# Characterization of the Body-to-Body Propagation Channel for Subjects during Sports Activities
## 4 The Channel Model
In the simulation model, samples of good and bad states are generated from the corresponding \(D_{g}\) and \(D_{b}\) distributions for the specified \(T_{g}\) and \(T_{b}\) periods of time respectively. The outputs are then multiplied by \(L(t)\), which is the large-scale fading component. The time series is then passed through the lowpass filter with appropriate cutoff frequency for spectrum shaping. The output from the simulator is a signal envelope that incorporates the overall fading characteristics of body-to-body channels under sporting activities. Figure 8: Channel simulator for BBWNs during running and cycling. \(L(t)\) is the component of the large scale fading, \(T_{g}\) and \(T_{b}\) are the period of good and bad states, respectively. To validate the proposed model, TSSMM channel simulations were performed using parameters given in Tables 2 and 3, and the first and second order statistics of the received signal power were calculated from the simulation results. The resulting statistics were then compared with the statistics obtained from the measurement data. We start the comparison with the cumulative distribution function (CDF), which is the probability of a signal being below a certain value. This information is commonly used in performance evaluation of the channel with regard to the channel capacity and outage probability. Figure 9 shows a good agreement between the measurement results, and the proposed simulation model results for all scenarios and activities. For second order statistics, the level crossing rate (LCR) and the average fade duration (AFD) were used for comparison. These statistics are important in comparing the time-varying properties of a channel, as they quantify how often the signal crosses a certain threshold and how long it stays below it. Figures 10 and 11 show the comparison of the LCR and AFD of the received signal normalized to their root mean square (RMS) values. We observe a good agreement between the measurement results and the developed simulation model results. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameters** & **Scenario 1** & **Scenario 2** \\ \hline Good & Lognormal & Lognormal \\ distribution, \(D_{g}\) & \(\mu=0.54,\sigma=0.61\) & \(\mu=1.01,\sigma=0.16\) \\ \hline Bad & Lognormal & Lognormal \\ distribution, \(D_{b}\) & \(\mu=-1.72,\sigma=1.32\) & \(\mu=-1.42,\sigma=0.93\) \\ \hline Large-scale & Lognormal & Lognormal \\ distribution, \(L\) & \(\mu=-0.23,\sigma=0.26\) & \(\mu=-0.29,\sigma=0.26\) \\ \hline Good period, \(T_{g}\) & 312 ms & 256 ms \\ Bad period, \(T_{b}\) & 392 ms & 432 ms \\ Filter order & First & First \\ Cutoff frequency, \(f_{c}\) & 8 Hz & 15 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters used for simulation of running activity. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameters** & **Scenario 1** & **Scenario 2** \\ \hline Good & Nakagami-m & Lognormal \\ distribution, \(D_{g}\) & \(m=5.5,\omega=1.99\) & \(\mu=0.29,\sigma=0.04\) \\ \hline Bad & Nakagami-m & Lognormal \\ distribution, \(D_{b}\) & \(m=1.79,\omega=0.23\) & \(\mu=-0.59,\sigma=0.73\) \\ \hline Large-scale & Lognormal & Lognormal \\ distribution, \(L\) & \(\mu=-0.05,\sigma=0.15\) & \(\mu=-0.14,\sigma=0.3\) \\ \hline Good period, \(T_{g}\) & 436 ms & 376 ms \\ Bad period, \(T_{b}\) & 460 ms & 392 ms \\ Filter order & Third & Third \\ Cutoff frequency, \(f_{c}\) & 45 Hz & 50 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters used for simulation of cycling activity. Figure 11: Comparison of AFD of the measurement results, and the developed simulated model results. (**a**) running; (**b**) cycling. Figure 10: Comparison of level crossing rate (LCR) of the measurement results, and the developed simulated model results. Figure 9: Comparison of cumulative distribution function (CDF) of the measurement results, and the developed simulated model results.