## 3 Communication Performance
### Results  
We used the uncoded bit error rate (BER) and the output SNR as the performance metrics. We investigated the impact of distributed diversity combining on the performances of BERs of Rx #1, as shown in Figure 7a as a function of the number of transmissions combined. We compared five different approaches: (1) individual performance without combining; (2) MRC with FDE; (3) MRC with convolution code; (4) MRC with HTFDE; and (5) MRC with HTFDE and convolution code. The BERs without combining were quite high (i.e., 13-22%). From one to three transmissions, the BER performance improved significantly with increasing diversity. After three transmissions (e.g., four and five transmissions), the performance improvement for the uncoded system was slight. For the MRC and FDE method, after five transmission combinations, the uncoded BER of Rx #1 was \(2.36\times 10^{-2}\), whereas the coded BER of Rx #1 with the convolution code was \(1.9\times 10^{-3}\). For the  
Figure 6: Estimated input SNRs (**a**), and drifting speed (**b**). Figure 7: Performance comparison between (**a**) top (Rx #1) and (**b**) bottom (Rx #8). Three different approaches are compared: (1) individual performance without combining; (2) MRC with FDE; (3) MRC with convolution code; (4) MRC with HTFDE; and (5) MRC with HTFDE and convolution code. MRC and HTFDE method, the uncoded BER of Rx #1 was \(6.6\times 10^{-3}\), whereas the coded BER with convolution code achieved error-free reception by five transmission combinations. Once the BER of the MRC-FDE was less than a certain level (10%), significant performance enhancement using HTFDE is achieved. To check the consistency of the results, we also plotted the performances of Rx #8 in Figure 7b. Other receivers at different depths achieved similar results. For comparison, we also plotted the BER results of conventional multichannel equalization with 1-8 channels for the first and fifth location in Figure 8. With an 8-channel receiver in one location, the uncoded BER was about \(7\times 10^{-2}\) using MRC and FDE and the coded BER was \(2\times 10^{-2}\). The uncoded BER using MRC and HTFDE is \(3.4\times 10^{-2}\) and the coded BER is \(5.3\times 10^{-3}\). As shown in Figure 8, the BER improvement using the five receiver elements at one location was far smaller than the improvement using the data of Rx #1 from five transmissions. This occurred because the channel correlation between the different elements was higher than the correlation between different transmissions. A linear array consisting of eight elements was used in the lake experiment. Figure 9 shows the BER performance using up to three contiguous elements with five transmissions. When we used elements from 1 to 3, the uncoded BER of MRC-FDE decreased from \(1.5\times 10^{-2}\) to \(3\times 10^{-3}\), whereas the uncoded BER of MRC-HTFDE decreased from \(6.6\times 10^{-3}\) to \(6.1\times 10^{-4}\). We demonstrated that error-free using three elements combined three transmissions, especially using MRC-HTFDE. Figure 10 shows the output SNRs using different elements and transmission numbers using MRC-FDE and MRC-HTFDE methods. With the same transmission number, the output SNR improvement reduced as we used more receiver elements. The output SNRs of the three transmissions with three receiver elements were 8 dB for MRC-FDE and 10.9 dB for MRC-HTFDE. With three contiguous elements, the 0.5-m-long linear array with three transmissions achieved error-free reception. Such a three-element array is low cost and acceptable for small underwater platforms, like UUVs. Through the use of multiple elements, the BER can be reduced significantly, thus reducing the required number of transmissions, shown in Figure 10.  
Figure 8: BER performance using conventional multichannel FDE and HTFDE at one location: (**a**) Location #1 and (**b**) Location #5.