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In orthogonal time frequency space (OTFS) modulation, information-carrying symbols reside in the delay-Doppler (DD) domain. By operating in the DD domain, an appealing property for communication arises: time-frequency (TF) dispersive…

Signal Processing · Electrical Eng. & Systems 2022-12-07 Franz Lampel , Alex Alvarado , Frans M. J. Willems

Orthogonal Time Frequency Space (OTFS) is a framework for communications and active sensing that processes signals in the delay-Doppler (DD) domain. It is informed by 6G propagation environments, where Doppler spreads measured in kHz make…

Information Theory · Computer Science 2024-02-16 Beyza Dabak , Venkatesh Khammammetti , Saif Khan Mohammed , Robert Calderbank

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

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

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

In Zak-OTFS (orthogonal time frequency space) modulation the carrier waveform is a pulse in the delay-Doppler (DD) domain, formally a quasi-periodic localized function with specific periods along delay and Doppler. When the channel delay…

Signal Processing · Electrical Eng. & Systems 2025-07-21 Saif Khan Mohammed , Amit Kumar Pathak , Muhammad Ubadah , Ronny Hadani , Ananthanarayanan Chockalingam , Robert Calderbank

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…

Information Theory · Computer Science 2024-03-22 Shuangyang Li , Peter Jung , Weijie Yuan , Zhiqiang Wei , Jinhong Yuan , Baoming Bai , Giuseppe Caire

In our first paper [2] we explained why 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…

Signal Processing · Electrical Eng. & Systems 2023-10-03 Saif Khan Mohammed , Ronny Hadani , Ananthanarayanan Chockalingam , Robert Calderbank

Millimeter-wave (mmWave) communication offers vast bandwidth for next-generation wireless systems but faces severe path loss, Doppler effects, and hardware impairments. Orthogonal Time Frequency Space (OTFS) modulation has emerged as a…

Signal Processing · Electrical Eng. & Systems 2025-11-12 Sabarinath Ramachandran , Venkatesh Khammammetti , Prasanthi Maddala , Narayan Mandayam , Ivan Seskar , Robert Calderbank

Zak-Orthogonal Time Frequency Space (Zak-OTFS) modulation has been shown to achieve significantly better performance compared to the standardized Cyclic-Prefix Orthogonal Frequency Division Multiplexing (CP-OFDM), in high delay/Doppler…

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

Orthogonal time frequency space (OTFS) modulation is a recently proposed multi-carrier transmission scheme, which innovatively multiplexes the information symbols in the delay-Doppler (DD) domain instead of the conventional time-frequency…

Information Theory · Computer Science 2022-08-26 Shuangyang Li

Orthogonal time frequency space (OTFS) modulation was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) in delay--Doppler channels. In order to detect OTFS modulated data, the…

Information Theory · Computer Science 2018-08-28 P. Raviteja , Khoa T. Phan , Yi Hong

Waveforms with ideal ambiguity functions are fundamental to integrated sensing and communication, to active sensing (radar), and to uplink multiple access. We describe a general method of constructing waveforms using the discrete Zak…

Signal Processing · Electrical Eng. & Systems 2025-04-01 Nishant Mehrotra , Sandesh Rao Mattu , Robert Calderbank

Zak-OTFS (orthogonal time frequency space) modulation is a communication framework that parameterizes the wireless channel in the delay-Doppler (DD) domain, where the parameters map directly to physical attributes of the scatterers that…

Signal Processing · Electrical Eng. & Systems 2025-07-21 Nishant Mehrotra , Sandesh Rao Mattu , Robert Calderbank

4G/5G wireless standards use orthogonal frequency division multiplexing (OFDM) which is robust to frequency selectivity. Equalization is possible with a single tap filter, and low-complexity equalization makes OFDM an attractive physical…

Signal Processing · Electrical Eng. & Systems 2025-09-25 Sandesh Rao Mattu , Nishant Mehrotra , Saif Khan Mohammed , Venkatesh Khammammetti , Robert Calderbank

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) is a framework for communication and active sensing that processes signals in the delay-Doppler (DD) domain. This paper explores three key features of the OTFS framework, and explains their value to…

Signal Processing · Electrical Eng. & Systems 2023-02-20 Saif Khan Mohammed , Ronny Hadani , Ananthanarayanan Chockalingam , Robert Calderbank

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

Orthogonal Time Frequency Space (OTFS) modulation has been recently proposed to be robust to channel induced Doppler shift in high mobility wireless communication systems. However, to the best of our knowledge, none of the prior works on…

Information Theory · Computer Science 2024-10-30 Saif Khan Mohammed
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