## 4 Performance Assessment  
### Channel Responses Measured in an Actual Experiment  
The performance of the proposed method was assessed based on a group of channel responses measured in an MIMO-FMT TR acoustic communication experiment carried out in an indoor pool of 45 m in length, 6 m in width, and 5 m in depth. Four sides of the pool were covered with acoustic absorbent materials. The surface and bottom reflected the acoustic signal. In the experiment, two hemispherical transducers placed at 1.5 m and 2 m below the surface were used to transmit two user signals. Two spherical hydrophones deployed at 0.7 m and 0.9 m below the surface provided a vertical array for receiving. The communication distance was 15 m. The other parameters settings are shown in Table 1.  
In the experiment, the input signal-to-noise ratio (SNR) at the receiver was approximately 24 dB and, therefore, the effect of noise on channel estimation was very mild and could be ignored.  
Figure 5 shows the measured composite channel responses for two users after the TR process. In Figure 5, \(q^{(\alpha,\alpha),(m,m)}(t)\) represented by red dash-dotted line is a continuous time form corresponding to the composite channel response \(q^{(\alpha,\alpha),(m,m)}(IT,nT)\), which is normalized with respect to its maximum amplitude; \(q^{(\alpha,\tau),(m,m)}(t),\alpha\
eq\gamma\) represented by the blue dotted line, is the continuous time form corresponding to the composite channel response \(q^{(\alpha,\tau),(m,m)}(IT,nT)\) and that is normalized with respect to the maximum amplitude of \(q^{(\alpha,\alpha),(m,m)}(t)\). Combined with Equation (9), the amplitude of the mainlobe in \(q^{(\alpha,\alpha),(m,m)}(t)\) reflects the intensity of the desired signal, the range of sidelobes in \(q^{(\alpha,\alpha),(m,m)}(t)\) indicates the intensity and range of ISI, and the amplitude and range of \(q^{(\alpha,\tau),(m,m)}(t),\alpha\
eq\gamma\) shows the intensity and range of CCI. Two observations can be obtained from Figure 5. Firstly, although the side lobe of \(q^{(\alpha,\alpha),(m,m)}(t)\) is much smaller than its main lobe, it is not fully compressed, and the symbol range of impact is relatively large. This observation indicates that the residual ISI after TR processing is still relatively large. Secondly, the amplitude of \(q^{(\alpha,\tau),(m,m)}(t),\alpha\
eq\gamma\) is much lower than the main lobe of \(q^{(\alpha,\alpha),(m,m)}(t)\), but it has not been compressed completely. This observation reveals that there is still residual CCI that needs to be removed.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Setting** \\ \hline Communication frequency band & 8–16 kHz \\ \hline Carrier modulation mode & FMT \\ \hline The number of subbands & 4 \\ \hline Roll-off factor & 0.5 \\ \hline Symbol rate on each subband & 4000/3 \\ \hline Constellation & Binary phase shift keying (BPSK) \\ \hline Number of symbol for channel estimation & 250 \\ \hline Algorithm for channel estimation & Recursive least square \\ \hline Forgetting factor & 0.999 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the experiment.  
Figure 5: Composite channel responses after TR process: (**a–d**) the channel responses of user1 from the 1 st subband to the 4 th subband; (**e–h**) the channel responses of user2 from the 1 st subband to the 4 th subband.