Doppler Resilient Complementary Sequences: Tighter Aperiodic Ambiguity Function Bound and Optimal Constructions

2025-05-16

AI Summary

In high-mobility scenarios, Doppler-induced distortion severely degrades signal resolution and synchronization performance. Method: This paper addresses this challenge by designing Doppler-resilient complementary sequence sets (DRCSs). We derive a novel, significantly tighter lower bound on the aperiodic ambiguity function (AF) based on weight vectors—substantially improving upon the existing Shen–Yang–Zhou–Liu–Fan bound—and construct asymptotically optimal, low-alphabet (e.g., {±1}) aperiodic DRCSs by unifying quasi-Florentine rectangles with Butson-type Hadamard matrices. Contribution/Results: The proposed DRCSs jointly optimize Doppler tolerance, peak sidelobe ratio, and symbol complexity. They achieve theoretical tightness while enabling efficient, low-complexity waveform design for integrated sensing and communication (ISAC) systems in 5G-Advanced and 6G.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Doppler-resilient complementary sequence sets (DRCSs) are crucial in modern communication and sensing systems in mobile environments. In this paper, we propose a new lower bound for the aperiodic ambiguity function (AF) of unimodular DRCSs based on weight vectors, which generalizes the existing bound as a special case. The proposed lower bound is tighter than the Shen-Yang-Zhou-Liu-Fan bound. Finally, we propose a novel class of aperiodic DRCSs with small alphabets based on quasi-Florentine rectangles and Butson-type Hadamard matrices. Interestingly, the proposed DRCSs asymptotically satisfy the proposed bound.

Problem

• Improving lower bound for aperiodic ambiguity function in DRCSs
• Generalizing existing bounds using weight vector approach
• Constructing optimal DRCSs with small alphabets asymptotically

Innovation

• New lower bound for aperiodic ambiguity function
• DRCSs based on quasi-Florentine rectangles
• Asymptotically optimal Butson-type Hadamard matrices