Simulation and Design of Three 5G Antennas

Abstract

In the context of 5G networks, this paper investigates microstrip array antennas and mobile terminal MIMO array antennas. It introduces two innovative designs and, based on these, develops and fabricates a mobile terminal antenna. The first of these designs, a 4 × 4 microstrip array antenna operating in the LTE band 42 (3.4–3.6 GHz), is researched and fabricated and an innovative approach, combining embedded and coaxial feeding methods, is proposed and employed. Measurement results indicate a bandwidth of 373 MHz (3.321–3.694 GHz), achieving a relative bandwidth of 10.7%. The antenna exhibits a high gain of 12.7 dBi, with an undistorted radiation pattern, demonstrating excellent directional characteristics. The second of these designs, a “loop-slot” MIMO antenna designed for 5G mobile devices with metal frames, is investigated. By opening slots in the metal frame and integrating them into the antenna’s feeding structure, the decoupling principle is analyzed from the perspective of characteristic mode theory. This design shares resonant modes between the loop and slot antennas, allowing for the overlapping placement of the two antenna units. Experimental results confirm an isolation level exceeding 21 dB, with significantly reduced dimensions. Finally, an eight-unit MIMO antenna is designed and fabricated for 5G mobile devices with metal frames. Continuous optimization of the “loop-slot” module layout and unit spacing leads to a compact and miniaturized antenna structure. Measurement results show an isolation level exceeding 17 dB, radiation efficiency ranging from 65.8% to 73.7%, and an envelope correlation coefficient (ECC) below 0.03. Finally, an analysis of specific absorption rate (SAR) demonstrates excellent MIMO performance in terms of human body radiation exposure.

1. Introduction

Microstrip antennas offer advantages, such as their compactness, their lightness of weight, their cost effectiveness, and their flexibility in shape [1], that make them suitable for various applications in crucial fields. However, the ever-increasing demands of wireless communication systems have rendered the conventional designs with single antenna units obsolete, as they are no longer suitable for the complex and diverse communication systems of today. To meet these evolving requirements, the approach of combining multiple antenna units in various configurations to form antenna arrays has become essential, particularly in the context of 5G microstrip array antennas, which holds profound significance.

In the realm of mobile terminals, the development of wireless communication technologies has exacerbated the issue of spectrum scarcity [2]. The shortage of available spectrum resources poses limitations on the growth of wireless communication systems [3]. Consequently, the emergence of multiple-input multiple-output (MIMO) technology was timely [4]. Although the transmitter’s power remains constant, MIMO technology significantly increases the channel capacity when compared with conventional single-antenna systems. To meet the demands of future 5G cellular communication systems, there is a necessity to continually boost the channel capacity of smartphones by integrating six or eight antenna units. Thus, the design of MIMO array antennas holds substantial practical value.

Different feeding methods for antennas have varying impacts on microstrip antenna performance. The comparison in [5] was made to investigate the effects of embedded feedline feeding, coaxial feedline feeding, coupling feedline feeding, and probe coupling feedline feeding on antenna performance, and confirmed that embedded feedline and coupling feedline feeding yield superior results [5]. In another study, ref. [6] employed a rectangular microstrip antenna with coaxial feeding and rendered it more compact by modifying the antenna patch design. However, the size of the single antenna unit still reached 14 mm × 14 mm × 1.6 mm, failing to achieve genuine miniaturization. In contrast, ref. [7] utilized circular patches with embedded microstrip lines for feeding, aiming to achieve a wider impedance bandwidth. The simulated results show an impedance bandwidth of only 7.1% (5.73–6.14 GHz). Furthermore, the antenna’s thickness reached 120 mm due to the use of a tapered dielectric rod, posing significant challenges during fabrication and constraints in practical use.

When operating array antennas, antennas placed in proximity typically experience mutual coupling, which can significantly impact antenna performance. To address this issue, researchers have proposed various structural solutions. In [8], a series-fed millimeter-wave microstrip line array antenna was designed. When 16 antenna elements were evenly serially distributed, the antenna’s gain increased to 15.7 dB. However, this led to higher sidelobe levels, thus degrading antenna performance. In another work, ref. [9] introduced a feed network composed of multiple branched microstrip lines, achieving decoupling with an 18 dB improvement in isolation.

Designing MIMO array antennas suitable for the 5G frequency bands presents new challenges, primarily related to antenna miniaturization and the mitigation of the influence of metal environments on antenna performance. To address these challenges, several methods have been developed by researchers. Ref. [10] proposed an eight-element metal frame mobile MIMO antenna array operating in LTE band 42 (3.4–3.6 GHz). Within the working frequency range, the array achieved an isolation of over 12 dB, with a measured overall efficiency of 45–58%. In another study, ref. [11] investigated the use of slot antennas in metal frame mobile terminals, confirming the continued excellent performance of slot antennas in such environments. Moreover, ref. [12] integrated antennas into the metal frame of mobile devices, where the metal frame acted as both a structural component and a radiation element. This innovative design effectively mitigated the impact of the metal frame on antenna performance. In [13], L-shaped monopole slot antennas and C-shaped coupled feed antennas were mutually orthogonally designed to create an 8-element MIMO array antenna with an isolation of over 12.5 dB, without the need for external decoupling structures. Despite the enhanced isolation achieved in these studies, the MIMO array antennas designed were relatively large. Therefore, there is a pressing need to minimize the MIMO array size while improving isolation.

The structure of this paper is organized as follows:

Research and development of a 4 × 4 microstrip array antenna operating in the LTE band 42 (3.4–3.6 GHz). A novel approach to antenna array feeding is introduced, combining embedded feeding and coaxial feeding, utilizing rectangular microstrip line patches with embedded structures for feeding. By adjusting the depth and width of the embedded microstrip lines, a relatively wide bandwidth is obtained, while the entire array utilizes coaxial feeding to suppress coupling between antenna elements, achieving effective decoupling. Simulation and measurement results demonstrate that the array provides coverage in the 5G LTE band 42 (3.4–3.6 GHz). In comparison with traditional patch antennas, this chapter’s array antenna achieves a bandwidth of 373 MHz (3.321–3.694 GHz), corresponding with a relative bandwidth of 10.7%. The antenna exhibits a gain of 12.7 dBi and maintains excellent directivity without distortion.

A study of a two-element “ring-slot” MIMO antenna for 5G metal frame mobile terminals. The impact of integrating a metal frame on mobile terminal signal strength is analyzed. Subsequently, a ring antenna unit and a slot antenna unit are designed as the basis for the two-element “ring-slot” MIMO antenna structure. After simulating and optimizing the ring and slot antennas, their overlapping arrangement is determined. Without external decoupling structures, the antenna units still achieve high isolation. The paper delves into the theoretical principles underlying this design’s decoupling effectiveness, affirming its reliable performance.

Investigation of an eight-element MIMO array antenna for 5G metal frame mobile terminals, realizing coverage in LTE band 42 (3.4–3.6 GHz) [14]. Building upon the innovative “ring-slot” structure introduced in Chapter 4, the study analyzes the impact of three different placement methods on antenna performance. The optimal “ring-slot” module layout and inter-element spacing are determined, achieving a compact and miniaturized antenna structure. Furthermore, a T-shaped decoupling structure is etched on the ground plane between adjacent “ring-slot” structures along the longer edges of the antenna, effectively enhancing antenna performance. Simulation and measurement results highlight an isolation of over 17 dB, radiation efficiency ranging from 65.8% to 73.7%, and a low envelope correlation coefficient. The paper also analyzes the antenna-specific absorption rate (SAR) concerning human exposure, demonstrating favorable MIMO performance.

A concluding summary of the three innovations presented in the paper is followed by an analysis of design limitations and future directions.

2. Materials and Methods

2.1. Theoretical Analysis of Microstrip Antenna Arrays

With the rapid development of 5G communication, there is increased demand for antennas in various aspects. Individual antenna units can no longer meet the requirements of modern production and daily life. Therefore, it is necessary to connect multiple antenna units to create higher gain and more directional array antennas. Typically, identical antenna units are used, arranged in various combinations to form array antennas with different numbers of elements, enabling the array to perform different functions. Arrays with regularly spaced identical antenna units are more convenient for design and calculations.

The overall performance of array antennas depends not only on the characteristics of the individual antenna units but also on the number of elements, spacing, arrangement, and the amplitude and phase of the excitation [15]. The most common array antenna configurations include two types: one is characterized by the placement of multiple antenna units at equal intervals along a straight line and centered around an axis, known as a linear array antenna; the other is an extension of the linear array, forming a planar arrangement, and is known as a planar array antenna. In the following sections, we will provide a detailed explanation of linear array antennas and planar array antennas.

2.1.1. Linear Array

A linear array antenna consists of multiple antenna elements arranged in a straight line [16]. When each antenna element has the same structure and they are evenly spaced, it forms a uniform linear array antenna. As shown in Figure 1, this represents a uniform linear array antenna arranged along the x-axis.

