# Feasibility of Ultra-Wideband Channels at Millimeter Wavelengths Faded by Rain in GeoSurf Satellite Constellations

^{*}

## Abstract

**:**

## 1. Satellite Constellations with Zenith Propagation Paths at Any Site

## 2. Rain Attenuation and Phase Delay Due to Rain in Zenith Propagation Paths

## 3. Ultra-Wideband Channels Distorted by Rain

## 4. Experimental Interference

^{®}. We have simulated the transmission of a sequence of ${10}^{4}$ symbols drawn from a quadrature phase-shift keying (QPSK) modulation of long sequences of independent bits at the bit rate $\rho $ (bits per second, bps) according to the value of the roll-off factor $r$. Since the baseband width is fixed to $B=5$ GHz, the bit rate is a function of $r$, given by

- (1)
- The three sites, although in different climatic zones, are practically indistinguishable in all cases.
- (2)
- All histograms show even symmetry; therefore, indicating that for about 50% of the time, we can consider the channel factor to be either $\mu <0$ (dB), therefore, $\gamma <\mathsf{\Gamma}$; or $\mu >0$ (dB), therefore, $\gamma >\mathsf{\Gamma}$.
- (3)
- Histograms with only ISI and with ISI + QI are distinguishable.
- (4)
- With ISI only, the lowest range of attenuation (10 dB) shows more marked peaks at $\mu =0$ dB and $\mu \approx \pm 0.3$ dB. These peaks are largely smoothed when QI is also added.
- (5)
- The roll-off factor $r$ plays a small role because the values of the peaks change a little, especially for $r=1$.

## 5. Modeling Interference

## 6. Channel Capacity Loss

## 7. Conclusions

- (1)
- The three sites considered, although in different climatic zones, are practically indistinguishable in all cases.
- (2)
- The channel factor $\mu $ can be either $\mu <0$ (dB), therefore, $\gamma <\mathsf{\Gamma}$; or $\mu >0$ (dB), therefore, $\gamma >\mathsf{\Gamma}$ with equal probability.
- (3)
- Histograms with only ISI or with ISI + QI are diverse.
- (4)
- With ISI only, the lowest range of attenuation (10 dB) shows more marked peaks in the relative frequency histograms at $\mu =0$ dB and $\mu \approx \pm 0.3$ dB. These peaks are largely smoothed when QI is added.
- (5)
- The roll-off factor $r$ plays a small role because the peaks change only for $r=1$.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Annual probability distribution (%) $P\left(\mathrm{R}\right)$ of exceeding the value indicated in abscissa at Spino d’Adda, Madrid and Tampa.

**Figure 2.**(

**a**) Annual probability distribution (%) $P\left(\mathrm{A}\right)$ of exceeding the value indicated in abscissa at Spino d’Adda, Madrid and Tampa; (

**b**) annual probability distribution (%) $P\left(\mathsf{\Phi}\right)$ of exceeding the value indicated in abscissa at Spino d’Adda, Madrid and Tampa, at 80 GHz and with circular polarization.

**Figure 3.**Rain rate time series $R\left(t\right)$ recorded at Tampa on 27 September 1997. According to the rain gauge collecting rainfall, the rain event started at 7:34:27 AM, local time. Samples are averaged in 1 min.

**Figure 4.**SST simulated event at Tampa, 27 September 1997, started at 7:34:27 AM local time. (

**Upper panel**): rain attenuation $A\left(t\right)$ (dB) at 80 GHz (circular polarization). (

**Lower panel**): relative attenuation at the extremes of a 10 GHz bandwidth. Sampling time is 1 min.

**Figure 5.**SST simulated event at Tampa, 27 September 1997, started at 7:34:27 AM, local time. (

**Upper panel**): phase delay $T\left(t\right)$ (picoseconds) at 80 GHz (circular polarization). (

**Lower panel**): relative phase delay at the extremes of a 10 GHz bandwidth. Sampling time is 1 min.

**Figure 6.**Flowchart of the baseband receiver in ideal conditions. $S\left(f\right)$ is the two-sided spectrum of the Nyquist pulse, $\sqrt{S\left(f\right)}$ is its matched filter, $n\left(t\right)$ is the receiver total additive Gaussian white noise.

