Understanding the details of OTFS and its use for communication and sensing requires that the reader goes outside of the comfort zone of a Fourier analysis that is commonly used in communication theory. For instance, Figure 1 depicts a block marked as ISFFT (Inverse Symplectic Finite Fourier Transform), which is not really the first off-the-shelf tool used by a communication engineer. Let us, though, try to illustrate the main contribution of the paper. A downlink scenario is considered, where a multi-antenna Base Station (BS) transmits to K randomly distributed User Equipments (UEs), each with a single antenna. From the figure it can be seen that the OTFS modulation is supplemented with two modules. One of them is used for precoding and power allocation, which is a way to combat multi-path interference. The next module does spatial spreading to combat interference after spatial multiplexing. The actual variant of OTFS used in this work is spatially spread orthogonal time frequency space (SS-OTFS). Given a sufficient number of antennas, the spatial spreading and de-spreading is used to approximately eliminate the interference due to multipath and multiuser transmissions.

JSAC: Could you briefly and intuitively explain the main idea behind OTFS and provide some thoughts on its possible possibilities and obstacles to be adopted in standardization?

OTFS is a novel delay-Doppler (DD) domain communication scheme, which multiplexes the information symbols in the DD domain rather than the time-frequency (TF) domain as adopted for conventional OFDM modulation. The DD domain symbol multiplexing allows a direct interaction between the information symbols and the DD domain channel responses, which are generally quasi-static, compact, and separable. From a discrete signaling point of view, the DD domain connects to the TF domain by the symplectic finite Fourier transform (SFFT), which consists of two-pairs of DFT/IDFT along both the time and frequency dimensions, while it connects to the time domain (also called time-delay (TD) domain) by the discrete Zak transform, which can be interpreted as a DFT operation followed by a block interleaving. OTFS can be viewed as a 2D-preoded OFDM modulation (in TF domain). The OTFS waveform behaves locally like TDMA (localized in the time domain), globally like OFDM (orthogonal tones in the frequency domain) and spreading like CDMA (2D-spreaded in the TF domain), thus inheriting their beneficial properties, and having the potentials of achieving full channel diversity. Recently, OTFS has motivated researchers to develop other delay-Doppler plane modulation with orthogonal pulses, such as the orthogonal delay-Doppler division multiplexing (ODDM), which can achieve orthogonality in accordance with delay and Doppler resolutions that are generally much smaller than the symbol duration and subcarrier spacing in conventional OFDM and match channel’s delay and Doppler resolutions. 

OTFS, or delay-Doppler plane modulation, has a high possibility to be adopted in future wireless standards, e.g., beyond 5G, as a promising waveform not only because it has a robust performance in high-mobility channels but also because it directly interacts with the DD domain channel, which mirrors the underlying physical geometries of the environment. This fact provides numerous new opportunities for future wireless networks, where the interferences can be separated or exploited in the DD domain at a low cost, because different resolvable paths generally have different physical attributes, yielding different delay or Doppler responses. Therefore, OTFS is generally attractive for transmissions with strong interference from different sources/physical scatterers, whereas conventional TF domain channel is complex or hard to be exploited, such as multi-user MIMO, satellite communication, underwater acoustic communications, and space-air-ground integrated network (SAGIN). On top of that, OTFS also has a natural alignment with radar sensing, because OTFS operates in the DD domain where the delay and Doppler estimation can be implemented linearly. Thus, it also enjoys high potential in integrated sensing and communication (ISAC) transmissions.

From a standardization perspective, the main obstacles to the application of OTFS modulation may be the latency issue, detection complexity, pulse designs. Note that OTFS spreads the DD domain information symbol to the whole TF domain. Consequently, the OTFS demodulation can only be done once the whole block of TF symbols are received, which may incur a higher latency compared to OFDM. Meanwhile, OTFS generally requires a higher detection complexity, because the received OTFS signal is essentially the superposition of the time-delayed and frequency-shifted versions of the transmitted signal. Consequently, a message-passing type of receiver may be required to obtain a good error performance. Furthermore, pulse designs for OTFS have not been fully studied in the literature. Without a carefully designed pulse, OTFS may experience high out-of-band emissions (OOBE) and other practical related issues. In conclusion, the transceiver designs for OTFS are important for its standardization.

JSAC: What do you think is the weak point of your approach? Was there a criticism from the reviewers that led you to rethink part of your work?

The weak point of the proposed approach may be the fact of spreading the OTFS signals from the angular domain to the spatial (antenna) domain usually requires a large number of antennas. In other words, the proposed approach may not perform very well without a massive MIMO setup. To address this problem, it is necessary to derive a system model that reflects the effect of spatial domain power leakage when the number of antennas is limited. Furthermore, practical designs on precoding and detection need to be developed based on the derived model to facilitate the ISAC design. Currently, we are working on extensions of the proposed approaches aiming to address the aforementioned weak points.

The reviewer’s comments were generally very positive. One of the reviewers raised important criticism against our derivations related to the spatial-spreading and the pair-wise error probability. To address this criticism, we have reevaluated the suitability of the proposed spatial-spreading and precoding in ISAC transmissions, where new derivations and discussions were provided. In particular, we have adopted new simulations to verify the derivations. Furthermore, we have also presented representative examples to demonstrate the physical insights behind the concept of spatial-spreading and explained why it is suitable for ISAC transmissions. This paper is merely a humble attempt to apply OTFS for ISAC transmissions. We hope our work can stimulate more studies on this topic.