If the linear array antenna consists of N identical antenna elements, each spaced at a distance of ‘d’, without considering mutual coupling between the antenna elements, then, when excited with amplitudes of the same magnitude and a phase variation interval of ‘α’, the excitation current amplitude of the antenna elements can be represented by Equation (1).

$${\dot{\mathrm{I}}}_{\mathrm{n}}={\mathrm{I}}_{\mathrm{n}}\mathrm{e}\mathrm{x}\mathrm{p}\left(\mathrm{j}\mathrm{n}\mathsf{\alpha }\right),$$

(1)

By calculating the weighted direction function of the antenna elements, the array factor, representing the overall directionality of the antenna array, is obtained [17]. This can be represented using the expression S(θ, φ), as given in Equation (2).

$$\mathrm{S}(\mathsf{\theta },\mathsf{\phi })={\sum }_{\mathrm{n}=0}^{\mathrm{N}-1}{\mathrm{I}}_{\mathrm{n}}\mathrm{e}\mathrm{x}\mathrm{p}\left[\mathrm{j}\mathrm{n}(\mathrm{k}\mathrm{d}\mathrm{c}\mathrm{o}\mathrm{s}\mathsf{\phi }+\mathsf{\alpha })\right],$$

(2)

When the uniform array antenna forms a specific angle with the x-axis, we assume the angle is β and, in this case, cos(θ) sin(φ) = cos(β). Then, the above equation can be rewritten as Equation (3).

$$\mathrm{S}(\mathsf{\theta },\mathsf{\varphi })={\sum }_{\mathrm{n}=0}^{\mathrm{N}-1}{\mathrm{I}}_{\mathrm{n}}\mathrm{e}\mathrm{x}\mathrm{p}\left[\mathrm{j}\mathrm{n}(\mathrm{k}\mathrm{d}\mathrm{c}\mathrm{o}\mathrm{s}\mathsf{\beta }+\mathsf{\alpha })\right],$$

(3)

Because all antenna elements are loaded with the same excitation current, we have I₀ = I_n, and after simplifying the above equation, we can obtain Equation (4).

$$\left|\mathrm{S}(\mathsf{\theta },\mathsf{\varphi })\right|={\mathrm{I}}_0\left|{\displaystyle \frac{\mathrm{s}\mathrm{i}\mathrm{n}\frac{\mathrm{N}(\mathrm{k}\mathrm{d}\mathrm{c}\mathrm{o}\mathrm{s}\mathsf{\beta }+\mathsf{\alpha })}{2}}{\mathrm{s}\mathrm{i}\mathrm{n}\frac{(\mathrm{k}\mathrm{d}\mathrm{c}\mathrm{o}\mathrm{s}\mathsf{\beta }+\mathsf{\alpha })}{2}}}\right|,$$

(4)

When u = kdcos(β)+α = 0, the array factor of the antenna array is maximized, and the corresponding maximum radiation direction angle is as given in Equation (5).

$${\mathsf{\beta }}_{\mathrm{m}\mathrm{a}\mathrm{x}}=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{c}\mathrm{o}\mathrm{s}\left(-{\displaystyle \frac{\mathsf{\alpha }}{\mathrm{k}\mathrm{d}}}\right),$$

(5)

To sum up, within a uniform linear array, the spacing between antenna elements ‘d’ and the phase difference ‘α’ have the most pronounced influence on the maximum radiation direction. Consequently, when designing a practical uniform linear array antenna, the careful choice of antenna element spacing ‘d’ and phase difference ‘α’ is of paramount importance.

2.1.2. Planar Array

On the basis of a linear array, we can arrange several linear arrays in a planar configuration. This is known as a planar array antenna. Here, we will introduce the rectangular planar array as a classic arrangement, where the elements consist of identical antenna units. This is illustrated in Figure 2, which represents a schematic of a rectangular planar array.

In Figure 2, a three-dimensional coordinate system is established, with the (0, 0) antenna unit placed at the origin, and a planar array set in the xoy plane. Assuming the direction parallel to the x-axis is termed ‘columns’, each column contains N_x antenna units, and the distance between adjacent units in a column is denoted as ‘d_x’. Similarly, the direction parallel to the y-axis is termed ‘rows’, with each row containing N_y antenna units, and the distance between adjacent units in a row is ‘d_y’. Therefore, the coordinates of a particular antenna unit (m, n) can be expressed using Equation (6).

$$\left\{\begin{array}{c}{\mathrm{x}}_{\mathrm{m}}={\mathrm{m}\mathrm{d}}_{\mathrm{x}},0\le m\le {\mathrm{N}}_{\mathrm{x}}-1\\ {\mathrm{y}}_{\mathrm{n}}={\mathrm{n}\mathrm{d}}_{\mathrm{y}},0\le n\le {\mathrm{N}}_{\mathrm{y}}-1\end{array}\right.,$$

(6)

Based on the earlier assumptions, the planar array antenna is composed of N_x × N_y individual antenna units. Under ideal conditions, the current flowing through the antenna unit located at position (m, n) is denoted as ${\dot{I}}_{mn}$. The expression for the array factor $S(\theta ,\varphi )$ of the planar array antenna can be derived as shown in Equation (7).

$$S(\theta ,\varphi )={\sum }_{m=0}^{N_x-1}{\sum }_{n=0}^{N_y-1}{\dot{I}}_{mn}exp\left[jk({md}_{x}cos\varphi +n{d}_{y}sin\varphi )sin\varphi \right],$$

(7)

Assuming the current flowing through each antenna unit parallel to the x-axis varies with a phase difference of α_x and has equal magnitudes, the current in the x-axis direction is described as in Equation (8).

$${\dot{\mathrm{I}}}_{\mathrm{x}\mathrm{m}}={\mathrm{I}}_{\mathrm{x}\mathrm{m}}\mathrm{e}\mathrm{x}\mathrm{p}(-\mathrm{j}\mathrm{m}{\mathsf{\alpha }}_{\mathrm{x}}),$$

(8)

Similarly, assuming that the current passing through each antenna unit aligned parallel to the y-axis varies with a phase difference of α_y and has the same magnitude, the current in the y-axis direction is as represented in Equation (9).

$${\dot{\mathrm{I}}}_{\mathrm{y}\mathrm{n}}={\mathrm{I}}_{\mathrm{y}\mathrm{n}}\mathrm{e}\mathrm{x}\mathrm{p}(-\mathrm{j}\mathrm{n}{\mathsf{\alpha }}_{\mathrm{y}}),$$

(9)

Consequently, the current passing through the planar array antenna is expressed as in Equation (10).

$$\dot{\mathrm{I}}={\dot{\mathrm{I}}}_{\mathrm{x}\mathrm{m}}·{\dot{\mathrm{I}}}_{\mathrm{y}\mathrm{n}}={\mathrm{I}}_{\mathrm{x}\mathrm{m}}{\mathrm{I}}_{\mathrm{y}\mathrm{n}}\mathrm{e}\mathrm{x}\mathrm{p}[-\mathrm{j}\left(\mathrm{m}{\mathsf{\alpha }}_{\mathrm{x}}+\mathrm{n}{\mathsf{\alpha }}_{\mathrm{y}}\right)],$$

(10)

Another expression for the array factor S(θ, φ) can be derived as shown in Equation (11).

$$\left\{\begin{array}{c}\mathrm{S}(\mathsf{\theta },\mathsf{\varphi })={\mathrm{S}}_{\mathrm{x}}(\mathsf{\theta },\mathsf{\varphi })·{\mathrm{S}}_{\mathrm{y}}(\mathsf{\theta },\mathsf{\varphi })\\ {\mathrm{S}}_{\mathrm{x}}(\mathsf{\theta },\mathsf{\varphi })=\sum _{\mathrm{m}=0}^{{\mathrm{N}}_{\mathrm{x}}-1}{\mathrm{I}}_{\mathrm{x}\mathrm{m}}\mathrm{e}\mathrm{x}\mathrm{p}\left[\mathrm{j}\mathrm{m}\right({\mathrm{k}\mathrm{d}}_{\mathrm{x}}\mathrm{c}\mathrm{o}\mathrm{s}\mathsf{\varphi }\mathrm{s}\mathrm{i}\mathrm{n}\mathsf{\theta }-{\mathsf{\alpha }}_{\mathrm{x}})\\ {\mathrm{S}}_{\mathrm{y}}(\mathsf{\theta },\mathsf{\varphi })=\sum _{\mathrm{n}=0}^{{\mathrm{N}}_{\mathrm{y}}-1}{\mathrm{I}}_{\mathrm{y}\mathrm{n}}\mathrm{e}\mathrm{x}\mathrm{p}\left[\mathrm{j}\mathrm{n}\right({\mathrm{k}\mathrm{d}}_{\mathrm{y}}\mathrm{s}\mathrm{i}\mathrm{n}\mathsf{\varphi }\mathrm{s}\mathrm{i}\mathrm{n}\mathsf{\theta }-{\mathsf{\alpha }}_{\mathrm{y}})\end{array}\right.,$$

(11)

Hence, it is apparent that the array factor S(θ, φ) of the planar array antenna is the product of the array factors in the x-axis and y-axis directions, in line with the principles of the array antenna radiation pattern theory [18].

