# Characteristic Mode-Based Neutralization Line Design for MIMO Antenna

Authors: Yitian Sun; Minmin Tian; G. S. Cheng
Journal: International Journal of Antennas and Propagation
 (2022)

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## Abstract

Based on the theory of characteristic modes (TCMs), this paper proposes a systematic design procedure to guide the design of a neutralization line (NL) for a dual-band multiple-input-multiple-output (MIMO) antenna to achieve high isolation. According to the direction of the current flow of significant characteristic modes, coupling and uncoupling modes are identified and a metal NL is appropriately designed to cancel the coupling modes. More specifically, it introduces new currents opposite in direction to the original coupling characteristic currents, thus reducing mutual coupling. Compared with the traditional NL design method, the proposed approach simplifies the optimization process and saves lots of optimal design time. As an illustration of the proposed design method, we design another dual-band antenna operating in the WLAN bands with a compact size of 50 mm × 48 mm × 0.8 mm and minimum edge‐to‐edge space between the radiating elements with 0.033λ0 of the lower band. The impedance bandwidths for S11 ≤ -10 dB are 0.42 GHz (2.27–2.69 GHz) and 0.24 GHz (5.6–5.84 GHz). A fabricated prototype shows good agreement between the measured and simulated results. The introduced NL improves the isolation degree by about 18 dB for the 5.8 GHz band, and the total efficiency of the antenna was also improved. In addition, the proposed antenna also has a low envelop correlation coefficient (ECC < 0.3), high diversity gains, and low total active reflection coefficient (TARC) in the frequency band of interest. Measurement results show that the proposed MIMO antenna system is suitable for WLAN applications.


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## Body

## 1. Introduction

With the rapid development of wireless communication, how to use the limited spectrum resources to improve the communication quality and signal transmission rate in a harsh environment has always been a hot spot, and multiple-input multiple-output (MIMO) technology is one of the most promising solutions. MIMO system adopts multiple antennas or antenna arrays at both ends of the transceiver, which can provide an additional degree of freedom to increase channel capacity, ensure communication quality, and improve transmission rate by utilizing the multipath characteristics of space channel without increasing transmission power and communication bandwidth [1]. The mutual coupling of antennas on transmitter and receiver should be low for good quality of communication and channel capacity [2].However, the rapid development of mobile communication equipment makes the space for the integration of antennae becomes smaller and smaller. A load of multiple antennas in a limited space will inevitably produce large mutual coupling, which leads to poor impedance matching and bad diversity performance of the MIMO system. In recent years, researchers have proposed several methods to improve the isolation between antenna elements, such as decoupling networks [3–5], metasurfaces and metamaterials [6–9], electromagnetic-bandgap (EBG) structures [10–14], defective ground structures (DGS) [15–18], split-ring resonators (SRRs) [19], and neutralization line (NL) technique [20–23]. NL technique has been studied extensively because it does not require additional space or changing the ground plane. The working principle of NL is to connect the antenna element with a metal strip and cancel each other out by introducing a new current in the opposite direction of the original coupling current. However, it is difficult to determine the loading position and the specific parameters of NL, which requires a lot of optimization time.The theory of characteristic modes (TCM) was studied by Harrington and Mautz [24] and is widely adopted in antenna design [25–35]. One of the most attractive properties of TCM is that both the characteristic current and the characteristic field at infinity satisfy the property of orthogonality. By taking advantage of this property, TCM is widely adopted in the MIMO system because good envelope correlation coefficient (ECC) performance can be realized.Characteristic mode analysis of two adjacent planar inverted-F antenna (PIFA) elements was reported to show how a shorted line could help reduce the mutual coupling [32]. However, the design of the NL in [32] was still based on the traditional electromagnetic analysis and optimization algorithm. The TCM was only used to analyze and verify why the loaded NL could achieve the effect of decoupling from the perspective of mode theory. In this study, based on the initial preliminary work in [23], a TCM-based design procedure to systematically guide the design of NL is proposed. The characteristic mode analysis is performed for the initial MIMO antenna without NL. According to the direction of the significant characteristic currents, coupling and uncoupling modes are identified. A metal NL is appropriately designed according to the characteristic current distribution of the coupling modes to cancel the mutual coupling. More specifically, the shape of NL is determined qualitatively based on the characteristic currents of the coupling mode. Then, HFSS was used to optimize the critical parameters of NL and determine it quantitatively. Compared with the traditional optimization design method, the proposed TCM-based design procedure can save lots of optimal design time. Experimental results show that 21 dB of isolation between the ports is achieved, and good agreement is observed between the measured and simulated results.


## 2. Characteristic Mode Analysis and Design Procedure

### 2.1. Introduction of TCM

The TCM provides a clear physical concept, which can essentially explain the radiation mechanism of an antenna and facilitate the guidance of antenna design, such as the essential physical characteristics of antenna structure and appropriate feed structure as well as the feed location to excite a characteristic mode (CM). More specific derivations of TCM and its application in antenna design are detailed in [33].The CMs of arbitrarily shaped perfectly electrically conducting (PEC) bodies can be obtained fromXJn=λnRJn, where λn is eigenvalues, Jn is eigenvectors or the characteristic currents, and R and X are real and imaginary Hermitian parts of the generalized impedance matrix Z = R + jX resulting from electric field integral equation (EFIE) [33]. The eigenvalue λn is a handy parameter because it can reveal the resonance and radiation information of its corresponding CM. In fact, there are several other preferred variables that can provide resonance and radiation information. The modal significance (MS), defined as MSn = |1/(1+ jλn)|, is the inherent and excitation source-independent property of each mode. It converts the variation range of eigenvalues [−∞, +∞] to [0, 1]. The characteristic mode is resonant when λn is zero, while MSn = 1. The CMs form a complete set of orthogonal modes so that the induced current (J) of a conducting object excited by an excitation source can be expanded as J=ΣαnJn, where αn is the modal weighting coefficients determined by the MSn, external excitation source, and characteristic current of the nth mode [33]. In the following section, the TCM analysis of the proposed antennas is carried out using the commercial simulation software FEKO.


