###### Abstract
Nevertheless, the potential of employing OTFS modulation for radar sensing remains largely untapped. To illustrate, the complexity of the algorithm introduced in [31] increases almost threefold with respect to the size of the OTFS frame, indicating a relatively elevated computational load. Conversely, the investigation carried out in [32] solely accounts for integer-valued DD shifts. Nonetheless, this approach might prove impractical in real-world wireless networks, where temporal resources are constrained, leading to inadequate Doppler resolution. As a result, the inclusion of fractional Doppler components becomes inevitable. Furthermore, achieving precise sensing performance mandates an exploration of radar sensing with limited frequency resources, even though integer delay suffices for communication design in most cases. Consequently, considering both fractional DD indices becomes imperative for effective radar sensing. These concerns collectively drive the motivation to develop an approach that facilitates radar sensing through OTFS signaling, accommodating fractional DD shifts. The practical implementation of OTFS modulation is facilitated by its compatibility with conventional OFDM and pulse-shaped OFDM transceiver structures. This is achieved through the straightforward addition of pre-processing and post-processing blocks. The choice of shaping pulses in a communication or sensing system can significantly impact the overall performance and the spectral efficiency, especially in the context of sensing where accurate channel estimation and signal recovery are crucial. Shaping pulses are waveforms that are used to shape the transmitted signal and, when appropriately chosen, can enhance various aspects of the sensing performance. By using pulses with well-designed spectral characteristics, it is possible to optimize the use of available bandwidths. The choice of shaping pulses influences the duration and bandwidth of the transmitted signal. Depending on the sensing requirements and the characteristics of the environment, it may be desirable to use pulses with specific durations and bandwidths. In addition, to achieve full diversity in TF (time frequency) considerations, effective detection methods are essential. Implementing the maximum a posteriori algorithm (MAP) for each symbol, as detailed in reference [33; 34; 35; 36; 37; 38], represents an optimal approach for data detection within interference channels. The MAP algorithm can be represented by an intuitive cyclic factor graph. However, it is crucial to note that the MAP algorithm becomes computationally infeasible since the number of computation-interfering elements grows exponentially. This exponential growth renders it impractical for scenarios involving multiple signal paths, which requires a low-complexity detector. In an effort to mitigate this computational burden, numerous approximate methods have been developed. For instance, in reference [39], an alternative MAP algorithm is introduced, which leverages Gaussian approximation (GA) to reduce the complexity of these procedures. Reference [9] explores the use of detectors founded on approximate message passing (AMP). Furthermore, reference [40] introduces a unitary approximate message passing detector, which has the same detection performance as the minimal mean square error (MMSE). Lastly, reference [41] presents a detector based on variational Bayes (VB), which has significantly lower computational demands while ensuring convergence with significantly lower computational demands. This paper introduces a method for estimating fractional DD method. First, the radar receiver captures the echoes reflected by targets in the DD domain and subsequently carries out 2D matched filtering involving the DD domain symbols between the receiver and transmitter. With the correlation matrix in hand, we deploy a difference-based technique that entails computing the discrepancy between the indices corresponding to the highest and second highest magnitudes in the correlated matrix.