# Orthogonal Chirp Division Multiplexing for Underwater Acoustic Communication
## 4 Results
### Water Tank Channel  
The tank experiment allowed comparing the performance of OCDM against conventional OFDM in a static scenario, meaning that neither Doppler shift, nor Doppler spread effects were observed in the received signal. However, multiple reflections on the surface, bottom and tank edges provided an extensive multipath effect. In order to avoid ISI, the CP length was set such that \(N_{CP}/B\) was much larger than the RMS channel delay spread. The performance of MSE and BER is plotted respectively in Figure 6a,b. Moreover, the performance in Additive White Gaussian Noise (AWGN) channel is drawn in both figures to provide a lower bound on performance. It can be concluded that fully-loaded OCDM provided a slight MSE enhancement compared with fully-loaded OFDM on the static channel. This MSE gain was logically converted to BER enhancement, as shown in Figure 6b. One can note that the BER gain was getting higher as \(N\) decreased. In fact, since \(R_{CP}\) is constant, by decreasing \(N\), the absolute CP duration was getting shorter. This phenomenon demonstrates the better robustness of OCDM against out of guard interval echoes. Furthermore, the performance gain can be explained by the better diversity exploitation provided by the OCDM approach where each information cell was spread over a full block duration and frequency band contrary to OFDM, which carried the information cell on a given sub-carrier. Besides, robustness gain would be larger without FEC  
\begin{table}
\begin{tabular}{c l c c} \hline \hline
**Symbol** & **Signification** & **Water Tank Channel** & **Watermark NOF1 Channel** \\ \hline \(B\) & Bandwidth for baseband signal & 4 kHz & 4 kHz \\ \(f_{s}\) & Sample frequency in passband & 120 kHz & 120 kHz \\ \(f_{c}\) & Center carrier frequency & 20 kHz & 14 kHz \\ \(g_{f}\) & FEC coder & \((156,123)_{o}\) & \((156,123)_{o}\) \\ \(R_{c}\) & FEC rate & 1/2 & 1/2 \\ \(M\) & Constellation order & 4 & 4 \\ \(R_{CP}\) & Cyclic prefix ratio & 1/4 & 1/4 \\ \(N\) & Number of waveforms & 512 or 1024 & 256 \\ \(N_{u}/N\) & Useful waveforms ratio & 1/2 or 1 & 1/8, 1/4, 1/2 or 1 \\ \(N_{d}\) & Number of data blocks per Frame & 3 & 3 \\ \(T_{g}\) & Guard interval time & 256 ms & 256 ms \\ \(N_{ps}\) & Preamble Sequence length & 512 or 1024 & 256 \\ \(T_{f}\) & Frame length & 960 or 1472 ms & 640 ms \\ \(D_{r}\) & Raw data rate & 1.2 or 2.4 kb/s & 0.3, 0.6, 1.2 or 2.4 kb/s \\ \hline \hline \end{tabular}
\end{table}
Table 2: System parameters.  
encoding and random interleaving, which provided frequency and time diversities [14].  
Results were substantially different in the underloaded scenario presented in Figure 7. When \(N_{u}/N=1/2\), OCDM achieved huge improvement w.r.t. OFDM, especially in the low SNR region. This performance gain was due to the spreading spectrum effect realized by OCDM in the underloaded configuration. The same behavior can be seen in the EDR curves depicted in Figure 7, where the half-loaded OCDM modulation achieved a steady EDR of 1.2 kb/s from an SNR of 7 dB, which represents an impressive performance gain w.r.t. half-/fully-loaded OFDM, as well as fully-loaded OCDM. Actually, underloaded OCDM was demonstrated to combine diversity and spreading gain efficiently, therefore leading to good robustness at low SNR.