### 2.2. TCM-Based NL Design

Figure1 shows the initial geometry of a MIMO antenna designed in this paper (named antenna#1), which consists of two symmetric antenna elements. The antenna unit is designed based on the traditional inverted L-shaped monopole antenna. By loading the horizontal radiation branch and bending it, the dual-band and miniaturization characteristics of the antenna are realized, respectively. The antenna is printed on an FR-4 substrate with a relative permittivity of 4.4, a loss tangent of 0.02, and a thickness of 1.6 mm. The antenna size is 54 mm × 32 mm × 1.6 mm.Figure 1
Structure of antenna#1 without NL: (a) perspective view and (b) end view.
(a)(b)The S-parameters of the MIMO antenna#1 are illustrated in Figure2. It can be seen that the mutual coupling without the NL is lower than −15 dB within 2.37–2.69 GHz while higher than −15 dB within 5.0–5.84 GHz. Therefore, an additional decoupling structure is needed to improve the isolation at the high-frequency band.Figure 2
Simulation of ECC (with NL) and S-parameters of antenna#1 with and without NL.The initial antenna structure is analyzed by TCM. Figure3 shows the MS of the significant modes of the antenna. MS is a good indicator to measure the coupling degree between each mode and the external excitation field and determine its radiation performance. In general, the mode with an MS value greater than 0.707 is considered the significant mode that plays an essential role in antenna radiation [33]. As can be seen from Figure 3, mode 1, mode 1’ and mode 2’ are significant modes at the frequency band of interest.Figure 3
MS for the dominant CMs of the MIMO antenna#1 without the NL.Figure4 gives the characteristic current distribution of significant modes. In the low-frequency band, mode 1 has current flowing from left to right, so mode 1 is defined as a coupling mode for this band. However, the coupling of the antenna at the low-frequency band is not strong, and there is no need to deal with it. It can be seen from Figure 4(c) that mode 1’ has a large amount of current flowing from the antenna unit on the left to the right, so this mode is defined as a coupling mode at the high-frequency band. Although mode 2’ is also a significant mode, it can be seen from the current distribution and flow direction (Figure 4(e)) that there is no current coupling between the two antenna elements, so this mode is defined as the uncoupling mode.Figure 4
Characteristic current distribution of the significant modes of antenna#1: (a) mode 1 at 2.45 GHz, (b) mode 1 at 2.45 GHz, (c) mode 1’ at 5.5 GHz, (d) mode 1’ at 5.5 GHz, (e) mode 2’ at 5.5 GHz, and (f) mode 2′ at 5.5 GHz.
(a)(b)(c)(d)(e)(f)According to the characteristic currents of the coupling mode shown in Figure4(c), the shape and loading position of NL is determined qualitatively, and different heights of arc NLs are loaded based on the coupling characteristic mode currents, just as is shown in Figure 5. The next step is to determine the specific parameters of NL quantitatively, and then the key parameters (H, W) of NL shown in Figure 5(a) are optimized using commercial software HFSS based on the antenna’s S parameter. The optimization process is given.Figure 5
Structure of antenna#1 with NL: (a) perspective view and (b) end view.
(a)(b)The variableH represents the height of NL. With the decrease of H, the resonance frequency, impedance matching, and isolation of the antenna at the low-frequency band do not change much, as shown in Figure 6. This is consistent with our original design. Just as can be observed from comparing characteristic currents before and after loading NL in Figures 4(a) and 4(b), the characteristic current at the low-frequency band does not change much after adding the NL. Therefore, the loaded NL will not affect the antenna of the low-frequency part too much. While at the high-frequency band, with the decrease of parameter H, the resonant frequency shifts to the right, but the bandwidth of S11 does not change much. The S21 decreases first and then increases, which means the isolation of the antenna gets better at first and then gets worse. The H value is determined from 10 mm to 11 mm based on the above analysis, and by further optimization, the optimal value of H is chosen as 10.1 mm.Figure 6
S-parameters of antenna#1 with different heights of the NL: (a) S11 and (b) S21.
(a)(b)Similarly, the width (W) of the NL has almost no effect on the S-parameters at the low frequency, as shown in Figure 7. While at the high-frequency band, with the increase of W, S11 slightly shifts to high frequency, and S21 becomes better first and then becomes worse. Reasonable compromise based on the S11 and S21, the optimal value of W is chosen as 0.5 mm based on the parameter scan result.Figure 7
S-parameters of antenna#1 with different widths of the NL: (a) S11 and (b) S21.
(a)(b)So parametersH and W mainly influence the antenna’s performance on the high-frequency band and have little influence on the low-frequency band, which is consistent with our analysis based on characteristic currents. The optimal values of H and W are chosen as 0.1 mm and 0.5 mm, respectively.The antenna#1 loaded with NL is shown in Figure5. The addition of NL changes the surface current distribution of the radiation element and thus affecting the matching of the antenna, just as shown in Figure 2. To compensate for this effect, the high-frequency radiation unit is designed to resonate at 5 GHz so that after the addition of NL, the resonance frequency of the whole antenna will be around the desired frequency of 5.5 GHz. It should be mentioned that although the distribution of characteristic current changes with the change of frequency, the distribution of characteristic current will remain relatively stable when the change of frequency is relatively small. In other words, we can still qualitatively guide the design of the NL (parameters such as position and shape) according to the characteristic current distribution of the coupling mode at the resonant frequency point of the original structure (without NL).Figures4(b), 4(d), and 4(f) show the characteristic current distribution of the antenna after adding NL. It can be seen that the loaded NL introduces a new current, whose current direction is opposite to that of the coupling mode (the directions of the mode current on the NL are indicated by gray arrows). It can also be seen from the distribution of characteristic current that the original coupling mode becomes uncoupling mode after the NL is added. This indicates that the loaded NL can improve the isolation effectively, just as shown in Figure 2. Results show that the isolation in the high-frequency band is improved by about 25 dB, and the low-frequency part is also improved a little. In addition, ECCs of the antenna were less than 0.3 in the working frequency bands, which means the MIMO antenna has good diversity gain performances [36, 37].