**Figure 7.**Flowchart of the quadrature baseband receiver in rain attenuation. $S\left(f\right)$ is the two-sided spectrum of the Nyquist reference pulse assumed to be positive, $\sqrt{S\left(f\right)}$ is the matched filter and $n\left(t\right)$ is the receiver total additive Gaussian white noise for each channel of equal power.

**Figure 8.**Relative frequency histogram of the channel factor $\mu $ (dB) with ISI (

**upper panel**) and with ISI and QI (

**lower panel**).

**Color key**: blue = Spino d’Adda; green = Madrid; red = Tampa.

**Curve key**: continuous $9\le {A}_{80\mathrm{GHz}}\le 11$ dB; dashed $18\le {A}_{80\mathrm{GHz}}\le 22$ dB; “+” $27\le {A}_{80\mathrm{GHz}}\le 33$ dB. Roll-off factor $r=0.25$.

**Figure 9.**Relative frequency histogram of the channel factor $\mu $ (dB) with ISI (

**upper panel**) and with ISI and QI (

**lower panel**).

**Color key**: blue = Spino d’Adda; green = Madrid; red = Tampa.

**Curve key**: continuous $9\le {A}_{80\mathrm{GHz}}\le 11$ dB; dashed $18\le {A}_{80\mathrm{GHz}}\le 22$ dB; “+” $27\le {A}_{80\mathrm{GHz}}\le 33$ dB. Roll-off factor $r=0.50$.

**Figure 10.**Relative frequency histogram of the channel factor $\mu $ (dB) with ISI (

**upper panel**) and with ISI and QI (

**lower panel**).

**Color key**: blue = Spino d’Adda; green = Madrid; red = Tampa.

**Curve key**: continuous $9\le {A}_{80\mathrm{GHz}}\le 11$ dB; dashed $18\le {A}_{80\mathrm{GHz}}\le 22$ dB; “+” $27\le {A}_{80\mathrm{GHz}}\le 33$ dB. Roll-off factor $r=1$.

**Figure 11.**Average relative frequency histogram of the channel factor $\mu $ (dB) in the presence of ISI and QI.

**Curve key**: black $9\le {A}_{80\mathrm{GHz}}\le 11$; blue $18\le {A}_{80\mathrm{GHz}}\le 22$; red $27\le {A}_{80\mathrm{GHz}}\le 33$. Curves are averaged over the sites and roll-off factors.

**Table 1.**Geographical coordinates, altitude (km), rain height ${H}_{R}$ (km), number of years of continuous rain rate time series measurements at the indicated sites.

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

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

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

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

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**MDPI and ACS Style**

Matricciani, E.; Magarini, M.; Riva, C.
Feasibility of Ultra-Wideband Channels at Millimeter Wavelengths Faded by Rain in GeoSurf Satellite Constellations. *Telecom* **2023**, *4*, 732-745.
https://doi.org/10.3390/telecom4040033

**AMA Style**

Matricciani E, Magarini M, Riva C.
Feasibility of Ultra-Wideband Channels at Millimeter Wavelengths Faded by Rain in GeoSurf Satellite Constellations. *Telecom*. 2023; 4(4):732-745.
https://doi.org/10.3390/telecom4040033

**Chicago/Turabian Style**

Matricciani, Emilio, Maurizio Magarini, and Carlo Riva.
2023. "Feasibility of Ultra-Wideband Channels at Millimeter Wavelengths Faded by Rain in GeoSurf Satellite Constellations" *Telecom* 4, no. 4: 732-745.
https://doi.org/10.3390/telecom4040033