# Hamming Distance Optimized Underwater Acoustic OTFS-IM Systems
## 4 Simulation Analysis
The number of active sub-grids in the index modulated OTFS block is less than in a conventional OTFS system; therefore, there is an improvement in energy efficiency. Secondly, when comparing the BER performance of two different receiver detection algorithms with the same sub-grid group size, we found that the smaller the number of active sub-grids, the better the BER performance of the system. When the number of active sub-grids in the system sub-grid group is 2, the system BER reaches 0 after the SNR is 26 dB, and when the number of active sub-grids is 1, the system BER reaches 0 after 22 dB. This performance gain is obtained through a reduction in spectral efficiency so OTFS-IM systems can obtain a trade-off between system BER performance and spectrum efficiency. Finally, the BER performance at the receiver end of the system is significantly better than the GD algorithm when the ML algorithm is used  
Figure 4: Time-varying underwater acoustic channel. for detection, but the GD detection algorithm outperforms the ML detection algorithm in terms of algorithm complexity. A comparison of the BER performance of the system produced by the Hamming distance optimized index mapping model with the random selection mapping model for a sub-grid group size of 4 with the number of activated sub-grids of 2 and for a sub-grid group size of 8 with the number of activated sub-grids of 3 is presented in Figures 7 and 8, respectively. It can be seen from the simulations that the use of the Hamming distance optimization model for the redundancy in the indexed combinatorial sequences brings a degree of optimization to the BER performance of the system. This optimization effect is more obvious at high SNR, which is reflected by both the ML detection algorithm and the GD detection algorithm at the system receiver. The BER performance improvement of the Hamming distance optimization model is more pronounced at the receiver side when the  
Figure 5: Spectral efficiency diagram for different values of \((n,k)\). Figure 6: Simulation comparison of the number of different active sub-grids. SNR is higher than 15 dB while using the ML detection algorithm and the GD detection algorithm. This is due to the fact that the signal is more heavily disturbed by noise at low SNR which interferes with the determination of the location of the active sub-grid during demodulation. By comparing the performance of two different detection algorithms when the index combination mapping model is optimized by the Hamming distance, the effect of the GD detection algorithm in the optimization of the index combination mapping model under the condition of high SNR is almost the same as that of the ML detection algorithm without the index mapping model. This means that a relatively good BER performance can be achieved at the same time when a relatively low complexity detection algorithm is used, and the system BER performance can be further improved when a relatively high complexity ML detection algorithm is adopted. Figure 8: Hamming distance optimized index mapping and random selection mapping performance comparison. Figure 7: Hamming distance optimized index mapping and random selection mapping performance comparison.