## 2.1. Introduction of TCM

The TCM provides a clear physical concept, which can essentially explain the radiation mechanism of an antenna and facilitate the guidance of antenna design, such as the essential physical characteristics of antenna structure and appropriate feed structure as well as the feed location to excite a characteristic mode (CM). More specific derivations of TCM and its application in antenna design are detailed in [33].The CMs of arbitrarily shaped perfectly electrically conducting (PEC) bodies can be obtained fromXJn=λnRJn, where λn is eigenvalues, Jn is eigenvectors or the characteristic currents, and R and X are real and imaginary Hermitian parts of the generalized impedance matrix Z = R + jX resulting from electric field integral equation (EFIE) [33]. The eigenvalue λn is a handy parameter because it can reveal the resonance and radiation information of its corresponding CM. In fact, there are several other preferred variables that can provide resonance and radiation information. The modal significance (MS), defined as MSn = |1/(1+ jλn)|, is the inherent and excitation source-independent property of each mode. It converts the variation range of eigenvalues [−∞, +∞] to [0, 1]. The characteristic mode is resonant when λn is zero, while MSn = 1. The CMs form a complete set of orthogonal modes so that the induced current (J) of a conducting object excited by an excitation source can be expanded as J=ΣαnJn, where αn is the modal weighting coefficients determined by the MSn, external excitation source, and characteristic current of the nth mode [33]. In the following section, the TCM analysis of the proposed antennas is carried out using the commercial simulation software FEKO.


## 2.2. TCM-Based NL Design

Figure1 shows the initial geometry of a MIMO antenna designed in this paper (named antenna#1), which consists of two symmetric antenna elements. The antenna unit is designed based on the traditional inverted L-shaped monopole antenna. By loading the horizontal radiation branch and bending it, the dual-band and miniaturization characteristics of the antenna are realized, respectively. The antenna is printed on an FR-4 substrate with a relative permittivity of 4.4, a loss tangent of 0.02, and a thickness of 1.6 mm. The antenna size is 54 mm × 32 mm × 1.6 mm.Figure 1
Structure of antenna#1 without NL: (a) perspective view and (b) end view.
(a)(b)The S-parameters of the MIMO antenna#1 are illustrated in Figure2. It can be seen that the mutual coupling without the NL is lower than −15 dB within 2.37–2.69 GHz while higher than −15 dB within 5.0–5.84 GHz. Therefore, an additional decoupling structure is needed to improve the isolation at the high-frequency band.Figure 2
Simulation of ECC (with NL) and S-parameters of antenna#1 with and without NL.The initial antenna structure is analyzed by TCM. Figure3 shows the MS of the significant modes of the antenna. MS is a good indicator to measure the coupling degree between each mode and the external excitation field and determine its radiation performance. In general, the mode with an MS value greater than 0.707 is considered the significant mode that plays an essential role in antenna radiation [33]. As can be seen from Figure 3, mode 1, mode 1’ and mode 2’ are significant modes at the frequency band of interest.Figure 3
MS for the dominant CMs of the MIMO antenna#1 without the NL.Figure4 gives the characteristic current distribution of significant modes. In the low-frequency band, mode 1 has current flowing from left to right, so mode 1 is defined as a coupling mode for this band. However, the coupling of the antenna at the low-frequency band is not strong, and there is no need to deal with it. It can be seen from Figure 4(c) that mode 1’ has a large amount of current flowing from the antenna unit on the left to the right, so this mode is defined as a coupling mode at the high-frequency band. Although mode 2’ is also a significant mode, it can be seen from the current distribution and flow direction (Figure 4(e)) that there is no current coupling between the two antenna elements, so this mode is defined as the uncoupling mode.Figure 4
Characteristic current distribution of the significant modes of antenna#1: (a) mode 1 at 2.45 GHz, (b) mode 1 at 2.45 GHz, (c) mode 1’ at 5.5 GHz, (d) mode 1’ at 5.5 GHz, (e) mode 2’ at 5.5 GHz, and (f) mode 2′ at 5.5 GHz.