2.2. The Unique Performance Parameters of MIMO Terminal Antennas

In MIMO antenna systems, the number of antenna elements, their spatial arrangement, correlation coefficient (ECC), average effective gain, and overall efficiency are all key parameters for performance evaluation.

2.2.1. Correlation

Diversity characteristics are one of the crucial attributes of MIMO antenna systems, and the evaluation of diversity performance can be achieved by analyzing the correlation coefficients ρ_ij. The envelope correlation coefficient (ECC) is expressed as the square of the correlation coefficient ρ_ij. When designing MIMO antennas, the specific calculation formula is given in Equation (12).

$${\mathsf{\rho }}_{\mathrm{e}\mathrm{i}\mathrm{j}}={\left|{\mathsf{\rho }}_{\mathrm{i}\mathrm{j}}\right|}^2={\displaystyle \frac{{\left|{{\mathrm{S}}^{\mathrm{*}}}_{\mathrm{i}\mathrm{i}}{\mathrm{S}}_{\mathrm{i}\mathrm{j}}+{{\mathrm{S}}^{\mathrm{*}}}_{\mathrm{i}\mathrm{j}}{\mathrm{S}}_{\mathrm{j}\mathrm{j}}\right|}^2}{(1-{\left|{\mathrm{S}}_{\mathrm{i}\mathrm{i}}\right|}^2-{\left|{\mathrm{S}}_{\mathrm{i}\mathrm{j}}\right|}^2)(1-{\left|{\mathrm{S}}_{\mathrm{i}\mathrm{j}}\right|}^2-{\left|{\mathrm{S}}_{\mathrm{j}\mathrm{j}}\right|}^2)}},$$

(12)

In this equation, ρ_eij represents the envelope correlation coefficient ECC between antenna units i and j. S_ii is the reflection coefficient for antenna unit i itself, while S_ij represents the transmission coefficient between antenna unit i and antenna unit j. The specific formula for calculating the correlation coefficient ECC between antenna units i and j in a MIMO antenna system with N antenna units can be derived as shown in Equation (13)

$${\mathsf{\rho }}_{\mathrm{e}\mathrm{i}\mathrm{j}}={\left|{\mathsf{\rho }}_{\mathrm{i}\mathrm{j}}\right|}^2={\displaystyle \frac{{\left|{{\mathrm{S}}^{\mathrm{*}}}_{\mathrm{i}1}{\mathrm{S}}_{1\mathrm{j}}+{{\mathrm{S}}^{\mathrm{*}}}_{\mathrm{i}2}{\mathrm{S}}_{2\mathrm{j}}+{{\mathrm{S}}^{\mathrm{*}}}_{\mathrm{i}3}{\mathrm{S}}_{3\mathrm{j}}+\cdots +{{\mathrm{S}}^{\mathrm{*}}}_{\mathrm{i}\mathrm{N}}{\mathrm{S}}_{\mathrm{N}\mathrm{j}}\right|}^2}{(1-{\left|{\mathrm{S}}_{1\mathrm{i}}\right|}^2-{\left|{\mathrm{S}}_{2\mathrm{i}}\right|}^2-\cdots -{\left|{\mathrm{S}}_{\mathrm{N}\mathrm{i}}\right|}^2)(1-{\left|{\mathrm{S}}_{1\mathrm{j}}\right|}^2-{\left|{\mathrm{S}}_{2\mathrm{j}}\right|}^2-\cdots -{\left|{\mathrm{S}}_{\mathrm{N}\mathrm{j}}\right|}^2)}},$$

(13)

Low coupling between antennas generally achieves high isolation, but, theoretically, isolation and correlation coefficient are two completely different parameters. The correlation coefficient calculated using Equation (12) only considers the factor of mutual coupling between different input ports of antennas, while it disregards the coupling between the radiation fields of the antennas. Considering the presence of spatial radiation and related issues, the antenna pattern can be used for calculation, and the formula for this calculation is given in Equation (14)

$${\left|{\mathsf{\rho }}_{\mathrm{i}\mathrm{j}}\right|}^2={\displaystyle \frac{{\left|\oint {\mathrm{A}}_{\mathrm{i}\mathrm{j}}\left(\mathsf{\Omega }\right)\mathrm{d}\mathsf{\Omega }\right|}^2}{\left|\oint {\mathrm{A}}_{\mathrm{i}\mathrm{j}}\left(\mathsf{\Omega }\right)\mathrm{d}\mathsf{\Omega }\oint {\mathrm{A}}_{\mathrm{i}\mathrm{j}}\left(\mathsf{\Omega }\right)\mathrm{d}\mathsf{\Omega }\right|}},$$

(14)

Therefore, in MIMO antenna systems, the level of mutual coupling or isolation cannot be the sole parameter by which to measure ECC. While achieving low mutual coupling and high isolation, it is also essential to ensure low correlation coefficients. This is necessary to obtain good diversity characteristics, and, typically, the value of ECC should be less than 0.5 to meet requirements.

2.2.2. Average Effective Gain (AEG)

The average effective gain (AEG) is defined as the ratio of the average received power to the average incident power on the antenna [19]. Unlike measuring the gain of an individual antenna unit in a microwave chamber, in real-world antenna applications, various factors, such as the antenna’s environment and terminal structure need to be considered. In such cases, the average effective gain (AEG) is used to accurately represent the antenna’s gain performance. The AEG of the antenna is typically obtained through simulation or measurement of the gain pattern. The calculation formula is given in Equation (15).

$$\mathrm{M}\mathrm{E}\mathrm{G}={\displaystyle \frac{1}{2\mathsf{\pi }}}{\int }_0^{2\mathsf{\pi }}[{\displaystyle \frac{\mathsf{\Gamma }}{1+\mathsf{\Gamma }}}{\mathrm{G}}_{\mathsf{\theta }}({\displaystyle \frac{\mathsf{\pi }}{2}},\mathsf{\phi })+{\displaystyle \frac{1}{1+\mathsf{\Gamma }}}\mathrm{G}\mathsf{\phi }({\displaystyle \frac{\mathsf{\pi }}{2}},\mathsf{\phi })]\mathrm{d}\mathsf{\phi },$$

(15)

In the equation, G_θ is the vertical component of the power gain pattern, and G_φ is the horizontal component of the power gain pattern. MEG is the parameter used to assess the antenna’s average effective gain. To meet the design requirements of a multi-antenna system, the MEG_i/MEG_j should be less than 3 dB.

2.2.3. Overall Efficiency

In MIMO antenna arrays consisting of N antenna units, overall efficiency is commonly used to represent the efficiency of the MIMO antenna array, as shown in Equation (16).

$${\mathsf{\eta }}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l},\mathrm{m}}={\mathsf{\eta }}_{\mathrm{r}\mathrm{a}\mathrm{d},\mathrm{m}}{\mathsf{\eta }}_{(\mathrm{m}\mathrm{i}\mathrm{s}+\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{p}),\mathrm{m}}={\mathsf{\eta }}_{\mathrm{r}\mathrm{a}\mathrm{d},\mathrm{m}}(1-{\left|{\mathrm{S}}_{\mathrm{m}\mathrm{m}}\right|}^2-{\sum }_{\mathrm{n}\ne \mathrm{m}}^{\mathrm{N}}{\left|{\mathrm{S}}_{\mathrm{m}\mathrm{n}}\right|}^2),$$

(16)

In the equation, η_totalm represents the overall efficiency of antenna unit m, while η_radm stands for the radiation efficiency of antenna unit; η_{(mis+coupm),m} represents the power loss efficiency due to coupling and mismatch in antenna unit m. S_mm represents the reflection coefficient of antenna unit m, and S_mn represents the transmission coefficient from antenna unit n to m. It is evident that mutual coupling between antenna units can reduce the overall efficiency of the MIMO antenna array.

3. Design of 5G Microstrip Array Antennas

3.1. Design and Simulation of Antenna Units

In this chapter, a 4 × 4 microstrip array antenna will be designed and simulated using a combination of coaxial and embedded feeding methods to achieve high gain and miniaturization for 5G microstrip array antennas.

3.1.1. Calculation and Optimization of Antenna Unit Parameters

As illustrated in Figure 3, we assume a resonant frequency $f_0$ 5 GHz for a rectangular microstrip patch antenna with a dielectric substrate of thickness h, width W, length L, and a relative dielectric constant e_r. Next, optimization and determination will be carried out for the selection of the substrate thickness h, width W, and length L of the rectangular microstrip patch.

Dielectric Substrate Thickness (h)

When designing microstrip antennas, parameters such as the dielectric substrate thickness (h), relative permittivity (e_r) and dielectric loss tangent (tanδ) have a significant impact on antenna performance [20]. A lower relative permittivity (e_r) can lead to a notable increase in antenna bandwidth, but also results in larger antenna dimensions. However, a higher dielectric loss tangent (tanδ) can reduce antenna efficiency, so it should be minimized. Choosing a thicker dielectric substrate can improve the antenna’s bandwidth to some extent but can also increase the excitation of surface waves, thus decreasing antenna performance. Therefore, selecting an appropriate thickness is crucial.

