## 4 Propagation Characteristics and Phenomena of LMS Communication
### Direct Wave  
The direct wave is the direct ray that arrives at the receiver site via a line-of-sight (LoS) path without reflection. Other than attenuation due to free space, an additional path loss, as a function of the elevation angle (\(\theta\)) of the station with respect to the ground, can be considered. Free space attenuation causes the received signal power to decrease with the distance between the transmitter and receiver. The receiver power at a distance \(d\) between the transmitter and receiver is expressed by the following formula, known as the Friis or free space loss (FSL) equation:  
\[P_{r}(d)=P_{t}G_{t}G_{r}\cdot\frac{\lambda^{2}}{(4\pi d)^{2}}, \tag{1}\]  
where \(P_{t}\) is the transmitted power, \(G_{t}\) and \(G_{r}\) are the antenna gain of the transmitter and receiver, respectively, and \(\lambda\) is the wavelength expressed in meters. For frequencies up to about 10 GHz, the propagation is not affected by rain.  
The optimal conditions are when the transmission of the LoS component is not obstructed by obstacles. The LoS component is unaffected by shadowing, and the entire receiving signal is made up of the LoS (dominant) component plus a large number of independently fading multipath components that follow the Rice distribution [22], whose probability density function (PDF) is represented by:  
\[p_{Rice}(a)=\frac{a}{\sigma^{2}}exp\left[-\frac{a^{2}+v^{2}}{2\sigma^{2}} \right]I_{0}\left(\frac{av}{\sigma^{2}}\right), \tag{2}\]  
where \(a\) is the received signal level, \(\sigma^{2}\) represents the average power received caused by multipath, and \(I_{0}\) represents the zero-order Bessel function. The Rice factor, indicated with \(K\), is defined as the ratio between the average power of the direct component (\(v^{2}/2\)) and that due to the multipath (\(\sigma^{2}\)):  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Description** \\ \hline \(P_{r}\) & Receiver power \\ \(P_{t}\) & Transmitted power \\ \(d\) & Distance \\ \(G_{t}\) & Transmitted antenna gain \\ \(G_{r}\) & Receiver antenna gain \\ \(\lambda\) & Wavelength \\ \(p(a)\) & Probability density function (PDF) \\ \(a\) & Received signal level \\ \(\sigma^{2}\) & Received average power for multipath \\ \(I_{0}\) & Bessel function of order zero \\ \(K\) & Rice factor \\ \(\frac{v^{2}}{\mu}\) & Direct component average power \\ \(\mu\) & Mean of shadowed receiver signal component \\ \(\sigma^{2}\) & Variance of shadowed receiver signal component \\ \((A_{p})_{u}\) & Atmosphere corrective factor for uplink channel \\ \((A_{p})_{d}\) & Atmosphere corrective factor for downlink channel \\ \(\Lambda\) & Faraday rotation \\ \(f\) & Frequency \\ \(f_{d}\) & Doppler frequency \\ \(s\) & Mobile terminal speed \\ \hline \hline \end{tabular}
\end{table}
Table 3: Symbols used in Propagation Characteristics and Phenomena of LMS Communication section.  
\[K=\frac{v^{2}}{2\sigma^{2}}. \tag{3}\]  
Some works, such as [23], propose the use of the Nakagami-Rice distribution for the LoS condition whose PDF is:  
\[P_{Nakagami-Rice}(a)=\frac{v}{\sigma^{2}}exp^{-(v^{2}+a^{2})/2\sigma^{2}}I_{0}( \frac{va}{\sigma^{2}}). \tag{4}\]