**4. Fabrication and experiment**

To verify, a transmitarray and two patch antennas were fabricated. **Figure 13** shows that the prototype is verified in the anechoic chamber.

**Figure 13.** *The prototype is verified in the anechoic chamber. Reprinted with permission from Ref. [22]; copyright 2022 IEEE.*

**Figure 14.**

*(a) The simulated and measured patterns of the patch antenna at 25 GHz. (b) The simulated and measured |S11| of the interferometric phase transmitarray excited by the patch antenna. Reprinted with permission from Ref. [22]; copyright 2022 IEEE.*

**Figure 14a** shows the patterns at 25 GHz of the patch antenna, and the simulated and measured curves are similar. **Figure 14b** shows the simulated and measured |S11| of the interferometric phase transmitarray excited by the patch antenna.

**Figure 15** shows the simulated and measured patterns at 25 GHz of the interferometric phase transmitarray excited by the patch antenna. The simulated realized gain is 18.4 dBi, which is 0.9 dBi higher than the measured realized gain. In addition, the simulated and measured sidelobe level is around -15 dB, within a reasonable range. Minor differences between curves are mainly caused by the measurement environment.

### **5. MIMO behavior**

To evaluate the performance of the proposed interferometric phase MIMO system, a same-size unifocal transmitarray antenna with a focus on (18 mm, 0, 30 mm) is introduced for simple comparison. **Figure 16** shows the simulated pattern.

#### **Figure 15.**

*The simulated and measured patterns at 25 GHz of the interferometric phase transmitarray excited by the patch antenna. (a) xoz-plane. (b) yoz-plane. Reprinted with permission from Ref. [22]; copyright 2022 IEEE.*

*Interferometric Phase Transmitarray for Millimeter-Wave MIMO System DOI: http://dx.doi.org/10.5772/intechopen.112468*

**Figure 16.** *The simulated pattern of the unifocal transmitarray antenna at 25 GHz.*

**Figure 17.**

*The simulated 3D pattern of the unifocal transmitarray antenna at 25 GHz.*

**Figure 17** shows the 2 � 2 MIMO system integrated by four unifocal transmitarray. It is assumed that the distance between two unifocal transmitarrays on one side is 100 mm and the transmission distance is 1000 mm, then the angle of the cross weak channels is *θ* = 6°. **Figure 18** shows the simulated xoz-plane pattern of the unifocal transmitarray antenna at 25 GHz. It can be seen from **Figure 18** that when *θ* = 6°, the gain is 15.2 dBi.

The channel capacity can be calculated by Eq. (7) as follows

$$\mathbf{C} = B \log \mathbf{2} (\mathbf{1} + \mathbf{S}/\mathbf{N}) \tag{7}$$

where *B* is bandwidth, and *S*/*N* represents signal noise ratio. In MIMO links, the higher the receiving power, the greater the *S*/*N*, and the larger the channel capacity. The receiving power can be expressed as Eq. (8).

$$P\_r = P\_t \frac{G\_t G\_r \lambda\_0^2}{16\pi^2 d^2} \tag{8}$$

**Figure 18.** *The simulated xoz-plane pattern of the unifocal transmitarray antenna at 25 GHz.*

where *Pr* and *Pt* represent receiving power and transmitting power, *Gr* and *Gt* represent the gain of the receiving antenna and the transmitting antenna, λ<sup>0</sup> is the wavelength in free space, and *d* is the distance between transmitter and receiver.

Therefore, the channel capacity is positively correlated with the gain of the receiving antenna and transmitting antenna. To compare the two MIMO systems in **Figures 1** and **2**, it is assumed that all environments are the same, except for antenna gain differences. The gains of the receiving and transmitting antennas in the 2 2 MIMO system integrated by interferometric phase transmitarray are all 18.4 dBi. Normalize the channel capacity of each link to 1, and the channel capacity of the 2 2 MIMO system is 4. By comparison, there are two strong channels and two weak channels in the 2 2 MIMO system in **Figure 17**. The gains of the receiving and transmitting antennas are 19.5 dBi in strong channels and 15.2 dBi in weak channels. In the 2 2 MIMO system in **Figure 17**, the 18.4 dBi of the antenna gain is still used to normalize the channel capacity. After normalization, the channel capacity of the strong channel is 1.056, and the weak channel is 0.823 in **Figure 17**. Therefore, the channel capacity of the 2 2 MIMO system in **Figure 17** is 3.758, which is lower than the 2 2 MIMO system integrated by interferometric phase transmitarray. In addition, the distance between transmitter and receiver *d* will also affect the channel capacity of the MIMO system in **Figure 17**. Since when *d* decreases, the angle of the cross weak channels *θ* increases, resulting in a decrease in antenna gain in weak channels. When d increases, the result is the opposite.

Therefore, through simple comparison, it can be found that the channel capacity of the 2 2 MIMO system integrated by interferometric phase transmitarray is higher than the 2 2 MIMO system integrated by unifocal transmitarray.

### **6. Conclusions**

The proposed interferometric phase transmitarray can adjust two EM waves to the boresight of the transmitarray. When the plane wave illustrates the proposed transmitarray, the transmitted plane wave will be scattered and focused on two

positions. The MIMO system integrated by the interferometric phase transmitarray breaks the limitations of weak channels in conventional lens MIMO. In addition, the proposed method of the MIMO system can be extended to more channels.
