## 4 WBANs: The Key M2M Area Network Technology for mHealth Applications
### WBAN Channel Modeling
#### 4.2.1 On-Body Radio Propagation Model  
This section summarizes the most important findings related to the path loss and the small-scale fading of on-body radio channels. Path loss Model:According to [32; 33; 34; 35], propagated waves are more likely to diffract around the human body, rather than penetrate it. Hence, traditional formulas for wireless communications can be applied, such as the Friis equation that calculates the path loss as a function of the distance \(d\)[36]: \begin{table}
\begin{tabular}{c c c c c} \hline
**PHY Layer** & **Frequency Band (MHz)** & **Bandwidth (MHz)** & **Available Channels** & **Rates (kbps)** \\ \hline \multirow{8}{*}{Narrowband (NB)} & 402–405 (MICS) & 0.3 & 10 & 75.9–455.4 \\  & 420–450 & 0.32 & 12 & 75.9–187.5 \\  & 863–870 & 0.4 & 14 & 101.2–607.1 \\  & 902–928 (ISM) & 0.4 & 60 & 101.2–607.1 \\  & 950–958 & 0.4 & 16 & 101.2–607.1 \\  & 2,360–2,400 & 1 & 39 & 121.4–971.4 \\  & 2,400–2,483.5 (ISM) & 1 & 79 & 121.4–971.4 \\ \hline \multirow{8}{*}{Ultra-Wideband (UWB)} & 3,000–5,000 & 499.2 & 3 & Non-coherent: \\  & & & & 394.8–12,636 \\ \cline{1-1}  & & & & Differentially coherent: \\ \cline{1-1}  & 6,000–10,000 & 499.2 & 8 & 487–15,600 \\ \cline{1-1}  & & & & FM: \(202.2\) \\ \hline Human Body & & & & \\ \cline{1-1} Communications (HBC) & 21 (center frequency) & 5.25 & 1 & 164.1–1,312.5 \\ \hline \end{tabular}
\end{table} 
Table 2: IEEE 802.15.6 frequency bands and supported rates. \[\text{Path loss}\sim G_{r}G_{t}\left(\frac{\lambda}{4\pi}\right)^{2}\left(\frac{1}{d }\right)^{n} \tag{1}\]  
where \(G_{t}\) and \(G_{r}\) are the respective transmitter and receiver antenna gains, \(\lambda\) is the wavelength, and \(n\) is the path loss exponent that depends on the propagation environment. In free space propagation environments, the path loss exponent is equal to \(n=2\). In the context of WBANs, however, \(n\) has a higher value, depending on the scenario. In particular, when the transmit and receive antennas are placed at the same side of the body (Line-of-Sight-LOS situation), it has been estimated that the values of \(n\) range between \(3\) and \(4\), depending on the position of the device (_i.e._, the path loss on the arm is lower that the one on the trunk). Then, in Non-LOS (NLOS) cases that occur when the antennas are placed at different sides of the body, \(n\) assumes higher values, between \(5\) and \(7.4\)[33, 35]. It is important to mention that in the context of WBANs, frequency does not significantly affect the path loss [37]. On the other hand, the current user activity and the antenna height (defined as the distance from the body) are the two major contributors to the path loss characteristic of wearable WBANs. Regarding the former, the impact of user activity (_i.e._, walking) on the path loss has been experimentally studied in [38]. The obtained results show that the subject's mobility causes significant deviations in the path loss, with respect to the average path loss values obtained when the subject remains static. Concerning the antenna height, the authors in [39] claim that the closer the antenna is to the body, the higher is the path loss. A difference of more than 20 dB can be obtained by comparing the path loss for antennas placed at 5 mm and 5 cm from the body surface. Small-scale fading:Small-scale fading is different in on-body WBANs with respect to other wireless environments. Several distributions have been proposed to model small-scale fading in different frequency bands [15, 40]. However, traditional Rayleigh and Rician distributions have been proven inefficient, while the lognormal distribution seems to be the best fit [41]. In addition, measurements in [40] have indicated that the multipath components can be divided into two clusters. The first cluster is due to the initial wave diffraction around the body and the second is due to reflections on the ground. The correlation between the bins of the two clusters is very weak, and therefore the bins from the different clusters can be considered as statistically independent.