Taking all these factors into account, this design opts for FR4-epoxy, which is an epoxy glass fiber board with a relative permittivity (e_r) of 4.4 and a dielectric loss tangent (tanδ) of 0.02. This material offers stable electrical insulation, standard thickness tolerance, heat and moisture resistance, and good mechanical processability, making it suitable for crafting high-performance antennas. Commonly used thicknesses include 0.8 mm, 1.0 mm, 1.2 mm, 1.6 mm, 1.8 mm, and 2.0 mm.

Figure 4 illustrates the impact of the dielectric substrate thickness (h) on the S₁₁ parameter. It is evident that, as the dielectric substrate thickness (h) increases from 0.8 mm to 2.0 mm, the antenna’s resonant frequency gradually decreases. The S₁₁ initially decreases and then increases, and the S₁₁ curve becomes smoother, resulting in a broader bandwidth. When the dielectric substrate thickness is set to h = 1.6 mm, the antenna’s resonant frequency aligns with the 3.5 GHz requirement for this design. Therefore, the choice of a 1.6 mm thick FR4-epoxy substrate material is confirmed to meet the design specifications.

Antenna Element Width (W)

Once the dielectric substrate thickness (h), relative permittivity (e_r), and dielectric loss tangent (tanδ) for the selected substrate material are determined, the initial calculation of the width W of the rectangular patch element can be made using empirical Formula (17). However, it is essential to limit the range of W, as an excessively large width can generate higher-order modes and affect the antenna’s performance.

$$\mathrm{W}\le {\displaystyle \frac{\mathrm{c}}{2{\mathrm{f}}_0}}{\left({\displaystyle \frac{{\mathsf{\epsilon }}_{\mathrm{r}}+1}{2}}\right)}^{-{\displaystyle \frac{1}{2}}},$$

(17)

In the formula, c represents the speed of light, $c=3.0\times {10}^8 \mathrm{m}/\mathrm{s}$. $f_0$ is the resonant frequency and is set to 3.5 GHz in this design. The relative permittivity (εr) is fixed at 4.4. Through calculations, it is found that W should be limited to ≤26.082 mm.

As shown in Figure 5, it illustrates the impact of the antenna element width (W) on the S₁₁ parameter. Within the range of antenna element widths from 18 mm to 27 mm, it is evident that changes in the antenna element width W significantly affect the S11 parameter. Additionally, the antenna achieves the best matching at around 22 mm. Further optimization of W will be carried out in subsequent simulations.

Antenna Element Length (L)

In theory, the length (L) of the rectangular microstrip patch antenna is approximately half-wavelength [21]. It can be calculated using Equation (18).

$$\mathrm{W}\le {\displaystyle \frac{\mathrm{c}}{2{\mathrm{f}}_0}}{\left({\displaystyle \frac{{\mathsf{\epsilon }}_{\mathrm{r}}+1}{2}}\right)}^{-{\displaystyle \frac{1}{2}}},$$

(18)

where λ₀ is the wavelength in a vacuum area that can be found by Equation (3), and ${\epsilon }_e$ is the effective dielectric constant of the substrate material that can also be given by Equation (19).

$${\mathsf{\epsilon }}_{\mathrm{e}}={\displaystyle \frac{{\mathsf{\epsilon }}_{\mathrm{r}}+1}{2}}+{\displaystyle \frac{{\mathsf{\epsilon }}_{\mathrm{r}}-1}{2}}(1+12{\displaystyle \frac{\mathrm{h}}{\mathrm{W}}}{)}^{-{\displaystyle \frac{1}{2}}},$$

(19)

In practical applications, due to the influence of edge effects, the actual patch length ‘L’ should be determined as per Equation (20).

$$\mathrm{L}={\displaystyle \frac{\mathrm{c}}{2{\mathrm{f}}_0\sqrt{{\mathsf{\epsilon }}_{\mathrm{e}}}}}=-2\mathsf{\Delta }\mathrm{L},$$

(20)

In this equation, ΔL represents the equivalent radiating aperture length, which can be computed as shown in Equation (21).

$$\mathsf{\Delta }\mathrm{L}=0.412\mathrm{h}{\displaystyle \frac{({\mathsf{\epsilon }}_{\mathrm{e}}+0.3)(\raisebox{1ex}{$\mathrm{W}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{h}$}\right.+0.264)}{\left({\mathsf{\epsilon }}_{\mathrm{e}}-0.258\right)\left(\raisebox{1ex}{$\mathrm{W}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{h}$}\right.+0.8\right)}},$$

(21)

The calculated value for ΔL is 0.734 mm, and the resulting patch length ‘L’ is 19.987 mm.

As shown in Figure 6, the impact of antenna unit length ‘L’ on the S₁₁ parameter was examined by scanning the antenna unit length within the range of 19.3 mm to 20.3 mm. As ‘L’ increases, the resonant frequency gradually decreases, and the S₁₁ curve exhibits an overall leftward shift. When ‘L’ is set to 19.6 mm, the antenna unit resonant frequency is measured at 3.5 GHz.

An overview of the various parameters for the microstrip antenna unit is provided in

Table 1. Antenna unit parameters.

Parameters	Value	Units
$\mathrm{Resonant}\mathrm{Frequency}(f_0$)	3.5	GHz
Relative dielectric constant (εᵣ)	4.4	\
Substrate thickness (h)	1.6	mm
Patch width (W)	22	mm
Effective dielectric constant (εe)	3.99	\
Equivalent radiating aperture length (ΔL)	0.734	mm
Patch length (L)	19.6	mm

.

3.1.2. Simulation of Antenna Units

In HFSS, the designed antenna unit is modeled and simulated. The created antenna unit model is shown in Figure 7.

At this point, the antenna unit model is a simple rectangular microstrip patch, and its input impedance can be calculated using empirical Formula (22).

$$\mathsf{\Delta }{\mathrm{Z}}_{\mathrm{i}\mathrm{n}}={\displaystyle \frac{60{\mathsf{\lambda }}_0}{\mathrm{W}}},$$

(22)

In the equation, λ₀ is the wavelength in a vacuum, and Zin is the input impedance of the antenna, which is calculated to be approximately 90 Ω.

To facilitate the subsequent design of the antenna array, the microstrip antenna unit is adjusted to 50 Ω using a feeding mechanism. Traditional end-fed methods often result in high input impedance. Therefore, this design employs the inset-fed method in microstrip feeding. This feeding method positions the feed point closer to the center, reducing the input impedance. As the current follows a sinusoidal distribution, moving a distance R from the end increases the current by cos(R/πL), resulting in a phase difference of πR/L. The scale factor for the input impedance is calculated as Z = V/I, where the scaling factor is Formula (23).

$${\mathrm{Z}}_{\mathrm{i}\mathrm{n}}(\mathrm{R})=\mathrm{c}\mathrm{o}{\mathrm{s}}^2({\displaystyle \frac{\mathsf{\pi }\mathrm{R}}{\mathrm{L}}}){\mathrm{Z}}_{\mathrm{i}\mathrm{n}}(0),$$

(23)

In the equation, Z_in(0) represents the input impedance for the end-fed configuration. For example, when R = L/4, it results in cos(πR/L) = cos(π/4), making $\left[cos\right(\mathsf{\pi }/4){]}^2=1/2$, so a 1/8 wavelength inset reduces the input impedance by 50%. This method determines the inset length and achieves a 50Ω input impedance. The inset-fed design effectively reduces the size of the antenna unit, enabling antenna miniaturization [22]. Moreover, the inset-fed configuration is more suitable for developing high-gain microstrip array antennas. Figure 8 depicts the model of an antenna unit with the inset-fed configuration:

At this point, the length Y0 of the embedded feedline has the most significant impact on the antenna’s input impedance. Figure 9 illustrates the resonance frequency of the embedded feed antenna unit as Y0 varies. The resonant frequency changes with the increase of Y0. Taking all factors into consideration, the performance of the antenna unit becomes optimal when it reaches Y0 = 5.25 mm. The specific dimensions of the embedded feeding structure are provided in

Table 2. Parameters of the microstrip antenna unit.

Parameters	Values (mm)
Microstrip feedline width (Wf)	1
Embedding depth (Y0)	5.25
Embedding width (g)	1.5

.

The simulation of the embedded-fed antenna unit using HFSS provides the reflection coefficient VSWR as shown in Figure 10. Within the operating frequency range of 3.4 GHz to 3.6 GHz, the VSWR remains below 2. At the central frequency of 3.5 GHz, the return loss reaches −35 dB, and the VSWR $\le$1.1. This indicates that the embedded-fed antenna unit achieves excellent impedance matching.

As shown in Figure 11, the gain pattern of the microstrip antenna unit at a frequency of 3.5 GHz is presented. Figure 11a represents the 3D gain pattern of the antenna unit, and Figure 11b shows the gain polar pattern. From the figures, it can be observed that the maximum radiation direction of the microstrip antenna unit is perpendicular to the antenna’s center, and the gain reaches 3.8 dB in the maximum radiation direction.

