# Cognitive Routing in Software-Defined Underwater Acoustic Networks
## 3 Proposed Cognitive Acoustic Software-Defined Underwater Network
### Spectrum Sensing and the Channel Model  
In this subsection, we explain how all communicating nodes in the ocean perform spectrum sensing to detect the presence of the PU signal in an underwater acoustic channel. One might think about how a sound signal from marine mammals is detected by CA users. Here, we briefly discuss the assumptions we make for sound signals produced by marine mammals. Various studies have been carried out to measure and detect different sound patterns produced by different marine mammals [27; 28]. The methods marine scientists use to measure animal sounds are not part of this work. Our motive is to protect the signal produced by either marine mammals or sonar systems from interference by CA users. Basically, the sound patterns of marine animals like whales, dolphins, etc., have pauses of a few seconds, and multipath arrivals of sound with echoes are considered noise. Moreover, mammals can hear each other at up to 6 miles apart [28]; beyond that distance, the sound signal is also considered noise. Therefore, the spectrum can be utilized even when marine mammals are communicating with each other, either during pauses or when CA users are far enough from legitimate users to safeguard PU signals. For that reason, we model PU activity as an exponential on/off activity pattern. With SONAR systems as a PU, we assume that both transmitters and receivers are equipped with transducers. However, for natural acoustic systems, receivers only are equipped with transducers. We consider an OFDM-based cognitive acoustic system in which the PU-OFDM system consists of S subcarriers. Spectrum sensing is done with an energy detection scheme to determine which subcarriers are free from PU activity. In an OFDM modulation scheme [29], the symbols of the PU first pass through a serial-to-parallel converter to generate parallel streams, and they then enter the \(S\)-point inverse fast Fourier transform (IFFT) block, which generates transmission samples. Then, multiplexing is done to generate serial streams of PU symbols, after which a cyclic prefix is added to the original samples. Finally, the OFDM-based PU samples are transmitted through an underwater acoustic channel. On the receiver side, CA users receive samples from the acoustic channel, remove the cyclic prefix, and allow these samples to pass through a serial-to-parallel converter to enter the \(S\)-point FFT block. The receiver detects the total number of subcarriers that can be used by CA users for communicating with each other. Therefore, the received signal after the FFT operation is defined as:  
\[y_{q,i}(n)=s_{q,i}(n)+w_{q,i}(n) \tag{6}\]  
where \(q=1,\ldots,S-1\) is the subcarrier index. To detect the presence or absence of a PU signal on the underwater acoustic channel, the received signal is then modeled as a binary hypothesis test, as follows:  
\[y_{q,i}(n)= \begin{cases}w_{q,i}(n),\quad H_{0}\\ s_{q,i}(n)+w_{q,i}(n),\,H_{1}\end{cases}  \tag{7}\]  
where \(i=1,\ldots,C,s_{q,i}(n)\) is a complex PU signal at subcarrier \(q\), and \(w_{q,i}(n)\) is noise. The energy-based test statistic in a discrete domain is given as follows:  
\[y_{E_{q,i}}=\sum_{n=1}^{W}\,y_{q,i}[n]\widetilde{y}_{q,i}[n] \tag{8}\]  
where \(W\) is the time-bandwidth product, and \(\widetilde{y}_{q,i}[n]\) is the conjugate signal of \(y_{q,i}[n]\). The acoustic propagation speed in the underwater realm is the key parameter, which is assumed to be 1500 m/s in most of the literature. However, in acoustics theory, the propagation speed is mainly affected by depth (pressure), salinity, and temperature, and can be modeled in meters per second as follows [10]:  
\[q(z,s,T)=1449.05+45.7T-5.21T^{2}+0.23T^{3}+(1.333-0.126T+0.009T^{2})(s-35)+16.3z+0.18z^{2} \tag{9}\]  
where \(z\) is the depth in kilometers, \(s\) is the salinity in parts per trillion, and \(T\) = (temperature in \({}^{\circ}\)C)/10. The dependence of path loss \(A(d,f)\) (dB) on signal frequency \(f\) (kHz) is another peculiar property of an underwater acoustic channel.