# Cognitive Routing in Software-Defined Underwater Acoustic Networks
## 3 Proposed Cognitive Acoustic Software-Defined Underwater Network
### Spectrum Sensing and the Channel Model
This path loss affects the received signal power while traveling over distance \(d\) (m), which in turn changes the signal-to-noise-ratio (SNR) (dB) for each user transmitting on \(f\). Therefore, each sensor node experiences a different SNR, which is calculated as follows [30]:  
\[SNR(d,f)=\frac{P_{T}}{A(d,f)N(f)\triangle f} \tag{10}\]where \(P_{T}\) is the transmitted power, \(\triangle f\) is the width of frequencies, and \(N(f)\) is the noise power spectral density in dB re \(\mu\) Pa, which is calculated as:  
\[N(f)=N_{t}(f)+N_{\mathrm{s}}(f)+N_{w}(f)+N_{th}(f) \tag{11}\]  
The right-hand side of (11) refers to the superposition of four components: turbulence \((t)\), shipping and other human activities \((s)\), wind and waves \((w)\), and thermal noise \((th)\). These four components are calculated as follows [31]:  
\[ \begin{split} N_{t}(f)=17-30\mathrm{log}_{10}(f)\\ N_{\mathrm{s}}(f)=40+20(s-0.5)+26\mathrm{log}_{10}(f)-60\mathrm{ log}_{10}(f+0.03)\\ N_{w}(f)=50+7.5\sqrt{w}+20\mathrm{log}_{10}(f)-40\mathrm{log}_{10}(f +0.4)\\ N_{th}(f)=-15+20\mathrm{log}_{10}(f)\end{split}  \tag{12}\]  
\(A(d,f)\) in (10) is defined as \(A(d,f)=d^{k}a(f)^{d}\), where \(k\) is the path loss exponent that models the geometry (spherical and cylindrical) of propagation, and \(a(f)\) (\(\mathrm{dB/km}\)) is the absorption coefficient, which can be obtained by [PERSON]'s formula [32]:  
\[A(f)=\frac{0.11f^{2}}{1+f^{2}}+\frac{44f^{2}}{4100+f^{2}}+2.75\times 10^{-4}f^{2 }+0.003 \tag{13}\]  
where \(A(f)=10\mathrm{log}_{10}a(f)\). Acoustic communications in underwater systems present various challenges due to environmental conditions that are primarily related to accurate modeling of the channel behavior [33]. To propose an appropriate routing algorithm for software-defined cognitive underwater networks, an introductory requirement is to design a relatively accurate channel model. [PERSON] et al. [34] showed the significant difference in using a ray tracing tool over empirical propagation formulas. The empirical equations cannot model complex phenomena, such as sound speed profile, bathymetry, and sound propagation in bottom sediments, whereas a Bellhop ray tracing tool provides accurate emulation of sound propagation and a relatively accurate channel model. However, the authors also claimed that accuracy provided by a Bellhop simulator is only limited to channel attenuation. For modeling noise in an underwater channel environment, empirical equations are still used in simulations. Also, [PERSON] and [PERSON] [35] claimed that ray theory seems to be a viable solution for providing an accurate picture of an underwater acoustic channel. We second them; therefore, like [PERSON] et al. [36] and [PERSON] et al. [37], in this study, we use beam tracing tools, such as the Bellhop [38], to compute channel attenuation to take into account ineluctable channel variations. Now, the term \(ch\) in (1) and (4) shows the common idle channel between two communicating acoustic nodes that is free from PU activity. We explain the summary of the proposed algorithm by considering an example scenario, as shown in Figure 1. Assume that the MC and all LCs have the global and the localized view of the network, respectively. Source \(S\) is looking for a stable route to reach destination \(D\). The source reaches gateway \(G\) by making hop-to-hop links using (1). \(G\) forwards the request packet to an LC. The LC checks its flow table and does not find a match. It forwards the packet to the MC, which calculates a stable route using (4). The MC sends this packet to the LC, which sends it back to the source node. The source finally forwards the data packet to the destination via the prescribed route. The flow chart of the complete algorithm is shown in Figure 2.