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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 con- sequence 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.

Saif Khan Mohammed
Indian Institute of Technology Delhi, New Delhi, India
Ronny Hadani
University of Texas at Austin, Austin, TX, USA
Ananthanarayanan Chockalingam
Indian Institute of Science, Bangalore, India

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