# A Weighted Turbo Equalized Multi-Band Underwater Wireless Acoustic Communications
## 4 Experimental Result  
To prove the efficiency of the proposed algorithm, a flowchart of the performance evaluation has been depicted in Figure 7.  
After receiving the distorted signals induced by Doppler, multi-paths, and other factors, multi-band signals were divided into a single band of \(N_{b}\), by a band-pass filter number. Synchronizations including Doppler and phase compensation were performed, based on the preamble data which were known to the transmitter and the receiver. It also acquired the beginning of data fields. After synchronization, we calculated the BER of each band, using the compensated preamble data. To apply the proposed threshold algorithm, if the calculated BER of each band was lower than the threshold, the demodulated data of that band was passed to the summation block, else, it was multiplied by the weighting factor and passed on to the summation block.  
Based on Figure 7, the underwater experiment was performed by using the packet structure of Figure 6b. Table 2 presents the average error rates of data that were transmitted, repeti  
Figure 5: Frequency division.  
Figure 6: Transmission signal packet structure: (**a**) Individual band packet structure; (**b**) multi-band packet structure.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(N_{b}\)} & \multirow{2}{*}{\(f_{c}\)} & \multirow{2}{*}{**Preamble BER**} & \multicolumn{6}{c}{**Number of Iterations of Turbo Equalization**} \\ \cline{3-9}  & & & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline
1 & \(f_{1}\) & \(10^{-0.696}\) & \(10^{-0.30  
As shown in Table 2, when the number of bands increased from 1 to 4, the performance improved. When four multi-bands were used and the total iteration number of 6 was applied between the equalizer and the decoder, all of the data were decoded without error. The error rates of preamble data used in each band were analyzed. It turned out that, when the number of bands increased, the error rate of the preamble had both improved and degraded. The four multi-band worsened the error rate of preamble data of \(f_{4}\) band. We have tried to re-transmit these same, four, multi-band signals, after several minutes (denotes \(N_{b}=4^{*}\)). The performance was worse than the single and double band ones, in this case, because the performance in one particular band affected the output from the entire range of bands. To improve the performance, the proposed threshold-setting algorithm was applied based on the preamble error rates. Table 3 presents the results of this application.  
In order to improve the BER performance, it was very important to decide the weighting value for each frequency band. The relationship between the BER of the un-coded preamble sequence and that of the coded data field depended on what kind of coding methods and coding rates were used. Generally, BER of un-coded preamble sequence had under a \(10^{-1}\), BER of the coded data field with a guarantee for the QEF region, in the case of turbo pi codes with rates of \(1/3\). In the case of \(N_{b}=4\) and \(N_{b}=4^{*}\), different weighting values were applied, for each specific frequency band. In order to find the optimal weighting value for each frequency band, based on their relationship, we assigned different weighting values to each frequency band, in the range of 0.1 to 1. Since the four bands (\(N_{b}=4\)) showed poor error rates for the preamble data of \(f_{4}\) band, the threshold value of the data was set to 0.1 to minimize the impact on the entire data. Consequently, when the total iteration number of turbo equalization was 1, all of the data could be decoded without error. Similar to that of \(N_{b}=4^{*}\), when the total iteration number of turbo equalization was 2, all of the data could be decoded without error.