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Characterization of Fading Statistics of mmWave (28 GHz and 38 GHz) Outdoor and Indoor Radio Propagation Channels^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Overview of Measurement Setup and Used Data-Extraction Method

#### 2.1. Case 1: Outdoor Urban Environment at 38 GHz

#### 2.2. Case 2: Indoor Corridor Environment at 28 GHz and 38 GHz

#### 2.3. Case 3: Indoor Office Environment at 28 GHz

#### 2.4. Data Extraction and Calibration

## 3. Channel Statistics

#### 3.1. Definition of Angular Spread Quantifiers

#### 3.2. Characterization of Angular Spread for Outdoor and Indoor Radio Propagation Channels

#### 3.3. Definition of SOFS Quantifiers

#### 3.4. Characterization of SOFS for Outdoor and Indoor Radio Propagation Channels

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Angular distribution of multipath power with respect to azimuth angle of arrival (AoA) for different outdoor mmWave (38 GHz) radio propagation environments; obtained after data calibrations, and normalization operations performed on the measurement results provided in [4]. (

**a**) Tx-Rx separation < 150 m; (

**b**) Tx-Rx separation > 150 and < 250 m; (

**c**) Tx-Rx separation > 250 m Figure 7 of [4].

**Figure 2.**Angular distribution of multipath power with respect to azimuth AoA for different mmWave (38 GHz and 28 GHz) indoor corridor environments; obtained after data calibrations, and normalization operations performed on the measurement results provided in [7]. (

**a**) Tx-Rx separation = 3 m; (

**b**) Tx-Rx separation = 5 m; (

**c**) Tx-Rx separation = 6 m Figure 13 of [7].

**Figure 3.**Angular distribution of multipath power with respect to azimuth AoA for different indoor mmWave (28 GHz) radio propagation environments; obtained after performing numerical integration along delay domain, data calibrations, and normalization operations on the measurement results provided in [6]. (

**a**) LoS Scenario, Figure 8b of [6]; (

**b**) NLoS Scenario 1, Figure 8e of [6]; (

**c**) NLoS Scenario 2, Figure 8h of [6].

**Figure 4.**Level-crossing-rate (LCR) and average fade duration (AFD) plotted against different values of maximum Doppler shift in (

**a**,

**b**), respectively; for different scenarios of outdoor mmWave (case 1; 38 GHz) radio propagation environments. (m = 1, $\rho $ = 2).

**Figure 5.**Spatial auto-covariance and coherence distance (CD) for different scenarios of outdoor mmWave (case 1; 38 GHz) radio propagation environments in (

**a**,

**b**), respectively. (m = 1, ${f}_{d}$ = 1 Hz).

**Figure 6.**LCR and AFD plotted against different values of maximum Doppler shift in (

**a**,

**b**), respectively; for different scenarios of indoor mmWave (Case 2 (a); 28 GHz) radio propagation environments. (m = 1, $\rho $ = 2).

**Figure 7.**Spatial auto-covariance and CD for different scenarios of indoor mmWave (Case 2 (a); 28 GHz) radio propagation environments in (

**a**,

**b**), respectively. (m = 1, ${f}_{d}$ = 10 Hz).

**Figure 8.**LCR and AFD plotted against different values of maximum Doppler shift in (

**a**,

**b**), respectively; for different scenarios of indoor mmWave (Case 2 (b); 38 GHz) radio propagation environments. (m = 1, $\rho $ = 2).

**Figure 9.**Spatial auto-covariance and CD for different scenarios of indoor mmWave (Case 2 (b); 38 GHz) radio propagation environments in (

**a**,

**b**), respectively. (m = 1, ${f}_{d}$ = 10 Hz).

**Figure 10.**LCR and AFD plotted against different values of threshold levels in (

**a**,

**b**), respectively; for different scenarios of indoor mmWave (Case 3; 28 GHz) radio propagation environments. (m = 4 for LoS Scenario and m = 1 for NLoS Scenarios, ${f}_{d}$ = 1 Hz).

**Figure 11.**Spatial auto-covariance and CD for different scenarios of indoor mmWave (Case 3; 28 GHz) radio propagation environments in (

**a**,

**b**), respectively. (m = 4 for LoS Scenario and m = 1 for NLoS Scenarios, ${f}_{d}$ = 10 Hz).

Measurement Scenario | Propagation Environment | Frequency Band | Channel Statistics | |
---|---|---|---|---|

Available | Proposed Extension | |||

Case 1 [4] | Outdoor Urban | 38 GHz | Path Loss, Root Mean Square (RMS) Delay Spread, AoA | Azimuthal Spread Quantification, LCR, AFD, CD, Auto-Correlations |

Case 2 [7] | Indoor Corridor | 28 and 38 GHz | Path Loss, RMS Delay Spread, AoA | Azimuthal Spread Quantification, LCR, AFD, CD, Auto-Correlations |

Case 3 [6] | Indoor Office | 28 GHz | Delay Spread, AoA, Time of Arrival | Azimuthal Spread Quantification, LCR, AFD, CD, Auto-Correlations |

