There is significant recent interest in designing new modulation schemes for doubly-selective channels with large delay and Doppler spreads, where legacy modulation schemes based on time-frequency signal representations underperform. Multiple modulation schemes, e.g., in the delay-Doppler, chirp, time-sequency, and other domains, have been proposed in the literature for this purpose, with varying implementation details. In this letter, we establish that all previously proposed modulation schemes for doubly-selective signaling are instances of a single family of complex Hadamard-modulated pulse trains. When the delay and Doppler spread of the doubly-selective channel is limited to a certain support, all modulation schemes in this waveform family offer equivalent, full diversity achieving performance with no symbol fading and low channel estimation overhead. The existence of this waveform family also enables flexible, multi-waveform co-existence -- allowing a common transceiver architecture to generate multiple waveforms in the family, that may each be flexibly allocated to different users and services.

翻译：近年来，针对具有大时延扩展和多普勒扩展的双选择性信道设计新型调制方案受到广泛关注，而基于时频信号表示的经典调制方案在此类信道中性能欠佳。为此，文献中已提出多种调制方案，例如在时延-多普勒域、线性调频域、时序域及其他域中的方案，但其实现细节各不相同。本文指出，所有先前提出的双选择性信道调制方案均属于复哈达玛调制脉冲序列的统一框架。当双选择性信道的时延扩展和多普勒扩展被限制在特定支撑集内时，该波形族中的所有调制方案均能实现等效的、达到全分集增益的性能，且无符号衰落并具有较低的信道估计开销。该波形族的存在还支持灵活的多波形共存——允许通用收发机架构生成该族中的多种波形，每种波形均可灵活分配给不同用户与服务。