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

2024/02/01 by Lingsheng Meng, Meng, Lingsheng, Yong Liang Guan +7 · 1 citation
Computer Science · Mathematics · #Coding theory and cryptography #Cognitive Computing and Networks #FOS: Computer and information sciences #FOS: Electrical engineering #Information Theory (cs.IT) #Mathematical Approximation and Integration #Signal Processing (eess.SP) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2402.00455

openalex publication_date 2024/02/01 · openalex created_date 2024/02/03 · openalex updated_date 2026/07/28

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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