# Hamming Distance Optimized Underwater Acoustic OTFS-IM Systems  
[PERSON]  
Correspondence: [EMAIL_ADDRESS]  
[PERSON]  
Correspondence: [EMAIL_ADDRESS]  
[PERSON]  
(PAPR). Subsequently, in the context of multi-user underwater acoustic communication, [PERSON] [13] combined OTFS modulation techniques with MIMO to investigate a large-scale MIMO-OFDM-based OTFS multi-user underwater acoustic communication scheme. At the receiving end of the system, [PERSON]. [14] proposed an optimal coordinate descent infinite parametric constrained equilibrium algorithm for the problem of high complexity of the linear minimum mean square error (LMMSE) algorithm, which reduces the complexity of the system while ensuring the BER performance of the system. In contrast, [PERSON]. [15] also proposed a two-dimensional passive time-reversal receiver to reduce the complexity of the algorithm at the receiver side of the system and verified the proposed algorithm in simulated and measured channels to obtain a better system BER performance with lower complexity. [PERSON]. [16] proposed a method of Doppler compensation for OTFS systems that mitigates the severe Doppler effect in underwater acoustic communication systems and avoids problems caused by fractional Doppler shifts through the design of channel estimation. With continuous research on multi-carrier modulation techniques, inspired by the orthogonal frequency division multiplexing with index modulation (OFDM-IM) [17] technique, the [18] combined index modulation techniques with OTFS to propose orthogonal time frequency space with index modulation (OTFS-IM), which transmits information through constellation symbols and index bits in the DD domain, achieves better BER performance at high spectral efficiency compared to the OFDM-IM system. At the same time, the addition of index bits improves the spectral efficiency and system performance of the OTFS system.  
A series of indexed modulation techniques such as OFDM-IM are widely used in underwater acoustic communications [19; 20; 21]. However, it is difficult to realize robust work in the face of a strong Doppler environment in the time-varying underwater acoustic channel, and it is limited in a series of dynamic underwater acoustic communication scenarios. The OTFS-IM modulation technique is based on the OTFS modulation technique and combined with index modulation, which inherits the characteristic that OTFS has of a strong anti-Doppler effect in DD domain. Additionally, because the addition of index modulation enables the OTFS-IM system to have more flexible and controllable SE and BER than the OTFS system, it can achieve a better compromise between transmission reliability and SE in time-varying channels, but OTFS-IM underwater acoustic communication systems are just starting.  
This paper constructs the OTFS-IM underwater acoustic communication system and proposes a Hamming distance optimization model for the problem of redundancy in activator grid combinations generated by the specific index combination method at the transmitter side of the system. Encoding the activation states of sub-grid groups, using the Hamming distance between the encoded and activated sub-grid combinations, and selecting the sequence of index combinations with a maximum Hamming distance for modulation avoids redundant combinations in a particular index combination. In contrast, the maximum likelihood (ML) detection algorithm was used on the receiver side to verify against the greedy detection (GD) detection algorithm.