Antenna structure

The detailed and physical dimensions of the proposed eight element MIMO array are displayed in Fig. 1(a). The antenna elements are placed symmetrically on the inner surface of the frame of the mobile phone. The mobile phone frames have thickness of 0.8 mm and height of 7 mm that are placed perpendicularly on the PCB board. The size of the substrate is 150 and 75 mm which is a typical size of 5.5-inch smartphone. FR4 substrate (relative permittivity = 4.4, loss tangent = 0.02) is considered as the printed circuit board (PCB) of system and side-edge frame. Each dual-band antenna consists of an L-shaped open slot antenna on the ground and comb-shaped monopole antenna. The monopoles are fed by the 50 Ω microstrip line that is connected by a 50 Ω SMA connector at point A. The monopole is connected to the ground plane at points B and C.

Fig. 1. (a) The geometry of the proposed eight elements and (b) the simulated reflection coefficient of single element.

Parametric analysis

Figure 1(b) shows the simulated reflection coefficient of single element antenna. It is observed that the two desired bands are fully covered under the condition of −10 dB return loss. In this design, the comb-shaped monopole antenna and the L-shaped open slot antenna are used to generate the 5.5 and 3.5 GHz resonant, respectively. To further verify the resonant mode of the two proposed antenna, the simulated surface current and E-field distributions at 3.5 and 5.5 GHz are depicted in Figs 2(a) and 2(b). At 3.5 GHz, as shown in Fig. 2(a) it can be easily seen that strong surface current distributions are mainly concentrated on the closed end of the slot, showing the L-shaped open slot antenna operates at the fundamental quarter-wavelength resonant mode. Hence, the first resonance is determined by the length of L-shaped open slot antenna (d), as shown in Fig. 3(a). It is also seen in Fig. 2(b), that there are two current nulls along monopole, which indicates the first higher order mode at high band. Similarly, for H and L fixed, impedance matching and resonant frequency of high band can be fine-tuned by parameter l, as shown in Fig. 3(b). It is also observed that the two modes can be tuned separately. The optimized parameters of the proposed single antenna are displayed in Table 1.

Fig. 2. Simulated surface current and E-field distributions at (a) 3.5 GHz and (b) 5.5 GHz.

Fig. 3. Simulated reflection coefficient for different (a) length of slots and (b) length of monopoles.

Table 1 Optimized parameters of antenna.

Array design

In dual-element antenna array, there are two kinds of arrangement, namely mirrored and shifted configurations that is illustrated in Figs 4(a) and 4(b), respectively. The simulated transmission coefficients of two configurations with different space between them (d₁₂), are shown in Fig. 5. It is observed that in the mirrored case, transmission coefficient S₂₁ is less than −15 and −20 dB in the low band and high band for d₁₂ = 14 mm, while in shifted case, the same S₂₁ value is not achieved even for larger d d₁₂. Therefore, we will use the mirrored configuration for designing eight-element MIMO antenna array.

Fig. 4. Two arrangement of dual-element array (a) mirrored and (b) shifted configuration.

Fig. 5. Simulated transmission coefficient of two configuration (a) mirrored and (b) shifted.

Array configuration and performances

Two different arrangements of 8 × 8 MIMO antenna array are presented namely, cases I and II as illustrated in Fig. 6. In case I, all of the elements are symmetrically located on the two-long edges of smartphone, but in the case II, four elements are located on the two long edges and four other antennas on the top and bottom edges. Based on the result of [Reference Parchin, Al-Yasir, Ali, Elfergani, Noras, Rodriguez and Abd-Alhameed19], the configuration of case I is considered hereafter. The 3D radiation patterns of Ant1-Ant4 at 3.5 and 5.5 GHz are shown in Figs 7(a) and 7(b), respectively. It can be seen that each side of the space has been fully covered.

Fig. 6. Two different configurations of eight-elements of MIMO antennas array (a) case I and (b) case II.

