IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 17, NO. 10, OCTOBER 2018 6501
Interference Cancellation and Iterative Detection for
Orthogonal Time Frequency Space Modulation
P. Raviteja , Student Member, IEEE, Khoa T. Phan , Member, IEEE, Yi Hong , Senior Member, IEEE,
and Emanuele Viterbo , Fellow, IEEE
Abstract—The recently proposed orthogonal time–frequency–
space (OTFS) modulation technique was shown to provide signif-
icant error performance advantages over orthogonal frequency
division multiplexing (OFDM) over delay-Doppler channels.
In this paper, we ﬁrst derive the explicit input–output relation
describing OTFS modulation and demodulation (mod/demod).
We then analyze the cases of: 1) ideal pulse-shaping waveforms
that satisfy the bi-orthogonality conditions and 2) rectangular
waveforms which do not. We show that while only inter-Doppler
interference (IDI) is present in the former case, additional inter-
carrier interference (ICI) and inter-symbol interference (ISI) occur
in the latter case. We next characterize the interferences and
develop a novel low-complexity yet efﬁcient message passing (MP)
algorithm for joint interference cancellation (IC) and symbol
detection. While ICI and ISI are eliminated through appropriate
phase shifting, IDI can be mitigated by adapting the MP algo-
rithm to account for only the largest interference terms. The MP
algorithm can effectively compensate for a wide range of channel
Doppler spreads. Our results indicate that OTFS using practical
rectangular waveforms can achieve the performance of OTFS
using ideal but non-realizable pulse-shaping waveforms. Finally,
simulation results demonstrate the superior error performance
gains of the proposed uncoded OTFS schemes over OFDM under
various channel conditions.
Index Terms—Delay–Doppler channel, OTFS, message
passing, time–frequency modulation.
IFTH-GENERATION (5G) mobile systems are expected
to accommodate an enormous number of emerging wire-
less applications with high data rate requirements such as
real-time video streaming, and online gaming, connected
and autonomous vehicles. While the orthogonal frequency
division multiplexing (OFDM) modulation scheme currently
deployed in fourth-generation (4G) mobile systems can
achieve high spectral efﬁciency for time-invariant frequency
selective channels, it is not robust to time-varying channels
with high Doppler spread (e.g., high-speed railway mobile
communications). Hence, new modulation techniques that
Manuscript received November 30, 2017; revised April 28, 2018; accepted
July 14, 2018. Date of publication August 2, 2018; date of current version
October 9, 2018. This work was supported by the Australian Research Council
through the Discovery Project under Grant DP160100528. The associate editor
coordinating the review of this paper and approving it for publication was K.
Huang. (Corresponding author: Emanuele Viterbo.)
The authors are with the ECSE Department, Monash University, Clayton,
VIC 3800, Australia (e-mail: firstname.lastname@example.org; khoa.phan@
monash.edu; email@example.com; firstname.lastname@example.org).
Color versions of one or more of the ﬁgures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identiﬁer 10.1109/TWC.2018.2860011
are robust to channel time-variations have been extensively
To cope with time-varying channels, one existing approach
is to shorten the OFDM symbol duration so that the chan-
nel variations over each symbol appear inconsequential .
However, one major drawback is the reduced spectral efﬁ-
ciency due to cyclic preﬁx (CP). Another approach exploits
time–frequency signaling , . In  the authors have intro-
duced the frequency-division multiplexing with frequency-
domain cyclic preﬁx (FDM-FDCP), which can efﬁciently
compensate for channel Doppler spread. In high-Doppler low-
delay spread channels, FDM-FDCP is shown to outperform
OFDM at the same spectral efﬁciency. The performance of
FDM-FDCP under other channel conditions are yet to be
A new time–frequency modulation technique called orthog-
onal time frequency space (OTFS) was recently proposed
in  and , which shows signiﬁcant advantages over OFDM
in delay–Doppler channels. The delay–Doppler domain pro-
vides an alternative representation of a time-varying channel
geometry modeling mobile terminals and reﬂectors , .
Leveraging on this representation, the OTFS modulator
spreads each information symbol over a two dimensional (2D)
orthogonal basis function, which spans across the entire time–
frequency domain required to transmit a frame. The set of
basis functions is speciﬁcally designed to combat the dynamics
of the time-varying multi-path channels. In , a general
framework of OTFS based on ideal pulse-shaping waveforms
was introduced. A coded OTFS system with turbo equaliza-
tion was compared with coded OFDM, showing remarkable
gains. In , since mm-wave channels incur high frequency
dispersion, OTFS is shown to outperform OFDM signiﬁcantly.
In this paper, we analyze the input–output relation describ-
ing OTFS mod/demod for delay–Doppler channels using gen-
eral pulse-shaping waveforms. The relation reveals the effects
of the inverse symplectic ﬁnite Fourier transform (ISFFT)
and SFFT operations interpreted as pre- and post-processing
blocks applied to a time–frequency signaling scheme. We then
analyze the cases of (i) ideal pulse-shaping waveforms
that satisfy the bi-orthogonality conditions, and (ii) practi-
cal rectangular waveforms which do not. Unlike previous
works , , , we assume no CP in the second case.
While the OTFS input-output relation derived in  is com-
plex, and does not provide insights, our work presents a simple
relation characterizing the interference. Speciﬁcally, we show
1536-1276 © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
Authorized licensed use limited to: SOUTHWEST JIAOTONG UNIVERSITY. Downloaded on September 24,2022 at 13:44:02 UTC from IEEE Xplore. Restrictions apply.