On the equivalence of OSDM and OTFS

In this paper, we show the mathematical equivalence of two popular modulation schemes: OSDM and OTFS. The former is mainly used in underwater acoustic communications, while the latter scheme is a promising modulation technique in radio-frequency communications. Although literature suggests a link between the two modulation schemes by connecting them to related modulation schemes like V-OFDM and A-OFDM, to the best of the authors' knowledge, a direct mathematical comparison between the schemes has not been presented yet. The main purpose of this paper is therefore to show the mathematical equivalence of the two schemes. In addition, by combining the knowledge of acoustic and radio-frequency communications, we give insight in the performance of OSDM/OTFS in terms of intersymbol interference (ISI) and intercarrier interference (ICI) by analyzing its signal structure.