Fig. 7. Simulated 3D radiation pattern of Ant1–4 at (a) 3.5 GHz and (b) 5.5 GHz.

Thus, the proposed MIMO antenna array presents good radiation coverage which makes it more appropriate to be used in future mobile phones. Also, it can be observed that the maximum radiating orientations of antenna are in different directions, hence, diversity pattern is achieved which, is an advantage for good MIMO performance. Figure 8 depicts the simulated total efficiency. It is seen that, the total efficiencies are better than 60 and 80% in the 3.5 and 5.5 GHz band, respectively.

Fig. 8. Simulated total efficiency of Ant1–4.

S-Parameters

The simulated and measured S parameters are shown in Fig. 10. Due to the symmetrical structure, only the results of the Ant 1–4 are given. It is observed that, the measured S₁₁, S₂₂, S₃₃ and S₄₄ are smaller than −6 dB in the two desired frequency band, and the measured isolations between two adjacent ports (S₁₂, S₂₃, S₃₄, and S₂₄) are better than 11.5 and 15 dB whit in the low band and high band, respectively. Therefore, there are good agreement between the simulated and measured S parameters and the little differences are due to the connector and fabrication losses.

Fig. 10. Simulated and measured results of (a) reflection coefficient and (b) transmission coefficient.

Radiation pattern

The measured and simulated total realized gain patterns of Ant1–4 in the xoy plane at two different frequency 3.5 and 5.5 GHz are illustrated in Figs 11 and 12, respectively. Although in some direction the measured pattern has not tracked the corresponding simulation result, the overall trend of the two results are similar and the slight difference possibly is due to the test environment errors and other external disturbances. Also, it is observed that Ant1–Ant4 have strong radiation in the φ = 315°, φ = 210°, φ = 180°, and φ = 65°, respectively, in the 3.5 GHz frequency. As shown in Fig. 12, in the 5.5 GHz frequency, maximum radiation is oriented in at the φ = 330°, φ = 90°, φ = 270°, and φ = 30°, respectively. In conclusion, because of difference in the maximum radiating orientations, diversity pattern is achieved which, is an advantage for good MIMO performance.

Fig. 11. Simulated and measured total realized gain pattern Ant1–4 at 3.5 GHz.

Fig. 12. Simulated and measured total realized gain pattern Ant1–4 at 5.5 GHz.

MIMO performance

Beside the other radiation performance of antenna, it is important to investigate ECC, mean effective gain (MEG), and channel capacity to evaluate diversity performance of the proposed MIMO antenna. The ECC values are calculated from measured complex radiation far field of antenna by formula explained in [Reference Taga20] and are depicted in Fig. 13. It is observed that the calculated ECC values were smaller than 0.15 which is better than its acceptable threshold.

Fig. 13. Simulated ECC values between some adjacent elements.

The MEG of Ant1–4 under propagation conditions Gaussian/uniform (XPR = 5 dB, m_v = 10°, m_H = 10°, σ_v = 15°, σ_H = 15°) [Reference Taga20] were computed directly from CST by the simulated 3D far-field radiation patterns. Then, branch power ratio (k) was calculated for the two antennas by following formula [Reference Sharawi21]:

(1)$$k_{i, j} = \min \left({\displaystyle{{MEG_i} \over {MEG_j}}, \;\displaystyle{{MEG_j} \over {MEG_i}}} \right)$$

The calculated MEG and branch power ratio (k) of Ant1–4 are shown in Table 2. It is observed that k is more than −3 dB which is essential to obtain the maximum diversity gain and avoid significant loss in the diversity performance of the MIMO antenna system [Reference Sharawi21].

Table 2 MEG and branch power ratio (K).

If the transmitter does not know the channel state information (CSI) and the transmit power is equally allocated to every transmit antenna, the ergodic channel capacity can be achieved by the formula given in [Reference Tian, Lau and Ying22]

(2)$$C = E\left\{{{\rm lo}{\rm g}_2\,\det \left({I + \eta \displaystyle{{SNR} \over N}HH^H} \right)} \right\}$$

where I is the identity matrix, SNR denotes the mean SNR, N is the rank of the matrix HH ^T, H is the channel matrix, and H ^H denotes the Hermitian transpose of matrix. The channel matrix H is calculated by the Kronecker channel model [Reference Li, Du, Takahashi, Saito and Ito23].

