## 5 Analysis of the Results
### Multipath Component  
The system loss model for off-body communication (Equation (1)) also takes the small-scale fading component \(\Delta L_{MF}\) into account. It represents the impact of the user's motion and the multipath effect. Due to the random nature of this phenomenon, \(\Delta L_{MF}\) also has a random character and is represented by a random variable. Extraction of \(\Delta L_{MF}\) is possible by subtracting the value of the composite component \(\overline{L_{SL}(d)}\) (Equation (4)) from instantaneous values of the system loss \(L_{SL}\), i.e. :  
\[\Delta L_{MF(\text{dB})}=L_{SL(\text{dB})}-\overline{L_{SL}(d)_{(\text{dB})}} \tag{6}\]  
The methodology of determining the empirical distribution of the small-scale fading component and fitting the theoretical PDFs is very similar to that used for the body shadowing component, \(\Delta L_{BS}\), and is also performed in the linear domain (\(\Delta L_{MF}\)). Based on the literature dealing with the small-scale fading distributions, both for NB and UWB channels, the most frequently used ones were selected for fitting, i.e., lognormal, Rice, Rayleigh, Weibull, and Nakagami-\(m\). For WBAN channels, the lognormal, Weibull, and Nakagami-\(m\) distributions were indicated as those that most accurately represent the small-scale fading amplitude distribution. Statistically, Rice and Rayleigh distributions are less often used for these channels [38]. In Figure 5, the exemplary results of the selected PDFs fitted to the empirical distribution of multipath fading is shown. Rice- and Rayleigh-fitted PDFs' distribution parameters were similar. This may be caused by the fact that, in a strong multipath environment like the investigated one, there is no dominant direct component, and the received signal is a sum of a large number of reflected components. Apparent asymmetry of the empirical distribution around the mean value makes the lognormal distribution the best fitting one. Apart from the subjective assessment, the GoF test has been performed using the correlation coefficient and the chi-square test. To present the results in a tabular form, a unified description of the P\({}_{1}\) and P\({}_{2}\) distributions' parameters was used, where:  
* for Rice distribution, P\({}_{1}\) is the non-centrality parameter \(s_{R}\) and P\({}_{2}\) is the scale parameter \(\sigma_{R}\),
* for Nakagami-\(m\) distribution, P\({}_{1}\) is the shape parameter \(m\) and P\({}_{2}\) is the scale parameter \(\Omega\),
* for Weibull distribution, P\({}_{1}\) is the shape parameter \(\alpha_{W}\) and P\({}_{2}\) is the scale parameter \(\beta_{W}\),
* for Rayleigh distribution, P\({}_{1}\) is a scale parameter \(\sigma_{RAY}\), and
* for lognormal distribution, P\({}_{1}\) is the mean value \(\mu\) and P\({}_{2}\) is the standard deviation \(\sigma\), both expressed in (dB). Figure 5: Exemplary results of the selected PDFs fitted to the empirical distribution of multipath fading (for DEP, AB\({}_{L}\), NB, and LOS). Tables 3-5 show the detailed list of fitted distributions' parameters for different MN placements and scenarios. The threshold value of the chi-square test is the same as for the body shadowing case. For the majority of NB cases, the correlation coefficients satisfy the acceptance criteria. The best results were obtained for the lognormal distribution, although, in some cases, Nakagami-\(m\) also gives acceptable results. It may be observed that lognormal distribution fulfills the acceptability criteria for both GoF tests, regardless of the analyzed case. For the lognormal distribution, a significantly higher correlation coefficient was obtained compared to the other distributions. Thus, considering the data in the linear scale, the short-term fading is best described by the lognormal distributed random variable. Similarly, all distributions fitted to the empirical UWB channel data are within the range of the acceptability of the chi-square test.