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The fundamental concepts and challenges of orthogonal time frequency space (OTFS) modulation have been reviewed in Part I of this three-part tutorial. In this second part, we provide an overview of the state-of-the-art transceiver designs…

Information Theory · Computer Science 2022-09-13 Shuangyang Li , Weijie Yuan , Zhiqiang Wei , Robert Schober , Giuseppe Caire

This tutorial derives the mathematical foundations of what it means for a carrier waveform to be predictable and non-selective. We focus on Zak-OTFS, where each carrier waveform is a pulse in the delay-Doppler (DD) domain, formally a…

Information Theory · Computer Science 2026-04-21 Sandesh Rao Mattu , Nishant Mehrotra , Venkatesh Khammammetti , Robert Calderbank

Wireless communications over fast fading channels are challenging, requiring either frequent channel tracking or complicated signaling schemes such as orthogonal time frequency space (OTFS) modulation. In this paper, we propose…

Information Theory · Computer Science 2020-11-30 Hongyang Zhang , Xiaojing Huang , J. Andrew Zhang

Orthogonal Time Frequency Space ({OTFS}) modulation offers significant advantages over Orthogonal Frequency Division Multiplexing ({OFDM}), particularly in high speed environments. Hence, we consider {OTFS} transmission over high-Doppler…

Signal Processing · Electrical Eng. & Systems 2026-05-12 Xinyu Feng , Chao Zhang , Mohammed EL-Hajjar , Chao Xu , Lajos Hanzo

Orthogonal delay-Doppler (DD) division multiplexing (ODDM) modulation has recently emerged as a promising paradigm for ensuring reliable communications in doubly-selective channels. This work investigates the spectra and orthogonality…

Signal Processing · Electrical Eng. & Systems 2025-11-20 Akram Shafie , Jun Tong , Jinhong Yuan , Taka Sakurai , Paul Fitzpatrick , Yuting Fang , Yixuan Xie

In this paper, we rethink delay Doppler channels (also called doubly selective channels). We prove that no modulation schemes (including the current active VOFDM/OTFS) can compensate a non-trivial Doppler spread well. We then discuss some…

Signal Processing · Electrical Eng. & Systems 2025-04-01 Xiang-Gen Xia

In this paper, we propose a Doppler pre-compensation scheme for high-mobility orthogonal frequency division multiplexing (OFDM) uplink, where a high-speed terminal transmits signals to the base station (BS). Considering that the…

Information Theory · Computer Science 2017-04-24 Wei Guo , Weile Zhang , Pengcheng Mu , Feifei Gao , Bobin Yao

High-mobility scenarios in next-generation wireless networks, such as those involving vehicular communications, require ultra-reliable and low-latency communications (URLLC). However, rapidly time-varying channels pose significant…

Information Theory · Computer Science 2025-10-21 Zhaowei Guan , Wenkun Wen , Peiran Wu , Chen Wang , Minghua Xia

**PLEASE FIND THE FULL EXTENDED ARTICLE "From OTFS to AFDM: A Comparative Study of Next-Generation Waveforms for ISAC in Doubly-Dispersive Channels" (Accepted for publication at the IEEE Signal Processing Magazine - Special Issue on Signal…

Orthogonal time frequency space (OTFS) modulation is a two-dimensional modulation scheme designed in the delay-Doppler (DD) domain, exhibiting superior performance over orthogonal frequency division multiplexing (OFDM) modulation in…

Information Theory · Computer Science 2025-12-09 Tengfei Qi , Yifei Yang , Xiong Deng , Zhinan Sun , Ziqiang Gao , Xihua Zou , Wei Pan , Lianshan Yan

Orthogonal Time Frequency Space (OTFS) modulation has recently attracted significant interest due to its potential for enabling reliable communication in high-mobility environments. However, the effectiveness of OTFS receivers relies on the…

Signal Processing · Electrical Eng. & Systems 2026-02-11 Xiaoqi Zhang , Zhitong Ni , Weijie Yuan , J. Andrew Zhang , Tony Q. S. Quek

This paper investigates the effect of oscillator phase noise in orthogonal time frequency space (OTFS) systems. The paper provides in-depth analysis of the interference due to phase noise in the delay-Doppler domain and derives expressions…

Signal Processing · Electrical Eng. & Systems 2026-05-15 Stephen McWade , Arman Farhang

The primary objective of this paper is to establish a generalized framework for pulse-shaping on the delay-Doppler plane. To this end, we classify delay-Doppler pulse-shaping techniques into two types, namely, circular and linear…

Signal Processing · Electrical Eng. & Systems 2023-11-14 Mohsen Bayat , Arman Farhang

Orthogonal time frequency space (OTFS) modulation offers superior robustness to high-mobility channels compared to conventional orthogonal frequency-division multiplexing (OFDM) waveforms. However, its explicit delay-Doppler (DD) domain…

Signal Processing · Electrical Eng. & Systems 2026-04-03 Junyao Zheng , Chung-Hsuan Tung , Yuncheng Yao , Nishant Mehrotra , Sandesh Mattu , Zhenzhou Qi , Danyang Zhuo , Robert Calderbank , Tingjun Chen

Orthogonal time frequency space (OTFS) modulation can effectively convert a doubly dispersive channel into an almost non-fading channel in the delay-Doppler domain. However, one critical issue for OTFS is the very high complexity of…

Information Theory · Computer Science 2019-09-04 Junqiang Cheng , Hui Gao , Wenjun Xu , Zhisong Bie , Yueming Lu

Orthogonal time frequency space (OTFS) modulation is a recently developed multi-carrier multi-slot transmission scheme for wireless communications in high-mobility environments. In this paper, the error performance of coded OTFS modulation…

Information Theory · Computer Science 2020-10-27 Shuangyang Li , Jinhong Yuan , Weijie Yuan , Zhiqiang Wei , Baoming Bai , Derrick Wing Kwan Ng

The Orthogonal-Time-Frequency-Space (OTFS) signaling is known to be resilient to doubly-dispersive channels, which impacts high mobility scenarios. On the other hand, the Orthogonal-Frequency-Division-Multiplexing (OFDM) waveforms enjoy the…

Signal Processing · Electrical Eng. & Systems 2023-10-20 I. Zakir Ahmed , Hamid R. Sadjadpour

Next-generation networks explore the opportunistic assistance of airliner/high-altitude platforms (HAPs) in delivering high data rates for terrestrial networks to ensure consistent and reliable communication. When an airliner/HAP moves at…

Information Theory · Computer Science 2026-01-22 Ashok S Kumar , Shashank Shekhar , Gokularam Muthukrishnan , Muralikrishnan Srinivasan , Sheetal Kalyani

The rapid evolution of the International Mobile Telecommunications (IMT) landscape has prompted the International Telecommunications Union Working Party 5D (ITU WP5D) to outline the framework for IMT-2030 and beyond. This next-generation…

Signal Processing · Electrical Eng. & Systems 2024-09-16 Koteswara Rao Gudimitla , Sibgath Ali Khan M , Kiran Kuchi

Wireless users with different characteristics will be expected to share spectrum in next generation communication networks. One of the great strengths of wireless networks based on Orthogonal Frequency Division Multiplexing (OFDM) is the…

Signal Processing · Electrical Eng. & Systems 2025-07-22 Imran Ali Khan , Saif Khan Mohammed , Ronny Hadani , Ananthanarayanan Chockalingam , Robert Calderbank