Fundamentals of Delay-Doppler Communications: Practical Implementation and Extensions to OTFS
CoRR(2024)
摘要
The recently proposed orthogonal time frequency space (OTFS) modulation,
which is a typical Delay-Doppler (DD) communication scheme, has attracted
significant attention thanks to its appealing performance over doubly-selective
channels. In this paper, we present the fundamentals of general DD
communications from the viewpoint of the Zak transform. We start our study by
constructing DD domain basis functions aligning with the time-frequency
(TF)-consistency condition, which are globally quasi-periodic and locally
twisted-shifted. We unveil that these features are translated to unique signal
structures in both time and frequency, which are beneficial for communication
purposes. Then, we focus on the practical implementations of DD Nyquist
communications, where we show that rectangular windows achieve perfect DD
orthogonality, while truncated periodic signals can obtain sufficient DD
orthogonality. Particularly, smoothed rectangular window with excess bandwidth
can result in a slightly worse orthogonality but better pulse localization in
the DD domain. Furthermore, we present a practical pulse shaping framework for
general DD communications and derive the corresponding input-output relation
under various shaping pulses. Our numerical results agree with our derivations
and also demonstrate advantages of DD communications over conventional
orthogonal frequency-division multiplexing (OFDM).
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