# Earth-to-Earth Microwave Rain Attenuation Measurements: A Survey On the Recent Literature
## 3 Theoretical and Experimental Framework
### Signal and Rainfall Measurement Parameters  
A typical measurement setup of rain attenuation includes a transceiver system with a distance L between transmitter and receiver, as they are depicted in Figure 2. The received power is given through the fundametal equation for a link budget calculation:  
\[P_{r}=P_{t}+G_{total}-L_{total}-A_{path} \tag{7}\]  
where \(P_{t}\) stands for the transmitter power output; \(G_{total}=\sum\limits_{i=1}^{N}G_{i}\) are the transmitter/receiver gains while \(L_{total}=\sum\limits_{i=1}^{M}L_{i}\) are the total transmitter and receiver losses. Both the gains and the losses could be multiple in number. They are generally depended on the complexity of the transmitter and receiver chains. \(A_{path}\) stands for the path loss. The path loss for a specific frequency of operation, constant transmitter, receiver setup in general is given by:  
\[A_{path}=A_{dry}+A_{rain}, \tag{8}\]  
where \(A_{rain}\) are the losses due to rain and \(A_{dry}\) are the losses due to path. Therefore the difference in power at the receiver for dry weather minus the difference in strength due to rain gives us the signal attenuation due to rain. \[P_{r}\big{|}_{dry}-P_{r}\big{|}_{rain}=A_{rain}, \tag{9}\]  
This is a straightforward approach for the rain attenuation measurement over the distance L under the condition that the received power remains constant over time when there is no rain. In practice, as it can be seen from Figure 3, the baseline, i.e., the received power when \(A_{rain}=0\) is not constant, since power affected by interference, noise, multipath propagation and several other meteorological parameters such as water vapor, humidity, wind, etc., affect the measurements significantly. In Figure 4, during a very high rainfall event, it is clear that there is a significant signal attenuation due to rain. Figure 2: Typical measurement setup of rain attenuation. As it is shown in figure after the rain, there is more considerable signal fluctuation \(\pm 0.2\) dB in the received power. The signal fluctuation after the precipitation event is attributed to the corresponding change in atmospheric humidity and the concentration of small water droplets in the atmosphere. A fundamental quantity in the calculation of rain attenuation is the specific rain attenuation (\(A\)) which is given in dB/km. The losses due to rain (\(A_{min}\)) are related to specific rain attenuation, in the case whereas the rainfall is uniformly distributed along the physical path length with \(L\)[25] between the transmitter and the receiver:  
\[A_{rain}=AL, \tag{10}\]  
The general equation relating losses due to rain with specific rain attenuation along \(L\) is given by [26]:  
\[A_{rain}=\int\limits_{L_{TX}}^{L_{RX}}A(l)dl, \tag{11}\]  
where \(L_{TX}\), \(L_{RX}\) is the location of the transmitter and the receiver respectively related to the physical path length by \(L=|L_{TX}-L_{RX}|\). According to [PERSON] [27], the relationship correlating specific rain attenuation to rain rate is given by:  
\[A=aR^{b}, \tag{12}\]  
where the coefficients \(\alpha\), b depends on the frequency, polarization, temperature, and drop size distribution. The most common instrument for rainfall measurement is a typical typing bucket with usually 60 to 1 min integration times. According to P.837-6-Annex1 recommendation, the exact reported specification is that \"rainfall rate statistics with a 1-min integration time are required for the prediction of rain attenuation in the earth to earth links\" [28]. Several models have been proposed to convert rain rates from various integration times to one minute [29; 30]. In order to have the best possible correlation, the path length must be small so that the rainfall is considered uniform or there are several rain gauges along the path. Further validation of rain attenuation measurements is possible through two-dimensional video, OTT Parsivel, and laser optical disdrometers that measure rainfall intensity [31].