Design for the proposed antenna

Antenna structure and principle

Figure 1(a) shows the positions of antennas for a MIMO antenna array in a mobile phone. The size of the mobile phone is 150 mm (length) × 75 mm (width) × 7 mm (height). The blue part on the back of the FR4 substrate that is 0.8 mm thick is the system ground plane (ε _r = 4.4, tanδ = 0.02). The antennas for the proposed 12 × 12 MIMO antenna array are placed on two side edges of the mobile phone. Figure 1(b) and (c) shows the geometric and the detail parameters for the proposed single antenna element. Figure 1(b) and (c), respectively, shows the front view and the lateral view of the proposed single antenna element. The single antenna element is composed of a serpentine-structure loop antenna and an inverted-L feeding structure. The serpentine-structure loop antenna has a resonance frequency of 3.5 GHz. The length of the loop antenna is 43.8 mm, which is around half the wavelength of 3.5 GHz.

Figure 1.

(a) The position of the MIMO antenna array in a mobile phone; the detail parameters for the proposed single antenna element in (b) the front view and (c) the lateral view.

The inverted-L feeding structure, which is a capacitive coupling structure, is connected to a 50 Ω transmission line. In Fig. 1(b) and (c), the red rectangle is the feeding point for the proposed antenna and the blue area is the ground plane in the mobile phone. The size of a single antenna element is 5.85 × 4.9 mm² (0.068λ ₀ × 0.057λ ₀). The width of all lines for the proposed antenna is 0.2 mm, except lines that are marked with a yellow T, which are 0.3 mm, and all gaps between line and line of the antenna are 0.25 mm except for gaps that are marked with a red G, which are 0.3 mm, as shown in Fig. 1(c). The simulated reflection coefficients for the proposed MIMO antenna array are shown in Fig. 2, and the 6-dB impedance bandwidth covers 3.4–3.6 GHz.

Figure 2.

Reflection coefficients for the proposed MIMO antenna array.

Antenna design process and current distribution

In Fig. 3(a), the bilateral-symmetry serpentine loop antenna, which is called Ref.1, initially had a T-shape feeding structure. Ref.1 excites three resonating modes at around 3.3, 5.4, and 7.5 GHz and the reflection coefficient is shown in Fig. 3(b). Ref.1 is a bilateral-symmetry structure, so the current distribution is 5.4 GHz on the right-hand side and the left-hand side of Ref.1, as shown in Fig. 3(c). Therefore, Ref.1 can be divided into two identical half-antennas. The half-antenna that is fed by an L-shape feeding structure and is connected by a straight strip to the ground is called Ref.2, as shown in Fig. 3(d). The L-shape feeding structure in Ref.2 is split from the T-shape feeding structure in Ref.1. The L-shape feeding structure is compressed, so line ab and line cd are shorter, as shown in Fig. 3(d).

Figure 3.

The antenna design process shows (a) Ref. 1, (d) Ref. 2, and (g) the proposed Ant. The reflection coefficients are for (b) Ref. 1, (e) Ref. 2, and (h) the proposed Ant. The current distributions are for (c) Ref. 1, (f) Ref. 2, and (i) the proposed Ant.

Ref.2 uses a straight strip that is connected to the ground, so Ref.2 is longer than half of the length of Ref.1. Therefore, the first resonant frequency of Ref.2 is lower than the second resonant frequency of Ref.1. The first resonant frequency for Ref.2 is 4.6 GHz and the length of the current path, which is about 0.5λ ₀ at 4.6 GHz, is 32 mm, as shown in Fig. 3(e). However, the operating band is still not close to the desired band of 3.4–3.6 GHz. Extending the length of the current path for Ref.2 forms the proposed antenna, as shown in Fig. 3(g). The size of the proposed antenna is also increased to 5.85 × 4.9 mm². The reflection coefficient for the proposed antenna is shown in Fig. 3(h). The resonant frequency is around 3.5 GHz, and the operating bandwidth covers the required band of 3.4–3.6 GHz. The current distribution for the proposed antenna at 3.5 GHz is shown in Fig. 3(i). The length of the proposed antenna is 43.8 mm, which is half of the wavelength for the resonant frequency of 3.5 GHz.

