# Closed-Form Performance Analysis of the Inverse Power Lomax Fading Channel Model
## 4 Simulation and Results' Analysis
### Experimental Verification  
Although the theoretical comparison of the IPL model with other well-known models demonstrated its high flexibility and usefulness, it does not justify its practical applicability. Therefore, further clarification is needed. To resolve this issue, one should rely on real-life experimental data and synthetic data generated via certified models. The current research assumes both approaches. To this extent, four datasets were considered:  
1. Experimental data from a 5.8 GHz device-to-device (D2D) communication system with on-body devices forming a body area network (BAN) in indoor and outdoor line-of-sight and non-line-of-sight environments [56]. 2. Experimental data from a 868.3 MHz two-user D2D system operating outdoors in a line-of-sight environment, with distances between the users ranging from 1 to 15 m [42; 57]. 3. Experimental measurements of a 4G LTE network functioning in a densely populated smart city [58]. 4. Synthetic computer-generated datasets compliant with the COST 2100 model, employed for a channel multipath clustering assessment [60; 61]. The first and second datasets presented experimental data from D2D communication between on-body devices. The assumed use cases involved a BAN with two users in indoor and outdoor environments, and the tests were conducted to assess the impact of the surrounding environment on link quality. In both datasets, the extracted data represented histogram values of the normalized envelope. Therefore, for fitting the IPL model, its SNRstatistics (i.e., the PDF) were converted into envelope statistics using the standard random variable transformation technique. The third dataset focuses on real-world network-performance indicators. Measurements were collected from an accessible 4G LTE network operating at a frequency of 1876.6 MHz with a bandwidth of 10 MHz. The tests involved a moving vehicle traveling up to 30 km/h and three static base stations over a distance of approximately 2 km. For this study, the SINR values were extracted from the site labeled \"site 1\" and converted from decibels to dimensionless quantities for analysis. The fourth dataset is based on a simulated semi-urban environment at 5.3 GHz, also with a bandwidth of 10 MHz. This dataset was initially proposed for assessing the multipath clustering effects as outlined in the COST 2100 channel model. The extracted data, representing the relative power of different components from the power-delay profile, were normalized based on the sample variance, producing dimensionless values for further analysis. For the first two datasets, the resulting data provided the sample PDF values. For the last two datasets, the extracted data were further processed using Wolfram Mathematica by generating the histogram list with fixed bins (obtained using the conventional Sturges binning). The results are presented in Figures 5-8 with black markers. All the data are accompanied by the fitting PDF curves of the corresponding models (i.e., \(\kappa-\mu/\kappa-\mu\) for Figure 5, \(\alpha-\mathcal{F}\) for Figure 6, and fdRLoS for Figures 7 and 8). The parameters for each channel were chosen in accordance with [42; 56; 59]. For each of the assumed datasets, the corresponding IPL PDF was obtained by selecting the channel model parameters (i.e., \(\bar{\gamma},\alpha,\beta\)) that provided the best fit (in terms of the minimum mean squared error (MSE)). The resulting curves are depicted in Figures 5-8 as blue curves, with the corresponding MSE denoted in the legend. It can be observed that in most cases, the IPL model produces a better fit (in terms of the MSE) than the best of the models applied to the current data. In cases where the IPL has a greater MSE than that of the initial model, the loss is generally insignificant for practical applications. Moreover, in these cases, it performs better than the other models referenced in [42; 56; 59] (i.e., only the best-fitting models were considered here). Furthermore, it should be highlighted that the IPL provides a much better fit in the distribution tails.