3.2. Design and Simulation of 4 × 4 Antenna Units

In general, microstrip antenna units have relatively low gain and may not meet the requirements for real-life antenna applications. To achieve higher gain, it is necessary to configure them into a microstrip array antenna using a feeding network. The design of the array antenna involves considerations such as the number of antenna elements, their arrangement, the spacing between array elements (denoted as ‘d’), and the design of the feeding network.

3.2.1. Analysis and Simulation of Element Spacing

After selecting the antenna elements and considering the mutual coupling effects between these elements, the key factor influencing the performance of the array antenna is the element spacing ‘d’ [23]. To simplify the simulation and analysis process, a linear polarization mode is chosen for this design, with all antenna elements excited with equal amplitude and fixed directional electric field vectors. When $u=kdcos\beta +\alpha =0$, the array factor S(u) has its maximum beamforming value S_max and the corresponding maximum radiation direction angle β_max, which represents the main lobe in the array antenna’s radiation pattern. When u = ± 2π, sidelobes will appear, and to suppress the sidelobes’ impact on the antenna performance, it is recommended to choose $\left|u\right|<2\pi$, as shown in Equation (24)

$$\mathrm{d}<{\displaystyle \frac{\mathsf{\lambda }}{{\left|\mathrm{c}\mathrm{o}\mathrm{s}\mathsf{\beta }-\mathrm{c}\mathrm{o}\mathrm{s}{\mathsf{\beta }}_{\mathrm{m}\mathrm{a}\mathrm{x}}\right|}_{\mathrm{m}\mathrm{a}\mathrm{x}}}},$$

(24)

Given that 0 ≤ β ≤ π, and considering Equation (25).

$${\left|\mathrm{c}\mathrm{o}\mathrm{s}\mathsf{\beta }-\mathrm{c}\mathrm{o}\mathrm{s}{\mathsf{\beta }}_{\mathrm{m}\mathrm{a}\mathrm{x}}\right|}_{\mathrm{m}\mathrm{a}\mathrm{x}}=1+\left|\mathrm{c}\mathrm{o}\mathrm{s}{\mathsf{\beta }}_{\mathrm{m}\mathrm{a}\mathrm{x}}\right|,$$

(25)

Therefore, we can derive Equation (26).

$$\mathrm{d}<{\displaystyle \frac{\mathsf{\lambda }}{1+\left|\mathrm{c}\mathrm{o}\mathrm{s}{\mathsf{\beta }}_{\mathrm{m}\mathrm{a}\mathrm{x}}\right|}},$$

(26)

For a uniform planar array with edge radiation, βmax = π/2, thereby calculating d < λ, which means that, in general array antenna designs, the element spacing is typically less than one wavelength. According to Balanis’ antenna theory book, array element spacing must exceed 0.5 wavelengths to avoid overlap. When the number of elements is fixed, smaller spacing results in a narrower main lobe, but excessively small spacing can cause strong mutual coupling between elements. In this design, the resonant frequency is 3.5 GHz, with a spatial wavelength of λ = 85 mm, implying an element spacing in the range 42.5 mm < d < 85 mm. For simulation and analysis, we chose d = 50 mm, d = 60 mm, and d = 70 mm. Figure 12 illustrates the simulated radiation pattern in the xoz plane at 3.5 GHz.

From Figure 12, it can be observed that when d = 50 mm, the antenna elements are relatively close, resulting in stronger mutual coupling, appearance of sidelobes, and lower gain at the maximum radiation direction. However, as d increases from 50 mm to 60 mm, the main lobe width of the antenna array decreases while the gain increases. On the other hand, as d increases from 60 mm to 70 mm, the gain at the maximum radiation direction decreases. In summary, an optimal choice for the element spacing should be d = 60 mm.

3.2.2. The Design and Simulation of the Feeding Network

In the actual design of array antennas, the excitation of the antennas is typically achieved through feeding networks, and it is essential to consider principles such as wide bandwidth and simplicity in the design.

Series feeding involves connecting individual antenna units in a serial manner via feed lines. However, the coupling between these units limits the operating bandwidth, resulting in a relatively narrow frequency range. In contrast, parallel feeding uses a power distributor to allocate input power to antenna units in specific proportions [24]. This approach offers a simpler and more easily implementable structure and achieves a broader frequency range. Nevertheless, it comes at the cost of a larger footprint for the feeding network. Considering the losses in the feed lines, antenna efficiency may be reduced.

In the design of the feeding network, a quarter-wavelength impedance transformer is introduced to achieve impedance matching for the circuit. The impedance matching principle is illustrated in Figure 13.

To achieve impedance matching for Z_in = Z₀, it is essential to meet the requirements outlined in Equation (27).

$${\mathrm{Z}}_{01}=\sqrt{{\mathrm{Z}}_0{\mathrm{R}}_{\mathrm{L}}},$$

(27)

To achieve a wide bandwidth and optimal matching characteristics, the incorporation of a multi-section impedance transformer is required [25]. In this instance, a T-type power divider structure is employed to facilitate the design of the multi-section impedance transformer. Figure 14 serves as an illustrative representation of the principles underlying the T-type power divider structure.

To achieve impedance matching for the T-type power divider, it is necessary to satisfy Equation (28).

$${\mathrm{Y}}_{\mathrm{i}\mathrm{n}}=\mathrm{j}\mathrm{B}+{\displaystyle \frac{1}{{\mathrm{Z}}_1}}+{\displaystyle \frac{1}{{\mathrm{Z}}_2}}={\displaystyle \frac{1}{{\mathrm{Z}}_0}},$$

(28)

As illustrated in Figure 15, we have a parallel-fed T-junction structure composed of a 50 Ω microstrip line, a 100 Ω microstrip line, and a quarter-wavelength impedance transformer.

3.2.3. Simulation of a 4 × 4 Array Antenna

Once the antenna elements and the feeding network have been determined, they can be combined to create the 4 × 4 microstrip array antenna, as depicted in Figure 16.

In this design, the feeding point for the entire array antenna is positioned at the center of the array, and coaxial feeding is utilized. The coaxial probe connects through small apertures to the radiating element of the antenna, enabling the feeding of the antenna. With the feeding point located inside the patch, it minimizes the impact on the antenna radiation. Figure 17 illustrates the coaxial feeding point of the array antenna.

After performing HFSS simulations on the 4 × 4 array antenna, the reflection coefficient S11 plot, as shown in Figure 18, is obtained. From the results in the graph, it can be observed that the array antenna provides full coverage of the LTE band 42 (3.4–3.6 GHz) frequency range. When the antenna operates at the central frequency of 3.5 GHz, the return loss reaches approximately −26.1 dB. With a return loss less than −6 dB, the achieved bandwidth is 373 MHz (3.321–3.694 GHz), corresponding to a relative bandwidth of 10.7%.

Figure 19 represents the radiation pattern of the microstrip array antenna at a frequency of 3.5 GHz. From the 3D gain pattern in Figure 19a, it is evident that the maximum radiation direction is perpendicular to the antenna center, with a peak gain of 12.7 dBi in the maximum radiation direction. Figure 19b presents the polar gain pattern of the array antenna.

3.2.4. Fabrication of a 4×4 Array Antenna Prototype

In this design project, the fabrication and soldering of the array antenna were carried out entirely within the laboratory. The process involved the use of the ProtoLaser STC series products from LPKF, in conjunction with the CircuitPro PL software-driven system. Figure 20 illustrates the laboratory fabrication environment.

To achieve the best experimental results and to simultaneously fabricate multiple array antenna boards, manual soldering of the feeding SAM connectors was performed. Figure 21 presents the physical fabrication diagram of the array antenna, where Figure 21a provides an overview of the front side patch illustration and Figure 21b depicts the schematic representation of the rear side with feeding SAM connectors.

3.2.5. Physical Measurement and Result Analysis

First, VSWR parameters of the physical array antenna were measured. As shown in Figure 22, the measured VSWR plot of the array antenna falls below 2 within the 5G LTE band 42 (3.4–3.6 GHz) frequency range, meeting the antenna design requirements.

Subsequently, a vector network analyzer was used to measure the return loss, and the measured S parameters are displayed in Figure 23.

Comparing the measured S parameters of the array antenna with the simulated S parameters, it is observed that the measured results exhibit a slight overall upward shift, with a slight leftward deviation in the center frequency to approximately 3.48 GHz, resulting in a return loss of approximately −25.9 dB. Nevertheless, these measured results closely align with the simulation results.

In Figure 24, the microwave anechoic chamber measurement environment is depicted. Figure 25 displays the radiation pattern of the antenna measured in the microwave anechoic chamber at a frequency of 3.5 GHz. When compared with the simulation results, no distortion is observed, indicating that the designed 4 × 4 array antenna exhibits favorable radiation characteristics.