Parametric analysis

The parameter H, which is the distance between the upper and lower arms of the S-shaped strip line for the proposed antenna, is shown in Fig. 4(a). The reflection coefficients are specified relative to the variations in the parameter H, as shown in Fig. 4(b). As the value for the parameter H increases, the current path becomes longer and the resonant frequency decreases. As the value of the parameter H decreases, the resonance frequency shifts increase. Therefore, a value for H of 2.1 mm equates to the lowest resonance frequency of 3.25 GHz and a value for H of 1.1 mm equates to a resonating frequency of 3.8 GHz. The optimal value for H is 1.6 mm because the 6-dB impedance frequency covers the desired band.

Figure 4.

(a) The parameter H for the proposed antenna and (b) the variation in the reflection coefficient as H varies.

The width (parameter W) of the straight shorting line that is connected to the ground is also studied, as shown in Fig. 5(a). The value of the parameter W is used to fine-tune the resonance frequency. As W becomes wider, the resonance frequency increases slightly. The optimal value for parameter W is 0.2 mm because the 6-dB impedance bandwidth is from 3400 to 3730 MHz and covers 3400–3600 MHz, as shown in Fig. 5(b). Adjusting the length (parameter F) of the L-shaped feeding structure in Fig. 6(a) affects the impedance matching. From Fig. 6(b), it can be observed that the longer parameter F has better impedance matching. However, a greater value for parameter F creates a small value for gap1, which is the gap between the feeding structure and the serpentine antenna, as shown in Fig. 6(a). gap1 is too small to be fabricated so the optimal value for the parameter F is 4.95 mm and impedance matching is sufficient (reflection coefficient is around −30 dB). The value for the parameter S (Fig. 7(a)) is used to fine-tune the operating frequency such as the parameter W, as shown in Fig. 7(b). As the value for the parameter S is increased, the resonance frequency decreases slightly. The optimal value for the parameter S is 4.3 mm, and the 6-dB impedance bandwidth covers the LTE42 band.

Figure 5.

(a) The parameter W for the proposed antenna and (b) variation in the reflection coefficient as W varies.

Figure 6.

(a) The parameter F for the proposed antenna and (b) variation in the reflection coefficient as F varies.

Figure 7.

(a) The parameter S for the proposed antenna and (b) variation in the reflection coefficient as S varies.

Measurements and discussion

Figure 8(a–c) shows front, rear, and lateral views of the proposed MIMO antenna. The simulated and measured reflection coefficients for Ant1 to Ant6 are shown in Fig. 9. The solid lines in Fig. 9 are measurements and the dotted lines are simulations. The MIMO antenna is symmetrical, so only Ant1 to Ant6 are measured. All of the measured reflection coefficients are similar to the simulated results, but the frequency shifts slightly. The 6-dB impedance bandwidth for the entire antenna covers the LTE42 band.

Figure 8.

Photographs of the fabricated 12-element MIMO antenna: (a) front, (b) back, and (c) lateral view of the single antenna element.

Figure 9.

Reflection coefficients for simulation and measurement.

Figure 10 shows simulated and measured transmission coefficients for Ant1, Ant2, and Ant3 to other antennae. Only the transmission coefficients between Ant1 to Ant3 and other antennae are shown because the arrangement of those antennas is symmetrical in the mobile phone. Figure 10(a) and (b) shows the simulated and measured transmission coefficients between Ant1 and other antennae. Figure 10(c) and (d) shows the simulated and measured transmission coefficients between Ant2 and other antennae. Figure 10(e) and (f) shows the simulated and measured transmission coefficients between Ant3 and other antennae. All of the measured transmission coefficients are less than −12 dB. Figure 10 shows that there is good agreement between the measured and simulated results.

Figure 10.

Transmission coefficients for simulation and measurement (a) between Ant1 and Ant2 to 6, (b) between Ant1 and Ant7 to 12, (c) between Ant2 and Ant3 to 6, (d) between Ant2 and Ant7 to 12, (e) between Ant3 and Ant4 to 6, and (f) between Ant3 and Ant7 to 12.

