# A Comparison of Distribution Models for Fast Variations in the Indoor Radio Channel at 5G Frequency Range 1 Microwave Bands

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Measurement Procedure

_{21}, in module and phase format sweeping a spectrum band around the central frequency. Both antennas were azimuth-omnidirectional EM-6865 manufactured by Electro-Metrics. The transmitting antenna, connected to port 1 of the VNA, was placed in a static location, and it is represented in Figure 1 as a green triangle. The receiving antenna (another green triangle at Figure 1) was moving along a positioner, following a 2.5-m-long straight path. An indexer drove the step by step motor that controlled the movement along the positioner; thus, the location of the receiving antenna at each measurement spot is meticulously defined anytime. A tailor made software, based on Matlab

^{®}and running on a PC, governed the process of both the movement and the electromagnetic equipment: this allows the repetition of the experiments reducing the human errors during the measurement campaigns.

#### 2.2. Measurement Environments

#### 2.3. Data Processing

_{tx}− P

_{rx}= PL

_{0}− 10 n log

_{10}(d/d

_{0}) [dBm],

- PL
_{0}: Path Loss at a reference distance (d_{0}) [dBm]. - n: path loss exponent, indicating the rhythm of decay.
- d: distance between transmitter and receiver [m].
- d
_{0}reference distance (for simplicity it is usually 1 m) [m].

- L is the value of log-likelihood,
- w is the size of the sample,
- k is the number of parameters estimated in the model.

## 3. Results

^{2}test, the models that have >5% acceptance among all the data vectors of all environments resulted to be, in alphabetical order:

- Log-Normal.
- Nakagami.
- Normal.
- Rayleigh.
- Rice.
- Weibull.

#### 3.1. Results at 3 GHz Band

#### 3.2. Results at 5 GHz Band

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Environment schemes for measurements in the 3 GHz band (

**a**) auditorium; (

**b**) small lab #1; (

**c**) small lab #2; and (

**d**) corridor.

**Figure 3.**Environment schemes for measurements in the 5 GHz band (

**a**) large lab LoS; (

**b**) large lab NLoS; (

**c**) office #2; and (

**d**) small lab #3.

**Figure 5.**Comparison among distributions best-fitting the measured fast variations, in terms of percentage of acceptation of Pearson’s goodness-of-fit χ

^{2}test.

**Figure 6.**Cumulative distribution functions fitting fast variations within the corridor at 3.5 GHz in LoS conditions.

**Figure 8.**Cumulative distribution functions fitting fast variations within the corridor at 3.5 GHz in NLoS conditions.

**Figure 10.**Cumulative distribution functions fitting fast variations within the auditorium at 3.5 GHz in LoS conditions.

**Figure 11.**Percentage of best fitted distribution functions regarding fast variations within the auditorium at 3 GHz band in LoS conditions.

**Figure 12.**Cumulative distribution functions fitting fast variations within the small lab #1 at 3 GHz, in LoS conditions.

**Figure 13.**Cumulative distribution functions fitting fast variations within the small lab #2 at 3 GHz. (

**a**) Furnished; and (

**b**) empty.

**Figure 14.**Cumulative distribution functions fitting fast variations within the large lab at 5.8 GHz in LoS conditions.

**Figure 15.**Cumulative distribution functions fitting fast variations within the large lab at 5.8 GHz in NLoS conditions.

**Figure 16.**Cumulative distribution functions fitting fast variations within the office at 5.8 GHz. (

**a**) Empty; and (

**b**) furnished.

**Figure 17.**Cumulative distribution functions fitting fast variations within the small lab #3 at 5.8 GHz in LoS conditions.

**Figure 18.**Rice distribution fitting fast variations within the small lab #3 at 5.8 GHz in empty conditions.

Environment | Visibility Conditions | Distribution | |||||
---|---|---|---|---|---|---|---|

Normal | Rayleigh | Weibull | Rice | Nakagami | Lognormal | ||

Corridor | LoS | 192 | 279 | 19 | 285 | BIC* | 163 |

NLoS | 338 | 535 | BIC* | 540 | 20 | 53 | |

Auditorium | LoS | 312 | 365 | BIC* | 371 | 31 | 52 |

Small lab #1 | OLoS | 113 | 153 | 3 | 158 | BIC* | 73 |

Small lab #2 | Furnished | 103 | 150 | BIC* | 154 | 7 | 11 |

Empty | 49 | 57 | BIC* | 61 | BIC* | 24 |

Environment | Visibility Conditions | Distribution | |||
---|---|---|---|---|---|

Weibull | Nakagami | ||||

Scale (a) | Shape (b) | Shape (µ) | Scale (Ω) | ||

Corridor | LoS | 1.7317 | 1.1280 | 0.4287 | 4.5627 |

NLoS | 1.9761 | 0.8586 | 0.2930 | 10.6208 | |

Auditorium | LoS | 1.6840 | 1.0833 | 0.4027 | 5.1147 |

Small lab #1 | OLoS | 1.7352 | 1.0981 | 0.4128 | 4.8834 |

Small lab #2 | Furnished | 1.7027 | 1.0514 | 0.3880 | 5.4965 |

Empty | 1.7172 | 1.0275 | 0.3757 | 5.8678 |

Environment | Visibility Conditions | Distribution | ||||
---|---|---|---|---|---|---|

Normal | Rayleigh | Weibull | Rice | Nakagami | ||

Large lab | LoS | 4 | 107 | 3 | BIC* | 14 |

NLoS | 33 | 17 | BIC* | 1 | 1 | |

Office | Furnished | 28 | 19 | BIC* | 1 | 1 |

Empty | 26 | 18 | 2 | BIC* | 3 | |

Small lab #3 | LoS | 8 | 66 | 1 | BIC* | 6 |

Environment | Visibility Conditions | Distribution | |||
---|---|---|---|---|---|

Weibull | Rice | ||||

Scale (a) | Shape (b) | Distance (ν) | Scale (σ) | ||

Large lab | LoS | 1.1820 | 3.4461 | 1.0005 | 0.3509 |

NLoS | 1.2323 | 2.7783 | 0.9766 | 0.4652 | |

Corridor | Furnished | 1.2328 | 2.7367 | 0.9705 | 0.4728 |

Empty | 1.2376 | 2.6863 | 0.9641 | 0.4870 | |

Small lab #3 | LoS | 1.2030 | 3.2252 | 0.9953 | 0.3929 |

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**MDPI and ACS Style**

Malo-Torreiro, S.; Seijas-Iglesias, M.; Cuiñas, I.
A Comparison of Distribution Models for Fast Variations in the Indoor Radio Channel at 5G Frequency Range 1 Microwave Bands. *Electronics* **2022**, *11*, 449.
https://doi.org/10.3390/electronics11030449

**AMA Style**

Malo-Torreiro S, Seijas-Iglesias M, Cuiñas I.
A Comparison of Distribution Models for Fast Variations in the Indoor Radio Channel at 5G Frequency Range 1 Microwave Bands. *Electronics*. 2022; 11(3):449.
https://doi.org/10.3390/electronics11030449

**Chicago/Turabian Style**

Malo-Torreiro, Sergio, Marta Seijas-Iglesias, and Iñigo Cuiñas.
2022. "A Comparison of Distribution Models for Fast Variations in the Indoor Radio Channel at 5G Frequency Range 1 Microwave Bands" *Electronics* 11, no. 3: 449.
https://doi.org/10.3390/electronics11030449