## 4 Simulation Tests Using Watermark Replay Channel Simulator  
The additional simulation tests of DSSS transmission were performed using the Watermark simulator. This is a freely available benchmark for physical-layer schemes for underwater acoustic communications. Its core is a replay channel simulator driven by at-sea measurements of the time-varying impulse response. For testing DSSS signals, all five communication channels available at Watermark were used, represented by impulse responses measured in Norway-Oslofjord (NOF1), Norway-Continental Shelf (NCS1), Brest Commercial Harbor (BCH1), and in shallow water off the western side of Kauai, HI, USA (KAU1 and KAU2). NOF1 and NCS1 impulse responses were recorded between a stationary source and a stationary single-hydrophone receiver. The BCH1 channel was measured with a source and a four-element array lowered into the water column from two docks. KAU1 and KAU2 impulse responses were recorded between a towed source and a vertically suspended array with 16 receivers. The main difference between KAU2 with KAU1 is the larger range, which attenuates delayed arrival clusters more rapidly [19]. The basic Watermark channels' parameters and sounding conditions are shown in Table 3.  
During the simulation tests, the DSSS signals of parameters shown in Table 1 were transmitted. Similarly, as in case tests performed using the measurement pool simulator, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Channel** & **NOF1** & **NCS1** & **BCH1** & **KAU1** & **KAU2** \\ \hline Environment & Fjord & Shelf & Harbour & Shelf & Shelf \\ \hline Range & 750 m & 540 m & 800 m & 1080 m & 3160 m \\ \hline Water depth & 10 m & 80 m & 20 m & 100 m & 100 m \\ \hline
\begin{tabular}{c} 3 dB \\ frequency \\ band \\ \end{tabular} & 10–18 kHz & 10–18 kHz & 32.5–37.5 kHz & 4–8 kHz & 4–8 kHz \\ \hline Delay coverage & 128 ms & 32 ms & 102 ms & 128 ms & 128 ms \\ \hline Doppler coverage & 7.8 Hz & 31.4 Hz & 9.8 Hz & 7.8 Hz & 7.8 Hz \\ \hline Type & SISO & SISO & SIMO & SIMO & SIMO \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Watermark channels’ parameters and sounding conditions [19]. three types of spreading sequence were used, all of rank 8. Depending on the Watermark channel type, different carrier frequencies and maximum possible bandwidths were used to fit the DSSS signal to the frequency band in which the impulse responses of the given channel have been measured. In the case of the NOF1 and NCS channels, the maximum bandwidth was equal to 8 kHz, and carrier frequency was equal to 14 kHz. For the BCH1 channel these values were equal to 5 kHz and 35 kHz, respectively. In the case of KAU channels, the maximum bandwidth was equal to 4 kHz, and the carrier frequency was equal to 6 kHz. Based on the BER values obtained, the coding rate of BCH error correction coding necessary to obtain the reliability expressed as BER less than 0.01 and 0.001 was estimated. Than the possibility of obtaining such an error rate was confirmed in additional simulations using Watermark. Tables 4-8 present the results of all simulation tests performed using the Watermark software. Each table shows the results for one replay channel. The second and the third columns present BER values and transmission rates achieved without BCH coding. In the following pairs of columns, the BCH code rates required to obtain BER < 0.01 and BER < 0.001 and the corresponding transmission rates are presented. The code rate is defined as \(C_{r}=L_{i}/L_{msg}\), where \(L_{i}\) is a number information bits and \(L_{msg}=2^{m}-1\) is message length, \(m\in\{3,4,5,6,7,8,9,10,11,12,13\}\).