(a)(b)(c)(d)(e)(f)According to the characteristic currents of the coupling mode shown in Figure4(c), the shape and loading position of NL is determined qualitatively, and different heights of arc NLs are loaded based on the coupling characteristic mode currents, just as is shown in Figure 5. The next step is to determine the specific parameters of NL quantitatively, and then the key parameters (H, W) of NL shown in Figure 5(a) are optimized using commercial software HFSS based on the antenna’s S parameter. The optimization process is given.Figure 5
Structure of antenna#1 with NL: (a) perspective view and (b) end view.
(a)(b)The variableH represents the height of NL. With the decrease of H, the resonance frequency, impedance matching, and isolation of the antenna at the low-frequency band do not change much, as shown in Figure 6. This is consistent with our original design. Just as can be observed from comparing characteristic currents before and after loading NL in Figures 4(a) and 4(b), the characteristic current at the low-frequency band does not change much after adding the NL. Therefore, the loaded NL will not affect the antenna of the low-frequency part too much. While at the high-frequency band, with the decrease of parameter H, the resonant frequency shifts to the right, but the bandwidth of S11 does not change much. The S21 decreases first and then increases, which means the isolation of the antenna gets better at first and then gets worse. The H value is determined from 10 mm to 11 mm based on the above analysis, and by further optimization, the optimal value of H is chosen as 10.1 mm.Figure 6
S-parameters of antenna#1 with different heights of the NL: (a) S11 and (b) S21.
(a)(b)Similarly, the width (W) of the NL has almost no effect on the S-parameters at the low frequency, as shown in Figure 7. While at the high-frequency band, with the increase of W, S11 slightly shifts to high frequency, and S21 becomes better first and then becomes worse. Reasonable compromise based on the S11 and S21, the optimal value of W is chosen as 0.5 mm based on the parameter scan result.Figure 7
S-parameters of antenna#1 with different widths of the NL: (a) S11 and (b) S21.
(a)(b)So parametersH and W mainly influence the antenna’s performance on the high-frequency band and have little influence on the low-frequency band, which is consistent with our analysis based on characteristic currents. The optimal values of H and W are chosen as 0.1 mm and 0.5 mm, respectively.The antenna#1 loaded with NL is shown in Figure5. The addition of NL changes the surface current distribution of the radiation element and thus affecting the matching of the antenna, just as shown in Figure 2. To compensate for this effect, the high-frequency radiation unit is designed to resonate at 5 GHz so that after the addition of NL, the resonance frequency of the whole antenna will be around the desired frequency of 5.5 GHz. It should be mentioned that although the distribution of characteristic current changes with the change of frequency, the distribution of characteristic current will remain relatively stable when the change of frequency is relatively small. In other words, we can still qualitatively guide the design of the NL (parameters such as position and shape) according to the characteristic current distribution of the coupling mode at the resonant frequency point of the original structure (without NL).Figures4(b), 4(d), and 4(f) show the characteristic current distribution of the antenna after adding NL. It can be seen that the loaded NL introduces a new current, whose current direction is opposite to that of the coupling mode (the directions of the mode current on the NL are indicated by gray arrows). It can also be seen from the distribution of characteristic current that the original coupling mode becomes uncoupling mode after the NL is added. This indicates that the loaded NL can improve the isolation effectively, just as shown in Figure 2. Results show that the isolation in the high-frequency band is improved by about 25 dB, and the low-frequency part is also improved a little. In addition, ECCs of the antenna were less than 0.3 in the working frequency bands, which means the MIMO antenna has good diversity gain performances [36, 37].


