English

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

Information Theory 2025-05-12 v3 Signal Processing math.IT

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

Cite

@article{arxiv.2402.00455,
  title  = {Generalized Arlery-Tan-Rabaste-Levenshtein Lower Bounds on Ambiguity Function and Their Asymptotic Achievability},
  author = {Lingsheng Meng and Yong Liang Guan and Yao Ge and Zilong Liu and Pingzhi Fan},
  journal= {arXiv preprint arXiv:2402.00455},
  year   = {2025}
}

Comments

Accepted for publication in IEEE Transactions on Information Theory (Accepted date: 8 May 2025)