# Outage Probability versus Carrier Frequency in GeoSurf Satellite Constellations with Radio-Links Faded by Rain

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## Abstract

**:**

## 1. The GeoSurf Satellite Constellations

## 2. The Synthetic Storm Technique Applied to Zenith Paths

## 3. Outage Probability Factor

## 4. Model of the Average Outage Probability Factor

## 5. In-Band Outage Probability Factor

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Annual average probability $P\left(A\right)$(%) of exceeding the rain attenuation $A$ (dB) indicated in abscissa, at the indicated sites: Spino d’Adda (SP, blue continuous line); Gera Lario (GL, black continuous line); Fucino (FC, cyan continuous line); Madrid (MD, green continuous line); Prague (PR, magenta continuous line); Tampa (TM, cyan dashed line); Norman (NR, magenta dashed line); White Sands (WS, green dashed line), at 16 GHz in zenith paths. When the power margin in the zenith radio-links of the GeoSurf satellite constellations is equal to $A$ (dB), $P\left(A\right)$ represents the outage probability.

**Figure 2.**Annual average probability $P\left(A\right)$(%) of exceeding the rain attenuation $A$ (dB) indicated in abscissa, at the indicated sites: Spino d’Adda (SP, blue continuous line); Gera Lario (GL, black continuous line); Fucino (FC, cyan continuous line); Madrid (MD, green continuous line); Prague (PR, magenta continuous line); Tampa (TM, cyan dashed line); Norman (NR, magenta dashed line); White Sands (WS, green dashed line), at 30 GHz in zenith paths. When the power margin in the zenith radio-links of the GeoSurf satellite constellations is equal to $A$ (dB), $P\left(A\right)$ represents the outage probability.

**Figure 3.**Annual average probability $P\left(A\right)$(%) of exceeding the rain attenuation $A$ (dB) indicated in abscissa, at the indicated sites: Spino d’Adda (SP, blue continuous line); Gera Lario (GL, black continuous line); Fucino (FC, cyan continuous line); Madrid (MD, green continuous line); Prague (PR, magenta continuous line); Tampa (TM, cyan dashed line); Norman (NR, magenta dashed line); White Sands (WS, green dashed line), at 40 GHz in zenith paths. When the power margin in the zenith radio-links of the GeoSurf satellite constellations is equal to $A$ (dB), $P\left(A\right)$ represents the outage probability.

**Figure 4.**Annual average probability $P\left(A\right)$(%) of exceeding the rain attenuation $A$ (dB) indicated in abscissa, at the indicated sites: Spino d’Adda (SP, blue continuous line); Gera Lario (GL, black continuous line); Fucino (FC, cyan continuous line); Madrid (MD, green continuous line); Prague (PR, magenta continuous line); Tampa (TM, cyan dashed line); Norman (NR, magenta dashed line); White Sands (WS, green dashed line), at 80 GHz in zenith paths. When the power margin in the zenith radio-links of the GeoSurf satellite constellations is equal to $A$ (dB), $P\left(A\right)$ represents the outage probability.

**Figure 5.**Probability factor $\rho \left(A,f\right)$ as function of frequency, for fixed values of $A$ ranging approximately from 3 to about 30 dB in 0.2 dB steps (blue continuous curves): (

**a**) for Spino d’Adda; (

**b**) Prague. The red curve is the average value ${\rho}_{m}\left(f\right)$, a parameter independent of attenuation. Notice the different ordinate range.

**Figure 6.**Probability factor $\rho \left(A,f\right)$ as function of frequency, for fixed values of $A$ ranging approximately from 3 to about 30 dB in 0.2 dB steps (blue continuous curves): (

**a**) Tampa; (

**b**) White Sands. The red curve is the average value ${\rho}_{m}\left(f\right)$, a parameter independent of attenuation. Notice the different ordinate range.

**Figure 7.**Mean error (%) produced by Equation (3) as frequency increases from 16 GHz to 100 GHz. Spino d’Adda (SP, blue continuous line); Gera Lario (GL, black continuous line); Madrid (MD, green continuous line); Prague (PR, magenta continuous line); Tampa (TM, cyan dashed line); Norman (NR, magenta dashed line); White Sands (WS, green dashed line).

**Figure 8.**In-band probability factor ${I}_{p}$, Equation (4), versus frequency, Equation (5), at the indicated sites for ${B}_{w}=1$ GHz: Spino d’Adda (SP, blue continuous line); Gera Lario (GL, black continuous line); Fucino (FC, cyan continuous line); Madrid (MD, green continuous line); Prague (PR, magenta continuous line); Tampa (TM, cyan dashed line); Norman (NR, magenta dashed line); White Sands (WS, green dashed line), in zenith paths.

**Table 1.**Geographical coordinates, altitude (km), rain height H

_{R}(km), and number of years of continuous rain rate measurements at the indicated sites.

Site | Latitude N (°) | Longitude E (°) | $\mathbf{Altitude}{\mathit{H}}_{\mathit{S}}\left(\mathbf{km}\right)$ | Precipitation Height H_{R} (km) | Rain Rate Data Bank (Years) |
---|---|---|---|---|---|

Spino d’Adda (Italy) | 45.4 | 9.5 | 0.084 | 3.341 | 8 |

Gera Lario (Italy) | 46.2 | 9.4 | 0.210 | 3.483 | 5 |

Fucino (Italy) | 42.0 | 13.6 | 0.680 | 2.905 | 5 |

Madrid (Spain) | 40.4 | 356.3 | 0.630 | 3.001 | 8 |

Prague (Czech Republic) | 50.0 | 14.5 | 0.250 | 3.051 | 5 |

Tampa (Florida) | 28.1 | 277.6 | 0.050 | 4.528 | 4 |

Norman (Oklahoma) | 35.2 | 262.6 | 0.420 | 4.145 | 4 |

White Sands (New Mexico) | 32.5 | 253.4 | 1463 | 4.744 | 5 |

Site | $\mathit{a}$ | $\mathit{b}$ |
---|---|---|

Spino d’Adda (Italy) | 0.937 | 0.753 |

Gera Lario (Italy) | 1.008 | 0.756 |

Fucino (Italy) | 1.123 | 0.823 |

Madrid (Spain) | 1.007 | 0.518 |

Prague (Czech Republic) | 0.828 | 0.623 |

Tampa (Florida) | 0.532 | 0.315 |

Norman (Oklahoma) | 0.655 | 0.411 |

White Sands (New Mexico) | 0.711 | 0.495 |

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**MDPI and ACS Style**

Matricciani, E.; Riva, C.
Outage Probability versus Carrier Frequency in GeoSurf Satellite Constellations with Radio-Links Faded by Rain. *Telecom* **2022**, *3*, 504-513.
https://doi.org/10.3390/telecom3030027

**AMA Style**

Matricciani E, Riva C.
Outage Probability versus Carrier Frequency in GeoSurf Satellite Constellations with Radio-Links Faded by Rain. *Telecom*. 2022; 3(3):504-513.
https://doi.org/10.3390/telecom3030027

**Chicago/Turabian Style**

Matricciani, Emilio, and Carlo Riva.
2022. "Outage Probability versus Carrier Frequency in GeoSurf Satellite Constellations with Radio-Links Faded by Rain" *Telecom* 3, no. 3: 504-513.
https://doi.org/10.3390/telecom3030027