## 3. Another Similar Antenna Design and Porotype Verification

### 3.1. Design of Another Dual-Band Antenna

Using the same design method, a more complex MIMO antenna is designed and processed, which covers the 2.4 GHz and 5.8 GHz bands of WLAN.Similarly, the antenna unit is also composed of a bent monopole structure. The geometry of the antenna is depicted in Figure8 (named antenna#2). The left bend branch works at low frequency, while the right bend branch works at high frequency. The low-frequency part uses the antenna layout to obtain a good isolation degree, while the high-frequency part introduces the NL technology to improve the isolation degree. The antenna is also printed on an FR-4 dielectric substrate with a relative dielectric constant of 4.4 and a loss tangent angle of 0.02. The overall size is 50 mm × 48 mm, and the thickness is 0.8 mm.Figure 8
Overall structure of the MIMO antenna#2.The S-parameters of antenna#2 with and without loading NL are shown in Figure9. It can be seen that after the NL is loaded, the isolation of the antenna changes little at 2.4 GHz but increases by about 18 dB at 5.8 GHz.Figure 9
S-parameters of antenna#2 with and without NL: (a) S11 and (b) S21.
(a)(b)To confirm the design idea of using TCM to improve mutual coupling and the working mechanism of NL proposed above, the characteristic currents of significant modes for the antenna at 2.45 GHz and 5.8 GHz are given in Figure10. The significant mode at low frequency is mode 1. As can be seen from Figure 10(a), the characteristic current flow at 2.45 GHz is mainly from top to bottom, so there is very weak current coupling between antenna units, which indicates that the antenna has good isolation at low frequency.Figure 10
Characteristic current distribution of the significant modes of antenna#2: (a) mode 1 at 2.45 GHz, (b) mode 2 at 5.8 GHz, (c) mode 3 at 5.8 GHz, (d) mode 1 at 2.45 GHz, (e) mode 2 at 5.8 GHz, and (f) mode 3 at 5.8 GHz.
(a)(b)(c)(d)(e)(f)As is shown in Figure10(d), after the NL is added, characteristic current on NL cancels out, indicating that the isolation of the antenna at the low-frequency band will not change much. Figures 10(b) and 10(c) show the significant modes’ current distribution of the antenna at the high-frequency band; it is observed that the coupling between the antenna unit is mainly caused by mode 2. The current flow of mode 3 is primarily from top to bottom, just like mode 1, and has little effect on coupling. So mode 2 is defined as coupling mode, and mode 3 is defined as uncoupling mode. The loaded NL should generate a current flow in the opposite direction to mode 2 to achieve a decoupling effect.According to the direction of characteristic currents of mode 2 shown in Figure10(b), the shape and loading position of NL are determined qualitatively, just as shown in Figure 11. The next step is to determine the specific parameters of NL quantitatively, and then the key parameters (offset, L) of NL shown in Figure 11 are optimized using commercial software HFSS.Figure 11
Structure of antenna#2 with NL.The influences of the loading position of NL (offset) and the length of NL (L) on the S-parameter are analyzed. The variable offset represents the loading position of NL relative to the port. As can be seen from Figure 12, for the low-frequency band, with the increase of offset, the loading position of the NL is gradually away from the port; the bandwidth of S11 becomes wider; and the isolation becomes better. While for the high-frequency band, the notch curves of S11 and S21 move to high-frequency gradually with the increase of offset. So there is an optimal solution for variable offset, making the antenna cover the 5.8 GHz band and obtain an isolation degree greater than 15 dB in this band. We choose the optimal value of offset = 14 mm.Figure 12
S-parameter of antenna#2 with differentoffsets of the NL: (a) S11 and (b) S21.
(a)(b)The variableL represents the length of NL. As can be seen from Figure 13, for the low-frequency band, with L increase from 15 mm to 18 mm, impedance matching is improved, but it has almost no effect on S21. That is because the NL is loaded far away from the port, and the current on NL is weak. No matter how the length of NL changes, the current on the NL will always be weak, so L does not have much effect on S21 for the low-frequency band. For the high-frequency band, L has a significant influence on both S11 and S21, just as shown in Figure 13. As the variable L increases, the resonant point at the high-frequency band shifts to low frequency. Similarly, as the value of L increases, the notch curve of S21 moves towards low frequency. Therefore, variable L has an optimal value to cover the 2.4 GHz and 5.8 GHz bands effectively. By further optimization, the optimal value of L is chosen as 16.8 mm.Figure 13
S-parameter of antenna#2 with different lengths of the NL: (a) S11 and (b) S21.
(a)(b)The characteristic current distribution after adding NL is shown in Figures10(d), 10(e), and 10(f). As mentioned before, it has little influence on the antenna at the low-frequency band. The coupling of the antenna is mainly generated by mode 2. After adding NL, it can be seen from Figure 10(e) that part of the current that used to flow from the left to the right of the antenna becomes a loop current. Moreover, the current generated on NL flows in opposite direction to the current causing coupling, indicating that the added NL can improve the isolation of the antenna effectively. For modes 1 and 3, the currents generated on NL cancel each other out, with little effect on antenna isolation. It is consistent with Figure 9; the isolation in the 5.8-GHz band improved a lot while in the 2.4 GHz band did not change much. Figure 14 displays the radiation patterns of MIMO antenna with and without NL; the loaded NL will have some effect on the far-field patterns and slightly distort the radiation pattern for the xz-plane in the 5.8 GHz band.Figure 14
Simulated normalized radiation patterns of antenna #2 with and without NL.Gθ with NL, GΦ with NL, Gθ without NL, and GΦ without NL. (a) xz-plane at 2.4 GHz, (b) xz-plane at 5.8 G, (c) yz-plane at 2.4 GHz, and (d) yz-plane at 5.8 GHz.
(a)(b)(c)(d)