4. Metal Frame Mobile Terminal Dual-Element “Loop-Groove” MIMO Antenna Design

4.1. The Impact of Metal Frame on Mobile Terminals

Metal frame smartphones have gained popularity due to their durability and aesthetic appeal. Led by Apple’s iPhone, earlier iPhone models like the iPhone 4, 4s, 5, and 6, among others, featured metal frames or bodies. Some brands like Meizu MX3 and Xiaomi 4 utilized austenitic 304 stainless steel. Later, many smartphones began using materials like aluminum and magnesium alloys, which provide better protection against wear and impact. Furthermore, metal frames facilitate heat dissipation by quickly transferring heat generated during operation to the surrounding air, resulting in improved cooling efficiency. These reasons contribute to the preference for metal-framed smartphones by many users.

However, as 5G communication systems have developed, the number of 5G smartphones with metal bodies in the market has decreased. This change is primarily due to the nature of wireless signals, as metal frames can affect the signal quality. A metal body can attenuate signals, thus influencing connection speed and strength, especially when the user’s hand covers the antenna areas during calls. For instance, signal strength often weakens when entering elevators because elevators are enclosed metal spaces, effectively creating a metallic shield that significantly interferes with wireless signal reception. In simple terms, metal has a shielding effect on electromagnetic waves. As 5G operates at higher frequencies and uses pulse waves, it is even more sensitive to the presence of metal.

To simulate the impact of using a metal body on signal quality with 5G, a Huawei P40 Pro (5G) smartphone was selected for experimentation. Although the phone’s rear cover is made of precision ceramic material, the screen frame is still constructed of stainless steel. Given the innovative design of the phone’s curved screen, the metal frame makes up only one-third of the phone’s width. Figure 26 depicts the initial signal strength tests with the phone in a bare state.

Subsequently, a metal phone case was installed to simulate a widened metal frame, and its impact on signal quality was tested in the same environment, as shown in Figure 27.

As evident in Figure 26, when the smartphone is tested in its bare state, the 5G signal strength is within the range of (−67 dBm, 73 asu). However, after installing the metal phone case, as depicted in Figure 27, the 5G signal strength decreases to (−94 dBm, 46 asu).

To meet the demand for metal frame smartphones, higher standards are required when designing antennas for 5G terminal products. Nevertheless, due to the presence of metal frames, integrating multiple antennas together with high isolation becomes increasingly challenging. Previous research on metal frame smartphones has shown that some suffer from low isolation across the entire operating frequency band, failing to meet the required isolation standards. Additionally, some solutions have relatively larger dimensions, compromising the aesthetics of smartphones. Therefore, this section aims to design a new dual-element MIMO antenna with high isolation, specifically suitable for 5G metal frame smartphones.

4.2. The Dual-Element “Loop-Groove” MIMO Antenna Design Process

In this chapter, a dual-element “loop-groove” MIMO antenna structure is designed to operate within the LTE band 42 (3.4–3.6 GHz) frequency range, with a central frequency around 3.5 GHz. The design utilizes an FR4 dielectric substrate with a relative permittivity of 4.4 and a thickness of 0.8 mm. A 0.6 mm thick copper strip is placed around the perimeter of the dielectric substrate to simulate the metal frame within a mobile terminal. To create the dual-element “loop-groove” MIMO antenna structure, the initial step involves designing a loop antenna element and a slot antenna element, which serve as the foundational components for this structure.

4.2.1. Design and Simulation of the Loop Antenna

First, we designed a loop antenna operating at 3.5 GHz. We created a rectangular slot on the ground plane to form the circular architecture of the loop antenna. To mitigate the interference of the metal frame with the antenna’s performance, we chose to design a slot in the metal frame and treat the metal boundary as part of the antenna’s feeding structure [26]. Additionally, we designed a rectangular feeding branch, with its ends connected to the rectangular slot on the ground plane and the metal frame to effectively excite the loop antenna. Figure 28 illustrates the schematic diagram of the loop antenna structure.

In balanced mode, the ground currents between antennas can be effectively suppressed, leading to improved MIMO antenna isolation [27]. For this reason, the loop antenna’s perimeter is chosen to be approximately λ and, given that width W = 0.012λ_3.5GHz = 1 mm, the length L of the loop antenna can be calculated as L ≈ λ/2 − W ≈ 40.6 mm.

The gap width in the metal frame is another critical factor affecting antenna performance. As shown in Figure 29, the curve illustrates the change in the loop antenna’s S parameters as the gap width in the metal frame increases from 0.5 mm to 1.5 mm.

From Figure 29, it can be observed that, as the gap width in the metal frame gradually increases, the isolation of the loop antenna remains around −10 dB. However, the resonance frequency of the antenna tends to shift to the right, resulting in improved impedance matching and an expanded operating bandwidth. This is because, as the metal frame widens, the radiation of electric field energy becomes more convenient, optimizing antenna performance. Nevertheless, considering the aesthetics of mobile terminals, the gap width should not be excessively large. After considering various factors, a gap width of 1 mm was ultimately chosen, achieving high isolation for the loop antenna while integrating the metal frame as part of the antenna.

4.2.2. Design and Simulation of the Slot Antenna

In this section, a slot antenna operating at 3.5 GHz is designed. Similar to the previous section’s loop antenna, a rectangular slot is created on the ground plane, and an L-shaped feeding line consisting of a 50 Ω microstrip line and a feeding branch is designed to achieve impedance matching for the slot antenna. Figure 30 illustrates the schematic diagram of the slot antenna structure.

In this design, a slot antenna with closed ends at the gap is selected, exciting the 0.5λ resonant mode. Therefore, the slot antenna’s gap length is chosen to be half a wavelength, L = 0.5λ, which is approximately 41.6 mm, and the width is set to W = 1 mm = 0.012λ_3.5GHz. It is evident that the dimensions of the designed slot antenna, both in terms of width and length, are relatively close to those of the loop antenna, laying the foundation for subsequent design.

Next, we shall discuss the impact of varying the width, W1, of the feeding branch on the performance of the slot antenna. The comparative changes in the slot antenna’s S parameters when the width of the feeding branch varies from 0.3 mm to 0.5 mm are illustrated in Figure 31.

The feed branch appears in Figure 30b, where S is isolation of the loop antenna. From Figure 31, it is evident that, as the feed branch width (W1) increases, the S parameter curves of the antenna shift to the right, indicating improved impedance matching and a wider bandwidth for the slotted antenna. Additionally, when the feed branch width is W1 = 0.5 mm, the resonant center frequency of the slotted antenna is around 3.5 GHz, signifying the optimal performance of the designed antenna.

4.2.3. Implementation of a Dual-Element “Ring Slot” MIMO Antenna

Once the ring antenna and slot antenna have been individually designed, the next step is to arrange these two antenna elements in a manner that ensures high isolation and achieves antenna miniaturization.

Initially, the placement of the ring antenna and slot antenna is considered to be horizontally aligned along the longer edge, as depicted in Figure 32.

In this traditional placement method, in order to avoid mutual coupling between the antenna elements and prevent a decrease in isolation, the ring antenna and slot antenna are spaced apart by a certain distance. Consequently, this conventional arrangement increases the horizontal length of the antenna, resulting in a larger overall size for the designed MIMO antenna array. This can be limiting for mobile terminal devices with limited space, reducing the number of antenna elements that can be accommodated and thus hindering the achievement of true miniaturization in antenna design. Therefore, a new placement approach needs to be considered.

As discussed in Section 4.2, the rectangular slots on the ground for the designed ring antenna and slot antenna have dimensions that are very close in both length and width. Hence, it is feasible to explore a novel placement method where the ring antenna and slot antenna are designed to overlap within a shared rectangular slot, as illustrated in Figure 33, which represents a schematic structure for the co-located placement of the ring antenna and slot antenna.

To achieve impedance matching for the ring antenna and slot antenna, it is necessary to connect an inductor in series with the “ring-slot” structure. The design of the inductor connected between the metal frame and the midpoint of the rectangular slot in the ground can optimize the overall antenna performance. Figure 34 is an illustrative diagram of the dual-element “ring-slot” antenna structure.

4.3. Optimization of the “Ring-Slot” Structure Parameters

For the dual-element “ring-slot” antenna structure mentioned above to achieve higher performance, it is necessary to optimize its parameters, including the metal frame height, ground slot length, and chip inductor.

4.3.1. Optimization of Metal Frame Height

As explained in Section 4.1, the presence of the metal frame has a significant impact on the overall antenna performance. However, it is important to note that the variations in metal frame height primarily affect the ring antenna due to its feeding structure, whereas the impact on the slot antenna’s resonant frequency is relatively minor.

Next, we shall investigate the influence of changes in metal frame height on the reflection coefficient of the ring antenna within the dual-element “ring-slot” structure. As shown in Figure 35, when the metal frame height increases from 5.2 mm to 7.2 mm (with a 1 mm increment), the resonant frequency of the ring antenna decreases from 3.58 GHz to 3.39 GHz. Good impedance matching is achieved when the metal frame height is d = 6.2 mm. Therefore, the optimized metal frame height is determined to be 6.2 mm.

4.3.2. Optimization of Ground Slot Length

The resonant frequency of the slot antenna is closely related to the electrical length of the rectangular ground slot. Consequently, variations in the ground slot length (L) have a significant impact on the slot antenna while the impact on the ring antenna can be neglected. We shall now explore the changes in the reflection coefficient of the slot antenna in the dual-element “ring-slot” structure with respect to the length (L) of the rectangular ground slot, as illustrated in Figure 36.