Using this model, the complex channel matrix H can be expressed as

(3)$$H = {\rm \Phi }_R^{1/2} H_w{\rm \Phi }_T^{1/2} $$

where Φ_R and Φ_T are the receive and transmit antenna correlation matrix, respectively and {.}^1/2 denotes the matrix square root. H _w is the white channel matrix that describes the properties of the propagation scenario. When an independent and identically distributed (i.i.d.) Rayleigh fading channel is assumed, the entries of H _w are zero-mean circularly symmetric complex Gaussian random variables. It should be noted that the impact of the total efficiency on the antenna correlation matrix is considered here, as explained in [Reference Yun and Vaughan24]

(4)$$\eqalign{{\rm \Phi }_R = & \eta _{\rm r}^{1/2} {\rm \Psi }_{\rm R}^{1/2} \eta _{\rm r}^{1/2} \cr {\rm \Phi }_T = & \eta _{\rm t}^{1/2} {\rm \Psi }_{\rm T}^{1/2} \eta _{\rm t}^{1/2} } $$

where η _r and η _t are the receive and transmit diagonal matrices containing the total efficiencies of the receive and transmit antenna elements. By assuming all the antenna elements at transmitter are uncorrelated, i.e., zero-correlation coefficient, the (i, j)^th entry of Ψ_R is calculated by [Reference Kiani, Altaf, Abdullah, Muhammad, Shoaib, Anjum, Damaševičius and Blažauskas25]

(5)$$\eqalign{& \Psi _R^{( i, j) } = \displaystyle{{\mu _{ij}} \over {\sqrt {\mu _{ii}\mu _{\,jj}} \;}} \cr & \mu _{ij} = \int {E\{ [ A_i( \Omega ) h( \Omega ) ] [ A_j^\ast ( \Omega ) h^\ast ( \Omega ) ] {\rm d}\Omega \} } } $$

where A _i(Ω) and $A_j^\;( \Omega )$ represent the field patterns of antenna element i and j, h(Ω) represent incoming wave, { }* denotes conjugate operation, E{ } represents expectation. The mobile wireless environment defined in [Reference Guo, Liu, Liu, Huang and Du26] has a series of reasonable assumptions: the fading envelope being Rayleigh distributed, the incoming wave arriving in horizontal plane only, the incoming wave's orthogonal polarizations being uncorrelated, the individual polarizations being spatially uncorrelated, and finally the time-averaged power density per steradian being constant. Based on these approximations and the derivation in [Reference Yun and Vaughan24], can be written as

(6)$$\mu _{ij} = \int_0^{2\pi } {\left[{{\rm \Gamma }A_{i\theta }\left({\displaystyle{\pi \over 2}, \;\phi } \right)A_{\,j\theta }^\ast \left({\displaystyle{\pi \over 2}, \;\phi } \right) + A_{i\phi }\left({\displaystyle{\pi \over 2}, \;\phi } \right)A_{\,j\phi }^\ast \left({\displaystyle{\pi \over 2}, \;\phi } \right)} \right]\;{\rm d}\phi } $$

where Γ is the cross-polarization discrimination (XPD) of the incoming wave, that, in this paper is set to 0 dB. As shown in Fig. 14, the channel capacity is achieved by assuming the propagation scenario is independent and identically distributed (i.i.d.) Rayleigh-fading channel. It is observed that, the calculated channel capacity is 32, and 38.7 bps/Hz, for 17 and 20 dB SNR in the receiver, respectively, whereas the ideal 8 × 8 MIMO system by assuming zero correlation and 100% efficiency is about 43.96 bps/Hz.

Fig. 14. Calculated channel capacity from measured result.