Generalized OTFS Waveform: Overcoming Fractional Doppler in Delay-Doppler Localization

Orthogonal Time Frequency Space (OTFS) waveform has emerged as a promising solution for future communication systems, particularly in high-Doppler environments such as Joint Communication and Sensing and Integrated Sensing and Communication. In this work, we present a mathematical generalization of the standard OTFS formulation, referred to as the generalized OTFS-based waveform. Through a unified matrix representation, we demonstrate that OTFS is a special case of this broader family of waveforms. This generalization preserves the key characteristics of OTFS used in radar systems for localization, namely the circular row and column shifts caused by a delay-Doppler channel, and enables modulation schemes capable of addressing known OTFS performance limitations, such as those caused by fractional Doppler shifts.