Sensing Fast and Distant Targets in Overspread Channels with Zak-OTFS and Modular Arithmetic
Abstract
Delay-Doppler (DD) modulations, such as Zak-transform-based orthogonal time frequency space (Zak-OTFS) modulation, represent the channel as a sparse set of delay and Doppler shifts, which makes them well suited for radar sensing. Sensing with a single DD frame, however, is unambiguous only when the channel spread factor, i.e., the product of the delay and Doppler spreads, is below one. Long-range mobility scenarios, including drones, airplanes, low Earth orbit (LEO) satellites, and underwater acoustic links, typically violate this crystallization condition, so that a single frame aliases the target delays, Doppler shifts, or both. Existing methods add a time-frequency pilot to a conventional DD frame and resolve the aliasing in only one dimension. We propose a frame design that combines multiple DD bases with different delay and Doppler periods, which together cover an overspread channel, on the same bandwidth and frame size. For two frames, we show that modular arithmetic on the wrapped peak positions uniquely recovers each target by pairing the peaks through their common projection and their gains, and we derive the condition under which this pairing is ambiguous. We implement the design with two superimposed Zak-OTFS frames and propose two receivers: dual-frame sensing (DS), which performs the joint detection directly, and DS with cross-pilot cancellation (DS-XC), which additionally cancels the cross-pilot interference, re-estimates the gains by joint least squares, and removes ghost targets. Both receivers keep a detection rate close to one as the spread factor grows, and DS-XC also achieves the lowest false-alarm rate and channel normalized mean squared error (NMSE). In a 100 km drone scenario, DS-XC detects 98% of the targets, compared with 81% for the best baseline, with a complexity that grows near-linearly with the time-bandwidth product for a fixed number of targets.
Related
- Joint Identification, Transmission, and Sensing over State-Dependent Channels with Noiseless Feedback
- Secure Deterministic Identification with Feedback and Sensing over State-Dependent Wiretap Channels
- Arithmetic duality for p -adic pro-étale cohomology of analytic curves
- Higher arithmetic degrees of dominant rational self-maps
- Exponential Growth of Mean Multiplicities in Length Spectra of Semi-Arithmetic Surfaces of Arbitrary Arithmetic Dimension
BibTeX
@misc{novero2026sensing,
title = {{Sensing Fast and Distant Targets in Overspread Channels with Zak-OTFS and Modular Arithmetic}},
author = {Andrea Novero and Mudasir Ahmad Sheikh and Danish Nisar and Saif Khan Mohammed and Michele Zorzi and Robert Calderbank},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39110},
eprint = {2610.39110},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39110},
}
RIS
TY - UNPB
TI - Sensing Fast and Distant Targets in Overspread Channels with Zak-OTFS and Modular Arithmetic
AU - Andrea Novero
AU - Mudasir Ahmad Sheikh
AU - Danish Nisar
AU - Saif Khan Mohammed
AU - Michele Zorzi
AU - Robert Calderbank
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39110
UR - https://arxiv.org/abs/2610.39110
AB - Delay-Doppler (DD) modulations, such as Zak-transform-based orthogonal time frequency space (Zak-OTFS) modulation, represent the channel as a sparse set of delay and Doppler shifts, which makes them well suited for radar sensing. Sensing with a single DD frame, however, is unambiguous only when the channel spread factor, i.e., the product of the delay and Doppler spreads, is below one. Long-range mobility scenarios, including drones, airplanes, low Earth orbit (LEO) satellites, and underwater acoustic links, typically violate this crystallization condition, so that a single frame aliases the target delays, Doppler shifts, or both. Existing methods add a time-frequency pilot to a conventional DD frame and resolve the aliasing in only one dimension. We propose a frame design that combines multiple DD bases with different delay and Doppler periods, which together cover an overspread channel, on the same bandwidth and frame size. For two frames, we show that modular arithmetic on the wrapped peak positions uniquely recovers each target by pairing the peaks through their common projection and their gains, and we derive the condition under which this pairing is ambiguous. We implement the design with two superimposed Zak-OTFS frames and propose two receivers: dual-frame sensing (DS), which performs the joint detection directly, and DS with cross-pilot cancellation (DS-XC), which additionally cancels the cross-pilot interference, re-estimates the gains by joint least squares, and removes ghost targets. Both receivers keep a detection rate close to one as the spread factor grows, and DS-XC also achieves the lowest false-alarm rate and channel normalized mean squared error (NMSE). In a 100 km drone scenario, DS-XC detects 98% of the targets, compared with 81% for the best baseline, with a complexity that grows near-linearly with the time-bandwidth product for a fixed number of targets.
ER -