# Orthogonal Chirp Division Multiplexing for Underwater Acoustic Communication
## 4 Results
### Watermark NOF1 Channel  
In this section, the UWAC systems with OCDM and OFDM are compared over the Watermark NOF1 channel that replays a real experiment. As shown in Section 3, the time coherence of the NOF1 channel was much smaller than that of water tank channel, leading to non-negligible Doppler shift and Doppler spread effects in the received stream.  
Figure 6: Performance comparison of fully-loaded OCDM and OFDM over the water tank channel.  
Figure 7: Performance comparison of the full and underloaded OCDM and OFDM over the water tank channel.  
As a benchmark, we also provided the performance of an SC transmission system associated with an iterative FDE [9; 20]. By performing joint equalization and FEC decoding, the iterative receiver provided excellent performance against ISI and high spectral efficiency, while keeping low arithmetic complexity at the receiver side, making such an approach a reference for UWAC systems [9]. The choice of FDE instead of Time Domain Equalization (TDE) in the iterative loop [7] made the comparison with the proposed OCDM systems as fair as possible. The SC-FDE transmission system can use the same frame structure depicted in Figure 2, leading to a similar data rate and bandwidth. In this article, we have implemented a feed-forward linear equalizer associated with a feedback interference canceler, both optimized under the MMSE criterion (see [9] for details). For the considered channel, six iterations were required for the turbo-equalization process to converge.  
Figure 7(a),b provides the BER and PER performances of the OCDM, OFDM and SC-FDE systems. In the case of the fully-loaded scenario, conventional OFDM outperformed OCDM. This phenomenon can be explained by noise enhancement induced by the MMSE equalizer in the case of Doppler spread, which cannot be efficiently balanced by the better diversity exploitation offered by OCDM. However, we can see that the SC-FDE system provided higher robustness than fully-loaded OFDM. On the one hand, the turbo-equalization process removed ISI terms induced by the multipath channel efficiently, and on the other hand, SC transmission was less sensitive to CFO due to Doppler spread effects than OFDM waveforms for which CFO larger than inter-carrier spacing resulted in ICI [13]. However, compared to the OCDM and OFDM decoders, the iterative receiver used for the SC transmission system had a higher complexity since several loops of equalization and channel decoding processes were required [20].  
In the half-loaded case, OCDM achieved a significant enhancement in the relatively low SNR region, reaching a BER of \(10^{-4}\) at an \(\text{SNR}=10\) dB, resulting in a 3-dB gain w.r.t. conventional OFDM at the same load. By reducing the load ratio, OCDM still provided BER and PER improvements and converged to the AWGN boundary, while the underloaded performance OFDM of remained slightly improved. This phenomenon is explained by the fact that underloaded OCDM provided both spreading and diversity gain, whereas underloaded OFDM provided only better robustness against CFO due to the inter-carrier spacing increase. As a result, SC-FDE and underloaded OFDM have comparable BER performance.  
Figure 8: Cont.  
When analyzing the EDR of the considered systems, SC-FDE outperformed both full-load OCDM and OFDM for high SNR. In fact, SC-FDE was relatively robust against the UWAC channel without sacrificing spectral efficiency. However, at low SNR, the proposed underloaded OCDM provided higher EDR than other studied systems, demonstrating the interest in the this approach for robust UWAC applications. Furthermore, the performance of SC-FDE may be moderated by the fact that the OCDM (and OFDM) system considered in this study could be improved by a turbo-equalization process similar to that employed in SC-FDE.