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 SC-FDE, 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.