## 3 Underwater Channel Characterization
### Path Loss  
Path loss is a major channel characteristic for any medium that is considered for designing an efficient and robust UW system. Whenever an EM wave propagates in any channel (UW or free space), it degrades with an increase in the distance. The amount of degradation over a particular distance from the transmitter to the receiver is indicated from a term called Path Loss Attenuation or Path Loss. The factors that cause path loss are channel and frequency specific. In free space, the factors that cause path loss are diffraction, reflection, free-space loss or coupling losses, and terrain contours from different environments (urban or rural) [16]. It also gets affected by vegetation and foliage, propagation medium (dry or moist air), the distance between the transmitter and the receiver, and the height and location of antennas [16]. For underwater medium, the factors causing path loss for EM waves are the EM properties of water, multipaths, absorption losses, _etc._ These factors act differently over different frequency bands in a UW channel. In both scenarios, the relationship between signal power and distance is shown in Equation (1) [16].  
\[P_{r}\propto d^{-n} \tag{1}\]  
where \(P_{r}\) is a received signal power, \(d\) is the distance, and \(n\) is the path loss exponent. The relation states the simultaneous decrease in signal power as it propagates with respect to distance.  
The factor that characterizes path loss in different environments is called Path Loss Exponent. The path loss exponent characterizes the loss of signal strength when it propagates in different environments [16].  
Table 2 shows the values of the path loss exponent for different environments. A higher value of \(n\) characterizes lossy environments [16]. In some environments, such as buildings, stadiums and other indoor environments, the value of \(n\) ranges between 4 and 6 [16]. On the other hand, a tunnel may act as a waveguide, resulting in a path loss exponent less than 2. For a UW environment, which is a harsh environment, the path loss exponent ranges between 2 and 4 [17]. Depending on the type of environment for communication; various models have been designed to calculate the path loss. In our case, we use the Log Distance Model [16] to estimate path loss by calculating Received Signal Strength (RSS) in Equation (2) at different distances in UW environments.  
\[RSS=10\times n\times log(d)+C \tag{2}\]  
where RSS is the loss in dBs, \(n\) is the path loss exponent; \(d\) is the separation distance between transmitter and receiver usually in meters, and \(C\) indicates the system losses.  
In order to calculate the path loss exponent in any environment, the strength of the signal needs to be estimated at a particular power from different discrete distance points. This will give an overall approximation of how signal strength decreases with increasing distance in that particular environment. Since power of signal decreases with increasing distance, the factor \(n\) will be a linear regression line [18]. As in Equation (3),  
\[y=m\times d+C \tag{3}\]  
where \(y\) is a straight line, \(m\) is the slope of the line, \(d\) is the distance along which the values are calculated, and \(c\) is constant. Using Equations (2) and (3), we can extract the path loss exponent as \(n=m/10\). This relation will be used to estimate the path loss exponent of both of the environments, _i.e._, UW and terrestrial indoor environments.