## 2 Antenna Design  
### Single Element  
The proposed antenna is designed based on an ultra-thin 0.254 mm RO5880 substrate with relative permittivity of 2.3. The antenna has an overall length and width of \(12\times 10\) mm. The antenna comprises three strips closely connected to each other with 0.35 mm strips at top-right and bottom-left sides. Figure 1 shows the proposed S-shape antenna design, front and back, in detail. The ground plane consists of a square-shape slot incorporated at the top-middle side. Figure 2 explains the evolution of design through three different steps. To attain the anticipated resonance, the proposed single-monopole antenna element is attained with insertion of stubs. These stubs are then parametrically optimized for achieving optimum response.  
In stage 1, a simple l-shape resonator was introduced that showed the resonance response from 36 to 42 GHz with central frequency of 39 GHz. This was further modified with the insertion of an inverted L-shape stub on the right hand side of the l-shape strip. The stub enhanced the bandwidth response to dual-band characteristics, which in stage 3 was modified to a wide bandwidth with the insertion of L-shape stub on left side of the resonating structure.  
The proposed MIMO antenna has been evolved in number of parametric steps. Parametrical studies are conducted to see the antenna's resonance response by altering different paths of currents. Figure 3 shows the wideband response achieved through  
Figure 1: Proposed Antenna (**a**) Front (**b**) Back.  
Figure 2: Design Evolution of the proposed Antenna.  
different parametrical studies conducted. The parameters optimized were Z, Y, K and XX. At the start, parameter Z was parametrically optimized. The starting value was kept at 2 mm and was analyzed up to 4 mm. Five different values in this range were analyzed, each with a difference of 0.5 mm. It was observed that with every increment in value, the design response changed rapidly. It was observed that the resonance value increases with every increment in parameter Z. At 2 mm, a resonance of nearly 7 GHz was achieved from 31 to 38 GHz. At 2.5 mm, the resonance starts at 27 GHz and ends at 38 GHz, giving an approximately 11 GHz bandwidth. The optimal response was achieved at 3 mm, from 25 to 39 GHz. After this optimum value, any further increase resulted in effecting the resonance response. From Figure 3a, it can be seen that the resonances become abrupt. Similarly, in Figure 3b, parameter Y, which is feed length, was analyzed with five samples from 6.25 to 7.25 mm. The optimum response was achieved at 6.25 mm. With further increases in length, the resonance response shifted backwards. The K parameter in Figure 3c showed the optimal response at 3.5 mm. Any further increases and decreases showed that although the resonance bandwidth remains uncertain, the reflection coefficient value becomes abrupt. The trunked ground-plane square slot was optimized from 1.3 to 1.7 mm. The length and width of the square slot was kept same, and Figure 3d shows resonance behavior with antenna parameter XX. Figure 4 shows the single-element radiation patterns and gain over frequency. The gain ranges between 3.9 and 5.2 and efficiency ranges between 85 and 98%.  
Figure 3: Parametric Studies conducted (**a**) \(Z\) (**b**) Y (**c**) K (**d**) XX.