# Frequency-Selective Wallpaper for Indoor Interference Reduction and MIMO Capacity Improvement

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Wallpaper Design

#### 2.1. Frequency-Selective Surfaces

#### 2.2. Wallpaper with Low Transmission at 5 GHz

_{i}is the height. The FSS dimensions were selected using a parameter study that led to these optimal values: w = 0.4 mm, t = 1.3 mm, and a = 11.1 mm.

#### 2.2.1. Wallpaper with Gypsum Wall

^{−2}and a permittivity of ε

_{r}= 5.

#### 2.2.2. Gypsum Wall Only

^{−2}), as indicated in Figure 7.

#### 2.2.3. Wallpaper Attached onto Other Structures

#### Wallpaper with Gypsum–Wood Wall

_{r}= 5, σ = 0 Am

^{−2}, and a thickness of T’ = 102.9 mm were assumed for the wood layer. Dimensions and material properties for the gypsum layer remained the same as those considered in previous sections.

#### Wallpaper with Gypsum–Air–Gypsum Wall

## 3. Ray-Launching Method

_{N×N}). For each simulation, a calculation is made of the coefficient G(n,m), being the coherent sum of every ray received by the antenna m with transmissions only coming from the antenna n.

_{1}), multiple reflected (E

_{2}), multiple transmitted (E

_{3}), multiple diffracted (E

_{4}), multiple reflected/diffracted (E

_{5}), multiple transmitted/diffracted (E

_{6}), and multiple transmitted/reflected (E

_{7}) rays. Thus, the matrix G for any specific receiver position is found with [15]:

_{o}represents emitted field strength, k the wave number, p the total number of contributions considered, r and r

_{i}the propagation path lengths from source n to receiver m, s’ the path length from source to the diffracting wedge, s the path length from diffracting wedge to receiver, D

_{i}the diffraction coefficient for finitely conducting wedges shown in [16], T

_{i}the transmission coefficient, and R

_{i}the reflection coefficient. For this instance, T

_{i}and R

_{i}are dependent on the incident wave polarization, angle of incidence, conductivity, and permittivity.

## 4. Results and Discussion

#### 4.1. SISO Case

^{2}rooms, each having two apertures corresponding to squared windows of 1.6 m width; the experiment assumes that the rooms have a height of 3 m. The T × 1 transmitter is located within Room 2, providing coverage in that location. T × 2 is located within Room 1 so that when its signal enters Room 2, it becomes an interference.

- Omnidirectional antennas
- Frequency: 5 GHz
- Soft Polarization
- T × 1 and T × 2 bearing a 1 m height
- Number of rays launched: 7200
- Number of considered reflections: 14
- Number of considered reflections of diffracted rays: 4
- Number of considered transmissions: 4
- Number of considered transmissions of diffracted rays: 2.

- Omnidirectional antennas
- Frequency: 5 GHz
- Hard Polarization
- T × 1 and T × 2 bearing a 1 m height
- Number of rays launched: 7200
- Number of considered reflections: 14
- Number of considered reflections of diffracted rays: 4
- Number of considered transmissions: 4
- Number of considered transmissions of diffracted rays: 2.

#### 4.2. MIMO Case

^{T}G and GG

^{T}) as a function of frequency with both unpapered and papered walls. The simulation parameters considered in this case in the ray-launching code were the following:

- Omnidirectional antennas
- Hard Polarization
- 4 Tx and 4 Rx bearing a 1 m height
- Number of rays launched: 7200
- Number of considered reflections: 9
- Number of considered reflections of diffracted rays: 4
- Number of considered transmissions: 4
- Number of considered transmissions of diffracted rays: 3.

^{T}and G

^{T}G, concerning the antenna arrays T × 1 and R × 1, can be observed in Figure 25 for a frequency of 5 GHz and the two types of walls under study.

^{T}and G

^{T}G, present the lobes (at 120° in the transmitter and −60° in the receiver), making reference to the line of sight (LoS) path.

_{Nr}is the Nr × Nr identity matrix, ( )H is the Hermitian transposition, and H is the normalized channel transfer matrix.

