# Path Loss Measurement of Outdoor Wireless Channel in D-band
## 2 Methods  
The electromagnetic waves propagation in Free-space is shown in Figure 2.  
Figure 2: LOS propagation in free space.  
According to the classic Friis transmission equation [30], the relationship between the transmit and the receive power of a wireless link consisting of transmit and receive antennas can be obtained. Its expression is given as:  
\[P_{r}=P_{t}+G_{t}+G_{r}-L \tag{1}\]  
where, \(G_{t}\) and \(G_{r}\) represent the gains of the transmit and receive antenna respectively; \(P_{r}\) and \(P_{t}\) represent the transmit and receive power; and \(L\) is free-space path loss (FSPL).  
The FSPL model describes the channel propagation characteristics in an ideal propagation environment. Its expression is given as:  
\[FSPL(d,f)=20\log_{10}(4\pi df/c) \tag{2}\]  
where, \(d\) is the wireless transmission distance;\(f\) is the transmission frequency; and \(c\) is the speed of light.  
It can be seen from the above formula that the free space path loss is only related to the transmission distance \(d\) and the frequency \(f\). When the transmission distance or frequency doubles, the loss is increased by 6 dB. The free-space propagation model is suitable for a wireless environment with an isotropic propagation medium (such as a vacuum), and, therefore, is not an ideal model to apply to real scenarios.  
Instead, path loss in the real world is highly dependent on the transmission environment. The FSPL model is not accurate enough to describe the actual propagation characteristics. In 5G, two path loss models--the short-range reference (CI) model and the floating intercept (FI) model--are commonly used to characterize the power attenuation during propagation. Both the CI and the FI models are single-frequency path loss models. They can only simulate the path loss at a certain frequency. The 1 m CI model (3) is one of the most frequently used large-scale path loss models to predict the signal strength over distances for various frequencies [31; 32]:  
\[PL^{CI}(f,d)=FSPL(f,d_{0})+10\beta\log 10(\frac{d}{d_{0}})+X_{\sigma}^{CI},d>d_{0} \tag{3}\]  
where, \(FSPL\) is the free space path loss at carrier frequency \(f\) with \(d_{0}=1\) m; \(d_{0}\) is a reference distance; \(\beta\) is the path loss exponent that characterizes the dependence of path loss on \(d\); and \(X_{\sigma}^{CI}\) is the large-scale shadow fading that can be modeled as a zero-mean Gaussian distributed random variable with standard deviation \(\sigma\) (in dB).  
The CI model has only one variable (\(\beta\)), which can be obtained by the least squares linear fitting method, that is, fitting the measurement data with the smallest error. Therefore, the complexity of the CI model is relatively low.  
The FI model is used in the WINNER II and the 3 rd Generation Partnership Project (3 GPP) [33; 34]. Its expression is given as:  
\[PL^{FI}(f,d)=\alpha+10\beta\log 10(\frac{d}{d_{0}})+X_{\sigma}^{FI},d>d_{0} \tag{4}\]  
where, \(\alpha\) is a floating intercept in dB that represents the free-space path loss at \(d_{0}=1\) m; \(d_{0}\) is a reference distance; \(\beta\) is the path loss exponent; and \(X_{\sigma}^{FI}\) is the large-scale shadow fading. Path loss model parameters \(\alpha\), \(\beta\), and \(\sigma\) are estimated by the least squares linear fitting method. Similar to the CI model, two variables (\(\alpha\) and \(\beta\)) can be obtained by minimizing \(\sigma\).