# FD-LTDA-MAC: Full-Duplex Unsynchronised Scheduling in Linear Underwater Acoustic Chain Networks
## 3 Simulation Scenarios
### Simulation Set-Up  
#### 3.2.1 Channel Model  
Although there are several available propagation models, such as ray tracing, normal mode, parabolic equation, wavenumber integration, energy flux, finite difference, and finite element models [31], the acoustic propagation model employed is based on the BELLHOP [26] beam tracing method described in [32]. The choice is influenced by computational cost and model efficiency with respect to topology and application scenarios. Spatially varying local environment can influence underwater acoustic propagation. In order to accurately provide a representation of acoustic propagation, the following environmental variables that serve as the model input data are considered: bathymetry, sea surface, ambient noise power, and sound speed profile, source, and receiver locations.  
The bathymetry (characteristics of the sea bed) influences the propagation pattern of the sound wave, in order to provide an accurate multi-path propagation pattern, this paper employed a generic bathymetry model presented in [32] where small-scale variations are described by the sinusoidal shape bathymetry [32; 33; 34] represented by the following model:  
\[z(x)=R(x)\times\frac{z_{max}}{2}\left(\sin(-\frac{\pi}{2}+\frac{2\pi x}{L_{hill }})+1\right), \tag{9}\]  
where \(z(x)\) is the random elevation of the hills along horizontal range, \(x\), \(z_{max}\) represents the maximum hill elevation, and the length of single hill is \(L_{hill}\), while, \(R(x)\) is a uniform random number between 0 and 1. For the acoustic propagation model assumed in this work, \(z_{max}\) is set to 10 and a generic sea bottom layer represents sand-silt with 1 g cm\({}^{-3}\) density [26; 31]; the generated bathymetry is shown in Figure 5.  
The Pierson-Moskowitz spectral model for fully developed wind seas [34; 35] is used to obtain realisations of the random surface waves. Additionally, Gaussian beam spreading model is utilised to estimate the total intensity at the receiver. In order to compute the total wideband received signal power, the BELLHOP based ray tracing is used to compute the channel impulse response comprising of attenuation, phase and delay of multi-path components. A well established ambient noise model [36] is used to calculate acoustic noise at the receiver with the power spectral density  
\[N_{ambient}(f)=logN_{t}(f)+N_{s}(f)+N_{w}(f)+N_{th}(f). \tag{10}\]  
The components in (10) are described as  
\[N_{t}(f) =17-30 logf, \tag{11}\] \[N_{s}(f) =40+20(s-0.5)+26 logf-60 log(f+0.03),\] (12) \[N_{w}(f) =50+7.5w^{\frac{1}{2}}+20 logf-40 log(f+0.4),\] (13) \[N_{th}(f) =-15+20 logf, \tag{14}\]  
Figure 5: Sinusoidal bathymetry with 200 m long hills and random hill height.  
where \(N_{t}\), \(N_{s}\), \(N_{w}\) and \(N_{th}\) are the turbulence, shipping, wind, and thermal noise components, respectively. The shipping activity factor, \(s\) is set between 0 and 1, representing low and high activity, respectively, and the wind speed \(w\) is given in m s\({}^{-1}\).  
The SNR is computed as  
\[\text{SNR}=\frac{GP_{\text{Rx}}}{\int_{f_{\text{min}}}^{f_{\text{max}}}N_{ \text{ambient}(f)df}}, \tag{15}\]  
where \(GP_{\text{Rx}}\) is the received signal power, \(G\) is the channel gain, \(P_{\text{Rx}}\) is the transmitted signal power and \(N_{\text{ambient}}(f)\) is the noise PSD between the lower and upper limit of the communication frequency band of the communication system. Figure 6 shows the SNR as a function of range and depth for the source at 480 m depth and source level of 170 dB re \(\upmu\)Pa at 1 m, 24 KHz center frequency and 7.2 KHz bandwidth. Assuming source placed at 480 m, and a minimum SNR of 0 dB is required to decode a signal (transmitted at 170 dB re 1 \(\upmu\)Pa at 1 m) at the receiver, then, the source-receiver range can be approximated as 3.5 km as can be seen in Figure 6. In this case, we neglect internal receiver noise characteristics and residual self-interference in the case of full-duplex nodes.