# Asynchronous Chirp Slope Keying for Underwater Acoustic Communication
## 5 Discussion
An additional phase offset correction before the summation of both matched filter outputs, i.e., before the JDS block, would move the secondary symbol levels closer to their ideal state and increase the overall performance, but is not included at this point. The general feasibility of our approach is thereby shown, but further practical verification is required. If we regard the results in Figure 11, the simulation of the transmission error probabilities through BER and PER does not include the multi-path response and, therefore, describes the idealized performance of the algorithm at that point. The approximate far field fading of acoustic signals in open water of approximately 20 dB km\({}^{-1}\) in seawater can be used to design the acoustic output to suitable levels, e.g., for a BER of up to 0.1% over a range of 2000 m, the overall channel losses of approximately 40 dB have to be countered by about a combined gain of transmitter and receiver of 33 dB in the single band case and 39 dB in the dual-band case. More generally, the dual-band transmission is shifted by approximately 6 dB, which confirms the assumptions from (44) that a reduction of the bandwidth \(B\) to half the single band value also halves the symbol power \(E_{\text{sym}}\). The addition of a channel impulse response with additional echoes is expected to increase the error probability for all scenarios, as it introduces additional interference. The PER follows the behavior of the BER, which is due to the definition that a packet is considered erroneous as soon as a single bit is demodulated wrongly. The error curves' behavior for lower SNR to approach values over \(10^{1}\) may be counter-intuitive for synchronized transmissions or when the number of symbols in a packet is known. Since we allow for arbitrary lengths and have no additional synchronization, for those conditions more packets are detected than were initially sent. This implies very short or fragmented packets, which can be disregarded on a higher level, if an additional protocol is implemented, e.g., that restricts the syntax of valid packages as in the NMEA 2000 standard of the National Marine Electronics Association [65]. If we regard the initially set application of acoustic communication in reverberating environments, the validation runs have shown that we can successfully transmit data even inside a very small body of water, while the simulation hints at the performance for larger ones, especially lakes and harbor areas, where there is little surf and most interference  
Figure 10: Time domain plot of the detected frames (red) and estimated symbols (blue dots). (**a**) Single band communication; (**b**) Dual-band communication. The symbol difference is not optimally detected, as the amplitude of the signal exceeds the amplitude of the estimated symbols. The histograms to the right of each time plot are normalized by the total number of samples (red) and symbols (blue) in each frame. stems from ship engines. The change of acoustic properties in salt-water compared to fresh water is proportional to the length of the signal propagation, therefore for close proximity communications negligible, but requires consideration for long distance links. Hence, we assume the results of the pool runs can be extended to application at sea, lakes or oceans, albeit not as an accurate performance indicator for open water communication, but rather a worst-case scenario, in a highly reverberating environment, e.g., if two maintenance divers try to communicate in bad sight conditions near the ground or close to a ship's hull.