### 3.2. Experimental Results and Discussion

The proposed dual-band MIMO antenna#2 has been fabricated as shown in Figure15. The S-parameters have been measured with a vector network analyzer. As can be seen from Figure 9, the measured result is consistent with the simulated one. There is a slight shift at the higher resonant frequency, possibly due to the fabrication and experimental tolerances.Figure 15
Fabricated prototype of the dual-band antenna#2: (a) testing environment and (b) front view.
(a)(b)Figure16 displays the simulated and measured normalized radiation patterns of antenna#2 (one monopole is excited, while the other is terminated with a 50 Ω load) at 2.4 GHz and 5.8 GHz, and a good agreement is observed. The slight differences are caused by the influences of feed cables and the misalignment of the antenna resonant frequency. It can be observed that both xz and yz planes have similar omnidirectional radiation patterns, which means the antenna can receive or transmit signals from all directions.Figure 16
Simulated and measured normalized radiation patterns of antenna#2 at 2.4 GHz and 5.8 GHz. HFSS Gθ,  HFSS GΦ,  Meas Gθ, and  Meas GΦ. (a) xz-plane at 2.4 GHz, (b) xz-plane at 5.8 GHz, (c) yz-plane at 2.4 GHz, and (d) yz-plane at 5.8 GHz.
(a)(b)(c)(d)The radiation efficiency and total efficiency of antennas#2 with and without NL are compared in Table1. As shown in Table 1, the radiation efficiencies of the antennas at both bands are almost equal to 90%. Thus, the loaded NL reduces the mutual coupling to decrease the correlation of the two elements to maximize the MIMO performance without introducing additional loss to the radiation efficiency. Moreover, the proposed NL can efficiently enhance the isolation at a high frequency between MIMO elements so that the total efficiency at the high frequency of the proposed MIMO antennas can be improved. The total efficiency improvement with the NL is observed clearly at high frequency, while there is no significant change at low frequencies. The relationship between total efficiency and radiant efficiency is as follows:(1)ηtotal=ηrad1−S112−S212.Table 1
Comparison of the radiation efficiency and total efficiency of antenna#2 w/wo NL.
At low frequencyAt high frequencyRadiation efficiency (%)Total efficiency (%)Radiation efficiency (%)Total efficiency (%)wo NL94.986.087.369.9w NL93.587.086.776.0To further validate the capability and performance of MIMO antenna#2, the envelope correlation coefficient (ECC), diversity gain (DG), total active reflection coefficient (TARC), and mean channel capacity have been evaluated.The pattern diversity performance of MIMO antenna#2 can be evaluated by the ECC, which is an important parameter to measure the fading ability of the antenna signal and signal transmission rate [36, 37]. The ECC calculation method adopted in this paper is based on radiation patterns given by (2), where Fiθ,φ or Fjθ,φ means the far-field radiation patterns of the antenna i or j fed separately while other ports were connected with matching loads.(2)ρci,j=∬4πFiθ,φ⋅Fj∗θ,φdΩ2∬4πFiθ,φ2dΩ⋅∬4πFjθ,φ2dΩ.The DG of the proposed MIMO antenna can be calculated using (3) to evaluate the diversity performance of the proposed antenna [38]. Figure 17 shows the measured ECC and DG of antenna#2 with and without loading NL. It can be observed that the loaded NL significantly improves the ECC and DG values of the proposed antenna at the high-frequency band. Furthermore, the ECC was below 0.3 across both bands, which is suitable for MIMO applications, and the DG of the antenna is larger than 9.5 dB in the frequency band of interest.(3)DG=101−ECC2.Figure 17
The ECC and DG of the proposed antenna#2 with and without NL: (a) 2.4 GHz and (b) 5.8 GHz.
(a)(b)TARC is defined as the ratio of the square root of total reflected power divided by the square root of total incident power [38, 39]. The TARC of the 2-port MIMO antenna can be calculated from the S-parameters using the following formula:(4)TARC=S11+S122+S21+S2222.The measured values of TARC are shown in Figure18. It is observed from Figure 18 that the loaded NL obviously improves the TARC value of the proposed antenna at dual frequency bands and the value of TARC for the proposed antenna is less than −30 dB for the working frequency bands.Figure 18
The TARC of antenna#2 with and without NL: (a) 2.4 GHz and (b) 5.8 GHz.
(a)(b)The mean channel capacities of antenna#2 with and without NL as a function of the SNR at 2.45 GHz and 5.8GHz are shown in Figure19 [37]. It can be seen that the mean channel capacities of the antenna with and without NL are nearly the same at 2.45 GHz and slightly lower than the ideal uncorrelated MIMO configuration. However, for the 5.8GHz band, the mean channel capacity becomes better and closer to the ideal uncorrelated configuration after loading NL.Figure 19
The mean channel capacities of antenna#2 with and without NL.Finally, to highlight the advantages and innovation of the proposed antenna, comparisons between the proposed antenna and the state-of-the-art MIMO antenna are given in Table2. The comparison almost represents the current state-of-the-art decoupling technology for MIMO antenna, although it is not comprehensive. The comparison results show that the antenna achieves a good balance in size, isolation, bandwidth, edge-to-edge distance, number of ports, and technical complexity.Table 2
Performance comparisons with the previously published literature.
Ref.Decoupling methodMax decoupling improvementNumber of portsBandwidthBandsEdge-to-edge distanceComplexity[3]Decoupling network15 dB2NarrowSingle0.055λ0Yes[5]Decoupling network10 dB2WideSingle0.084λ0Yes[8]Metamaterial32 dB for X-band27 dB for ku-band26 dB for K-band4WideSix0.26λ0Yes[9]Fractal metamaterial EBG17 dB for S1237 dB for S1317 dB for S144WideThree0.5λ0Yes[12]EBG10 dB2NarrowSingle0.5λ0Yes[13]Uniplanar compact EBG14 dB2NarrowSingle0.5λ0Yes[14]Fractal UC-EBG16 dB2NarrowSingle0.22λ0Yes[17]DGS40 dB2NarrowSingle0.031λ0No[18]DGS17.4 dB2NarrowSingle0.23λ0No[19]SRR10 dB2NarrowSingle0.25λ0Yes[21]NL23.7 dB2WideSingle0.079λ0No[22]NL16 dB2NarrowSingle0.114λ0NoThis workTCM + NL18 dB2NarrowTwo0.033λ0No


