## 3 Radio Wave Propagation Analysis
### Estimation of the Ricean K-Factor  
All measurement environments of this study were LOS environments, so the Nakagami-Rice distribution is used to understand small-scale fading. The Rician K-factor, which evaluates fading behavior, can be used to evaluate communication stability. The Rician K-factor for the measurement results or analytical data generated with Equation (1) is estimated using the moment method expressed by the following equation [48]:  
\[K=\frac{\left|V\right|^{2}}{\left|v(t)\right|^{2}}=\frac{\sqrt{Ga^{2}-Gv^{2}}}{ Ga-\sqrt{Ga^{2}-Gv^{2}}} \tag{2}\]  
where \(K\) indicates the estimated Rician K-factor; \(V\) denotes the direct wave signal; \(v(t)\) indicates the total scattered wave signal; \(G_{a}\) is the first moment of the power gain; and \(G_{v}\) is the second moment of the power gain about \(G_{a}\), which is the root mean square (RMS) fluctuation. \(G_{a}\) and \(G_{v}\) are calculated from the measured and the analytical data generated with Equation (1).  
Using the Rician K-factor estimated with Equation (2), the cumulative probability distribution curve was calculated from the following equation:  
\[F(x;K)=1-Q_{1}\bigg{(}\sqrt{2K},\sqrt{2(1+K)x}\bigg{)} \tag{3}\]  
where \(Q_{1}\) is the Markov-Q function, which represents the Nakagami-Rice \(n\) distribution and can be expressed as follows:  
\[Q_{1}(a,b)=\int_{b}^{\infty}x\exp\bigg{(}-\frac{x^{2}+a^{2}}{2}\bigg{)}\,I_{0 }(ax)dx \tag{4}\]  
The zeroth-order Bessel function \(I_{0}\) is expressed as follows:  
\[I_{0}(z)=\sum_{k=0}^{\infty}\frac{1}{\left(k!\right)^{2}}\Big{(}\frac{z}{2} \Big{)}^{2k} \tag{5}\]  
Figure 10 shows the CDF characteristics of the received power data in Figure 9 normalized by each median. The red-purple line shows the results of the ray-tracing analysis, the black line shows the outcome of the dummy fading signal generated with Equation (1), the blue line shows the measured data, and the gray line shows the cumulative probability distribution curve based on the Rayleigh distribution, which is an NLOS environment. The solid line is the CDF characteristic, and the dashed curve is the characteristic calculated with Equation (3) with the Rician K-factor estimated using the moment method.  
As shown in Figure 10, the CDF characteristic of the measured data has a steeper slope than that of the Rayleigh distribution, so the estimated Rician K-factor is 4.94 dB, indicating that the effect of the direct wave can be confirmed. The ray-tracing result shows that the slope of the cumulative probability distribution is extremely steep and inconsistent with the measured results because the fading in the actual environment is not sufficiently reproduced, as seen in Figure 9. In addition, the estimated Rician K-factor is 14.54 dB, which is higher than that of the measured data. In contrast, the cumulative probability distribution of the dummy fading signal generated based on the path information calculated with the ray-tracing method is very similar to that of the measured data, indicating that the estimated Rician K-factor agrees with that of the experimental results.  
The cumulative probability distribution of the measured and analytical data (solid line) generally agrees with the theoretical characteristic (dashed curve) based on the estimated Rician K-factor. But there is some discrepancy in the low signal power region. This discrepancy is due to the fact that when estimating the Rician K-factor using the first moment and RMS, if the number of sample points is small, the estimation error can be large for small values of the cumulative probability distribution value [48].