# Field Decorrelation and Isolation Improvement in an MIMO Antenna Using an All-Dielectric Device Based on Transformation Electromagnetics

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design Methodology

## 3. Proposed Design Details

#### 3.1. Radiating Elements

^{2}. For each frequency, choosing different dimensions of length (L) and width (W) of both patch elements allowed achieving resonant frequencies of 3 GHz, 5 GHz, and 7 GHz. The L/W values of both patch antenna elements at 3 GHz, 5 GHz, and 7 GHz were 25.23 mm/30.7 mm, 14.68 mm/18.5 mm, and 10.18 mm/12 mm, respectively. The center-to-center separation (S) between the antenna elements was 36.7 mm (0.37λ) at 3 GHz, 24.5 mm (0.41λ) at 5 GHz, and 16.29 mm (0.38λ) at 7 GHz, which resulted in an edge-to-edge separation of 6 mm (0.06λ), 6 mm (0.1λ), and 4.29 mm (0.1λ), respectively. Here, λ represents the free-space wavelength. Each antenna element at their resonance frequencies was excited by a coaxial feed with an offset distance of 4.2 mm, 2.7 mm, and 1.9 mm from the center of patch. The inner diameter of the conducting pin was 1.27 mm, whereas the outer conductor diameter was 4.2 mm, which was used to connect the ground of the antenna to the body of the coaxial connector. The overall length of the coaxial connector considered during numerical simulations was 12 mm.

#### 3.2. Dielectric Wave Tilting Structure (DWTS)

^{3}each. Figure 2d shows the permittivity value of each unit cell. It is important to note that the conformal module, which is a geometric quantity determined by the structure and containing the complete invariants of the structure, of the physical space was much larger than 1 compared to that of the virtual space, which was 1. As such, anisotropy in the material parameters tensor was introduced in the transformed medium [21]. However, for a possible experimental validation of the proposed DWTS using a simplified all-dielectric material, we propose to ignore the anisotropy in the material parameters tensor. Such a simplification led to a degradation of the beam steering characteristics, which was reduced to around 28° in the case of 3 GHz, as illustrated in Figure 2c.

#### 3.3. Realistic Design of the DWTS

_{eff}of the composite material comprising two materials, i.e., air and dielectric, can be evaluated as follows [19]:

_{h}and f

_{a}are the fractional volumes of the dielectric PLA material and air holes, respectively, and ε

_{h}and ε

_{a}are the relative permittivities of the dielectric and air, respectively.

#### 3.4. Complete Antenna System

^{3}. In order to mount the DWTS easily above the antenna elements, two supports of width 7 mm each with eight M3 holes were added at both edges. The structure was placed symmetrically above the two radiating elements such that its dielectric constant was 1 in the center and increased in steps moving on both sides along the x-axis with a maximum value of 2.65 at the edges. The structure was inserted symmetrically above the elements so that the branch power ratio remained close to 1, an attribute which is recommended for MIMO antennas.

## 4. Simulation and Measurement Results

#### 4.1. S-Parameters and Radiation Patterns

_{11}and S

_{22}below the −10 dB level, having fractional bandwidths of 1.6%, 2.2%, and 3.8%, respectively. The shifted resonance frequency of both elements in each case was 2987 MHz, 4948 MHz/4932 MHz, and 7015/6912 MHz, respectively. In addition, the measured isolation level S

_{21}between the two ports of closely spaced antenna elements improved by more than 3.9 dB, 3 dB, and 4.6 dB at each shifted resonance frequency, respectively.

#### 4.2. Correlation Coefficient and Other MIMO Parameters

_{i}(ø, ϕ) (i = 1,2) is the far-field complex 3D radiation field of the i-th antenna, when only the i-th element is excited, and ∗ is the Hermitian product.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Space mapping illustration. (

**a**) Virtual domain. (

**b**) Physical domain with anisotropic material parameters. (

**c**) Physical domain with simplified quasi-isotropic material parameters. (

**d**) DWTS permittivity (ε

_{zz}) profile (xoz-plane).

