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We communicate over wireless channels by first estimating and then equalizing the effective channel. In Zak-OTFS (orthogonal time frequency space) modulation the carrier waveform is a pulse in the delay-Doppler (DD) domain, formally a…

Signal Processing · Electrical Eng. & Systems 2025-07-08 Saif Khan Mohammed , Sandesh Rao Mattu , Nishant Mehrotra , Venkatesh Khammammetti , Robert Calderbank

The principle of orthogonal time-frequency-space (OTFS) signaling is firstly analyzed, followed by explaining that OTFS embeds another signaling scheme referred to as orthogonal short-time Fourier (OSTF). Then, the relationship among OTFS,…

Information Theory · Computer Science 2024-01-26 Lie-Liang Yang

In this paper, we identified the challenges and requirements for the waveform design of the fifth generation mobile communication networks (5G) and compared Orthogonal frequency-division multiplexing (OFDM) based waveforms with Filter Bank…

Signal Processing · Electrical Eng. & Systems 2018-03-09 Yinan Qi , Mohammed Al-Imari

Orthogonal frequency division multiplexing (OFDM) has been widely recognized as the representative waveform for 5G wireless networks, which can directly support sensing/positioning with existing infrastructure. To guarantee superior…

Signal Processing · Electrical Eng. & Systems 2024-03-21 Fan Zhang , Tianqi Mao , Ruiqi Liu , Zhu Han , Sheng Chen , Zhaocheng Wang

The Zak-OTFS input/output (I/O) relation is predictable and non-fading when the delay and Doppler periods are greater than the effective channel delay and Doppler spreads, a condition which we refer to as the crystallization condition. When…

Signal Processing · Electrical Eng. & Systems 2024-10-24 Jinu Jayachandran , Rahul Kumar Jaiswal , Saif Khan Mohammed , Ronny Hadani , Ananthanarayanan Chockalingam , Robert Calderbank

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

Affine frequency division multiplexing (AFDM) is an emerging waveform candidate for future sixth generation (6G) systems offering a range of promising features, such as enhanced robustness in heterogeneous and high-mobility environments, as…

Orthogonal time frequency space (OTFS) is a promising alternative to orthogonal frequency division multiplexing (OFDM) for high-mobility communications. We propose a novel multiple-input multiple-output (MIMO) integrated sensing and…

Signal Processing · Electrical Eng. & Systems 2023-06-13 Musa Furkan Keskin , Carina Marcus , Olof Eriksson , Alex Alvarado , Joerg Widmer , Henk Wymeersch

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

This letter is the first part of a three-part tutorial on orthogonal time frequency space (OTFS) modulation, which is a promising candidate waveform for future wireless networks. This letter introduces and compares two popular…

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

The discussion on using zero padding (ZP) instead of a cyclic prefix (CP) for enhancing channel estimation and equalization performance is a recurring topic in waveform design for future wireless systems that high spectral efficiency and…

Information Theory · Computer Science 2023-03-15 Koosha Pourtahmasi Roshandeh , Mostafa Mohammadkarimi , Masoud Ardakani

Recently, a new precoding technique called orthogonal time-frequency signaling (OTFS) has been proposed for time- and frequency-selective communication channels. OTFS precodes a data frame with a complete set of spreading sequences and…

Information Theory · Computer Science 2017-10-30 Thomas Zemen , Markus Hofer , David Loeschenbrand

Next-generation wireless networks require enhanced flexibility, efficiency, and reliability in physical layer waveform design to address the challenges posed by heterogeneous channel conditions and stringent quality-of-service demands. To…

Signal Processing · Electrical Eng. & Systems 2026-03-09 Xingyao Zhang , Haoran Yin , Yanqun Tang , Yao Ge , Yong Zeng , Miaowen Wen , Zilong Liu , Yong Liang Guan , Hüseyin Arslan , Giuseppe Caire

This paper presents a unified and system-agnostic analysis of the ambiguity function (AF) characteristics of four representative multicarrier waveforms, orthogonal frequency division multiplexing (OFDM), orthogonal time frequency space…

Signal Processing · Electrical Eng. & Systems 2025-10-14 Hyeon Seok Rou , Giuseppe Thadeu Freitas de Abreu

In the high-mobility scenarios of next-generation wireless communication systems (beyond 5G/6G), the performance of orthogonal frequency division multiplexing (OFDM) deteriorates drastically due to the loss of orthogonality between the…

Signal Processing · Electrical Eng. & Systems 2023-03-01 Yu Zhou , Haoran Yin , Jiaojiao Xiong , Shiyu Song , Jiajun Zhu , Jinming Du , Haibo Chen , Yanqun Tang

When the delay period of the Zak-OTFS carrier is greater than the delay spread of the channel, and the Doppler period of the carrier is greater than the Doppler spread of the channel, the effective channel filter taps can simply be read off…

Signal Processing · Electrical Eng. & Systems 2024-12-31 Jinu Jayachandran , Imran Ali Khan , Saif Khan Mohammed , Ronny Hadani , Ananthanarayanan Chockalingam , Robert Calderbank

In orthogonal time frequency space (OTFS) modulation, Zak transform approach is a natural approach for converting information symbols multiplexed in the DD domain directly to time domain for transmission, and vice versa at the receiver.…

Information Theory · Computer Science 2023-03-23 Vineetha Yogesh , Vighnesh S Bhat , Sandesh Rao Mattu , A. Chockalingam

Orthogonal frequency division multiplexing (OFDM) is one of the most widely adopted waveforms for integrated sensing and communication (ISAC) systems, owing to its high spectral efficiency and compatibility with modern communication…

Signal Processing · Electrical Eng. & Systems 2025-10-16 Kawon Han , Kaitao Meng , Alexandra Chatzicharistou , Christos Masouros

Integrated sensing and communication (ISAC) is a key feature of next-generation wireless networks, enabling a wide range of emerging applications such as vehicle-to-everything (V2X) and unmanned aerial vehicles (UAVs), which operate in…

Signal Processing · Electrical Eng. & Systems 2025-11-03 Haoran Yin , Yanqun Tang , Jun Xiong , Fan Liu , Yuanhan Ni , Qu Luo , Roberto Bomfin , Marwa Chafii , Marios Kountouris , Christos Masouros

Integrated sensing and communication (ISAC) is viewed as a crucial component of future mobile networks and has gained much interest in both academia and industry. Similar to the emergence of radio-frequency (RF) ISAC, the integration of…

Signal Processing · Electrical Eng. & Systems 2024-03-12 Yunfeng Wen , Fang Yang , Jian Song , Zhu Han