Weyl-Heisenberg Framework-Based Orthogonal Waveform Design for Doubly Selective Channels

This paper proposes a unified waveform design framework for doubly selective channels based on the Weyl-Heisenberg (WH) group. By linking waveform orthogonality to the ambiguity function and its zero set under unitary timefrequency shift operators, the proposed framework unifies SCFDE, OFDM, OTFS, and AFDM as different operator paths on the delay-frequency-shift grid. Within this framework, we further design a novel WH-based waveform with a constant-modulus prototype in both the time and frequency domains, yielding orthogonal basis signals with near-uniform time-frequency energy spreading. In doubly selective channels, this waveform exhibits BER performance close to the theoretical minimum mean-square error (MMSE) lower bound.