**1. Introduction**

Recently, mmW technology has been the top priority of the fifth-generation (5G) wireless network [1]. Multiple-input multiple-output (MIMO) has been recognized as the most effective application of 5G technology since it can increase the data transmission rate by expanding channel capacity [2]. Generally, elements in MIMO antennas are with wider beamwidth to ensure that each receiving antenna can receive the signals from each transmitting antenna. However, for mmW antennas, high-gain and narrower beamwidth antennas are employed to overcome channel fading. With high gain elements, conventional lens-based 2 2 MIMO systems are investigated [3–6] as shown in **Figure 1**. This kind of MIMO system requires multiple lenses, which is not conducive to the miniaturization of the MIMO transceiver. Moreover, the signals of Channel 1 and Channel 2 are robust and easy to be received, but the signals of Channel 3 and Channel 4 are weak and unable to transmit information effectively due to the narrow beamwidth of the elements. Besides, MIMO systems in the mmW band have

### **Figure 1.** *The 2 2 MIMO system integrated by the conventional lens.*

high requirements for antenna and circuit performance, which leads to high costs and complexity [7–9].

Current metamaterials have the characteristics of flexible control of electromagnetic (EM) waves and are widely used in mmW systems, such as radar, satellite communications, and imaging [10]. Metamaterials and their derivatives also have the advantages of thin thickness, small size, and lightweight, which can effectively solve problems such as cost and loss [11–13]. More importantly, metamaterials are widely used in transmitting and reflective arrays to realize beamforming and beam steering [14–21], which lays the foundation for realizing the miniaturization of the MIMO transceiver.

This paper proposes an interferometric phase transmitarray for the MIMO system. Its characteristic is that when multiple EM waves radiate toward the array, all the EM waves are beamforming into beams with high directivity. When the plane wave illuminates the interference phase transmitarray vertically, the transmissive plane wave will be scattered and focused to two different positions. Based on the above two characteristics, a novel MIMO system can be implemented, as shown in **Figure 2**. Compared with the MIMO system in **Figure 1**, the advantage of this novel MIMO system is that two antennas can share one transmitarray, which is beneficial to the miniaturization of the MIMO transceiver. All four channels can efficiently transmit information and increase channel capacity.

**Figure 2.** *The MIMO system integrated by the proposed lens.*

### **2. Theoretical study**

The theoretical study focuses on the phase distribution and incident field of the interferometric phase transmitarray.

#### **2.1 The phase distribution**

The ideal model of interferometric phase transmitarray is shown in **Figure 3**. Assuming the interferometric phase transmitarray is an N � N square array. When two EM waves are radiated by two feeds toward the array, the two transmitted EM waves are formed into a high-directivity beam.

For quantitative analysis, it is assumed that Omn (xm, yn, 0) is the position of the unit cell in row m and column n. The coordinate of the Feed 1 (x1, y1, z1). Here, for the convenience of calculation, the ideal point source model is selected for Feed 1. The phase distribution caused by the propagation path of the EM Wave 1 radiated by Feed 1 to the array is calculated by Eq. (1),

$$\phi\_1(\mathbf{x\_m}, \mathbf{y\_n}) = k\_0 \sqrt{(\mathbf{x\_m} - \mathbf{x\_1})^2 - \left(\mathbf{y\_n} - \mathbf{y\_1}\right)^2 + \mathbf{z\_1}^2} \tag{1}$$

where *k*<sup>0</sup> = 2π/λ<sup>0</sup> is the wavenumber. To make the phase distribution of EM waves consistent passing through the transmitarray, the phase of the array itself should be *ϕ*1(xm, yn). Similarly, the phase distribution caused by the propagation path of the EM Wave 2 radiated by Feed 2 to the array is calculated by Eq. (2),

$$\phi\_2(\mathbf{x\_m}, \mathbf{y\_n}) = k\_0 \sqrt{(\mathbf{x\_m} - \mathbf{x\_2})^2 - \left(\mathbf{y\_n} - \mathbf{y\_2}\right)^2 + \mathbf{z\_2}^2} \tag{2}$$