- Omnidirectional antennas
- Frequency: 5 GHz
- Hard Polarization
- Transmitting and receiving antennas bearing a 1 m height
- Number of rays launched: 7200
- Number of considered reflections: 9
- Number of considered reflections of diffracted rays: 4
- Number of considered transmissions: 4
- Number of considered transmissions of diffracted rays: 3.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Transmission coefficient for the structure considered in Figure 2.

**Figure 4.**Reflection coefficient for the structure considered in Figure 2.

**Figure 5.**Transmission coefficient for the structure considered in Figure 2 for frequency = 5 GHz.

**Figure 6.**Reflection coefficient for the structure considered in Figure 2 for frequency = 5 GHz.

**Figure 8.**Transmission coefficient for the structure considered in Figure 7.

**Figure 9.**Reflection coefficient for the structure considered in Figure 7.

**Figure 10.**Transmission coefficient for the structure considered in Figure 7 for frequency = 5 GHz.

**Figure 11.**Reflection coefficient for the structure considered in Figure 7 for frequency = 5 GHz.

**Figure 13.**Transmission coefficient for the structure considered in Figure 12.

**Figure 14.**Reflection coefficient for the structure considered in Figure 12.

**Figure 16.**Transmission coefficient for the structure considered in Figure 15.

**Figure 17.**Reflection coefficient for the structure considered in Figure 15.

**Figure 19.**The signal-to-interference ratio (SIR) over Room 2 (dB) considering (

**a**) regular gypsum walls (

**b**) F-S walls.

**Figure 22.**Power delay profile for the geometry in Figure 20.

**Figure 23.**Geometry of two rooms and multiple-input multiple-output (MIMO) transmitter/receiver locations (top view).

**Figure 24.**Singular values for the channel transfer matrix considering the geometry in Figure 23.

**Figure 25.**Radiation diagrams from the eigenvectors of GG

^{T}and G

^{T}G applied to (

**a**) the transmitter T × 1 and (

**b**) the receiver R × 1. Frequency = 5 GHz.

**Figure 28.**Singular values for the channel transfer matrix considering the geometry of Figure 26 (I).

**Figure 29.**Singular values for the channel transfer matrix considering the geometry of Figure 26 (II).

**Table 1.**Mean and standard deviation of the singular values (lambda 1 to 4) obtained for all transmitter and receiver positions of Figure 26.

Mean | Standard Deviation | ||
---|---|---|---|

Lambda1 | 1.5254 | 0.50602 | |

Regular | Lambda2 | 0.63897 | 0.14742 |

Walls | Lambda3 | 0.17615 | 0.064675 |

Lambda4 | 0.012362 | 0.0081471 | |

Lambda1 | 2.9068 | 0.68067 | |

Walls with | Lambda2 | 1.5055 | 0.49311 |

Wallpaper | Lambda3 | 0.53912 | 0.18192 |

Lambda4 | 0.19102 | 0.061508 |

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## Share and Cite

**MDPI and ACS Style**

Rodríguez, J.-V.; Gustafsson, M.; Molina-García-Pardo, J.-M.; Juan-Llácer, L.; Rodríguez-Rodríguez, I.
Frequency-Selective Wallpaper for Indoor Interference Reduction and MIMO Capacity Improvement. *Symmetry* **2020**, *12*, 695.
https://doi.org/10.3390/sym12050695

**AMA Style**

Rodríguez J-V, Gustafsson M, Molina-García-Pardo J-M, Juan-Llácer L, Rodríguez-Rodríguez I.
Frequency-Selective Wallpaper for Indoor Interference Reduction and MIMO Capacity Improvement. *Symmetry*. 2020; 12(5):695.
https://doi.org/10.3390/sym12050695

**Chicago/Turabian Style**

Rodríguez, José-Víctor, Mats Gustafsson, José-María Molina-García-Pardo, Leandro Juan-Llácer, and Ignacio Rodríguez-Rodríguez.
2020. "Frequency-Selective Wallpaper for Indoor Interference Reduction and MIMO Capacity Improvement" *Symmetry* 12, no. 5: 695.
https://doi.org/10.3390/sym12050695