# A Survey on Physical Layer Techniques and Challenges in Underwater Communication Systems
## 3 Modeling of UWA Channel Problems and Challenges
### Distance vs. SNR  
Most of the ocean noises fall under one of the four categories including thermal noise, shipping, turbulence, and wind. Turbulence prevails in the low-frequency band of 0-10 Hz, shipping noises dominate in the frequency zone of 10-100 Hz, and wind-driven wave noise exists in the frequency range of 100 Hz-100 kHz, while thermal noises are dominant above 100 kHz [163]. The unweighted sum of the four noise elements forms the total noise. The frequency function \(f\) in kHz is used to model the noise PSD and is estimated through Equation (29):  
\[10 log_{10}N(f)\approx N_{1}-nlog_{10}f \tag{29}\]where, \(n\) and \(N_{1}\) are the constants with values of 18 and 50, correspondingly [163]. The unit for the expression stated in Equation (29) is dB re. \(\mu\)Pa per Hz. The 100 Hz to 100 kHz is the usual acoustic communication frequency range. Hence, the generated wind noise overshadows. Having a few prominent exceptions of breaking ice and snapping shrimp, noise occurring in frequency range of the acoustic communication is successfully modeled by adopting the Gaussian random procedure [163; 165]. Generally, the path of noise is not white as the PSD is not flat. \(l\) defines the attenuation function, i.e., the length of the acoustic path) and \(f\) specifies the frequency of the signal) [166; 167]:  
\[A(l,f)=(l/l_{r})^{2}\alpha(f)^{l-l_{r}} \tag{30}\]  
where, \(l_{r}\) is defined as reference distance and \((f)\) means the coefficient of absorption.  
The absorption coefficient as a function of frequency has been estimated by [PERSON] in [168; 155]. The frequency is valid in the range of 500 Hz to 50 kHz. Most of the acoustic communication frequencies are categorized in this range. The absorption coefficient is expressed as:  
\[10 log_{10}\alpha(f)=0.11\frac{f^{2}}{1+f^{2}}+44\frac{f^{2}}{4100+f^{2}}+2.75 \times 10^{-4}f^{2}+0.003, \tag{31}\]  
where, \(f\) is expressed in kHz and \(10 log_{10}\alpha(f)\) is in dB/km. The other expression for frequencies below 500 Hz can be written as the following:  
\[10 log_{10}\alpha(f)=0.11\frac{f^{2}}{1+f^{2}}+0.11f^{2}+0.002 \tag{32}\]  
Equation (32) is a better estimate [163; 166]. [PERSON] and [PERSON] [156] interlinked these mathematical models with the chemical and physical composition of seawater. The signal-to-noise ratio (SNR) can be deduced as a function of distance and frequency if any multipath effects are ignored, and a narrowband approximation is employed:  
\[SNR(1,f)=\frac{P/A(l,f)}{N(f)Vf}=\frac{P}{A(l,f)N(f)Vf^{\prime}} \tag{33}\]  
The \(V\!f\) is defined as the receiver bandwidth and thus the noise received (narrowband estimation) [163]. The expression \(A(l\!f)N(f)\) includes the frequency-dependent part of this mathematical expression. P is defined as the complete source power through the existing bandwidth. Using the spreading coefficient \(k=1.5\), Figure 17 demonstrates the association between SNR and frequency [163]. It can be observed that the 3-dB bandwidth and optimum/optimal center frequency are equally reliant on the range of transmission.  
Figure 16: Ray tracing for the representation of multipath channel [164].  
[PERSON] and [PERSON] [169] conducted an interconnected analysis to determine the optimum frequency that well-adjusted the attenuation and propagation methods of the shallow water channels but noise power was not kept into account. The optimum frequency is considered a generalized characteristic of ducting propagation or waveguide and is strongly dependent on depth in the case of shallow water channels [150]. When the water depth is 100 m, the usual optimum frequencies range between 200-800 Hz. In comparison to the range of frequencies in [163] having the noise characterization, the above-expressed range is lower.