As the rectangular ground slot length (L) increases from 30 mm to 32 mm (in 1 mm increments), the resonant frequency of the slot antenna decreases from 3.54 GHz to 3.45 GHz. When L = 31 mm, the center frequency is around 3.5 GHz and fully covers the LTE band 42 frequency range. Therefore, the optimized ground slot length is determined to be 31 mm.

4.3.3. Optimization of the Chip Inductor

In Section 4.3, a chip inductor is connected in series within the “ring-slot” structure to optimize the impedance matching of the entire structure. Next, we shall investigate the impact of the chip inductor on the transmission coefficient between the ring antenna and the slot antenna, as depicted in Figure 37.

As the chip inductor increases from 8.5 nH to 8.9 nH (in increments of 0.2 nH), the transmission coefficient between the ring antenna and the slot antenna initially increases and then decreases. When the chip inductor is selected as 8.7 nH, the isolation between the two antennas is maximized at around −26 dB at 3.5 GHz, and the isolation remains superior to −22 dB within the LTE band 42 frequency range. Therefore, after optimization, the chip inductor should be chosen as 8.7 nH.

4.4. The Decoupling Principle of the “Ring-Slot” Structure

In MIMO antenna design, the characteristic mode theory is often used to address the issue of mutual coupling between antenna elements. However, when an antenna has multiple resonant modes, many of these modes may be closely spaced or adjacent within the specified frequency band. In such cases, it becomes impossible to excite only a single resonant mode in the MIMO antenna. Furthermore, regardless of how antenna elements are arranged, multiple resonant modes are often excited. The characteristic mode theory can be employed to analyze scenarios where two elements excite the same resonant modes. Typically, there are two situations:

• Both antenna elements excite completely different resonant modes. When this occurs, an analysis of the overall structure is needed to find the most suitable placement for the antenna elements. However, this approach has limitations in practical antenna design.
• Both antenna elements can excite partially similar or completely identical resonant modes. In this section, for a mobile terminal antenna with added metal frame, operating in the 3.4–3.6 GHz frequency range, the ring antenna element and the slot antenna element can excite multiple identical resonant modes. In a dual-element “ring-slot” MIMO antenna system, the radiated electric fields from the ring antenna and slot antenna can be represented as a superposition of characteristic electric fields.

$$E_{Ant1}={\alpha }_{\mathrm{1,1}}{E}_1+{\alpha }_{M,1}{E}_M+{\alpha }_{C_1,1}{E}_{C_1}+\cdots +{\alpha }_{C_{N1},1}{E}_{C_{N1}},$$

(29)

$$E_{Ant2}={\alpha }_{\mathrm{1,2}}{E}_1+{\alpha }_{M,2}{E}_M+{\alpha }_{D_1,2}{E}_{D_1}+\cdots +{\alpha }_{D_{N2},2}{E}_{D_{N2}},$$

(30)

In the equations α_n,1 and α_n,2 represent the mode weighting coefficients for the ring antenna and slot antenna, respectively. M represents the number of identical modes that the ring antenna and slot antenna can excite and which are the different resonant modes excited by the ring antenna and slot antenna. The envelope correlation coefficient in a MIMO system can be expressed as in Equation (31).

$${\rho }_c(i,j)={\displaystyle \frac{{\left|\sum _{n=1}^N{\alpha }_{n,i}{{\alpha }_{n,j}}^{\mathit{*}}\right|}^2}{\left(\sum _{n=1}^N{\left|{\alpha }_{n,i}\right|}^2\right)\left(\sum _{n=1}^N{\left|{\alpha }_{n,j}\right|}^2\right)}},$$

(31)

Substituting Equation (29) and Equation (30) into Equation (31), we obtain Equation (32).

$$|\sum _{n=1}^{M+N1+N2}{\alpha }_{n,i}{{\alpha }_{n,j}}^{\mathit{*}}{|}^2={\left|{\alpha }_{\mathrm{1,1}}{{\alpha }_{\mathrm{1,2}}}^{\mathit{*}}+{\alpha }_{\mathrm{2,1}}{{\alpha }_{\mathrm{1,2}}}^{\mathit{*}}+\cdots +{\alpha }_{M,1}{{\alpha }_{M,2}}^{\mathit{*}}\right|}^2,$$

(32)

From Equation (32), it is evident that the envelope correlation coefficient is solely dependent on the mode weighting coefficients associated with the M identical modes excited. Identical modes can be categorized into two types: in-phase modes and out-of-phase modes, with a phase difference of 180 degrees. Considering the influence of different phase factors in the mode weighting coefficients, Equation (32) can be reformulated as Equation (33).

$$\begin{array}{ll}|{\displaystyle \sum _{n=1}^{P+Q}}{\alpha }_{n,i}{{\alpha }_{n,j}}^{\mathit{*}}{|}^2& =|\left(\left|{\alpha }_{E\mathrm{1,1}}{\alpha }_{E\mathrm{1,2}}\right|+\cdots +\left|{\alpha }_{EP,1}{\alpha }_{EP,2}\right|\right)\\ & {-\left(\left|{\alpha }_{A\mathrm{1,1}}{\alpha }_{A\mathrm{1,2}}\right|+\cdots +\left|{\alpha }_{AQ,1}{\alpha }_{AQ,2}\right|\right)|}^2={\left|EC-AC\right|}^2,\end{array}$$

(33)

In the equation, among the M identical modes, assuming that there are P co-polar modes excited, α_En,1 and α_En,2 represent the mode weighting coefficients for the nth co-polar mode. Similarly, assuming that there are Q cross-polar modes excited, α_An,1 and α_An,2 represent the mode weighting coefficients for the nth cross-polar mode. EC and AC represent the products of co-polar mode weighting coefficients for the ring antenna and slot antenna, respectively, as well as the products of cross-polar mode weighting coefficients.

From the result on the right side of Equation (27), it can be observed that, if the difference between EC and AC is smaller, the resulting envelope correlation coefficient (ECC) will be smaller. Therefore, by providing reasonable excitation to the ring antenna and slot antenna, in order to achieve similar respective co-polar and cross-polar modes, the requirement of achieving a low ECC value can be met. Figure 38 shows the current distribution diagram for the dual-element “ring-slot” MIMO antenna structure.

From Figure 38, it can be observed that, when the ring antenna is excited, the current predominantly radiates along the long side of the dielectric substrate, resulting in relatively weaker current flow through the slot antenna, which mainly circulates around the rectangular gap on the ground plane along the y-axis direction.

Conversely, when the slot antenna is excited, the current radiates vertically to the long side of the dielectric substrate, accompanied by reverse currents around the rectangular gap. Therefore, in the dual-element “ring-slot” MIMO antenna structure, the ring antenna and slot antenna exhibit orthogonal current patterns, effectively suppressing coupling between the two antenna elements. Even without the addition of external decoupling structures, the ring antenna element and the slot antenna element achieve a high level of isolation. Furthermore, when compared with traditional antennas, the proposed antenna structure features a complete overlap of both antenna elements and, after optimization, the “ring-slot” structure’s length has been significantly reduced to 31 mm, contributing to the miniaturization of smartphones.

4.5. Results Analysis

As shown in Figure 39, these are the S parameter curves for the dual-element “ring-slot” structure. It is evident from the graph that, although there is a slight shift in the resonance frequencies, the structure still fully covers the operating frequency range of LTE band 42 (3.4–3.6 GHz). Even in the scenario where the rectangular ground slots are shared and the two elements are placed in complete overlap, without the addition of any decoupling structures, the isolation of this dual-element “ring-slot” structure remains higher than 21 dB, achieving a high level of isolation between the antennas.

As shown in Figure 40, based on the radiation pattern results for the E-plane and H-plane at a frequency of 3.5 GHz for the dual-element “ring-slot” MIMO antenna, there is no distortion in the antenna’s radiation pattern. The E-plane radiation pattern exhibits a dumbbell-shaped distribution, indicating effective coverage of the entire antenna’s dielectric substrate. On the other hand, the H-plane radiation pattern displays omnidirectional radiation characteristics, signifying that the dual-element “ring-slot” MIMO antenna structure can achieve favorable radiation characteristics, meeting the requirements for MIMO antenna design.

5. Design of an Eight-Element MIMO Array Antenna for Mobile Terminals with a Metal Frame

Fifth-generation mobile terminal antennas are designed to meet specific performance requirements while considering channel distribution and the impact of the human body on antenna performance [28]. To meet the demands of future cellular communication systems, there is a need to continually increase the channel capacity of smartphones. The design trend is to integrate six or eight antenna elements to form MIMO array antennas. However, as smartphones become thinner and lighter, physical space in real-world scenarios is increasingly limited, leading to reduced space for antenna utilization. This compression in design dimensions results in significant coupling between MIMO components. Therefore, the following exploration will focus on how to enhance the isolation between MIMO array antennas.

