TY - GEN
T1 - On the Zak Transform-based Interpretation of OTFS Modulation
AU - Bondre, Akshay S.
AU - Richmond, Christ D.
N1 - Funding Information:
*This work is sponsored by the Air Force Research Laboratory under contract award number FA8750-20-2-0504 via a Duke University subcontract.
Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - In this paper, we present a Zak transform-based development of the recently proposed orthogonal time frequency space (OTFS) modulation scheme. Unlike previous works, we focus on the interpretation of the spreading function as the Zak transform of the 'impulse train response' for general underspread linear time-varying (LTV) channels. For an underspread channel, the Zak transform of the output signal is given by the twisted convolution of the spreading function with the Zak transform of the input signal. This twisted convolution relationship provides a Zak domain input-output relationship for general underspread LTV channels. We extend these results to the discrete case, by presenting a development of the discrete Zak transform (DZT) similar to the one provided by Mohammed for the continuous Zak transform. We argue that the discrete Zak domain twisted convolution relationship for LTV channels provides a simple and concise input-output relationship for OTFS modulation, analogous to the frequency domain multiplication relationship for orthogonal frequency division multiplexing (OFDM) over linear time invariant (LTI) channels. Lastly, we discuss the impact of adding a cyclic prefix and zero-padding in delay and Doppler in the discrete Zak domain.
AB - In this paper, we present a Zak transform-based development of the recently proposed orthogonal time frequency space (OTFS) modulation scheme. Unlike previous works, we focus on the interpretation of the spreading function as the Zak transform of the 'impulse train response' for general underspread linear time-varying (LTV) channels. For an underspread channel, the Zak transform of the output signal is given by the twisted convolution of the spreading function with the Zak transform of the input signal. This twisted convolution relationship provides a Zak domain input-output relationship for general underspread LTV channels. We extend these results to the discrete case, by presenting a development of the discrete Zak transform (DZT) similar to the one provided by Mohammed for the continuous Zak transform. We argue that the discrete Zak domain twisted convolution relationship for LTV channels provides a simple and concise input-output relationship for OTFS modulation, analogous to the frequency domain multiplication relationship for orthogonal frequency division multiplexing (OFDM) over linear time invariant (LTI) channels. Lastly, we discuss the impact of adding a cyclic prefix and zero-padding in delay and Doppler in the discrete Zak domain.
KW - Linear time-varying channels
KW - OTFS modulation
KW - Zak transform
KW - spreading function
KW - underspread channels
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U2 - 10.1109/IEEECONF56349.2022.10051983
DO - 10.1109/IEEECONF56349.2022.10051983
M3 - Conference contribution
AN - SCOPUS:85150189731
T3 - Conference Record - Asilomar Conference on Signals, Systems and Computers
SP - 715
EP - 721
BT - 56th Asilomar Conference on Signals, Systems and Computers, ACSSC 2022
A2 - Matthews, Michael B.
PB - IEEE Computer Society
T2 - 56th Asilomar Conference on Signals, Systems and Computers, ACSSC 2022
Y2 - 31 October 2022 through 2 November 2022
ER -