# Ciphered BCH Codes for PAPR Reduction in the OFDM in Underwater Acoustic Channels
## 3 System Architecture
### Shallow Underwater Acoustic Channel  
The system is tested using a shallow water underwater channel model [45] based on Rician fading along with absorption path loss and UWA noise [46]. Due to the doubly selective behavior of the underwater channel, acoustic signals experience both time and frequency selectivity [47]. The carrier spacing is greatly reduced [48], since the available bandwidth is of the order of several kHz over longer distances due to the presence of ambient noise as well as losses incurred because of the absorption of acoustic waves underwater [49]. In addition, the propagation velocity of sound waves in water is lower compared to terrestrial radio signals [50]. Thus, the chances of an OFDM system experiencing ICI are greatly enhanced, deteriorating the communication. Equation (5) expresses an underwater acoustic channel response [47] with \(L\) multipaths as:  
\[H(t,\tau)=\sum_{x=1}^{L}A_{x}(t)\delta(\tau-\tau_{x}(t)) \tag{5}\]  
where \(\tau_{x}(t)\) represents the delay coefficients, \(A_{p}(t)\) is the amplitude of the \(x\)th multipath and \(\delta(t)\) is the Dirac delta function. The delay spread for underwater acoustic channels can be anything between approximately 10 ms to 100 ms [51]. The Doppler shifts affect different subcarriers differently since the channel is wideband in nature.  
Figure 3 details the channel model [45] used in this work. The transmitted signal represented by \(s(t)\) passes through the absorption loss block, followed by Rician distribution-based fading and the addition of frequency-dependent ambient noise.  
Figure 2: XOR encryption [43].  
The acoustic pathloss in an underwater channel is a result of the absorption and geometric spreading of the acoustic signals. Thus, the obtained channel transfer function \(H_{a}(f,d)\)[53; 54] can be written as:  
\[H_{a}(f,d)=A_{d}e^{-\gamma(f)d} \tag{6}\]  
where \(A_{d}\) is the scaling constant, \(d\) represents the transmitter-receiver separation in meters and \(\gamma(f)\) is the propagation constant, which is complex. The signal \(c_{1}(t)\), shown in Figure 3, is then computed as the convolution of the inverse Fourier transform of the transfer function and the transmitted signal \(s(t)\).  
\[c_{1}(t)=h_{a}(t,d)\ \otimes\ s(t) \tag{7}\]  
It is evident from experimental data fitting models that the fading observed in a sound signal in an underwater channel can be modelled using a Rician distribution [55; 56; 57]. The parameters used in this work are: \(k=2.0;\ m=0.4\)[56]. The signal \(c_{2}(t)\) becomes:  
\[c_{2}(t)=h_{r}(t)\ \otimes\ c_{1}(t)+n(t) \tag{8}\]  
where \(n(t)\) represents the additive channel noise and \(h_{r}(t)\) represents the inverse Fourier transform of transfer function [58]. Figure 4 shows an instance of the delay profile used in this work and the average path gains.  
Figure 4: Channel impulse response sample.  
Figure 3: UWA channel model [52; 45].  
For an underwater channel, the ambient noise is a combination of various frequency dependent noises, and major noise sources include thermal noise, shipping activity, noise from turbulence and wave noise [59]. Additionally, from the noise equation, it is evident that the noise is location dependent. Furthermore, the amplitude is higher at the low and high ends of the spectrum and at its minimum at the frequency of 60 kHz [60].