5.1. Design and Simulation of an Eight-Element MIMO Array Antenna

Based on the “ring-slot” MIMO antenna structure proposed in Section 4, research has been conducted on an eight-element MIMO array antenna suitable for mobile terminals with a metal frame to achieve improved antenna performance. This antenna operates in the LTE band 42 (3.4–3.6 GHz) frequency range, with a center frequency around 3.5 GHz. A substrate with a relative dielectric constant of 4.4, loss tangent of 0.02, and a thickness of 0.8 mm made of FR4 material is chosen as the system circuit board, with dimensions of 145 mm × 75 mm × 0.8 mm. A 0.6 mm-thick copper strip is placed around the perimeter of the dielectric substrate to simulate the metal frame within a mobile terminal.

In this design, eight-element MIMO array antennas are composed of four sets of dual-element “ring-slot” MIMO antenna modules. These modules are arranged along the longer sides of the system board; block 1 (Ant1, Ant2) and block 2 (Ant3, Ant4) are placed on one longer side, while block 3 (Ant5, Ant6) and block 4 (Ant7, Ant8) are symmetrically positioned on the other longer side. As shown in Figure 41, this is the schematic diagram of the eight-element MIMO array antenna structure.

5.2. Optimization of the Parameters for the Eight-Element MIMO Array Antenna

The placement of the “Ring-Slot” antenna units also affects the resonance frequency and bandwidth of the array antenna. Next, through simulation optimization, including adding T-type decoupling structures to the antenna array, selecting suitable antenna unit positions, and adjusting the spacing distance, the performance of the array antenna will be improved.

5.2.1. Adding T-Type Decoupling Structures

The coupling between antenna elements is primarily due to the interaction of currents between them. Typically, decoupling structures are added to antennas to suppress the transmission of coupled currents and improve antenna performance. To enhance the isolation between the “ring-slot” structures, this design improves isolation by etching a quarter-wavelength T-shaped structure in the gap between two “ring-slot” structures along the longer edge of the ground plane. To further investigate the decoupling mechanism of the T-type decoupling structure, simulations were conducted on the antenna currents.

Figure 42a shows the current distribution diagram of the array antenna before adding the T-type decoupling structure, and Figure 42b shows the current distribution diagram after the T-type decoupling structure is added.

From Figure 42, it can be observed that adding the T-type decoupling structure between the “ring-slot” structures along the longer edge effectively suppresses the transmission of coupled currents between the “ring-slot” structures and the ground plane, achieving a significant decoupling effect.

5.2.2. Layout of the “Ring-Slot” Unit Modules

Three layouts of the “ring-slot” unit modules are considered, as shown in Figure 43: Figure 43a: Layout 1, where all the slot antennas (Ant2, 4, 6, 8) have their L-shaped feed branches pointing in the same direction. Module 1 (Ant1, Ant2) and Module 2 (Ant3, Ant4), placed along one side, are axisymmetric to Modules 3 (Ant5, Ant6) and 4 (Ant7, Ant8) on the other side of the antenna ground plane. Figure 43b: Layout 2, where the L-shaped feed branches all point toward the interior of the antenna ground plane, and the four “ring-slot” modules are placed in a central symmetry arrangement. Figure 43c: Layout 3, where the L-shaped feed branches all point toward the exterior of the antenna ground plane, and the four “ring-slot” modules are also placed in a centrally symmetric manner.

As shown in Figure 44, the simulated S parameters for the array antenna are compared for three different layouts of the antenna units. From Figure 44a, it can be observed that the first layout with L-shaped feed branches placed in the same direction results in lower isolation between the array antenna elements, which is not conducive to achieving the desired high gain for MIMO array antennas. Figure 44b shows that the second layout with L-shaped feed branches directed inward has a narrower bandwidth and insufficient isolation. Figure 44c demonstrates that the third layout with L-shaped feed branches directed outward has higher isolation compared with the first layout and can completely cover the LTE band 42 frequency range when compared with the second layout. Therefore, the layout in which L-shaped feed branches are directed outward is chosen as the final antenna array configuration.

5.2.3. Optimization of the Spacing between the “Ring-Slot” Unit Modules

The spacing (d) between two different modules has a significant impact on the overall isolation of the MIMO system. As shown in Figure 45, as the spacing (d) increases, the resonance frequencies of the ring antenna and slot antenna shift towards higher frequencies. When the spacing (d) increases from 73.5 mm to 77.5 mm, the isolation between antenna 1 and antenna 2 decreases. Simultaneously, as the spacing (d) increases, the distance between antenna 1 and antenna 3, which are located in different modules, also increases, leading to improved isolation between antenna 1 and antenna 3. After considering the isolation within modules and between modules, the optimal spacing (d) is chosen as 75.5 mm.

5.3. Fabrication and Measurement of the Eight-Element MIMO Array Antenna

To validate the performance of the designed eight-element MIMO array antenna in real-world usage, the next step involves fabricating the antenna model for measurements. This will include measuring S parameters (reflection coefficients and isolation), radiation efficiency, radiation patterns, MIMO antenna correlation envelope coefficient (ECC), and channel capacity.

5.3.1. Fabrication of the Antenna

To facilitate the fabrication and soldering of the antenna’s metal frame, soldering points were designed between the antenna array and the metal frame, as shown in Figure 46, which displays the model for antenna fabrication.

Figure 44 shows the actual fabrication of the antenna array, including Figure 47a for the front view, Figure 47b for the back view, and Figure 47c for the side view. Soldering the 50 Ω SMA feeders directly to the antenna substrate or the metal frame would have a significant impact on the antenna’s feeding performance and result in stronger mutual coupling between antenna elements, preventing the antenna from achieving its simulated performance. For the loop antennas (Ant1/3/5/7), a feeder line is routed from the outside of the metal frame, and an SMA feeder head is mounted on the exterior of the antenna. Likewise, for the slot antennas (Ant2/4/6/8), feeder lines are brought in through the metalized holes, connecting to L-shaped feed branches for feeding. This soldering method keeps the SMA feeder heads at a distance from the antennas to prevent mutual coupling and maintain antenna performance.

5.3.2. Analysis of Antenna Performance Results

Figure 48 presents the measured S parameters of the eight-element array antenna. It is evident from the graph that the array antenna provides complete coverage of the LTE band 42 (3.4–3.6 GHz) frequency range, with an overall isolation exceeding 17 dB. Furthermore, the measured S parameters closely align with the simulated S parameters. However, some minor disparities were observed upon comparison. These discrepancies are attributed to slight deviations in the center frequency and a narrowed bandwidth in the actual measured antenna, which stem from losses incurred during the fabrication of the dielectric substrate and SMA connectors. Additionally, inherent errors resulting from the equipment and procedural aspects during fabrication are unavoidable. Nevertheless, it is crucial to note that these errors remain within acceptable limits, and they do not impede the practical use of the array antenna.

Efficiency and radiation pattern measurements were conducted within a microwave anechoic chamber, as depicted in Figure 49. The diagram illustrates the environmental conditions within the anechoic chamber during testing. When one unit is subjected to testing, the other seven units are terminated with 50 Ω matching loads [29].

Figure 50 depicts the measured radiation pattern of the eight-element array antenna at a frequency of 3.5 GHz. Due to the symmetry of the array antenna, the results for four selected ports are displayed here for illustration. It is evident from the diagram that the radiation pattern remains undistorted, and the antenna exhibits effective radiation on both the E-plane and H-plane, achieving omnidirectional antenna radiation.

Figure 51 presents the measured radiation efficiency diagram of the array antenna, with results from four selected ports for illustration. The diagram demonstrates that the MIMO antenna’s radiation efficiency falls within the range of 65.8% to 73.7%.

In addition to radiation efficiency, MIMO antennas also require good isolation and coupling characteristics. Therefore, during measurements, specific metrics such as the envelope correlation coefficient (ECC) need to be closely monitored. For MIMO mobile antennas, a lower ECC value signifies greater diversity gain. As illustrated in Figure 52, the envelope correlation coefficient (ECC) diagram is presented, with ECC values primarily calculated based on the measured three-dimensional far-field radiation patterns.

As shown in Figure 52, it can be observed that the ECC values calculated from actual measurements are all below 0.03. This signifies that the antenna designed in this study exhibits excellent isolation and a relatively high diversity gain.

6. Conclusions and Future Outlook

This study has presented the design of three high-performance, high-isolation array antennas suitable for 5G communication, including a 5G microstrip array antenna and two MIMO antennas designed for mobile devices with metal frames. While the research has achieved significant milestones, several challenges and areas for improvement have been identified:

The 5G microstrip array antenna designed in this study, though successful in covering 5G LTE band 42 (3.4–3.6 GHz) with notable improvements in bandwidth and gain, could be further developed into a multi-band antenna to cater to the varying frequency requirements in different scenarios.

As technology continues to advance, the trend towards larger screens in mobile phones has become more prominent. For metal-frame antennas, it will be necessary to design smaller ground clearance areas and ensure compatibility with a wider range of network generations, including 2G, 3G, 4G, 5G, as well as LTE/WLAN frequency bands. Subsequent adjustments and refinements should be made to address these specific requirements.