*2.3. Atmospheric Attenuation*

Atmospheric attenuation and weather e ffects are important for mmWave propagation. The atmospheric loss is generally defined in terms of decibel (dB) loss per kilometer of propagation. Since the fraction of the signal loss is a strong function of the distance travelled, the actual signal loss experienced by a specific mmWave link due to atmospheric e ffects depends directly on the length of the link. A simple model describing the attenuation of mmWave for the range of 1 to 100 GHz through atmosphere *AL* can be described as follows:

$$AL = A\_r + A\_\upsilon + A\_\upsilon + A\_p \text{ (dB)}\tag{8}$$

which primarily includes the attenuation e ffects of dry air (including oxygen), humidity, fog, and rain. Here, *Ar* refers to the attenuation caused by rain, *Av* represents the water vapor attenuation, *Ao* represents the attenuation due to dry air, and *Ap* is the attenuation as a result of other-than-rain precipitation (i.e., fog, sleet, snow).

There are other possible causes of losses (*OL*), such as the coaxial cable loss at the transmitter and receiver; temperature and water vapor a ffecting the stability of the transmit and receive signal terminals (equipment, circuits, etc.); wetness of the transmit and receive antenna surface causing considerable attenuation; and anything that obstructs the LOS channel introducing additional loss.

#### 2.3.1. Water Vapor Attenuation

Attenuation due to absorption by oxygen and water vapor is always present and should be included in the calculation of total propagation loss at frequencies above approximately 10 GHz. For the millimeter frequency range, the resonance lines for water vapor and oxygen are at 22.3, 183.3, 323.8 GHz; and 57–63 and 118.74 GHz, respectively.

To illustrate the electromagnetic signal attenuation due to dry air and water vapor, Figure 1 was plotted based on the equations given in [35], for a given barometric pressure and temperature. The first excess attenuation occurs at around 22 GHz due to water vapor, and the second at 60 GHz due to oxygen. Oxygen absorption has a maximum attenuation at 60 GHz and contributes to 7–15 dB/km in the received signal strength at the frequency range of 57–63 GHz. For 32 and 38 GHz, the signal is mainly a ffected by water vapor, and the attenuation is less than 0.15 dB for a 1 km link length. For signals in E-band, the attenuation due to humidity can reach approximately 0.5 dB/km [24,35].

**Figure 1.** Frequency-dependent attenuation of electromagnetic radiation in standard atmosphere (barometric pressure 1013 mbar, temperature 15 ◦C, water vapor density of 7.5 g/m3) and rain attenuation in dB/km at various rainfall rates.

#### 2.3.2. Rainfall Effects on Radio Signals

A power law empirical model is often used in the calculation of rain-induced attenuation *Ar* and the average rain rate *R* [28,29] along the path:

$$A\_I = aR^bL \text{ (dB)}\tag{9}$$

where the constants *a* and *b* are related to frequency, rain temperature, the rain drop size distribution, and polarization, depending on the rain attenuation model. In our study, *L* (km) is the length of the microwave link and *Ar* is the overall signal attenuation induced by rain between the transmitter and receiver. A set of commonly used power law coefficients can be found in International Telecommunication Union (ITU) Recommendation P. 838-3 [28]. The power law coefficients for vertical polarization (*aV*, *bV*) and horizontal polarization (*aH*, *bH*) at different frequencies are summarized in Table 1. Assuming vertical polarization, the power law coefficients *a* and *b* used in our measurement are given in Table 1.


**Table 1.** Power law coefficients for different frequencies.

The rain attenuation values for the considered millimeter frequency band in this study at various rainfall rates (*R*) are given in Table 2. We categorized the rainfall intensity into six groups, including very light rain (rain rate < 1mm/h), light rain (1 mm/h ≤ rain rate < 2 mm/h), moderate rain (2 mm/h ≤ rain rate < 5 mm/h), heavy rain (5 mm/h ≤ rain rate < 10 mm/h), very heavy rain (10 mm/h ≤ rain rate < 20mm/h), extreme heavy rain (rain rate ≥ 20 mm/h). The theoretical rain-induced signal attenuation per kilometer based on Equation (9) for our considered millimeter frequencies is presented in Figure 2a. Compared to other atmospheric factors, atmospheric attenuation due to rain is one of the most noticeable components of excess losses at our considered frequencies. It is not important for low frequency bands, but rain affects links in millimeter frequency ranges, especially for higher frequencies. For increasing rain rate, the rain attenuation experienced by E-band links becomes more severe compared to the 32 and 38 GHz links. For a very heavy rain event, the rain-induced signal attenuation can be up to 9.7 dB for the 82 GHz link at a rain intensity of 20 mm/h. Figure 2b gives the theoretical rain attenuation for our measurement setup. Both 32 and 38 GHz links are 7-km long, and both 72 and 82 GHz are 3 km long. Based on the power law coefficients given by ITU-R P. 838-3, a 7-km long 38 GHz link experiences similar or less signal attenuation compared to a 3 km E-band link for rain intensity lower than 7 mm/h. At 32 GHz, the rain attenuation is lower compared to an E-band signal, even if the link has more than double the deployment length.


