OTFS—A Mathematical Foundation for Communication and Radar Sensing in the Delay-Doppler Domain

Orthogonal time frequency space (OTFS) is a framework for communication and active sensing that processes signals in the delay-Doppler (DD) domain. This article explores three key features of the OTFS framework, and explains their value to applications. The first feature is a compact and sparse DD domain parameterization of the wireless channel, where the parameters map directly to physical attributes of the reflectors that comprise the scattering environment, and as a consequence these parameters evolve predictably. The second feature is a novel waveform/modulation technique, matched to the DD channel model, that embeds information symbols in the DD domain. The relation between channel inputs and outputs is localized, non-fading, and predictable, even in the presence of significant delay and Doppler spread, and as a consequence the channel can be efficiently acquired and equalized. By avoiding fading, the post equalization signal to noise ratio remains constant across all information symbols in a packet, so that bit error performance is superior to contemporary multicarrier waveforms. Further, the OTFS carrier waveform is a localized pulse in the DD domain, making it possible to separate reflectors along both delay and Doppler simultaneously, and to achieve a high-resolution DD radar image of the environment. In other words, the DD parameterization provides a common mathematical framework for communication and radar. This is the third feature of the OTFS framework, and it is ideally suited to intelligent transportation systems involving self-driving cars and unmanned ground/aerial vehicles, which are self/network controlled. The OTFS waveform is able to support stable and superior performance over a wide range of user speeds. In the emerging 6G systems and standards, it is ideally suited to support mobility-on-demand envisaged in next generation cellular and WiFi systems, as well as high-mobility use cases. Finally, the compactness and predictability of the OTFS input–output relation makes it a natural fit for machine learning and AI algorithms designed for the intelligent nonmyopic management of control plane resources in future mobile networks.