###### Abstract  
For the orthogonal time frequency space (OTFS) modulation, we generally multiplex symbols on a new type of carrier waveform in the delay-Doppler (DD) domain. These two parameters can be used to infer the range (R) and velocity (V) of the communication user and sensing target; thus, it is natural for the OTFS to be implemented in integrated sensing and communication (ISAC). A framework for ISAC based on OTFS modulation is proposed in this paper, in which the matched filter scheme with fractional parameter estimation is implemented for radar sensing. In addition, the hybrid message passing (MP) detection algorithm is developed for OTFS symbol demodulation. According to the simulation results, fractional DD shifts associated with multiple targets can be accurately obtained through the proposed framework. Meanwhile, the bit error rate under the proposed detector is less than \(10^{-4}\) when the signal-to-noise ratio is high enough. OTFS; radar sensing; fractional parameter estimation; hybrid message passing; delay-Doppler (DD) domain +
Footnote †: journal:  
0000-0002-4000-0000-0000-0000-0000-0000-0000-0000-0000-00000-0000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-000000  
frequencies. Additionally, instances of high mobility bring about the deterioration of subcarrier orthogonality due to the pronounced Doppler effect, thereby potentially leading to considerable degradation in communication performance. Moreover, the channel response in scenarios characterized by substantial mobility exhibits notable fluctuations across distinct coherence regions. In such scenarios, OFDM requires frequent channel estimation to obtain accurate channel state information, leading to a significant increase in signaling overhead. These difficulties serve as a source of inspiration for researchers, propelling them to devise an innovative modulation technique with the capacity to guarantee resilient communication performance in situations characterized by significant mobility. OFDM and OTFS modulation are different modulation and signal processing techniques designed to address distinct challenges in communication systems. While OFDM is widely used in various current systems, including 4G and 5G cellular networks, OTFS modulation is specifically designed to excel in high-mobility scenarios and challenging channel conditions. 1. Channel Characteristics: OTFS modulation is explicitly designed to handle time-varying channels, making it well suited to high-mobility scenarios. It excels in scenarios with rapid changes in the channel, such as vehicular communication or high-speed rail. 2. Mobility and Doppler Tolerance: OTFS modulation is designed to handle scenarios with high Doppler shifts. Its DD domain representation naturally separates signals, enabling effective mitigation of Doppler effects. 3. Multipath Handling: OTFS modulation excels in multipath environments due to its ability to separate signals in the DD domain, providing superior performance in challenging propagation conditions. OTFS modulation may have an increased computational complexity compared to OFDM. 4. Accuracy in Time-Varying Channels: OTFS modulation excels in accuracy in time-varying channels, offering robust communication and sensing capabilities in high-mobility environments. The newly unveiled OTFS modulation has garnered considerable attention on account of its prospective capability to enable reliable communication in contexts marked by elevated mobility and multi-path propagation, as pointed out in [13; 14; 15; 16; 17]. The OTFS modulation framework is designed to address challenges in communication systems operating in highly dynamic environments with severe multipath and time-varying channel conditions. Under environmental conditions with high interference levels or fluctuating signal strength, the OTFS modulation framework can also demonstrate its advantages. For example:  
1. Multipath Fading and Time Variability 1.