Single element antenna

In Fig. 1, the single flexible antenna is configured, which is etched on a 24 × 30 × 0.1 mm³ LCP substrate, with a dielectric constant = 2.9 and loss tangent = 0.002. This design is a slot antenna, which is composed of a circular monopole, a complementary split ring resonator (CSRR) slot, and a ring branch forming the antenna.

Figure 1. Single flexible UWB antenna design process: (a) structure, (b) schematic of proposed antenna, and (c) S₁₁ of the single antenna.

In this design, the total length of each CSRR slot and ring branch is set to one-half of the guide wavelength:

(1)\begin{equation}L = \frac{{{\lambda _g}}}{2} = \frac{C}{{2{f_{notch}}\sqrt {{\varepsilon _{eff}}} }},\end{equation}

(2)\begin{equation}{\varepsilon _{eff}} = \frac{{{\varepsilon _r} + 1}}{2} + \frac{{{\varepsilon _r} - 1}}{2}{\left( {1 + \frac{{12h}}{{{w_f}}}} \right)^{ - 0.5}}.\end{equation}

In these formulas, C means the light speed, f _notch means the center frequency of the notch band, Ɛ _r represents the relative dielectric constant of the proposed substrate, and Ɛ _eff represents the effective value of the dielectric constant.

After optimization in HFSS, the optimal parameter values in Fig. 1(b) are as follows: L1 = 30 mm, L2 = 15 mm, Lf = 6.25 mm, g = 1.35 mm, Wf = 1.5 mm, W1 = 24 mm, W2 = 22 mm, d = 0.2 mm, R1 = 4.6 mm, R2 = 3.7 mm, and R3 = 6.6 mm.

Figure 1(c) plots S-parameters for the above antennas. The Ant1 is a circular monopole antenna, which the impedance bandwidth is 2.65–11.97 GHz. Then, by adding a ring branch on the Ant1, the Ant2 has the first notch band at 7.5 GHz. Finally, by loading the outer and inner rings of the CSRR on the Ant2, respectively, the Ant3 has another notch band at 3.5 GHz, and the Ant4 has the last notch band at 5.25 GHz (Figure 2).

Figure 2. Distributions of surface current at: (a) 3.5 GHz, (b) 5.25 GHz, and (c) 7.5 GHz.

Four-element MIMO antenna

Figure 3(a) illustrates the structure of the entire system which is etched on a 65 × 65 × 0.1 mm³ LCP substrate. To increase isolation between four antenna units, a cross-shaped stub is placed in the middle, and the grounds of four units are not connected.

Figure 3. Four-element antenna: (a) schematic and (b) manufactured antenna.

The parameter values depicted in Fig. 3(a) are as follows: d1 = 1 mm, L3 = 59.3 mm, L = 65 mm, W = 65 mm, α = 9°. The angle β between the cross-shaped stub is 91 degrees.

Decoupling structure design process

Decoupling structure design process is shown in Fig. 4. For simplicity, only S11, S21, and S31 are studied since they are symmetrically arranged. In Fig. 4(a), four units are placed orthogonally with each other without any isolation in Ant5. Ant6 is the evolution of Ant5 with one cross-shaped stub in the center of the substrate. Ant7 has two paralleled cross-shaped stubs in the middle of the substrate. And, Ant8 has three paralleled cross-shaped stubs in the middle of the substrate.

Figure 4. Comparison of four-element antenna: (a) evolution of four-element antenna, (b) S11, (c) S21, (d) S31, and (e) ECC.

Through Fig. 4(b), it is clear that after adding the cross-shaped stub, the antenna can still cover the working frequency ranging from 2.58 to 11.32 GHz. But the second notch band in Ant5 and Ant6 is lower than others. To achieve a better notch band and a wider impedance bandwidth, the number of cross-shaped stubs is increased.

As depicted in Fig. 4(c) and (d), whether with or without the cross-shaped stub structure, the frequency range of S21 less than −20 dB is almost unchanged. However, the change of S31 is obvious. After loading the cross-shaped stub, especially with three paralleled stubs, the value of S31 in the low frequency part has dropped from about −15 dB to below −20 dB. The cross-shaped stub acts as a reflector to effectively improve the isolation and reduce electromagnetic coupling between four ports, especially the diagonal units.

Envelope correlation coefficient (ECC) generally characterizes the relationship between two elements, so MIMO systems will use multiple sets of ECC to characterize the independence between antennas. In Fig. 4(e), it can be easily found that all values of ECC are lower than 0.1 and the ECC in Ant8 is better than others. As a result, three paralleled cross-shaped stubs are chosen for better antenna performance.

