# Design of a Compact Multiband Monopole Antenna with MIMO Mutual Coupling Reduction
## 2 Design of Antenna Structure
### The Compact Multiband Monopole Antenna  
The proposed compact multiband monopole antenna in this paper evolves from the design presented in [22]. The structure and detailed dimensions of the compact multiband monopole antenna are shown in Figure 1 and Table 1. Figure 2 shows the evolutionary steps of the compact multiband monopole antenna structure. Step 1 is a quarter-wavelength monopole antenna for 2.45 GHz, calculated using Equation (1). In step 2, an arm is added to the left side for 3.5 GHz. In step 3, two arms are added to the ground at the bottom layer for 5-6 GHz. In Step 4, two elliptical cuts remove a bit of metal from the middle arm for better impedance matching, as shown in Figure 1d and published in [22]. In the proposed design, an arm (which can be seen as a piece of inductance) parallel to the middle arm creates more bandwidth from 4 GHz to 7.2 GHz compared to [22], which creates about 800 MHz bandwidth at the 4 GHz band, as shown in Figures 2 and 3. Figure 1: The structure of the compact multiband monopole antenna. (**a**) Front view. (**b**) Bottom view. (**c**) Back view. (**d**) Detail view. Here, \(L_{arm}\) represents the length of the arms, \(C_{0}\) represents the speed of light, \(f_{0}\) is the designed frequency resonance, and \(\epsilon_{\rm eff}\) represents the effective permittivity. \[L_{arm}=\frac{C_{0}}{4f_{0}\sqrt{\epsilon_{eff}}} \tag{1}\]  
Figure 3 shows the reflection coefficients of the five-step antennas. The under \(-10\) dB bandwidth becomes progressively wider with each evolution step, and the impedance matching improves, especially at higher bands. The reflection coefficient of the proposed antenna has six frequency resonant points: 2.46 GHz, 3.47 GHz, 4.41 GHz, 5.45 GHz, 6.32 GHz, \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \(L_{mt}\) & \(W_{m}\) & \(L_{d}\) & \(L_{d1}\) & \(L_{d2}\) & \(L_{d3}\) & \(L_{d4}\) & \(W_{a}\) & unit \\
30 & 10 & 5 & 14.5 & 15 & 2 & 11 & 3 & unit \\ \(W_{d1}\) & \(W_{d2}\) & \(W_{d3}\) & \(L_{s}\) & \(W_{s}\) & \(L_{g}\) & \(W_{g}\) & h & mm \\
0.5 & 1 & 3.5 & 6 & 0.6 & 4.5 & 4 & 1.6 & mm \\ \hline \end{tabular}
\end{table} 
Table 1: The dimensions of the compact multiband monopole antenna. Figure 3: The evolution reflection coefficients of the five-step antennas. The gray background bars represent the designed target bands. Figure 2: The evolutionary steps of the compact multiband monopole antenna structure. and 7.06 GHz, respectively. These frequency resonance points determine and satisfy the bandwidth and performance requirements for the compact multiband monopole antenna. Figure 4 illustrates the simulation current distributions and radiation patterns of the compact multiband monopole antenna at 2.46 GHz, 3.47 GHz, 4.41 GHz, 5.45 GHz, 6.32 GHz, and 7.06 GHz, respectively. These radiation patterns exhibit omnidirectional characteristics with gains of 1.43 dBi, 1.44 dBi, 2.71 dBi, 3.63 dBi, 3.35 dBi, and 4.7 dBi, respectively. Figure 4a shows the current distribution of the antenna at the resonance frequency of 2.46 GHz, which exhibits the standard quarter-wavelength current distribution along the middle arm. This means the maximum current occurs at the shorted end and decreases to zero at the open end. Figure 4b exhibits a U-shaped and half-wavelength current distribution along the left arm and the parallel arm at 3.47 GHz. This means the maximum current occurs in the middle of the U-shape and decreases to zero at the two open ends. Despite the opposite current directions, they do not cancel each other out and still radiate electromagnetic power effectively. Figure 4c shows the three-quarters wavelength current distribution along the middle arm at 4.41 GHz. This means the current flows from maximum to zero, then to another maximum, and back to zero, with the current direction remaining mostly in phase. This frequency resonance point is key to creating more bandwidth. Figure 4d exhibits another U-shaped and half-wavelength current distribution along the left arm of the ground and the middle arm at 5.45 GHz.