Vector OFDM (VOFDM) is equivalent to OTFS and is good for time-varying channels. However, due to its vector form, its signal spectrum is not as clear as that of the conventional OFDM. In this paper, we study the discrete spectrum of discrete VOFDM signals. We obtain a linear relationship between a vector of information symbols and a vector of the same size of components evenly distributed in the discrete VOFDM signal spectrum, and show that if a vector of information symbols is set to 0, then a corresponding vector of the same size of the discrete VOFDM signal spectrum is 0 as well, where the components of the 0 vector are not together but evenly distributed in the spectrum. With the linear relationship, the information symbol vectors can be locally precoded so that any of the discrete spectrum of VOFDM signals can be set to 0, similar to that of the conventional OFDM signals. These results are verified by simulations.

翻译：矢量OFDM（VOFDM）等效于OTFS，适用于时变信道。然而，由于其矢量形式，其信号频谱不如传统OFDM清晰。本文研究了离散VOFDM信号的离散频谱。我们得到了信息符号矢量与离散VOFDM信号频谱中均匀分布的相同尺寸分量矢量之间的线性关系，并证明若将信息符号矢量置零，则离散VOFDM信号频谱中对应尺寸的矢量也会相应置零，其中零矢量的分量并非连续分布而是均匀分散在频谱中。利用该线性关系，可通过局部预编码处理信息符号矢量，使得VOFDM信号的任意离散频谱分量均可置零，其效果类似于传统OFDM信号。仿真结果验证了上述结论。