## 5 Simulation Model and Results  
In this section we present the numerical results obtained from computer simulations of C-HARQ protocol for the underwater sensor network depicted in Figure 1. The entire system is modelled in a Matlab environment, where extensive Monte Carlo simulations are performed to numerically measure the performance of a protocol. The averaged values of the performance metrics obtained for C-HARQ are compared with those of CARQ and standard S&W ARQ under common network conditions. Further, the performance metrics are used to find the optimum values of the network parameters so as to optimize the overall performance. For convolution encoding, the constraint length (\(K\)) of the systematic encoder is set to 5. The generator polynomial pair {37 33} is used, \"37\" (octal representation) being the feedback polynomial, which delivers a code rate of 1/2. At the destination a hard decision Viterbi decoder, operating in '_trunc_' mode, with a trace-back length set equal to 5\(K\), is used for decoding the convolution codewords along with their punctured derivatives. Out of the three operating modes of Viterbi decoder in Matlab, _i.e._, \"_cont_\", \"_term_\" and \"_trunc_\", trunc mode is used because it incurs no delay before the appearance of first symbol at the output [16]. In general, the energy requirement of convolution encoding process is considered negligible [18,19], however the process of Viterbi decoding is quite energy-intensive. Assuming a StrongARM microprocessor (SA-1110) to be the on-board processing unit, the average energy required per useful bit (\(E_{dec}\)) to decode a punctured convolution code (code rate = 1/2, \(K\) = 5) using a Viterbi decoder, has been experimentally found to be approximately 0.02 mJ [19]. The encoding and decoding energies of CRC are neglected. The underwater acoustic channel for data transmission is basically modelled in Matlab by a binary symmetric channel (BSC), whose bit error probability value is taken from the \"average BER _vs._ inter-nodal distance\" graph obtained in previous woks on CARQ in UASNs [3]. The average BER is obtained for binary phase shift keying (BPSK) modulation under Rayleigh channel fading, where the signal-to-noise ratio (SNR) is primarily affected by frequency and distance dependence attenuation, and ambient noise modelled by turbulence, shipping, waves and thermal noise. For the source-to-destination link of length 1,000 m the average BER is found to be around 2.5 \(\times\) 10\({}^{-3}\); for the cooperative links varying from 100 m to 1,000 m the BER is found to vary in the range of 2 \(\times\) 10\({}^{-5}\) to 2.5 \(\times\) 10\({}^{-3}\). For the sensor nodes, the on-board acoustic modem is considered to be the LinkQuest UWM2000 acoustic modem [2]. The relevant specifications of the modem, along with some network parameter values, are given in Table 1.  
The main assumptions or relaxations taken into account for the simulation purpose are:  
1. Control signals and Header/Trailer part of a packet are immune from errors. 2. Collision-free transmission of \(C_{\mathit{Avl}}\) signals. 3. No limit to source's retransmission attempts. 4. 100% error detection capability of CRC. 5. Negligible processing time compared to the long propagation delays. \begin{table}
\begin{tabular}{l l} \hline
**PARAMETER** & **VALUE** \\ \hline Source-Destination distance & 1,000 m \\ Sound Speed & 1,500 m/s \\ _ACK/NACK_ packet size & 7 Bytes \\ \(C_{\mathit{Req}}/C_{\mathit{Avl}}\) packet size & 7 Bytes \\ Data rate & 20 kbps \\ Operating frequency & 25 kHz \\ Transmission power (\(P_{\mathit{Tx}}\)) & 8 W \\ Reception power (\(P_{\mathit{Rx}}\)) & 0.8 W \\ Idle mode power (\(P_{\mathit{Idle}}\)) & 8 mW \\ Decoding energy per useful bit (\(E_{\mathit{dec}}\)) & 0.02 mJ \\ \hline \end{tabular}
\end{table} 
Table 1: Simulation Parameters and Acoustic Modem Specifications.