When Feed 1 and Feed 2 are excited together, the phase distribution of the array aperture is interferometric superimposed by Eq. (3),

$$\Delta\phi(\mathbf{x}\_{\mathrm{m}},\mathbf{y}\_{\mathrm{n}}) = \arg\left(A\_{1}(\mathbf{x}\_{\mathrm{m}},\mathbf{y}\_{\mathrm{n}})\exp\left(j\phi\_{1}(\mathbf{x}\_{\mathrm{m}},\mathbf{y}\_{\mathrm{n}})\right) + A\_{2}(\mathbf{x}\_{\mathrm{m}},\mathbf{y}\_{\mathrm{n}})\exp\left(j\phi\_{2}(\mathbf{x}\_{\mathrm{m}},\mathbf{y}\_{\mathrm{n}})\right)\right) \tag{3}$$

#### **Figure 3.**

*The theoretical model of interferometric phase transmitarray. Reprinted with permission from Ref. [22]; copyright 2022 IEEE.*

#### **Figure 4.**

*The phase distribution of the interferometric phase transmitarray. Reprinted with permission from Ref. [22]; copyright 2022 IEEE.*

where A1(xm, yn) and A2(xm, yn) are the amplitudes of E-field. To make the phase distribution of EM waves consistent through the transmitarray, the phase of the array itself should be -Δ*ϕ*(xm, yn).

Establishing a MATLAB model. The two ideal point sources are set at (�1.5 λ0, 0, �2 λ0) and (1.5 λ0, 0, �2 λ0), and the phase distribution of the transmitarray is shown in **Figure 4**.

#### **2.2 The incident field**

Assume *fm, n* (*θ*, *φ*) is the radiation pattern of the element in row *m* and column *n*, the radiation pattern of the transmitarray can be expressed as Eq. (4),

$$F(\theta,\varphi) = f\_{m,n}(\theta,\varphi) \mathbb{S}\_a(\theta,\varphi) \tag{4}$$

where *θ* and *φ* are the elevation and azimuth angles. *Sa*(*θ*, *φ*) is expressed as Eq. (5),

$$S\_{\mathbf{a}}(\theta,\varphi) = \sum\_{m=1}^{N} \sum\_{n=1}^{N} \exp\left(-i\left(\phi\left(\mathbf{x}\_{\mathrm{m}},\mathbf{y}\_{\mathrm{n}}\right) + kD\sin\theta \times \left(\left(m-1/2\right)\cos\varphi + \left(n-1/2\right)\sin\varphi\right)\right)\right) \tag{5}$$

where *l* represents the length of the element. The phase *ϕ*(xm, yn) contains the phase of the unit itself *ϕ*p(xm, yn) and the phase difference caused by the propagation distance *ϕ*q(xm, yn). Furthermore, the directivity *Dir*(θ, φ) can be expressed as Eq. (6),

$$\operatorname{Dir}(\theta,\varphi) = 4\pi |F(\theta,\varphi)|^2 \Big/ \int\_0^{2\pi} \int\_0^{\pi/2} \left| F(\theta,\varphi) \right|^2 \sin\theta d\theta d\varphi \tag{6}$$

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

**Figure 5.**

*The incident field analysis of Feed 1: (a) the phase distribution of the transmitarray itself, (b) the phase distribution caused by the propagation distance, (c) the superimposed phase distribution, (d) the amplitude distribution, and (e) the 3-D pattern. Reprinted with permission from Ref. [22]; copyright 2022 IEEE.*

According to the above derivation, **Figure 5** shows the incident field of Feed 1. **Figure 5a** shows the phase distribution of the array itself, **Figure 5b** shows the phase distribution caused by the propagation distance, **Figure 5c** shows the superposition of **Figure 5a** and **5b**, **Figure 5d** shows the amplitude distribution, **Figure 5e** shows the 3- D pattern. Compared to **Figure 5b**, the phase distribution of **Figure 5c** is improved. Therefore, the beam shown in **Figure 5e** can achieve high directivity, and the peak is 18.8 dB.

**Figure 6** shows the incident field analysis of Feed 2. **Figure 6a** shows the phase distribution of the array itself, **Figure 6b** shows the phase distribution caused by the propagation distance, **Figure 6c** shows the superposition of **Figure 6a** and **6b**, **Figure 6d** shows the amplitude distribution, **Figure 6e** shows the 3-D pattern. Compared to **Figure 6b**, the phase distribution of **Figure 6c** is improved. Therefore, the beam shown in **Figure 6e** can achieve high directivity, and the peak is 18.8 dB.

