## 2 Background Study
### Earth-Space Link Budget  
For rain attenuation studies and measurement, link budgeting is concerned with the losses and gains at the receiver antenna. The link budget does not differ much from terrestrial links except that free space loss (FSL) is much higher due to the considerable distance between the transponder and the Earth station [23; 24; 25; 27].  
\[P_{r}=P_{t}+G_{tx}+G_{rx}-FSL-L \tag{1}\]  
where \(P_{t}\) is the transmitter power. This is the microwave carrier output power, expressed in \(dBm\) in Equation (1); \(L\) is losses due to the presence of atmospheric gases, vegetation, buildings, clouds, and fog; \(G_{tx}\) is the transmitter antenna gain, \(G_{rx}\) is the receiver antenna gain, FSL is the free space path loss in dB, and \(P_{r}\) is the received signal level in dBm. Compared to terrestrial links discussed in [17], FSL is higher, e.g., above 200 dB in Ka/Q bands [25]. The performance of a communication system is estimated based on the achievable signal-to-noise ratio (SNR) at the receiver. The term SNR (in dB) refers to the estimation of signal strength as a function of signal degradation and background noise. This SNR can be expressed as:  
\[SNR=\frac{P_{t}G_{tx}G_{rx}}{KTBL_{sys}}\left(\frac{4\pi l}{\lambda_{0}} \right)^{2} \tag{2}\]  
where \(L_{sys}\) is system loss at the receiver and transmitter; \(\lambda_{0}\) is free-space wavelength (m), which is determined from the frequency as \(\left(\lambda_{0}=\frac{0.3}{f(\text{GHz})}\right)\); \(G_{tx}\) and \(G_{rx}\) are transmitting and receiving antenna gains, respectively; \(k\) is the Boltzmann constant \(1.38\times 10^{-23}\) J/K ; \(B\) is the bandwidth in (Hz); \(l\) is the link distance (m); and \(T\) is the noise temperature (K) of the system, which is assumed to be 290 K.  
The receiver antenna noise figure can be computed as [28]:  
\[N(dBm)=10\log_{10}(KTB) \tag{3}\]  
\[N(dBm)=174(dBm/Hz)-10\log_{10}B(Hz) \tag{4}\]  
Equation (2) can equivalently be computed in unit decibels (dBm) as  
\[\begin{array}{c}SNR(dB)=P_{t}(dBm)+G_{tx}(dB)+G_{rx}(dB)-FSL(dB)-L_{sys}(dB) \\ \hskip 142.26378 pt+174(dBm/Hz)-10\log_{10}B(Hz)\end{array} \tag{5}\]  
\[SNR(dB)=P_{r}(dBm)-10\log_{10}B(Hz)+174(dBm/Hz) \tag{6}\]  
where \(P_{r}\) is determined from the link profile given parameters. In real-world radio links, for the communications system to acquire the least tolerable quality of service (usually termed as minimum SNR), the received power level often needs to be better than the threshold level. When the received signal magnitude is below the threshold value, a network outage will occur. As a result, the radio link performance evaluation is done by comparing the percentage of outage time with the total time duration. This design allowance for received power is termed as the link margin and defined as the difference between the design value of received power and the minimum threshold value of received power [25; 26]:  
\[LM=P_{r}(dBm)-P_{r,\min}(dBm) \tag{7}\]  
where \(LM\) denotes the link margin measured in \(dB\). \(LM\), which is used to account for fading effects, is sometimes referred to as fade margin.  
Clear Air SNR calculation: The received signal for clear-sky conditions is determined using Equation (1) and the SNR of this link in a clear-sky environment can be determined using (6).  
Rainy time SNR calculation: Here the received signal is additionally degraded by the total rain attenuation amount. Thus, SNR at a rainy time is calculated as [23]:  
\[SNR=(P_{r}-A_{\rm rain})-10\log_{10}B(Hz)+174(dBm) \tag{8}\]  
where \(A_{\rm rain}\) is the attenuation induced by rain. If the SNR at a rainfall rate of exceedance of 0.01% is required, it can be calculated by replacing \(A_{\rm rain}\) by total rain attenuation at a rainfall rate of exceedance of \(A_{0.01}\).