# Channel Estimation and Iterative Decoding for Underwater Acoustic OTFS Communication Systems
## 1 Introduction  
Integrated sensing technology for space-air-ground-ocean (SAGO) contexts is a key research focus for next-generation mobile communications [1]. Underwater communication technology plays a crucial role in SAGO integrated sensing and information transmission systems. Acoustic waves are the sole effective medium for long-range underwater information transmission. However, the underwater acoustic (UWA) channel has numerous drawbacks, including limited bandwidths, significant delay spreads, frequency-selective fading, complex time variability, and susceptibility to the Doppler effect [2, 3]. Orthogonal Frequency Division Multiplexing (OFDM) is a multi-carrier modulation technology in which the frequencies of multiplexed subcarriers are orthogonal to each other. This orthogonality ensures that the peak value of each subcarrier aligns with the zero value of other subcarriers. Consequently, even if subcarriers overlap in the spectrum, they do not interfere with each other at the peak of the desired subcarrier. Moreover, OFDM systemsavoid bandwidth efficiency loss, which is common in systems using non-orthogonal carrier sets. Compared to earlier systems, OFDM significantly enhances the spectral efficiency of UWA communication systems. Its low implementation complexity in terms of modulation and demodulation has led to its widespread adoption in high-speed UWA communication and network systems [4; 5; 6; 7; 8; 9; 10; 11; 12]. However, in high-speed motion scenarios, rapid movement result in Doppler frequency shifts and expansions within the communication system [13]. Additionally, the carrier frequency offset (CFO) present in received signals can impair the orthogonality among subcarriers in OFDM systems, resulting in inter-carrier interference (ICI) which severely compromises system performance [14]. Existing approaches aim to mitigate this phenomenon through shortening the OFDM symbol duration to reduce channel variations within each symbol. However, this method's primary drawback is reduced spectral efficiency due to symbol duration shortening [15]. Consequently, OFDM modulation is particularly vulnerable to Doppler spread when employed in UWA communication networks, resulting in severe system performance degradation. Addressing efficient data transmission in dynamic and mobile UWA communication scenarios is thus a critical challenge. Enhancing the spectral efficiency in UWA communication networks--particularly in high-Doppler and high-delay UWA channels--has emerged as a primary research focus for future advancements in UWA communication technology. In 2017, [PERSON] et al. introduced a novel two-dimensional modulation technology termed Orthogonal Time-Frequency Space (OTFS) [16]. OTFS modulation presents a significant advancement in addressing the challenges posed by severe Doppler effects and channel impairments in high-speed mobile communication systems. Unlike traditional OFDM modulation in the time-frequency (TF) domain, OTFS operates in the delay-Doppler (DD) domain for information modulation. The DD domain exhibits robust tolerance to both time delays and Doppler shifts, offering the potential for full diversity--a key factor supporting reliable communication. Furthermore, OTFS modulation effectively transforms a time-varying fading channel into a stationary and non-fading channel in the DD domain, thereby maintaining nearly constant channel gains across all modulation symbols [16]. OTFS can be conceptualized either as an alternative multi-carrier modulation scheme or as a two-dimensional spread spectrum technique applied to QAM symbols, which can subsequently be used with OFDM or other multi-carrier modulation schemes such as Generalized Frequency Division Multiplexing (GFDM) for modulation. The integration of OTFS technology in UWA communication systems addresses the performance degradation observed in OFDM technology when operating in complex and rapidly changing UWA channels.