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We investigate the relationship between Orthogonal Time Frequency Space(OTFS) modulation and Orthogonal Short Time Fourier (OSTF) signaling. OTFS wasrecently proposed as a new scheme for high Doppler scenarios and builds onOSTF. We first show that the two schemes are unitarily equivalent in thedigital domain. However, OSTF defines the analog-digital interface with thewaveform domain. We then develop a critically sampled matrix-vector model forthe two systems and consider linear minimum mean-squared error (MMSE) filteringat the receiver to suppress inter-symbol interference. Initial comparison ofcapacity and (uncoded) probability of error reveals a surprising observation:OTFS under-performs OSTF in capacity but over-performs in probability of error.This result can be attributed to characteristics of the channel matricesinduced by the two systems. In particular, the diagonal entries of OTFS matrixexhibit nearly identical magnitude, whereas those of the OSTF matrix exhibitwild fluctuations induced by multipath randomness. It is observed that bysimply replacing the unitary matrix, relating OTFS to OSTF, by an arbitraryunitary matrix results in performance nearly identical to OTFS. We then extendour analysis to orthogonal frequency division multiplexing (OFDM) and alsoconsider a more extreme scenario of relatively large delay and Doppler spreads.Our results demonstrate the significance of using OSTF basis waveforms ratherthan sinusoidal ones in OFDM in highly dynamic environments, and also highlightthe impact of the level of channel state information used at the receiver.

How is Time Frequency Space Modulation Related to Short Time Fourier Signaling?