The performance of the proposed MIMO antenna is determined using the envelope correlation coefficient (ECC) and the diversity gain (DG). The ECC represents the degree of correlation between the signal that is received by different antenna elements and DG measures the benefits of having multiple uncorrelated signals in the system [Reference Malviya, Panigrahi and Kartikeyan26]. ECC and DG are, respectively, defined as (1) and (2):

(1)\begin{equation}\rho_\text{e}=\frac{{\vert\int{}\int{{\overrightarrow E}_i(\theta,\phi)}{\overrightarrow E}_j{(\theta,\phi)}{}\text{d}\Omega\vert}^2}{{\vert{\overrightarrow E}_i{(\theta,\phi)}\vert}^2{\vert{\overrightarrow E}_j{(\theta,\phi)}\vert}^2{}\text{d}\Omega},\end{equation}

(2)\begin{equation}{\textrm{DG}} = 10\sqrt {1 - \rho _{\textrm{e}}^2} \end{equation}

[Reference Mashagba27]. Figure 11(a–c), respectively, shows the calculated values for ECC for Ant1, Ant2, and Ant3 to other antennae. These ECC values are less than 0.42 at 3.4–3.6 GHz. Figure 12(a–c), respectively, show the calculated DG values for Ant1, Ant2, and Ant3 to other antennas. The DG values are more than 9 dB at 3.4–3.6 GHz. The ergodic CC for the proposed MIMO antenna is determined using Equation (3) as [Reference Ahmad12, Reference Ullah, Ullah, Faisal, Ullah, Mabrouk, Hasan and Kamal28]:

(3)\begin{equation}{\textrm{CC}} = E\left\{ {{{\log }_2}\left[ {\det \left( {I + {{{\textrm{SNR}}} \over {{m_{{\textrm{tr}}}}}}} \right){\textrm{H}}{{\textrm{H}}^{\textrm{T}}}} \right]} \right\}.\end{equation}

Figure 11.

Calculated ECC values for (a) Ant1, (b) An2, and (c) Ant3 to other antennae.

Figure 12.

Calculated DG values for (a) Ant1, (b) Ant2, and (c) Ant3 to other antennae.

In Equation (3), an equal amount of power is allocated to each transmit antenna, but there is no prior knowledge of the channel state information included. The calculated CC value for the proposed MIMO antenna is between 45 and 50 bps/Hz at 3.4–3.6 GHz, as shown in Fig. 13. Figure 14 shows the simulated and measured total efficiency and peak gain for Ant1 to Ant3. The MIMO antenna is symmetrical so only Ant1 to Ant3 are shown. The simulated total efficiency for the proposed MIMO antenna is between 40% and 57%, and the measured total efficiency for the proposed MIMO antenna is between 39% and 56%, as shown in Fig. 14(a). Figure 14(b) shows that the simulated and measured peak gain for the proposed MIMO antenna is between 1 and 2.6 dBi and between 0 and 3.2 dBi, respectively.

Figure 13.

Calculated channel capacity for the proposed MIMO antenna array.

Figure 14.

Simulated and measured (a) total efficiency and (b) peak gain.

The 2D normalized radiation pattern for Ant1 to Ant3 in the xz-, yz-, and xy-planes at 3.5 GHz is shown in Fig. 15. Figure 15(a–c) shows the radiation patterns for Ant1 in the xz-, yz-, and xy-planes at 3.5 GHz. Figure 15(d–f) shows the radiation patterns for Ant2, and Fig. 15(g–i) shows the radiation patterns for Ant3. The loop antenna is a magnetic dipole so the Eϕ value for Ant1 to Ant3 in the xz-plane features an omnidirectional radiation pattern, as shown in Fig. 15(a), (d), and (g).

Figure 15.

Simulated and measured radiation patterns for the proposed MIMO antenna at 3.5 GHz: (a) xz-plane, (b) xy-plane, and (c) yz-plane for Ant1, (d) xz-plane, (e) xy-plane, and (f) yz-plane for Ant2, and (g) xz-plane, (h) xy-plane, and (i) yz-plane for Ant3.