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 journalArticlepeer-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 languageEnglish
JournalIEEE Transactions on Information Theory
DOIs
Publication statusAccepted/In press - 2025
Externally publishedYes

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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