internal components such as the battery and mainboard. As shown in Figure 3a, the four antenna ports (ANTs #1 to #4) are symmetrically positioned along the inner top edge of the device, creating a shared coupling structure with the metal frame. Several key structural parameters govern the resonant behavior and radiation performance of the antenna. The total antenna width along the top frame is W\({}_{1}\) = 57 mm. W\({}_{2}\) = W\({}_{3}\) = 28 mm; the configuration is geometrically balanced. The coupling gap between the metal frame and the antenna is C\({}_{\text{g}}\) = 0.6 mm, and both the radiator and ground widths (R\({}_{\text{W}}\) and G\({}_{\text{W}}\)) = 1 mm. The antenna coupling length (L) beneath the frame is 3 mm, the radiating length (R\({}_{\text{L}}\)) along the frame 15 mm, and the grounding length (G\({}_{\text{L}}\)) at the base 7.6 mm. Each antenna port is a slot-fed stub positioned beneath the frame and is electromagnetically coupled with the edge current. To suppress parasitic coupling and improve inter-port isolation, additional grounding paths and PCB cutouts are incorporated. The entire structure is fabricated on a 0.8 mm thick FR4 substrate, which is a standard commercial grade PCB material. Figure 3b shows the antenna layout within the smartphone housing (148 \(\times\) 86 mm). The battery is centrally located. The antenna array is integrated along the top edge within the mechanically reserved region (the red-dotted area). This zone ensures adequate clearance for the coupling length and other critical structural features, enabling effective resonance along the metal frame and robust interaction with the ground plane. The symmetrical arrangement and careful dimensional optimization of the antenna elements enhance both the spatial and polarization diversity, which is particularly useful in edge mounted implementations wherein mutual coupling tends to be more pronounced. The metal frame-integrated design supports compact multi-port operation without the need for an external radiator, thereby offering a highly practical solution when high volume mobile device integration is required. Figure 4 illustrates the simulated VSWR performance of the four-port sub-6 GHz antenna system across three primary 5G NR frequency bands: n78 (3.3-3.8 GHz), n77 (3.3-4.2 GHz) and n79 (4.4-5.0 GHz). The reference VSWR threshold of 3:1 is indicated by dashed lines in each subplot. As shown in Figure 4a, ANT #1 maintains a VSWR \(\leq\) 3 across the entire n78 band that also partially extends into the n79 band. Impedance matching is good from approximately 3.3 to 4.9 GHz. Similarly, Figure 4b shows that ANT #2 delivers effective broadband matching over the n77 and n79 bands, with only a slight degradation near 3.6-3.7 GHz within the acceptable limits for sub-6 GHz operation. Figure 4c,d illustrate the performance of ANTs #3 and #4, respectively, both of which exhibit wideband characteristics spanning the n78 and n79 bands. All four ports exhibit dual resonant behavior attributable to the shared coupling structure and frame-based excitation mechanism. The design ensures a wide impedance bandwidth without a need for discrete external matching components. Overall, the simulations confirm that all four antenna ports exhibit acceptable VSWR characteristics across the required 5G NR bands. The design allows for full 4 \(\times\) 4 MIMO implementation into compact smartphone platforms.