Interferometric Phase Transmitarray for Millimeter-Wave MIMO System

Abstract

A millimeter-wave (mmW) interferometric phase transmitarray for the multiple-input multiple-output (MIMO) system is proposed, and its phase distribution is the interference superposition of electromagnetic waves radiated by two patch antennas at different locations. Its characteristic is that when multiple EM waves illuminate the center of the array, the transmitted waves are formed into high-directivity beams. In addition, when the plane wave illuminates the interference phase transmitarray vertically, the transmissive plane wave will be scattered and focused to two different positions. A novel MIMO system can be implemented based on the above two characteristics. Compared with the conventional lens MIMO, the advantage of the MIMO system integrated by the interferometric phase transmitarray is that multiple antennas can share one transmitarray, which is beneficial to the miniaturization of the MIMO transceiver. More critically, all channels can efficiently transmit information and increase channel capacity.

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, 4, 5, 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 high requirements for antenna and circuit performance, which leads to high costs and complexity [7, 8, 9].

Figure 1.

The 2 × 2 MIMO system integrated by the conventional lens.

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, 12, 13]. More importantly, metamaterials are widely used in transmitting and reflective arrays to realize beamforming and beam steering [14, 15, 16, 17, 18, 19, 20, 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.

Figure 3.

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

For quantitative analysis, it is assumed that O_mn (x_m, y_n, 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),

$${\varphi }_1\left({\mathrm{x}}_{\mathrm{m}},{\mathrm{y}}_{\mathrm{n}}\right)={\mathit{k}}_0\sqrt{{\left({\mathrm{x}}_{\mathrm{m}}-{\mathrm{x}}_1\right)}^2-{\left({\mathrm{y}}_{\mathrm{n}}-{\mathrm{y}}_1\right)}^2+{{\mathrm{z}}_1}^2}$$E1

where k₀ = 2π/λ₀ is the wavenumber. To make the phase distribution of EM waves consistent passing through the transmitarray, the phase of the array itself should be - ϕ₁(x_m, y_n). 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),

$${\varphi }_2\left({\mathrm{x}}_{\mathrm{m}},{\mathrm{y}}_{\mathrm{n}}\right)={\mathit{k}}_0\sqrt{{\left({\mathrm{x}}_{\mathrm{m}}-{\mathrm{x}}_2\right)}^2-{\left({\mathrm{y}}_{\mathrm{n}}-{\mathrm{y}}_2\right)}^2+{{\mathrm{z}}_2}^2}$$E2

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

$$\mathrm{\Delta }\varphi \left({\mathrm{x}}_{\mathrm{m}},{\mathrm{y}}_{\mathrm{n}}\right)=arg\left({\mathit{A}}_1\left({\mathrm{x}}_{\mathrm{m}},{\mathrm{y}}_{\mathrm{n}}\right)exp\left(\mathit{j}{\varphi }_1\left({\mathrm{x}}_{\mathrm{m}},{\mathrm{y}}_{\mathrm{n}}\right)\right)+{\mathit{A}}_2\left({\mathrm{x}}_{\mathrm{m}},{\mathrm{y}}_{\mathrm{n}}\right)exp\left(\mathit{j}{\varphi }_2\left({\mathrm{x}}_{\mathrm{m}},{\mathrm{y}}_{\mathrm{n}}\right)\right)\right)$$E3

where A₁(x_m, y_n) and A₂(x_m, y_n) 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 -Δϕ(x_m, y_n).

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.

Figure 4.

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

2.2 The incident field

Assume f_{m, 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),

$$\mathit{F}\left(\theta ,\phi \right)={\mathit{f}}_{\mathit{m},\mathit{n}}\left(\theta ,\phi \right){\mathit{S}}_{\mathit{a}}\left(\theta ,\phi \right)$$E4

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

$${\mathit{S}}_{\mathit{a}}\left(\theta ,\phi \right)=\sum _{\mathit{m}=1}^{\mathit{N}}\sum _{\mathit{n}=1}^{\mathit{N}}exp\left(-\mathit{i}\left(\varphi \left({\mathrm{x}}_{\mathrm{m}},{\mathrm{y}}_{\mathrm{n}}\right)+\mathit{kD}sin\theta \times \left(\left(\mathit{m}-1/2\right)cos\phi +\left(\mathit{n}-1/2\right)sin\phi \right)\right)\right)$$E5

where l represents the length of the element. The phase ϕ(x_m, y_n) contains the phase of the unit itself ϕ_p(x_m, y_n) and the phase difference caused by the propagation distance ϕ_q(x_m, y_n). Furthermore, the directivity Dir(θ, φ) can be expressed as Eq. (6),

$$\mathit{Dir}\left(\theta ,\phi \right)=4\pi {\left|\mathit{F}\left(\theta ,\phi \right)\right|}^2/{\int }_0^{2\pi }{\int }_0^{\pi /2}{\left|\mathit{F}\left(\theta ,\phi \right)\right|}^{2}sin\theta \mathit{d}\theta \mathit{d}\phi$$E6

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 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.

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.

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.

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 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 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.

Figure 8.

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

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.

Figure 9.

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

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.

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.

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 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.

Figure 11.

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

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).

Figure 12.

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

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.

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 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 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 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.

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.

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 16.

The simulated 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.

Figure 17.

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

Figure 18.

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

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

$$\mathit{C}=\mathit{B}log2\left(1+\mathit{S}/\mathit{N}\right)$$E7

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).

$${\mathit{P}}_{\mathit{r}}={\mathit{P}}_{\mathit{t}}\frac{{\mathit{G}}_{\mathit{t}}{\mathit{G}}_{\mathit{r}}{{\lambda }_0}^2}{16{\pi }^2{\mathit{d}}^2}\begin{array}{ccc}& & \end{array}\begin{array}{cc}& \end{array}$$E8

where P_r and P_t represent receiving power and transmitting power, G_r and G_t represent the gain of the receiving antenna and the transmitting antenna, λ₀ 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.