Principle of MTS decoupling

A two-element MIMO antenna can be equivalent to a two-port network, and its relationship of input and output voltages is expressed by S-parameters [Reference Bait-Suwailam, Boybay and Ramahi14]:

(1)$$\left[{\matrix{ {V_1^{\rm o} } \cr {V_2^{\rm o} } \cr } } \right] = \left[{\matrix{ {S_{11}} & {S_{12}} \cr {S_{21}} & {S_{22}} \cr } } \right]\left[{\matrix{ {V_1^{\rm i} } \cr {V_2^{\rm i} } \cr } } \right]$$

where S ₁₁ and S ₂₂ are the reflection coefficients of two ports, S ₁₂ and S ₂₁ are the coupling coefficients, V ₁ⁱ, V ₂ⁱ, V ₁^o and V ₂^o are the input and output voltages of two ports, respectively. When the network is lossless, reciprocal and matched, formula (1) can be expressed as:

(2)$$\left[{\matrix{ {V_1^{\rm o} } \cr {V_2^{\rm o} } \cr } } \right] = \left[{\matrix{ 0 & {S_{12}} \cr {S_{21}} & 0 \cr } } \right]\left[{\matrix{ {V_1^{\rm i} } \cr {V_2^{\rm i} } \cr } } \right]$$

When S ₁₂ = S ₂₁, the mutual coupling between two antenna elements will disappear, and the mutual impedances Z ₁₂ and Z ₂₁ should be reactive, thus the single negative metamaterial can be employed to reduce mutual coupling.

The principle of MTS decoupling is shown Fig. 1. A two-element MIMO antenna is arranged along the x-axis, and a single negative MTS is placed above the antenna, when the Ant.1 is excited and the Ant.2 is terminated with a 50 Ω matched load. The coupled electromagnetic waves propagate along the positive x-direction. When loading a single negative metamaterial (ɛ _r < 0, μ _r > 0 or ɛ _r > 0, μ _r < 0), the wavenumber k can be expressed as [Reference Wang, Li and Yin6]:

(3)$$k = w\sqrt {\mu \cdot \varepsilon } = \omega \cdot \sqrt {\varepsilon _{\rm r}\varepsilon _0\cdot \mu _{\rm r}\mu _0} = jk_0\cdot \sqrt {\vert {\mu_{\rm r}} \vert \cdot \vert {\varepsilon_{\rm r}} \vert \;} $$

Fig. 1. Principle of MTS decoupling.

The electric field along the positive x-direction can be expressed as:

(4)$$E( {x, \;t} ) = E_0e^{\,jkx}e^{\,jwt} = E_0e^{{-}k_0\sqrt {\vert {\mu_{\rm r}} \vert \vert {\varepsilon_{\rm r}} \vert } \cdot x}\cdot e^{\,jwt}$$

Therefore, the coupled electric field along the x-axis is evanescent, and the electromagnetic wave mainly propagates along the z-direction. In a word, the mutual coupling between antenna elements can effectively reduce by loading the single negative MTS.

MTS unit cell

Figure 2 plots the configuration of an unsymmetrical double-layer MTS unit cell. It consists of pairs of elliptic patches with two different sizes and is printed on the F4B substrate with a dielectric contains of 2.2, a loss tangent of 0.002 and a thickness of 1 mm. The master-slave boundaries are assigned on the sidewalls, and a pair of Floquet ports are applied on the x–y plane, as plotted in Fig. 2(a). The reflection and transmission coefficients of the unsymmetrical double-layer MTS unit cell are simulated with ANSYS HFSS. As shown in Fig. 2(b), the reflective type MTS unit cell operates at 2.6 and 3.5 GHz, and the electromagnetic waves can radiate effectively due to the anisotropic nature of the MTS [Reference Liu, Guo, Zhao, Shen and Yin10]. The permittivity ɛ and permeability μ of the MTS unit cell are extracted using the standard parameter retrieval method [Reference Szabó, Park, Hedge and Li15] and the inversion algorithm [Reference Smith, Vier, Koschny and Soukoulis16] programmed by MATLAB in Appendix. Figure 2(c) plots the extracted ɛ and μ of the unit cell illuminated by y-polarized plane wave, it is observed that the results of two algorithms agree well. The ɛ and μ are positive and negative around 2.6 GHz while negative and positive around 3.5 GHz. Besides, the extracted permittivity has a spike at 3.2 GHz due to the coupling between the elliptic patches with different sizes in different layers.

Fig. 2. MTS unit cell, (a) simulation model; (b) S-parameters; (c) permittivity and permeability.

Closely coupled dual-band MIMO antenna based on MTS

The configuration of the closely coupled dual-band MIMO antenna is shown in Fig. 3. A double-layer MTS formed by the proposed unit cells is loaded above a two-port coupled dual-band MIMO antenna to reduce the mutual coupling between the antenna elements. A pair of open slots is etched on the antenna element to achieve dual-band and two C-shape slots with different lengths are etched to increase the matching bandwidths in the lower and upper band, respectively. Two rows of the MTS unit cells are chosen to obtain better decoupling performance, and the distance between the MTS and the coupled antenna is determined by the theory of Fabry–Perot (F–P) cavity [Reference Cao, Zhang and Li17]. The coupled MIMO antenna is fabricated on the F4B substrate with a dielectric contains of 2.2 and a loss tangent of 0.002. The edge-to-edge distance of two antenna elements is 1 mm (0.01λ ₀ at 2.6 GHz). All analysis and simulations are carried out by HFSS 13.0, and the dimensions are listed in Table 1. Figure 4 shows the simulated S-parameters of the antenna with/without MTS. It can be seen that, the bandwidth in the lower band is increased from 4.26% (2.53–2.64 GHz) to 8.43% (2.5–2.72 GHz) and that in the upper band is increased from 4.62% (3.38–3.54 GHz) to 8.18% (3.4–3.69 GHz). Also, after loading the MTS, the isolation in two bands is improved by 12.5 and 15.4 dB, respectively.

Fig. 3. Configuration of antenna structure, (a) side view; (b) top view of MTS; (c) top view of the coupled MIMO antenna.

Fig. 4. S-parameters of antenna with/without MTS.

Table 1. Dimensions of antenna structure (Unit: mm)

A thinner substrate minimizes the surface waves and the mutual coupling between the closely coupled antennas is mainly due to the near-field space waves. The surface current distribution for antenna with/without MTS is investigated to illustrate the working mechanism of the MTS for mutual coupling reduction. Figure 5 shows the surface current distribution of the antenna when the Ant.1 is excited and the Ant.2 is terminated by a 50 Ω load. It is observed that without the MTS, a strong coupling current is distributed on the Ant. 2. However, after loading the MTS, the coupling current on the Ant. 2 at two bands is dramatically reduced as shown in Figs 5(c) and 5(d). In other words, the MTS has the favorable decoupling capability for a dual-band MIMO antenna.

Fig. 5. Surface current distribution of antenna, (a) at 2.6 GHz without MTS; (b) at 3.5 GHz without MTS; (c) at 2.6 GHz with MTS; (d) at 3.5 GHz with MTS.