Redefining Orthogonal Co-Existence: A Mother Waveform Framework for DFT-Based Waveforms

In this paper, we introduce the concept of a mother waveform to address key challenges in 5th generation (5G) and 6th generation (6G) networks, including spectral efficiency, backward compatibility, enhanced flexibility, and the integration of joint sensing and communication (JSAC). We propose single-carrier interleaved frequency division multiplexing (SC-IFDM) as the mother waveform and demonstrate, through rigorous mathematical modeling, that it can generate all discrete Fourier transform (DFT)-based waveforms without requiring structural modifications. Specifically, by selectively configuring lattice indices and phase adjustments, SC-IFDM enables seamless adaptation to diverse waveforms, such as orthogonal frequency division multiplexing (OFDM), orthogonal chirp division multiplexing (OCDM), orthogonal time-frequency space (OTFS), affine frequency division multiplexing (AFDM), and frequency-modulated continuous wave (FMCW) within a unified framework. Critical aspects such as coexistence strategies and resource allocation are thoroughly explored. Simulation results demonstrate the proposed frameworks ability to deliver superior communication performance, robust sensing capabilities, and efficient coexistence, surpassing traditional waveform designs in scalability and adaptability.