# Coded-GFDM for Reliable Communication in Underwater Acoustic Channels
## 4 Simulation Setup and Results  
The proposed scheme utilizes the GFDM transceiver model based on [9] along with our shallow acoustic underwater channel. Table 1 details the simulation parameters of the coding schemes and the transceiver. A \(K\times M\) binary stream is generated randomly, and the channel encoding block applies the specified encoding technique. The encoded data then undergoes M-ary mapping for a specified modulation index. In this work we have used a QAM mapper. The mapped symbols then undergo modulation according to the pulse shape selected and its roll-off factor. An IFFT operation is applied, and CP is added to every sub-symbol M.  
Table 2 has the channel parameters used in MATLAB simulations. The Tx-Rx separation was varied from 500 m to 2.5 km. The Tx-Rx depth is fixed at 20 m and the maximum Doppler shift is 10 Hz. We use Matlab's RicianChannel object for multipath fading and mathematical models are implemented for absorption and frequency dependent oceanic noise. Figure 3 shows the error performance of the BCH encoded GFDM scheme. Figure 3a shows a comparison of selected BCH encoding schemes, i.e., BCH (31,21), BCH (31,16), BCH (31,11), and BCH (31,6) when matched filter receiver is used for the recovery of the transmitted information and the transmitter-receiver distance is kept at 1000 m. Figure 3b shows a comparison of the same encoding schemes when a zero-forcing equalizer is used at the receiver. Figure 3c,d show the error performance of the proposed system as a function of transmitter-receiver distances. We varied this distance from 500 m to 2.5 km. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline No. of subcarriers (\(K\)) & 128 \\ Number of time slot (\(M\)) & 9 \\ Mapping & 4-QAM \\ Active subcarriers (\(K_{on}\)) & 96 \\ Active subsymbols (\(M_{on}\)) & 7 \\ Roll-off factor (\(\alpha\)) & 0.4 \\ Bandwidth & 10 KHz \\ Channel coding & BCH, RS, Convolutional \\ Pulse shape & Raised cosine \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Transceiver parameters. \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Quantity** \\ \hline TX–RX distance & 500 m to 2.5 km \\ Depth & 20 m \\ Max doppler shift & 10 Hz \\ Gain vector & [0; \(-1.5;\)\(-2.5;\)\(-7\)] dB \\ Tau vector & [0; \(1;\)\(2;\)] ms \\ Atmospheric pressure & \(1.01325\times 10^{5}\) Pa \\ Salinity & 35 parts/1000 \\ Density & \(10^{3}\) Kg/m\({}^{3}\) \\ Water temperature & 25 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Channel parameters. Figure 4 shows the error performance of the RS encoded GFDM scheme. Figure 4a shows a comparison of selected RS encoding schemes, i.e., RS (15,7), RS (15,5), and RS (15,3) when matched filter receiver is used for recovery of the transmitted information and the transmitter-receiver distance is kept at 1000 m. Figure 4b shows a comparison of the same encoding schemes when a zero-forcing equalizer is used at the receiver. Figure 4c,d show the error performance of the proposed system as a function of transmitter-receiver distances. We varied this distance from 500 m to 2.5 km. Figure 3: BCH encoded 4 QAM-GFDM schemes. (**a**) Comparison of selected BCH schemes with MF equalizer. (**b**) Comparison of selected BCH schemes with ZF equalizer. (**c**) Error performance as a function of Tx-Rx distance for BCH (31,6) scheme with MF equalizer. (**d**) Error performance as a function of Tx-Rx distance for BCH (31,6) scheme with ZF equalizer. Figure 5 shows the error performance of four convolutionally encoded GFDM schemes. Figure 5a shows a comparison of four convolutionally encoded schemes, i.e., rate \(1/3\) with constraint length \(3\), rate \(1/4\) with constraint length \(3\), rate \(1/4\) with constraint length \(4\), and rate \(1/4\) with constraint length \(5\). The equalizer employed for the recovery of transmitted information is matched filter and the transmitter-receiver distance is kept at 1000 m. Figure 5b shows a comparison of the same encoding schemes when a zero-forcing equalizer is used at the receiver.