## 4 Analysis of the MCSK-VTRM System
### Experiments  
To verify the performance of the proposed MCSK-VTRM system, an experiment was also carried out in January 2018 in the channel pool of Harbin Engineering University. The pool is 45 meters long, 6 meters wide and 5 meters deep. It is surrounded by silent wedges and has a sandy bottom. Both the transducer and the receiving hydrophone used in the experiment are omnidirectional. They were placed 2 meters below the water surface, and the horizontal distance was 8.35 meters. We used Cool Edit Pro to send and receive signals, and the structure of the transmitted signal is as shown in Figure 11. Figure 13 shows pictures of experiment equipment and Figure 14 shows the layout of the experiment site.  
We used the MP algorithm to estimate the channel used in the experiment. The CIR of the pool channel is shown in Figure 15.  
The parameters of pool experiments were kept the same as those in the simulations, which are shown in Table 3. The spread spectrum sequences used in experiments are composed of kasami sequences and their cyclic shift sequences. The frequency band of the transducer was 8-16 kHz, and the transmitted image was a binary image with a size of 27.4 kilobits. In the MCSK system and the MCSK-VTRM system, one spread spectrum sequence carries 5 bits of information. Figure 16 compares the images received by DSSS, MCSK, and MCSK-VTRM when the transmitting power was the same. MCSK-VTRM system used the MP algorithm to estimate the channel. The received image in the DSSS system is the clearest compared to the original image, while the received image in the MCSK system is the blurriest.  
Figure 14: The layout of the experiment site.  
Figure 15: CIR of the pool channel.  
Table 4 shows the performance comparison of the three kinds of communications. The BER is calculated by transmitting a large amount of data in the pool in different communication systems. When the length of spread spectrum sequences is the same, the communication rate of MCSK is higher than that of DSSS, but the BER is worse. When VTRM is applied to MCSK, the BER decreases. It is verified that VTRM can effectively equalize UWA channels and suppress multi-path interference, thus improving the accuracy of correct judgment in communications.  
In the simulations, the BER of the MCSK-VTRM system is almost similar to that of the DSSS system. However, the performance of the MCSK-VTRM system is not close to that of the DSSS system in the poor experiments. This is because the sparsity of the channel in the experiment is not good enough. As can be seen in Figure 15, the channel in the experiment is multi-path concentrated and mostly concentrated near the main path. But as shown in Figure 9, the sparsity of channel used in the simulation is good, where most channel coefficients have smaller energy. The distribution of several taps with larger energy is far apart, and the time delay difference between each tap is unequal. From the discussion in Section 3, we know that the effect of VTRM is related to the multipath structure of the UWA channel. The multipath structure of the channel in the experiments is not ideal enough and leads to the results that do not reach the ideal state of simulations.  
\begin{table}
\begin{tabular}{c c c} \hline
**Communication System** & **Communication Rate** & **BER** \\ \hline DSSS & 133.3 bps & 1.11 \(\times\) 10\({}^{-4}\) \\ MCSK & 665 bps & 6.63 \(\times\) 10\({}^{-2}\) \\ MCSK-VTRM & 665 bps & 3.04 \(\times\) 10\({}^{-2}\) \\ \hline \end{tabular}
\end{table}
Table 4: Performance Comparison.  
Figure 16: Transmitted and received images. (**a**) Original image; (**b**) received image in DSSS system; (**c**) received image in MCSK system; (**d**) received image in MCSK-VTRM system.