## 3.1. Design of Another Dual-Band Antenna

Using the same design method, a more complex MIMO antenna is designed and processed, which covers the 2.4 GHz and 5.8 GHz bands of WLAN.Similarly, the antenna unit is also composed of a bent monopole structure. The geometry of the antenna is depicted in Figure8 (named antenna#2). The left bend branch works at low frequency, while the right bend branch works at high frequency. The low-frequency part uses the antenna layout to obtain a good isolation degree, while the high-frequency part introduces the NL technology to improve the isolation degree. The antenna is also printed on an FR-4 dielectric substrate with a relative dielectric constant of 4.4 and a loss tangent angle of 0.02. The overall size is 50 mm × 48 mm, and the thickness is 0.8 mm.Figure 8
Overall structure of the MIMO antenna#2.The S-parameters of antenna#2 with and without loading NL are shown in Figure9. It can be seen that after the NL is loaded, the isolation of the antenna changes little at 2.4 GHz but increases by about 18 dB at 5.8 GHz.Figure 9
S-parameters of antenna#2 with and without NL: (a) S11 and (b) S21.
(a)(b)To confirm the design idea of using TCM to improve mutual coupling and the working mechanism of NL proposed above, the characteristic currents of significant modes for the antenna at 2.45 GHz and 5.8 GHz are given in Figure10. The significant mode at low frequency is mode 1. As can be seen from Figure 10(a), the characteristic current flow at 2.45 GHz is mainly from top to bottom, so there is very weak current coupling between antenna units, which indicates that the antenna has good isolation at low frequency.Figure 10
Characteristic current distribution of the significant modes of antenna#2: (a) mode 1 at 2.45 GHz, (b) mode 2 at 5.8 GHz, (c) mode 3 at 5.8 GHz, (d) mode 1 at 2.45 GHz, (e) mode 2 at 5.8 GHz, and (f) mode 3 at 5.8 GHz.
(a)(b)(c)(d)(e)(f)As is shown in Figure10(d), after the NL is added, characteristic current on NL cancels out, indicating that the isolation of the antenna at the low-frequency band will not change much. Figures 10(b) and 10(c) show the significant modes’ current distribution of the antenna at the high-frequency band; it is observed that the coupling between the antenna unit is mainly caused by mode 2. The current flow of mode 3 is primarily from top to bottom, just like mode 1, and has little effect on coupling. So mode 2 is defined as coupling mode, and mode 3 is defined as uncoupling mode. The loaded NL should generate a current flow in the opposite direction to mode 2 to achieve a decoupling effect.According to the direction of characteristic currents of mode 2 shown in Figure10(b), the shape and loading position of NL are determined qualitatively, just as shown in Figure 11. The next step is to determine the specific parameters of NL quantitatively, and then the key parameters (offset, L) of NL shown in Figure 11 are optimized using commercial software HFSS.Figure 11
Structure of antenna#2 with NL.The influences of the loading position of NL (offset) and the length of NL (L) on the S-parameter are analyzed. The variable offset represents the loading position of NL relative to the port. As can be seen from Figure 12, for the low-frequency band, with the increase of offset, the loading position of the NL is gradually away from the port; the bandwidth of S11 becomes wider; and the isolation becomes better. While for the high-frequency band, the notch curves of S11 and S21 move to high-frequency gradually with the increase of offset. So there is an optimal solution for variable offset, making the antenna cover the 5.8 GHz band and obtain an isolation degree greater than 15 dB in this band. We choose the optimal value of offset = 14 mm.Figure 12
S-parameter of antenna#2 with differentoffsets of the NL: (a) S11 and (b) S21.
(a)(b)The variableL represents the length of NL. As can be seen from Figure 13, for the low-frequency band, with L increase from 15 mm to 18 mm, impedance matching is improved, but it has almost no effect on S21. That is because the NL is loaded far away from the port, and the current on NL is weak. No matter how the length of NL changes, the current on the NL will always be weak, so L does not have much effect on S21 for the low-frequency band. For the high-frequency band, L has a significant influence on both S11 and S21, just as shown in Figure 13. As the variable L increases, the resonant point at the high-frequency band shifts to low frequency. Similarly, as the value of L increases, the notch curve of S21 moves towards low frequency. Therefore, variable L has an optimal value to cover the 2.4 GHz and 5.8 GHz bands effectively. By further optimization, the optimal value of L is chosen as 16.8 mm.Figure 13
S-parameter of antenna#2 with different lengths of the NL: (a) S11 and (b) S21.
(a)(b)The characteristic current distribution after adding NL is shown in Figures10(d), 10(e), and 10(f). As mentioned before, it has little influence on the antenna at the low-frequency band. The coupling of the antenna is mainly generated by mode 2. After adding NL, it can be seen from Figure 10(e) that part of the current that used to flow from the left to the right of the antenna becomes a loop current. Moreover, the current generated on NL flows in opposite direction to the current causing coupling, indicating that the added NL can improve the isolation of the antenna effectively. For modes 1 and 3, the currents generated on NL cancel each other out, with little effect on antenna isolation. It is consistent with Figure 9; the isolation in the 5.8-GHz band improved a lot while in the 2.4 GHz band did not change much. Figure 14 displays the radiation patterns of MIMO antenna with and without NL; the loaded NL will have some effect on the far-field patterns and slightly distort the radiation pattern for the xz-plane in the 5.8 GHz band.Figure 14
Simulated normalized radiation patterns of antenna #2 with and without NL.Gθ with NL, GΦ with NL, Gθ without NL, and GΦ without NL. (a) xz-plane at 2.4 GHz, (b) xz-plane at 5.8 G, (c) yz-plane at 2.4 GHz, and (d) yz-plane at 5.8 GHz.
(a)(b)(c)(d)


