# Integrated Sensing and Communication Using Random Padded OTFS with Reduced Interferences
## 1 Introduction
However, the CSI-based approach extracts information about the radar target from the channel impulse response using pilots, so the pilot configuration in the case of CSI-based sensing plays an important role. A Zero-Padded OTFS (ZP-OTFS) [15; 16] has the simplest pilot configuration among all OTFS waveforms. It has a dedicated pilot zone in the DD domain with only one active carrier in its center. Due to a low number of active carriers and a large number of inactive carriers, ZP-OTFS is not very efficient and its modification, ZP-BOX-OTFS, was introduced in [21]. The ZP-BOX-OTFS waveform has more active carriers in the center of the pilot zone of the DD grid, but is more complex from a computational point of view and still uses the guard interval (with zero values) in delay and Doppler directions. In turn, a random padded OTFS (RP-OTFS), a hybrid method proposed recently, takes advantage of the OTFS technique for data and uses very short OFDM symbols for pilots [22; 23; 24; 25]. The CSI estimation itself is performed in the TF domain, by means of these very short pilot-only OFDM symbols. Basically, RP-OTFS is a compromise between the strictly DD pilot configuration, such as ZP-OTFS, and OFDM. The advantages of RP-OTFS are the low computational complexity and the ability to use the well-known OFDM channel estimation approaches to OTFS after some adaptations. However, too high Doppler in the channel may corrupt the estimation results, as pilots in RP-OTFS are still OFDM symbols. From a communication point of view, CSI estimation and bit detection are the most challenging parts of the processing, both for OTFS and OFDM waveforms. In the case of OTFS, additional difficulties arise when the reflection parameters (delay and Doppler offsets) are not consistent with the step size of the DD grid [27]. Reflection inconsistency with the DD grid could be in the delay direction, Doppler direction, or both at the same time. These effects are known as fractional delay, fractional Doppler frequency shift, or fractional reflection, respectively [28; 29]. Creating a guard interval (i.e., cyclic prefix with random values) between the pilot and the data zone in RP-OTFS adds additional overhead, so in this paper, we examine the problem of interference between pilot carriers and data carriers. Also, because of a limited number of estimated samples of the CSI in the case of RP-OTFS (and also in ZP-OTFS and others), the CSI oscillations from the fractional reflections cannot be estimated directly. In addition, the accuracy of the CSI estimation is extremely important not only for communication but also, as mentioned before, for radar. In the past few years, a substantial number of studies have been conducted on ISAC systems employing OTFS modulation. Several works have investigated the behavior of OTFS modulation in the presence of interferences and fractional reflections. The MIMO-OTFS sensing and communication model that takes into account both inter-symbol interference (ISI) and inter-carrier interference (ICI) is presented in [30]. In the radar part, the authors develop a generalized likelihood ratio test based multi-target detection and DD-angle estimation algorithm for MIMO-OTFS radar sensing that can simultaneously mitigate and exploit ISI and ICI effects. The authors in [31] propose a low-complexity impulse-based channel estimation algorithm for ZP-OTFS systems that effectively handles fractional reflections. Using the self-duality and invariance properties of a \"pulsone\" pilot (practically the ZP-OTFS pilot), the method achieves improved normalized mean squared error and bit error rate (BER) performance. The authors in [28] present the modified orthogonal matching pursuit algorithm [32] to estimate the delays and Doppler shifts that can be non-integer multiples of the system delay and Doppler resolutions, respectively.