# A Compact Ultra-Thin 4 \(\times\) 4 Multiple-Input Multiple-Output Antenna
## 3 Working Mechanism  
### Design Stages  
The design stages of this antenna pairs system are discussed in this section to obtain a deeper comprehension of its mechanism. As plotted in Figure 3a, Stage 1 is a plain rectangle microstrip plane without ground clearance, and a resonant frequency larger than 4 GHz may exist, as depicted in Figure 3b. The circuit model of Stage 1 is a series branch of resistance and the inductance of the plain rectangle plane. The input impedance was relatively low because of the small resistance of the rectangular strip. By digging an L-shaped slit on the radiating element and cutting two ground clearances with a dimension of 145 \(\times\) 1.8 mm\({}^{2}\) on the grounding plane, Stage 2 was generated. A more apparent resonant  
Figure 1: (**a**) The overall structure and (**b**) concrete construction of the designed AP system.  
Figure 2: Simulated S-parameters.  
mode around 3.7 GHz emerged; the resonant frequency shift is due to the effect of the parasitic capacitor brought by the introduced L-shaped slit. The utilization of the L-shaped slit greatly enhances the resistance of the radiating element. Hence, the port matching condition improved a lot. However, the isolation performance between Ant. 1 and Ant. 2 deteriorated a lot. To obtain a resonant frequency offset toward 3.5 GHz and isolation enhancement, two small rectangle slots with different areas were cut from the short edge of the L-shaped slit and the ground plane. One can see evidently from Figure 3b that the proposed AP resonated approximately at 3.55 GHz, and a slight improvement of about 3 dB of isolation performance was achieved in Stage 3. In the final designed structure, another rectangular slot was cut from the radiating elements, and the ground slot evolved into a T-shaped open-ended slot; the explored AP accurately resonated at 3.5 GHz, and the mutual coupling was also enlarged to 15.5 dB at 3.5 GHz. The equivalent circuit of an AP at each design step is illustrated in Figure 3c. R1(2) and L1(2) are the inherent resistance and inductance of Ant. 1(2) at each stage. Cpg1(2) and Lg1(2) are the parasitic capacitance between the radiating element 1(2) and the ground plane and the grounding inductance; Cp12 is the coupled capacitor between Ant. 1 and Ant. 2. C1(2) and C\({}_{\text{T-shaped slot}}\) are parasitic capacitance brought by the slot cut from the antenna element and ground plane. The newly added component at each stage and the main variation are clearly indicated in Figure 3c.  
Figure 4a shows the simulated current distribution of the designed AP without/with the T-shaped slot when Ant. 1 is excited at 3.5 GHz. The most substantial surface current can be observed around the upper section of Ant. 1 when the T-shaped slot had not yet been applied. After the T-shaped slot was utilized, the most considerable current density was allocated over the edge of the T-shaped slot. A very weak current was obtained in the radiating element, thus decreasing the mutual coupling between two elements of the AP  
Figure 3: Simulated (**a**) design procedures, (**b**) simulated curves at each process, and (**c**) equivalent circuit of an AP at each stage.  
The simulated outcomes of these two situations are plotted in Figure 4b. The exploited AP resonated at 3.5 GHz without a T-shaped slot, but the port impedance matching condition was not ideal enough. The \(-6\) dB bandwidth range was 3.38-3.64 GHz, while the isolation performance was just around 9 dB within the desired bands. By introducing the T-shaped slot on the ground plane, a significant improvement in the port impedance matching condition was achieved; the \(-10\) dB bandwidth was 3.31-3.76 GHz, and isolation between Ant. 1 and Ant. 2 was also lifted to 15 dB. It is quite noteworthy that a tremendous reduction of approximately 0.66 of ECC\({}_{12}\) was attained after utilizing the T-shaped slot, which dramatically enhanced the MIMO performance of the designed AP.