In this paper, a unified framework for chirp-domain waveforms, including orthogonal chirp division multiplexing (OCDM) and affine frequency division multiplexing (AFDM), is developed. Based on their continuous-time representations, we show that these waveforms fall within the conventional Weyl-Heisenberg (WH) framework for multicarrier (MC) waveforms, where the root chirp corresponds directly to the prototype pulse in the WH framework. Since the chirp is a constant-envelope signal and is transparent to subcarrier orthogonality, these waveforms can be further interpreted as pulse-shaped (PS) orthogonal frequency division multiplexing (OFDM). Within the developed PS-OFDM framework, the power spectral density of chirp-domain waveforms is derived analytically. We then discuss existing practical implementations of chirp-domain waveforms, which rely on sub-Nyquist discrete-time samples and therefore exhibit frequency aliasing. The resulting aliased waveform is analyzed, and the orthogonality among the embedded aliased chirps is discussed. It is shown that the aliased chirps are conditionally orthogonal, whereas the implemented approximate aliased chirps can maintain mutual orthogonality when an appropriate sample-wise pulse-shaping filter is applied. We further derive an exact input-output relation for the implemented chirp-domain waveform over a delay-Doppler (DD) channel, showing that the effective channel observed at a practical receiver does not, in general, admit a DD spreading-function model commonly assumed in the literature. The implementation complexity is also investigated and compared with that of orthogonal delay-Doppler division multiplexing (ODDM), the DD-domain MC waveform defined within the evolved WH framework. Finally, simulation results are provided to verify the analysis.

翻译：本文建立了一个包含正交啁啾分复用(OCDM)和仿射频分复用(AFDM)在内的啁啾域波形统一框架。基于其连续时间表示，我们证明这些波形属于传统的多载波(MC)波形Weyl-Heisenberg(WH)框架，其中根啁啾直接对应于WH框架中的原型脉冲。由于啁啾是恒包络信号且对子载波正交性透明，这些波形可进一步解释为脉冲成形(PS)正交频分复用(OFDM)。在所建立的PS-OFDM框架内，我们解析推导了啁啾域波形的功率谱密度。随后，我们讨论了现有啁啾域波形的实用实现方案，这些方案依赖于亚奈奎斯特离散时间采样，因此存在频率混叠现象。我们对所得混叠波形进行了分析，并讨论了其中嵌入的混叠啁啾间的正交性。研究表明，混叠啁啾具有条件正交性，而当采用适当的逐采样点脉冲成形滤波器时，实际实现的近似混叠啁啾能够保持相互正交性。我们进一步推导了所实现啁啾域波形在时延-多普勒(DD)信道上的精确输入输出关系，表明实际接收机观测到的等效信道通常不符合文献中普遍假设的DD扩展函数模型。本文还研究了实现复杂度，并与演进WH框架内定义的DD域多载波波形——正交时延-多普勒分复用(ODDM)进行了比较。最后，通过仿真结果验证了理论分析。