Angular Spread Quantifiers | Quantifiers and Measurement Details | Angular Spread [10] | True Standard Deviation [16,17] | Angular Constriction [10] | Direction of Maximum Fading [10] |

Mathematical Expression: | ${\mathrm{\Lambda}}_{\theta}=\sqrt{1-|{\overline{R}}_{1}{|}^{2}}$ | ${\sigma}_{\theta}=\sqrt{-2\mathrm{ln}\left(\right|{\overline{R}}_{1}\left|\right)}$ | ${\gamma}_{\theta}=\frac{|{\overline{R}}_{2}-{\overline{R}}_{1}^{2}|}{1-|{\overline{R}}_{1}{|}^{2}}$ | ${\theta}_{\mathrm{MF}}=\frac{1}{2}\mathrm{phase}\{{\overline{R}}_{2}-{\overline{R}}_{1}^{2}\}$ | |

Range of Quantifier: | 0∼1. | 0∼2$\pi $ (${0}^{\circ}$∼${360}^{\circ}$) | 0∼1 | $-\pi $∼$\pi $ ($-{180}^{\circ}$∼$+{180}^{\circ}$) | |

Description: | Denotes concentration of multipaths around a single direction. 0 indicates the concentration of energy around exactly one path, while 1 indicates no bias. | Denotes measure of energy dispersion in angular domain. Measures the spread in true scientific notation, i.e., radians or degrees. | Denotes concentration of multipaths about two directions. 1 indicates the concentration of energy about exactly two paths, while 0 indicates no bias. | Denotes the physical direction of maximum fading in radians. | |

Case 1: Outdoor Urban Environment at 38 GHz | Tx-Rx separation < 150 m | 0.9829 | ${105.37}^{\circ}$ | 0.163 | ${17.59}^{\circ}$ |

Tx-Rx separation > 150 m and < 250 m | 0.955 | ${89.6}^{\circ}$ | 0.0941 | $-{1.99}^{\circ}$ | |

Tx-Rx separation > 250 m | 0.891 | ${72}^{\circ}$ | 0.0698 | $-{13.72}^{\circ}$ | |

Case 2 (a): Indoor Corridor Environment at 28 GHz | Tx-Rx separation = 3 m | 0.8463 | ${64.30}^{\circ}$ | 0.7297 | $-{32.33}^{\circ}$ |

Tx-Rx separation = 5 m | 0.8789 | ${69.7}^{\circ}$ | 0.74 | $-{28.5}^{\circ}$ | |

Tx-Rx separation = 6 m | 0.9077 | ${75.50}^{\circ}$ | 0.6605 | $-{28.65}^{\circ}$ | |

Case 2 (b): Indoor Corridor Environment at 38 GHz | Tx-Rx separation = 3 m | 0.767 | ${54}^{\circ}$ | 0.705 | $-{33.9}^{\circ}$ |

Tx-Rx separation = 5 m | 0.969 | ${96.04}^{\circ}$ | 0.322 | ${88.8}^{\circ}$ | |

Tx-Rx separation = 6 m | 0.619 | ${39.82}^{\circ}$ | 0.852 | ${32.1}^{\circ}$ | |

Case 3: Indoor Office Environment at 28 GHz | LoS Scenario (Figure 8b of [6]) | 0.9049 | ${74.89}^{\circ}$ | 0.6834 | $-{3.27}^{\circ}$ |

NLoS Scenario 1 (Figure 8e of [6]) | 0.7906 | ${56.75}^{\circ}$ | 0.3881 | ${77}^{\circ}$ | |

NLoS Scenario 2 (Figure 8h of [6]) | 0.4125 | ${24.74}^{\circ}$ | 0.9212 | $-{72}^{\circ}$ |

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**MDPI and ACS Style**

Gulfam, S.M.; Nawaz, S.J.; Baltzis, K.B.; Ahmed, A.; Khan, a.N.M.
Characterization of Fading Statistics of mmWave (28 GHz and 38 GHz) Outdoor and Indoor Radio Propagation Channels. *Technologies* **2019**, *7*, 9.
https://doi.org/10.3390/technologies7010009

**AMA Style**

Gulfam SM, Nawaz SJ, Baltzis KB, Ahmed A, Khan aNM.
Characterization of Fading Statistics of mmWave (28 GHz and 38 GHz) Outdoor and Indoor Radio Propagation Channels. *Technologies*. 2019; 7(1):9.
https://doi.org/10.3390/technologies7010009

**Chicago/Turabian Style**

Gulfam, Sardar Muhammad, Syed Junaid Nawaz, Konstantinos B. Baltzis, Abrar Ahmed, and and Noor M. Khan.
2019. "Characterization of Fading Statistics of mmWave (28 GHz and 38 GHz) Outdoor and Indoor Radio Propagation Channels" *Technologies* 7, no. 1: 9.
https://doi.org/10.3390/technologies7010009