Discrete Spectrum Analysis of Vector OFDM Signals

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.