### **3. Realization of the interferometric phase transmitarray**

The unit of the interferometric phase transmitarray is shown in **Figure 7**. The metal layer contains a square ring and patch as shown in **Figure 7a**. The overall structure is five dielectric and six metal layers arranged alternately, as shown in **Figure 7b**.

**Figure 6.**

*The incident field analysis of Feed 2: (a) the phase distribution of the transmitarray itself, (b) the phase distribution caused by the propagation distance, (c) the superimposed phase distribution, (d) the amplitude distribution, and (e) the 3-D pattern. Reprinted with permission from Ref. [22]; copyright 2022 IEEE.*

**Figure 7.**

*The view of the unit. (a) Top view. (b) Overall view. Reprinted with permission from Ref. [22]; copyright 2022 IEEE.*

The substrate adopts F4B, and its dielectric constant is 2.65. The thickness of the substrate is *h* = 1.5 mm. *p* = 4 mm is the unit period, and *t* equals 0.05 mm. Size *a* represents the side length of the square metal patch, which is related to the transmission characteristics of the unit. Eight units with different *a* are for comparison. **Figure 8a** shows that the phase change of the unit contains 300°. It can be seen from

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

#### **Figure 8.**

*Transmission characteristics of the unit: (a) phases, (b) amplitudes. Reprinted with permission from Ref. [22]; copyright 2022 IEEE.*

**Figure 8b** that the transmission amplitude of the unit is higher than 2 dB, which indicates the EM waves can pass through the unit efficiently.

Utilize s a patch antenna as the feed. The substrate adopts RuiLong, and its dielectric constant is 2.2. **Figure 9a** shows the physical structure of the patch antenna. The parameters are *pa* = 4.5 mm, *pb* = 3.4 mm, and *pl* = 14 mm. To connect the adapter, two air holes with a radius of 1 mm are drilled on the substrate. **Figure 9b** shows the radiation pattern of the patch antenna at 25 GHz**,** and the realized gain is 7.3 dBi.

Establishing a CST Microwave Studio model. **Figure 10a** shows the phase distribution of the interferometric phase transmitarray, and **Figure 10b** shows the simulation model. **Figure 10c** and **d** illustrate the 3-D radiation patterns when the two feeds are excited respectively, and the realized gain of the proposed transmitarray antenna is 18.4 dBi at 25 GHz. Moreover, the radiation patterns shown in **Figure 10c** and **d** are symmetric about the yoz-plane.

The above results show that when multiple EM waves radiate toward the array, all the transmitted waves are formed into high-directivity beams. This process is characteristic of the transmitter of the MIMO system integrated by interferometric phase transmitarray. Next, analyze the characteristics of the receiver. When the plane wave illustrates the interferometric phase transmitarray vertically, the transmitted plane

#### **Figure 9.**

*(a) The physical structure of the patch antenna. (b) The simulated radiation pattern. Reprinted with permission from Ref. [22]; copyright 2022 IEEE.*

#### **Figure 10.**

*(a) The Phase distribution of the interferometric phase transmitarray, (b) the CST Microwave Studio model, (c) when the right feed is excited, the 3-D pattern at 25 GHz, (d) when the left feed is excited, the 3-D pattern at 25 GHz. Reprinted with permission from Ref. [22]; copyright 2022 IEEE.*

#### **Figure 11.**

*Simulation setup in CST time-domain solver. (a) xoz plane view. (b) 3D view.*

wave will be scattered and focused to two places. The proposed transmitarray is discretized and simulated using CST Studio Suite with the setup illustrated in **Figure 11**. Set the plane wave radiated along the z-axis to illuminate the transmitarray. A xoz plane square vacuum without thickness, as shown in **Figure 11a,** is set above the transmitarray to observe the focuses.

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

**Figure 12.** *The E-field distribution of the interferometric phase transmitarray under plane wave illumination.*

Set up the e-field monitor and the simulated result is shown in **Figure 12**. It can be seen that when the plane wave illustrates the interferometric phase transmitarray vertically, the e-field will form two focuses, and its central coordinates are (18 mm, 0, 24 mm) and (18 mm, 0, 24 mm).

In summary, when multiple EM waves radiate toward the transmitarray, all the EM waves are beamforming into high-directivity beams. When the plane wave illustrates the interferometric phase transmitarray vertically, the e-field will form two focuses, and its relative positions are consistent with the relative positions of the two feeds. These characteristics successfully enable the interferometric phase transmitarray to achieve the MIMO system, as shown in **Figure 2**.
