Generalized Arlery-Tan-Rabaste-Levenshtein Lower Bounds on Ambiguity Function and Their Asymptotic Achievability

Lingsheng Meng; Yong Liang Guan; Yao Ge; Zilong Liu; Pingzhi Fan

doi:10.1109/TIT.2025.3570212

Generalized Arlery-Tan-Rabaste-Levenshtein Lower Bounds on Ambiguity Function and Their Asymptotic Achievability

Lingsheng Meng, Yong Liang Guan, Yao Ge, Zilong Liu^*, Pingzhi Fan

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

This paper presents generalized Arlery-Tan-Rabaste-Levenshtein lower bounds on the maximum aperiodic ambiguity function (AF) magnitude of unimodular sequences under certain delay-Doppler low ambiguity zones (LAZ). Our core idea is to explore the upper and lower bounds on the Frobenius norm of the weighted auto- and cross-AF matrices by introducing two weight vectors associated with the delay and Doppler shifts, respectively. As a second major contribution, we demonstrate that our derived lower bounds are asymptotically achievable with selected Chu sequence sets by analyzing their maximum auto- and cross- AF magnitudes within certain LAZ.

Original language	English
Journal	IEEE Transactions on Information Theory
DOIs	https://doi.org/10.1109/TIT.2025.3570212
Publication status	Accepted/In press - 2025
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

ASJC Scopus Subject Areas

Information Systems
Computer Science Applications
Library and Information Sciences

Keywords

Ambiguity function
Chu sequences
delay-Doppler low ambiguity zone
lower bounds
unimodular sequences

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10.1109/TIT.2025.3570212

Cite this

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abstract = "This paper presents generalized Arlery-Tan-Rabaste-Levenshtein lower bounds on the maximum aperiodic ambiguity function (AF) magnitude of unimodular sequences under certain delay-Doppler low ambiguity zones (LAZ). Our core idea is to explore the upper and lower bounds on the Frobenius norm of the weighted auto- and cross-AF matrices by introducing two weight vectors associated with the delay and Doppler shifts, respectively. As a second major contribution, we demonstrate that our derived lower bounds are asymptotically achievable with selected Chu sequence sets by analyzing their maximum auto- and cross- AF magnitudes within certain LAZ.",

keywords = "Ambiguity function, Chu sequences, delay-Doppler low ambiguity zone, lower bounds, unimodular sequences",

author = "Lingsheng Meng and Guan, {Yong Liang} and Yao Ge and Zilong Liu and Pingzhi Fan",

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AU - Guan, Yong Liang

AU - Ge, Yao

AU - Liu, Zilong

AU - Fan, Pingzhi

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AB - This paper presents generalized Arlery-Tan-Rabaste-Levenshtein lower bounds on the maximum aperiodic ambiguity function (AF) magnitude of unimodular sequences under certain delay-Doppler low ambiguity zones (LAZ). Our core idea is to explore the upper and lower bounds on the Frobenius norm of the weighted auto- and cross-AF matrices by introducing two weight vectors associated with the delay and Doppler shifts, respectively. As a second major contribution, we demonstrate that our derived lower bounds are asymptotically achievable with selected Chu sequence sets by analyzing their maximum auto- and cross- AF magnitudes within certain LAZ.

KW - Ambiguity function

KW - Chu sequences

KW - delay-Doppler low ambiguity zone

KW - lower bounds

KW - unimodular sequences

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Generalized Arlery-Tan-Rabaste-Levenshtein Lower Bounds on Ambiguity Function and Their Asymptotic Achievability

Abstract

Bibliographical note

ASJC Scopus Subject Areas

Keywords

Access to Document

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