## 5 Path-Loss Models and Analysis  
We investigated different path-loss models for single and multiple frequencies. For a single frequency, we used the CI free space reference range model [16], as follows:  
\[P_{L}^{CI}(f,d)[dB]=P_{L}(f,d_{0})+10n\ \log_{10}\left(\frac{d}{d_{0}}\right)+W_{ \sigma}, \tag{1}\]  
where \(P_{L}(f,d)\) is the path loss at operating frequencies, with multiple separation ranges; \(n\) is the path-loss exponent (PLE); \(P_{L}(f,d_{0})\) is the path loss in dB at a close-in (CI) range, \(d_{0}\), of 1 m; and \(W_{\sigma}\) is a zero-mean Gaussian-distributed random variable with standard deviation \(\sigma\) dB (shadowing impact). Figure 2: Measurement environment. (**a**) floor plan, (**b**) Tx location in Corridor A, and (**c**) Rx location in Corridor B. The other model, with three parameters, is known as the ABG model. It includes a frequency-dependent term, \(\gamma\); a distance-dependent term, \(\alpha\); and an optimization factor, \(\beta\), to describe the path loss at various frequencies [13; 21; 30]. The ABG model equation is given by the following [13]:  
\[PL^{ABG}(f,d)[dB]=10\alpha\ \log_{10}\left(\frac{d}{d_{0}}\right)+\beta+10\gamma \ \log_{10}\left(\frac{f}{f_{ref}}\right)+W_{o}^{ABG} \tag{2}\]  
The minimum mean square error (MMSE) is the strategy by all of the parameters for the CI and ABG path-loss models [16]. The CI and ABG path-loss models for all of the measured frequencies are shown in Figure 3a-c. Figure 3a shows the variation in path loss and the Tx-Rx separation distance (scatter plot and best-fit CI model at 19 GHz in NLOS environments). The path loss varies as a function of distance, based on the number of multipath components (MPCs) with their gain. The constructive and destructive nature of MPCs induces changes in the path loss. Based on the PLEs for CI and ABG (\(n=0.4\) and \(\alpha=0.2\)) at 19 GHz, the environment represents a waveguide in which many reflected paths are added constructively. Moreover, the reflected paths have a higher power because of reflections from the surrounding environment, which derive from the concrete stairs, walls, and ribbed metal ceiling; the Tx horn antenna is directed toward the stairs. Figure 3a shows that the CI and ABG models totally matched at 19 GHz for the last locations (above a 7 m Tx-Rx separation distance). The path loss variation as a function of the Tx-Rx separation distance at 28 GHz is shown in Figure 3b. It can be noted that the fluctuations in path loss as a function of distance are the same as those shown in Figure 3a for 19 GHz. However, the path-loss measurement values increase as the frequency increases. The value of PLEs for CI and ABG models (\(n=0.8\) and \(\alpha=0.2\)) are also low, which indicates that the total power of the received signal is strong and decays minimally with distance (waveguide effects due to the physical structure of the environment). At 28 GHz, there is divergence between both CI and ABG models; however, the divergence becomes low above a 7 m separation distance, as shown in Figure 3b. Figure 3: _Cont._  
Figure 3c illustrates the path loss variations as a function of the separation distance at 38 GHz. This figure shows that the path-loss measurement values at 38 GHz exceed those at 19 and 28 GHz, due to the higher frequency. The PLE for the CI model is higher compared with the PLE for the CI models at 19 and 28 GHz. However, it is still low compared with the theoretical free-space PLE (FSPL = 2), due to the constructive phenomena of MPCs and the waveguide effects induced by the concrete walls, stairs, ribbed metal ceiling, and iron railing of the corridor, which surround the Rx and Tx antennas. According to above test, it is shown that measured data for a 38 GHz band at an I2O environment are comparable to the CI and ABG models. Figure 3: Path loss versus Tx–Rx separation distance using horn-omnidirectional antennas for the soft non-line-of-sight (NLOS) environment. Here, the ABG model has a high deviation from the CI model at all locations of measurement.