# Slotted E-Shaped Meta-Material Decoupling Slab for Densely Packed MIMO Antenna Arrays
## 2 Methodology of Design and Measurement Analysis
### Antenna Array with Slotted Meta-Material Decoupling Slab  
A slotted meta-material decoupling slab (S-MTM-DS) with dual reflexes, slotted E-shapes extended with an inductive stub is proposed. Its function was validated when located between two microstrip patch antenna elements to reduce the inter-element spacing, the mutual coupling, and the return losses. Figure 7 shows the slotted MTM-DS antenna array equivalent circuit. The radiator is presented in the equivalent circuit by a resonant circuit with resistance \(R_{e}\), capacitance \(C_{e}\), and inductance \(L_{e}\). The slotted MTM-DS has inductance \(L_{s}\) and the capacitance \(C_{s}\).  
Figure 6: The fabricated \(2\times 1\) antenna microstrip patch antenna array with MTM-DS. (**a**) Simulated and measured S-parameters results. (**b**) Connected antenna array photo with decoupling slab.  
Sloted MTM-DS in the middle of the array connecting the two antenna elements sections is modelled by inductance \(L_{c}\). The coupling between the Slotted MTM-DS and the patch is through the dominant capacitance \(C_{c}\) because the coupling between the patch and the Slotted MTM-DS is via the patch antenna non-radiating edge. The resonance frequency (\(f_{r}\)) of the slotted MTM-DS is dependent on the magnitude of \(L_{c}\) and \(C_{s}\) and is presented as follows:  
\[f_{r}=\frac{1}{2\pi\sqrt{L_{s}C_{s}}} \tag{1}\]  
The effectiveness of the slotted MTM-DS was determined by the simplified equivalent circuit model. Optimized values of the equivalent circuit model were determined by using an optimization tool in full-wave electromagnetic solver simulation by AWR. The magnitudes of these parameters are given in Table 1.  
From the previous simulations and measurements, it was necessary to insert the slotted MTM-DS between the two radiators as shown in Figure 8 to enhance the mutual coupling. The MTM-DS microstrip configuration has ground slots on each arm. By using this configuration, the gain and the bandwidth of the array of elements is not affected by the presence of the slots.  
The importance of the new designed slotted MTM-DS appears in suppressing the induced surface current that results from interaction between the two patches. It is observable in Figure 9 that strong current is induced on the array of the antenna that guarantees the effectiveness of the slotted MTM-DS. The distance between the two patch elements is \(0.57\lambda 0\), where \(\lambda 0\) is wavelength in free space at 9.4 GHz.  
MTM-DS was designed and implemented as previous on FR-4 lossy substrate with h = 1.6 mm, \(\varepsilon_{r}\) = 4.5, and tan \(\delta\) = 0.025 as shown in Figure 10. The simulated and measured results isolation and return loss response of the MTM-DS array of antenna is shown in Figure 11. In Figure 11 the frequency bandwidth is 1.51 GHz from 8.67:10.18 GHz, and the maximum isolation is \(-43.7\) dB.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Values** \\ \hline \(R_{f}\) & 54 Ohm \\ \(R_{e}\) & 1.9 Ohm \\ \(C_{e}\) & 0.65 pF \\ \(L_{c}\) & 4.29 nH \\ \(L_{c}\) & 0.18 nH \\ \(C_{c}\) & 2.66 pF \\ \(L_{s}\) & 0.68 nH \\ \(C_{s}\) & 4.05 pF \\ \hline \hline \end{tabular}
\end{table}
Table 1: Optimized values of the equivalent model representing the \(2\times 1\) antenna microstrip patch antenna array with slotted MTM-DS.  
Figure 7: Slotted MTM-DS antenna array equivalent circuit.  
Figure 8: Geometry of \(2\times 1\) microstrip patch antenna array with slotted MTM-DS.  
Figure 10: Photograph of the fabricated antenna array with slotted MTM-DS.  
Figure 9: Current density of \(2\times 1\) microstrip patch antenna array with slotted MTM-DS.  
S-parameter results are measured the three types of the array of antenna: MTM without DS, MTM-DS, and slotted MTM-DS are summarized in Table 2. For the first configuration (without DS), the average isolation over the proposed band width is \(-18\) dB. For the second (MTM-DS), it is \(-23.85\) dB, and for the last one (slotted MTM-DS), it is \(-36\) dB. On average the isolation is improved by \(18\) dB.