Figure 5 shows the surface current distribution with/without the cross-shaped stub at 5.5 GHz. From Fig. 5(a), it can be seen that in the absence of the cross-shaped stub, a large amount of current is coupled to the other ports. In contrast, in Fig. 5(b), when a cross-shaped stub is used, most of the current stops flowing to other ports, and the port isolation is greatly improved.

Figure 5. Surface current distributions: (a) without stub and (b) with stub.

MIMO antenna with connected ground

Four-port MIMO antenna with connected ground is also designed and analyzed.

In Fig. 6(c), when the isolation structure is connected to four units, the simulated bandwidth of the antenna is 2.45–10.68 GHz, filtering out three notch frequency bands of 3.06–3.98, 4.51–5.28, and 7.39–8.59 GHz, which can still filter WiMAX signals at 3.5 GHz, WLAN signals at 5.25 GHz and X-band signals at 7.5 GHz. The isolation in the entire working frequency is better than 15 dB.

Figure 6. Different relative positions between decoupling structures and antenna: (a) α = 9°, (b) α = 11°, and (c) α = 13°.

Due to the fact that the angle β between the cross-shaped stub is 91 degrees, when the decoupling structure is rotated centered around the midpoint of the substrate, three situations occur in Fig. 6. When the parameter α is 9 degrees, the isolation stubs are not connected with four elements. And when the parameter α is 11 degrees, the isolation stubs are connected with two diagonal elements. Finally, when the parameter α is 13 degrees, the isolation stubs are connected with four elements, respectively.

The influence of different α on S11, S21, and S31 is plotted in Fig. 7, adjusting α from 9 to 13 degrees. From Fig. 7(a), as α increasing, the impedance bandwidth of the antenna becomes narrow, and the second notch band shifts to the left slightly. From Fig. 7(b), when the frequency is from 2.3 to 3.3 GHz, S21 is slightly fluctuating around −20 dB and the isolation in the other band is all below −20 dB. It can be found in Fig. 7(c) that different relative positions have little influence on S31.

Figure 7. Different S-parameters when α equals to different values: (a) S11, (b) S21, and (c) S31.

S-parameter

MIMO antenna without connected ground was finally fabricated. S-parameters were measured using an Agilent E8362B network analyzer. Port 1 is excited during the measurement, while the rest ports are connected to 50-ohm loads. It can be seen in Fig. 8(a) that the measured return loss of that antenna is 2.54–10.69 GHz, except for the three frequency bands that fall between 2.54 and 10.69 GHz, namely 2.81–3.85, 5.11–5.98, and 7.34–8.69 GHz. As a result, the antenna can filter WiMAX signals at 3.5 GHz, WLAN signals at 5.5 GHz, and X-band signals at 8.1 GHz. According to Fig. 8(b), it is clear that the measured parameters are better than the simulated ones. In the entire band, measured S21 and S31 are all less than −22 dB.

Figure 8. Antenna measured and simulated results. (a) S11 of simulation and measurement, (b) isolation of simulation and measurement, (c) when Port 1 is excited, the location of E-plane and H-plane, (d) measured S-parameters of antenna, respectively, bent along different radius R at E-plane, (e) measured S-parameters of antenna, respectively, bent along different radius R at H-plane, and (f) S-parameters when antenna is on human body.

To clarify the bending characteristics of the MIMO antenna, the entire design was bent both along the E-plane and H-plane, with bending radii of 30 and 45 mm, respectively. When port 1 is excited, the E-plane and H-plane is shown in Fig. 8(c). From Fig. 8(d) and (e), it is obvious that the antenna’s S-parameters are influenced by bending conditions. Bending along the E-plane has a greater impact on the antenna’s return loss than along the H-plane. Bending along the E-plane, the isolations are all better than 24 dB. Bending along the H-plane, the isolations are all better than 21 dB. As a result, under bending conditions, this MIMO system exhibits good performances.

In Fig. 8(f), the S-parameters are measured when the antenna is set on the human body. When the processed antenna system is attached to different parts of human body, such as the arm, thigh, and chest, respectively, the S-parameters are measured. As a result, the measured notch bands become narrow, especially at the high frequency band. But WiMAX, WLAN, and X-band notch bands still remain covered. The isolations of the antenna are all better than 30 dB.

Radiation patterns

Three frequency points of 4.5, 6, and 9.3 GHz are selected as the test frequency points of the normalized far-field radiation pattern of the antenna. In Fig. 9, each figure contains the simulated and measured radiation patterns of the co-planar polarization and cross polarization of the E-plane and the H-plane. It can be observed from the figure that the proposed antenna has good radiation performance, except for some deteriorations in the high-frequency state due to imperfect testing environment, but this does not affect the ability of the antenna to receive and transmit signals.