## 3.2. Experimental Results and Discussion

The proposed dual-band MIMO antenna#2 has been fabricated as shown in Figure15. The S-parameters have been measured with a vector network analyzer. As can be seen from Figure 9, the measured result is consistent with the simulated one. There is a slight shift at the higher resonant frequency, possibly due to the fabrication and experimental tolerances.Figure 15
Fabricated prototype of the dual-band antenna#2: (a) testing environment and (b) front view.
(a)(b)Figure16 displays the simulated and measured normalized radiation patterns of antenna#2 (one monopole is excited, while the other is terminated with a 50 Ω load) at 2.4 GHz and 5.8 GHz, and a good agreement is observed. The slight differences are caused by the influences of feed cables and the misalignment of the antenna resonant frequency. It can be observed that both xz and yz planes have similar omnidirectional radiation patterns, which means the antenna can receive or transmit signals from all directions.Figure 16
Simulated and measured normalized radiation patterns of antenna#2 at 2.4 GHz and 5.8 GHz. HFSS Gθ,  HFSS GΦ,  Meas Gθ, and  Meas GΦ. (a) xz-plane at 2.4 GHz, (b) xz-plane at 5.8 GHz, (c) yz-plane at 2.4 GHz, and (d) yz-plane at 5.8 GHz.
(a)(b)(c)(d)The radiation efficiency and total efficiency of antennas#2 with and without NL are compared in Table1. As shown in Table 1, the radiation efficiencies of the antennas at both bands are almost equal to 90%. Thus, the loaded NL reduces the mutual coupling to decrease the correlation of the two elements to maximize the MIMO performance without introducing additional loss to the radiation efficiency. Moreover, the proposed NL can efficiently enhance the isolation at a high frequency between MIMO elements so that the total efficiency at the high frequency of the proposed MIMO antennas can be improved. The total efficiency improvement with the NL is observed clearly at high frequency, while there is no significant change at low frequencies. The relationship between total efficiency and radiant efficiency is as follows:(1)ηtotal=ηrad1−S112−S212.Table 1
Comparison of the radiation efficiency and total efficiency of antenna#2 w/wo NL.
At low frequencyAt high frequencyRadiation efficiency (%)Total efficiency (%)Radiation efficiency (%)Total efficiency (%)wo NL94.986.087.369.9w NL93.587.086.776.0To further validate the capability and performance of MIMO antenna#2, the envelope correlation coefficient (ECC), diversity gain (DG), total active reflection coefficient (TARC), and mean channel capacity have been evaluated.The pattern diversity performance of MIMO antenna#2 can be evaluated by the ECC, which is an important parameter to measure the fading ability of the antenna signal and signal transmission rate [36, 37]. The ECC calculation method adopted in this paper is based on radiation patterns given by (2), where Fiθ,φ or Fjθ,φ means the far-field radiation patterns of the antenna i or j fed separately while other ports were connected with matching loads.(2)ρci,j=∬4πFiθ,φ⋅Fj∗θ,φdΩ2∬4πFiθ,φ2dΩ⋅∬4πFjθ,φ2dΩ.The DG of the proposed MIMO antenna can be calculated using (3) to evaluate the diversity performance of the proposed antenna [38]. Figure 17 shows the measured ECC and DG of antenna#2 with and without loading NL. It can be observed that the loaded NL significantly improves the ECC and DG values of the proposed antenna at the high-frequency band. Furthermore, the ECC was below 0.3 across both bands, which is suitable for MIMO applications, and the DG of the antenna is larger than 9.5 dB in the frequency band of interest.(3)DG=101−ECC2.Figure 17
The ECC and DG of the proposed antenna#2 with and without NL: (a) 2.4 GHz and (b) 5.8 GHz.
(a)(b)TARC is defined as the ratio of the square root of total reflected power divided by the square root of total incident power [38, 39]. The TARC of the 2-port MIMO antenna can be calculated from the S-parameters using the following formula:(4)TARC=S11+S122+S21+S2222.The measured values of TARC are shown in Figure18. It is observed from Figure 18 that the loaded NL obviously improves the TARC value of the proposed antenna at dual frequency bands and the value of TARC for the proposed antenna is less than −30 dB for the working frequency bands.Figure 18
The TARC of antenna#2 with and without NL: (a) 2.4 GHz and (b) 5.8 GHz.
(a)(b)The mean channel capacities of antenna#2 with and without NL as a function of the SNR at 2.45 GHz and 5.8GHz are shown in Figure19 [37]. It can be seen that the mean channel capacities of the antenna with and without NL are nearly the same at 2.45 GHz and slightly lower than the ideal uncorrelated MIMO configuration. However, for the 5.8GHz band, the mean channel capacity becomes better and closer to the ideal uncorrelated configuration after loading NL.Figure 19
The mean channel capacities of antenna#2 with and without NL.Finally, to highlight the advantages and innovation of the proposed antenna, comparisons between the proposed antenna and the state-of-the-art MIMO antenna are given in Table2. The comparison almost represents the current state-of-the-art decoupling technology for MIMO antenna, although it is not comprehensive. The comparison results show that the antenna achieves a good balance in size, isolation, bandwidth, edge-to-edge distance, number of ports, and technical complexity.Table 2
Performance comparisons with the previously published literature.
Ref.Decoupling methodMax decoupling improvementNumber of portsBandwidthBandsEdge-to-edge distanceComplexity[3]Decoupling network15 dB2NarrowSingle0.055λ0Yes[5]Decoupling network10 dB2WideSingle0.084λ0Yes[8]Metamaterial32 dB for X-band27 dB for ku-band26 dB for K-band4WideSix0.26λ0Yes[9]Fractal metamaterial EBG17 dB for S1237 dB for S1317 dB for S144WideThree0.5λ0Yes[12]EBG10 dB2NarrowSingle0.5λ0Yes[13]Uniplanar compact EBG14 dB2NarrowSingle0.5λ0Yes[14]Fractal UC-EBG16 dB2NarrowSingle0.22λ0Yes[17]DGS40 dB2NarrowSingle0.031λ0No[18]DGS17.4 dB2NarrowSingle0.23λ0No[19]SRR10 dB2NarrowSingle0.25λ0Yes[21]NL23.7 dB2WideSingle0.079λ0No[22]NL16 dB2NarrowSingle0.114λ0NoThis workTCM + NL18 dB2NarrowTwo0.033λ0No


## 4. Conclusions

A TCM-based design procedure is proposed for the design of an NL in MIMO antenna configuration. By analyzing the characteristic current direction of the initial antenna structure, the coupling mode is first identified, and the form and position of the NL were determined qualitatively based on the characteristic currents of the coupling mode. Then, HFSS was used to optimize the critical parameters of NL and determine it quantitatively. Finally, a designed NL is loaded to introduce opposite currents to the coupling mode currents, thus reducing mutual coupling. The measured results of the fabricated prototype show that the isolation of antenna #2 at 5.8 GHz is improved by about 18 dB through adding NL, and the total efficiency has also been improved (69.9% to 76.0%); the impedance bandwidths of the antenna for S11 ≤ -10 dB are 16.9% (2.27–2.69 GHz) and 4.2% (5.6–5.84 GHz), respectively; the ECC is less than 0.3 in the operating frequency bands. The results are in reasonable agreement between measured and simulated results, demonstrating that the proposed TCM-based design procedure for NL can be used in other MIMO antenna designs.



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*Source: 9669114-2022-07-30.xml*