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arXiv · 2402.00455

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
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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.

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Lingsheng Meng, Yong Liang Guan, Yao Ge, Zilong Liu, Pingzhi Fan. 2024-02-01. Generalized Arlery-Tan-Rabaste-Levenshtein Lower Bounds on Ambiguity Function and Their Asymptotic Achievability. https://arxiv.org/abs/2402.00455

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