Figure 9. Simulated and measured radiation patterns: (a) 4.5, (b) 6, and (c) 9.3 GHz.

Gain and diversity performance

It can be seen from the Fig. 10(a) that in the UWB range, except for the three stop bands, the gain changes gently, and the measured gain varies between 3.6 and 6.87 dB.

Figure 10. Measured and simulated results: (a) gain, (b) ECC, and (c) DG.

To assess the correlation between MIMO antenna channels, ECC and diversity gain (DG) can be introduced. In general, the calculated ECC values are more accurate by equation (3) based on far-field radiation [Reference Blanch Boris, Romeu Robert and Corbella Sanahuja14] than equation (4) with S-parameters [Reference Zhang, Du and Wang15], and the DG can be estimated by equation (5) [Reference Tian, Lau and Ying16]. Figure 10(b) indicates that the ECC value in the UWB frequency band is less than 0.05 except for the three stopbands. The DG curve in Fig. 10(c) shows that DG is greater than 9.999 except for the three stopbands in the operating frequency band. It is evident from all of the above that the proposed antenna has good independence.

(3)\begin{equation}{\rho _e}\left( {i,j,N} \right) = {\left| {\frac{{\sum \nolimits_{n = 1}^NS_{i,n}^*{S_{n,j}}}}{{\left|{\prod \nolimits_{k = i,j}\left( {1 - \sum \nolimits_{n = 1}^NS_{k,n}^*{S_{n,k}}} \right)} \right|}^{\frac{1}{2}}}} \right|}^2,\end{equation}

(4)\begin{equation}{{{\rho }}_{\text{e}}}\left( {{\text{i}},{\text{j}}} \right) = \frac{{{{\left| {\mathop \iint \nolimits_{4{{\pi }}}^{ } {{{{\vec{\text{F}}}}}_{\text{i}}}\left( {{{\theta }},{{\varphi }}} \right) \cdot {{{{\vec {\text{F}}}}}_{\text{j}}}\left( {{{\theta }},{{\varphi }}} \right){\text{d}\Omega }} \right|}^2}}}{{\mathop \iint \nolimits_{4{{\pi }}}^{ } {{\left| {{{{{\vec{\text{F}}}}}_{\text{i}}}\left( {{{\theta }},{{\varphi }}} \right)} \right|}^2}{\text{d}\Omega } \cdot \mathop \iint \nolimits_{4{{\pi }}}^{ } {{\left| {{{{{\vec{\text{F}}}}}_{\text{j}}}\left( {{{\theta }},{{\varphi }}} \right)} \right|}^2}{\text{d}\Omega }}}\end{equation}

(5)\begin{equation}{\text{DG}} = 10\sqrt {1 - {{\left( {{\text{ECC}}} \right)}^2}} .\end{equation}

The total active reflection coefficient (TARC) is introduced to reflect the behavior of the MIMO antenna, which can reflect the coupling of the MIMO system. For a four-element antenna system, its calculation formula is as follows [Reference Pandit, Mohan and Ray17]:

(6)\begin{equation}{\text{TARC}} = {N^{ - 0.5}}\sqrt[\phantom{4}]{\sum\limits_N^{i = 1} {{\left| {\sum \limits_N^{k = 1} {S_{ik}}{e^{\,j{\theta _{k - 1}}}}} \right|}^2}} ,\end{equation}

where N is the number of antenna and denotes the phase angle of the excitation source input by the antenna. Figure 11 shows the simulated and measured TARC curves of the antenna when α = 0°, 60°, 120°, and 180°, respectively. It can be observed that the simulated TARC is similar to the simulated return loss, and the measured TARC is similar to the measured return loss. It shows that the coupling effect of the antenna is low and the radiation efficiency of the antenna is relatively high.

Figure 11. Simulated and measured TARC of the proposed antenna.

SAR

The specific absorption rate (SAR) represents the sum of electromagnetic radiation absorbed by human tissue in a given time period [Reference Pei, Du, Shi and Peng18]. The simulated SAR of the antenna is calculated by HFSS 18.0 software. The structure of the simulated human tissue model is depicted in Fig. 12. The total size of the model is 75 mm × 75 mm × 40 mm. The distance between the antenna system and the human body model is H1. The input power is 0.1 w, the variables H1 = 3 mm and 5 mm, and the simulated SAR values at 4.2, 6, and 9.2 GHz are shown in Table 1. It can be found from Table 1 that the simulated SAR values are far lower than the EU standard of 2 W/kg/10 g organization, which shows that the radiation energy of the antenna has a particularly small impact on human tissues (Table 2).

Figure 12. Model of human body tissue.

Table 1. Maximum SAR values on various conditions

Table 2. The parameters of human body tissue