# Path Loss Measurements and Model Analysis in an Indoor Corridor Environment at 28 GHz and 38 GHz
## 3 Path Loss Measurements and Models
### Path Loss Propagation Models
#### 3.2.2 The Floating Intercept (FI) Free Space Reference Distance Path Loss Prediction Model  
This model relies on two major integral parts, i.e., the line slope, as well as the floating intercept. The FI model is good at achieving the optimal minimum error fit for the path loss values, [39; 75]. It can be expressed by Equation (15);  
The equation of this path loss model is [39]:  
\[PL^{FI}(d)[dB]=\propto+10.\beta log_{10}(d)+X_{\sigma SF}^{FI} \tag{15}\]  
This model adopts \(\propto\) as the floating intercept in \(dB\), and the slope of the line is \(\beta\) (not as in PLE). Moreover, \(\propto\) and \(\beta\) were the two parameters adopted by this FI model to make it different from the CI model. The zero-Gaussian shadow fading (in \(dB\)) variable over the mean path loss on a specified distance was \(X_{\sigma SF}^{FI}\). The best fit, such as the CI model, entailed solving \(\propto\) and \(\beta\) and minimizing \(\sigma\); the closed-form optimized solutions are provided below. It is worth noting that the FI model requires two model parameters, whereas the CI model only requires one. Let \(B=PL^{FI}(d)[dB]\), and \(D=10.log_{10}(d)\)  
Then, Equation (15) becomes,  
\[B=\propto+\beta D+X_{\sigma SF}^{FI}. \tag{16}\]  
\[X_{\sigma SF}^{FI}=B-\alpha-\beta D \tag{17}\]  
polarizations. They still closely matched the V-H polarization than the V-V. When the experiment was run using 28 GHz V-V antenna polarization, the PLE value was 2.254. However, when the experiment was run using a V-H antenna polarization, the PLE value increased to 2.979, indicating that the signal degraded more in the V-H polarization than in the V-V mode. Moreover, the values of \(\alpha\) for the V-V and V-H were 58.8294 and 59.9354, respectively. Nevertheless, the value of \(\beta^{\rm FI}\) rose from 2.154 to 3.05. It was observed that the value of \(\alpha^{FI}\) declined from 1.7431 (for V-V) to 1.3008 (for V-H). When transitioning from the V-V to the V-H antenna polarizations in the 38 GHz frequency band, there was an increase of 0.4186 in the path loss exponent. This shows that while changing antenna polarizations at a 38 GHz frequency, signal degradation occurred. Figure 8: Path loss versus distance at 28 GHz for the LOS scenario and V-V polarization. Figure 9: Path loss versus distance at 28 GHz for the LOS scenario and V-H polarization. The curves are shown in Figures 10 and 11. When contrast to the 28 GHz frequency, the PLEs for both antenna polarizations were significantly larger at 38 GHz. This is because increased scattering and penetration losses were generated by an increase in the signal attenuations at higher frequencies. The various irregular materials, such as bricks, concrete, and other building materials (e.g., wooden doors and elevator doors), produce interference and may potentially impact the outcome. The standard deviation for shadow fading \(\sigma^{CI}\) for the V-V antenna polarization was 3.1874; nevertheless, it climbed slightly to 4.1001 for the V-H antenna polarization. This demonstrates that there are many signal fluctuations in both situations. Additionally, \(\alpha^{FI}\) has a 1.6439 increase from the V-V to the V-H. While \(\beta^{FI}\) goes from 3.1461 to 3.6625, the \(\sigma^{FI}\) min value rises from V-V to V-H by 0.8016. Figure 11: Path loss versus distance at 38 GHz for the LOS scenario and V–H polarization. Figure 10: Path loss versus distance at 38 GHz for the LOS scenario and V–V polarization. Figures 12 and 13 compare the LOS CI at 28 and 38 GHz for the two antenna polarizations considered. It was discovered that path loss was more pronounced at 38 GHz than at 28 GHz for the V-V polarization. This indicates that higher frequencies are subject to the numerous propagation effects and path losses. The correlations between the path loss values in FI (in Figures 14 and 15) are very close to V-H, but have larger differences in the V-V polarization (similar to the CI case). This means that in the LOS scenario, both CI and FI behave similarly.