## 3 Performance Assessment
### Simulation
#### 3.1.2 Simulation Results  
Based on the shallow water channel model, simulation results are provided to assess the advantages of the proposed method over the TR acoustic communication using SC modulation. Figure 4 compares the time domain response of each composite channel from the transmit filter to the matched filter for the TR process between the proposed method and the TR acoustic communication using SC modulation. It is noticed that the span of ISI in each composite channel is reduced using the proposed method compared with the TR acoustic communication using SC modulation and, moreover, the span of ISI decreases with the increasing number of subcarriers. However, the larger number of subcarriers leads to the smaller bandwidth of each subcarrier which  
Figure 4: Comparison of the time domain response of each composite channel from the transmit filter to the matched filter for the TR process between two communication methods: (**a**–**c**) the proposed method for \(M=8\), \(M=16\), and \(M=32\) ; and (**d**) the TR acoustic communication using SC modulation. demands the longer transmit filter with more complicated implementation for the purpose of maintaining high spectral containment. Therefore, in practice, the number of subcarriers in FMT cannot increase indefinitely and should be selected in consideration of maintaining high ISI suppression and relatively low implementation complexity of the transmit filter. Figure 5 compares the performance of the TR process between the proposed method and the TR acoustic communication using SC modulation. Bit error rate (BER) and the output mean square error (MSE) computed by the mean square difference between the transmit symbols and the estimate of transmit symbols are used as indicators to assess the performance, and the low values of BER and MSE imply the good performance. In Figure 5, \(E_{a}\) denotes the transmitted energy per symbol, and \(N_{0}\) denotes the power spectral density of the channel noise \(w\big{(}k\big{)}\), and the ratio \(E_{a}\big{/}N_{0}\) implies the effect of noise. Several observations can be made from Figure 5. Firstly, the BER and output MSE of the TR process in the proposed method is obviously lower than that in the TR acoustic communication using SC modulation under the same \(E_{a}\big{/}N_{0}\). The reason for this observation is that compared with the TR acoustic communication using SC modulation, the proposed method can reduce the effect of ISI through exploiting FMT to decrease the ISI span of composite channel shown in Figure 4. Therefore, when the effect of noise is the same, the performance of the TR processing in the proposed method is superior to that in the TR acoustic communication using SC modulation. Secondly, the BER and output MSE of the TR process in the proposed method decrease when the number of subcarriers increases under the same \(E_{a}\big{/}N_{0}\). The reason for this observation is that in the proposed method, the ISI span of composite channel decreases with the increasing number of subcarriers. Therefore, the performance of the proposed method increased with the decreasing effect of ISI when the effect of noise is same. Thirdly, when \(E_{a}\big{/}N_{0}\geq\)20 dB, the BER and output MSE of the TR process in two communication methods both tends toward saturation. The reason for this observation is that when the effect of noise can be neglected due to the high value of \(E_{a}\big{/}N_{0}\), the effect of ISI determined by the ISI span in composite channel shown in Figure 4 is the major factor influencing the performance. Therefore, the performance of the TR process in two communication methods both tends toward  
Figure 5: Comparison of the performance of the TR process between the proposed method and the TR acoustic communication using SC modulation: (**a**) BER; and (**b**) output MSE. saturation as the result of high \(E_{a}\big{/}N_{{}_{0}}\) and fixed ISI span in composite channel for the same number of subcarriers, \(M\).