# Comparative Study of Indoor Propagation Model Below and Above 6 GHz for 5G Wireless Networks
## 3 Propagation Channel Model  
The CI model can be defined as [39]:  
\[P_{L}{}^{CI}(f,d)[dB]=P_{L}(f,d_{0})+10n\log_{10}\biggl{(}\frac{d}{d_{0}} \biggr{)}+X_{\sigma} \tag{1}\]  
where \(P_{L}(f,d)\) is the path loss at different frequencies with various Tx-Rx separation distance, \(n\) is the path-loss exponent (PLE), \(P_{L}(f,d_{0})\) is the path loss in dB at a close-in (CI) distance, d\({}_{0}\), of 1 m, and \(X_{\sigma}\) is a zero-mean Gaussian-distributed random variable with standard deviation \(\sigma\) dB (shadowingeffect) [40]. The PLE and minimum standard deviation are derived by minimum mean square error (MMSE) approach [30]. The floating-intercept (FI) path loss model is used in the WINNER II and 3 GPP standards [35]. It is based on the floating-intercept (\(\alpha\)) and line slope (\(\beta\)) to provide a best minimum error fit of collected path losses as follows:  
\[PL^{FI}(d)[dB]=\alpha+10\beta\log_{10}(d)+\chi_{\sigma}^{FI} \tag{2}\]  
where \(\chi_{\sigma}^{FI}\) is a zero mean Gaussian shadow fading random variable with standard deviation of \(\sigma^{FI}\). As in the CI model, the MMSE is used as a best-fit and requires solving for \(\alpha\) and \(\beta\) to obtain the \(\sigma^{FI}\). To cover a broad range of frequencies and measurements, multi-frequency path loss models are used. The alpha-beta-gamma (ABG) model is utilized for this purpose. The proposed ABG model has 1 m as reference distance and 1 GHz as reference frequency (\(f_{ref}\) set to 1 GHz). The ABG model is given as:  
\[PL^{ABG}(f,d)[dB]=10\alpha\log_{10}\biggl{(}\frac{d}{d_{0}}\biggr{)}+\beta+10 \gamma\log_{10}\biggl{(}\frac{f}{f_{ref}}\biggr{)}+\chi_{\sigma}^{ABG} \tag{3}\]  
where \(\alpha\) and \(\gamma\) are constant coefficients which indicate the effect of frequency and distance on path loss, \(\beta\) is referred to as offset in path loss, \(f\) is frequency in GHz and \(\chi_{\sigma}^{ABG}\) is a Gaussian random variable with standard deviation of \(\sigma^{ABG}\). The ABG model is solved by MMSE to minimize \(\sigma\) by concurrently solving for \(\alpha\), \(\beta\) and \(\gamma\)[30]. The close-in free space reference distance path loss model, with frequency dependent path loss exponent (CIF), is a multi-frequency model that employs the same physically motivated free space path loss (FSPL) anchor at 1 m, as that of the CI model. The CIF model is defined as [36]:  
\[PL^{CIF}(f,d)[dB]=FSPL\Bigl{(}f,d_{ref}\Bigr{)}+10n\biggl{(}1+b\biggl{(}\frac{ f-f_{0}}{f_{0}}\biggr{)}\biggr{)}\log_{10}(d)+\chi_{\sigma}^{CIF}, \tag{4}\]  
where \(n\) denotes the distance dependence of path loss, and \(b\) is a linear frequency dependence factor of path loss over all considered frequencies. The parameter \(f_{0}\) is the reference frequency, which is the weighted frequency average of all measurements for each specific environment scenario, found by summing up, over all frequencies, the number of measurements at a particular frequency and scenario, multiplied by the corresponding frequency, and dividing that sum by the entire number of measurements taken over all frequencies for that specific environment and scenario [35]. Based on the environment and scenario and the number of measurements at a particular frequency in this work, \(f_{0}\) =10.5 GHz. The PLE and minimum standard deviation are derived by minimum mean square error (MMSE) [13]. The DL presents the diffraction loss from shadow edge and the FD presents the signal drop for high frequency band as compared with low band. The DL can be calculated by:  
\[DL(f,d)[dB]=\mathrm{Pr}_{LOS}(f,d_{0})-\mathrm{Pr}_{NLOS}(f,d_{0}) \tag{5}\]  
where the \(\mathrm{Pr}_{\mathrm{LOS}}\) represent the recived power in LOS scenario and \(\mathrm{Pr}_{\mathrm{NLOS}}\) is the recived power in NLOS scenario.