**Figure 3.**Unit cell of dielectric host material with air hole where P

_{x}= 5 mm, P

_{y}= P

_{z}= 3.5 mm. (

**a**) Unit cell for effective permittivity of 1.25. (

**b**) Unit cell for effective permittivity of 1.63. (

**c**) Unit cell for effective permittivity of 2.5.

**Figure 5.**Geometry of the two-element MIMO antenna with the proposed DWTS. (

**a**) Ideal DWTS. (

**b**) PLA-based DWTS.

**Figure 6.**Simulated and measured S−parameters of the MIMO antenna system with and without DWTS. (

**a**) Reflection coefficient at 3 GHz. (

**b**) Isolation at 3 GHz. (

**c**) Reflection coefficient at 5 GHz. (

**d**) Isolation at 5 GHz. (

**e**) Reflection coefficient at 7 GHz. (

**f**) Isolation at 7 GHz.

**Figure 7.**Simulated normalized 2D radiation pattern of MIMO antenna with and without the DWTS in xoz−plane. (

**a**) E1 and E2 at 3 GHz. (

**b**) E1 and E2 at 5 GHz. (

**c**) E1 and E2 at 7 GHz.

**Figure 8.**3D radiation pattern (in linear scale) of the two-element MIMO antenna with and without the DWTS. (

**a**) 3 GHz. (

**b**) 5 GHz. (

**c**) 7 GHz.

**Figure 11.**Simulated and measured radiation patterns (in the xoz−plane) for both configurations. (

**a**) E1 at 3 GHz. (

**b**) E2 at 3 GHz. (

**c**) E1 at 5 GHz. (

**d**) E2 at 5 GHz. (

**e**) E1 at 7 GHz. (

**f**) E2 at 7 GHz.

**Figure 12.**Correlation coefficient of the two-element MIMO antenna with and without the proposed DWTS. (

**a**) 3 GHz. (

**b**) 5 GHz. (

**c**) 7 GHz.

**Figure 13.**(

**a**) Diversity gain of the two−element MIMO antenna with and without the proposed DWTS. (

**b**) Multiplexing efficiency of the two-element MIMO antenna with and without the proposed DWTS.

Ref. | Radiating Element/Ports | Edge to Edge Spacing | Beam Tilt Angle | Isolation | Reduction in Correlation |
---|---|---|---|---|---|

[12] | Patch/2 | 0.13λ | 51° | Degrade | 95% |

[26] | DRA/6 | 0.31λ | 45° | Improve | 42.3% |

[27] | DRA/4 | 0.24λ | 35° | Improve | 43.2% |

[28] | Patch/4 | 0.23λ | 27° | Degrade | 65% |

[29] | Patch/2 | 0.03λ | 35° | Improve | Not given |

[30] | Patch/2 | 0.15λ | 0° | Improve | Inaccurate |

[31] | Patch/2 | 0.17λ | 0° | Improve | Not given |

This work | Patch/2 | 0.06λ | 44° | Improve | 62% to 99% |

at 3 GHz | |||||

0.1λ | 67° | 37% to 97% | |||

at 5 GHz | |||||

0.1λ | 76° | 57% to 95% | |||

at 7 GHz |

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**MDPI and ACS Style**

Qureshi, U.; Khan, M.U.; Sharawi, M.S.; Burokur, S.N.; Mittra, R.
Field Decorrelation and Isolation Improvement in an MIMO Antenna Using an All-Dielectric Device Based on Transformation Electromagnetics. *Sensors* **2021**, *21*, 7577.
https://doi.org/10.3390/s21227577

**AMA Style**

Qureshi U, Khan MU, Sharawi MS, Burokur SN, Mittra R.
Field Decorrelation and Isolation Improvement in an MIMO Antenna Using an All-Dielectric Device Based on Transformation Electromagnetics. *Sensors*. 2021; 21(22):7577.
https://doi.org/10.3390/s21227577

**Chicago/Turabian Style**

Qureshi, Usman, Muhammad Umar Khan, Mohammad S. Sharawi, Shah Nawaz Burokur, and Raj Mittra.
2021. "Field Decorrelation and Isolation Improvement in an MIMO Antenna Using an All-Dielectric Device Based on Transformation Electromagnetics" *Sensors* 21, no. 22: 7577.
https://doi.org/10.3390/s21227577