Signal due (dB/km).

to

rain

loss

**Table**

**2.**

**Figure 2.** The theoretical rain-induced signal attenuation for various rain rates at different frequencies: (**a**) per kilometer; (**b**) over a 7-km long 32 GHz 2 × 2 line-of-sight multiple-input multiple-output (LOS-MIMO) link, a 7-km long single-input single-output (SISO) 38 GHz link, a 3-km long 72 GHz link, and a 3-km long 82 GHz test link using our measurement scenario.

#### 2.3.3. Rain Rate Estimation Using the Receive Signal Levels from Millimeter-Wave Links

The use of microwave links for near-ground environmental monitoring is a new technology, and it has shown to be an effective tool for rainfall monitoring in over 20 countries. The method of retrieving the rain rate from the rain-induced attenuation in the received signal level is based on the power law model in Equation (9) from the recommendations of the ITU-R P. 838-3:

$$R = \sqrt[b]{\frac{A\_r}{aL}} \left(\text{mm/h}\right) \tag{10}$$

For a vertical polarized setup, the power law coefficients *a* and *b* for the frequencies considered in this study are presented in Table 1, derived from [28]. Therefore, the average rain rate along a link can be derived from the microwave link rain-induced attenuation. In order to determine the signal attenuation caused by rain, we will need to choose a reference level *Pref*, which can be calculated using the average of the received power in the previous 3 hours in dry weather before rain [36,37]. If there are *I* observations, then the rain attenuation for the *i*th observation becomes:

$$A\_{r,i} = P\_{ref} - P\_{R,i} \tag{11}$$

For the case of the LOS-MIMO system, we assume that link length *L* is the same for all MIMO data streams.

## *2.4. Outdoor Measurement*

We present here a summary of the measurements from three outdoor test mmWave links and local rainfall measurements using rain gauges. These measurements are also used to validate the accuracy of rain rate estimation.

The locations of the three test links are illustrated in Figure 3. The measurement setup parameters are given in Table 3. The transmitter and the receiver of the 32 GHz LOS-MIMO link and the 38 GHz link were closely installed between site A and B. Both links had a length of approximately 6.87 km. One side of the two links was on the roof of the Ericsson building (site A), close to water. Both the 32 GHz LOS-MIMO link and 38 GHz SISO link were operated in a line-of-sight environment. The 32 GHz LOS-MIMO link was horizontally deployed, with antenna separation at both sites. The antenna separation at one end (site B) was fixed and installed at 5 m, whereas antennas at the other end (site A) were installed on tripods, with an antenna separation distance of 7.93 m. The details of the measurement setup can be found in [38]. Here, the radio link operating in the forward transmission direction is referred to as link 1, while the radio link operating in the opposite transmission direction is referred to as link 2. The 32 GHz LOS-MIMO link employed 2 antennas at both the transmit and receive sides, while 2 data streams were transmitted in the forward direction and in the opposite direction over the radio link. Altogether, 4 data streams were in transmission simultaneously. Note that the data used in this study from the LOS-MIMO test link is recorded at the receiver without post-processing, but for practical deployment, the received data streams should be decoupled using carrier-to-interference (C/I) measurement. Since the rain attenuation is mainly distance dependent as shown in Equation (9), the actual wanted and interference signal power will not impact on the accuracy of rain retrieval analysis.

**Figure 3.** The measurement setup and locations in Gothenburgh, Sweden. SMHI, Swedish Meteorological and Hydrological Institute.



For the 38 GHz SISO link, one data stream was transmitted in the forward and reverse directions, and there were 2 data streams transmitting instantaneously over the radio link.

For the 3 km SISO E-band link, one end was also installed on the roof of the Ericsson building at site A and was deployed between sites A and C. The geographic locations of the E-band links are listed in Table 3. In the forward transmission the radio link operates at 72.625 GHz, while in the reverse transmission the radio link operates at 82.625 GHz.

All the mmWave links have a sampling interval of 30 seconds. Rain, humidity, temperature, air pressure, and wind information were provided by a weather station equipped with a rain gauge located at the rooftop of the Ericsson building. The accuracy of the rain gauge is of the order +/− 3% [39]. We used the measurement from this rain gauge for the analysis in the results section. As this weather station was located on the rooftop, we also selected the closest rain gauges operated by the Swedish Meteorological and Hydrological Institute (SMHI). The SMHI rain gauge reported the cumulative rain amount in mm over 1 day and its location is indicated in Figure 3.

## **3. Measurement Results**

During the outdoor trial measurements, the received signal level and path attenuation were recorded in changing weather conditions for the three mmWave links at 32 GHz, 38 GHz, and E-band ranges. All the links were in operation at the same time.
