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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. The…

信号处理 · 电气工程与系统科学 2025-07-01 Muhammad Ubadah , Saif Khan Mohammed , Ronny Hadani , Shachar Kons , Ananthanarayanan Chockalingam , Robert Calderbank

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…

信号处理 · 电气工程与系统科学 2023-10-03 Saif Khan Mohammed , Ronny Hadani , Ananthanarayanan Chockalingam , 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…

The Zak-transform-based Orthogonal Time Frequency Space (Zak-OTFS), offers a robust framework for high-mobility communications by simplifying the input-output (I/O) relation to a twisted convolution. While this structure theoretically…

信号处理 · 电气工程与系统科学 2026-02-10 Kecheng Zhang , Weijie Yuan , Yonghui Li

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…

信号处理 · 电气工程与系统科学 2024-12-31 Jinu Jayachandran , Imran Ali Khan , Saif Khan Mohammed , Ronny Hadani , Ananthanarayanan Chockalingam , Robert Calderbank

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…

信息论 · 计算机科学 2024-02-16 Beyza Dabak , Venkatesh Khammammetti , Saif Khan Mohammed , 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…

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…

信号处理 · 电气工程与系统科学 2025-07-21 Nishant Mehrotra , Sandesh Rao Mattu , Robert Calderbank

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…

信号处理 · 电气工程与系统科学 2025-07-21 Saif Khan Mohammed , Amit Kumar Pathak , Muhammad Ubadah , Ronny Hadani , Ananthanarayanan Chockalingam , Robert Calderbank

Zak-transform based orthogonal time frequency space (Zak-OTFS) is a delay-Doppler (DD) domain modulation scheme in which the signal processing is carried out in the DD domain. The channel when viewed in the DD domain is predictable.…

信号处理 · 电气工程与系统科学 2025-07-21 Sandesh Rao Mattu , Nishant Mehrotra , 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…

信息论 · 计算机科学 2026-04-21 Sandesh Rao Mattu , Nishant Mehrotra , Venkatesh Khammammetti , 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…

信号处理 · 电气工程与系统科学 2025-11-12 Sabarinath Ramachandran , Venkatesh Khammammetti , Prasanthi Maddala , Narayan Mandayam , Ivan Seskar , Robert Calderbank

Integrated sensing and communication (ISAC) through Zak-transform-based orthogonal time frequency space (Zak-OTFS) modulation is a promising solution for high-mobility scenarios. Realizing accurate bistatic sensing and robust communication…

信号处理 · 电气工程与系统科学 2026-01-08 Kecheng Zhang , Weijie Yuan , Maria Sabrina Greco

Zak-OTFS provides a framework for integrated sensing & communication (ISAC) in high delay and Doppler spread environments. Pulse shaping filter design enables joint optimization of sensing and communication performance. For sensing, a…

信号处理 · 电气工程与系统科学 2026-01-16 Nishant Mehrotra , Sandesh Rao Mattu , Robert Calderbank

The transceiver operations in the delay-Doppler (DD) domain in Zak-OTFS modulation, including DD domain filtering at the transmitter and receiver, involve twisted convolution operation. The twisted convolution operations give rise to…

信息论 · 计算机科学 2025-04-29 Arpan Das , Fathima Jesbin , Ananthanarayanan Chockalingam

In this paper, we consider the problem of estimating the delay-Doppler (DD) domain input-output (I/O) relation in Zak-OTFS modulation, which is needed for signal detection. Two approaches, namely, model-dependent and model-free approaches,…

信息论 · 计算机科学 2025-10-13 Sai Pradeep Muppaneni , Vineetha Yogesh , A. Chockalingam

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…

信号处理 · 电气工程与系统科学 2025-04-01 Nishant Mehrotra , Sandesh Rao Mattu , Robert Calderbank

The choice of delay-Doppler domain (DD) pulse shaping filter plays an important role in determining the performance of Zak-OTFS. Sinc filter has good main lobe characteristics (with nulls at information grid points) which is good for…

信息论 · 计算机科学 2025-02-07 Arpan Das , Fathima Jesbin , Ananthanarayanan Chockalingam

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…

信号处理 · 电气工程与系统科学 2025-07-08 Saif Khan Mohammed , Sandesh Rao Mattu , Nishant Mehrotra , Venkatesh Khammammetti , Robert Calderbank

Looking towards 6G wireless systems, frequency bands like the sub-terahertz (sub-THz) band (100 GHz - 300 GHz) are gaining traction for their promises of large available swaths of bandwidth to support the ever-growing data demands. However,…

信号处理 · 电气工程与系统科学 2025-04-23 Claire Parisi , Venkatesh Khammammetti , Robert Calderbank , Lauren Huie
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