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

TL;DR

This paper introduces a new, tighter lower bound for the aperiodic ambiguity function of Doppler-resilient complementary sequence sets and proposes novel constructions that asymptotically meet this bound, enhancing robustness in mobile communication systems.

Contribution

It presents a generalized, tighter lower bound for the aperiodic AF of DRCSs and introduces new sequence constructions based on quasi-Florentine rectangles and Hadamard matrices.

Findings

The new bound is tighter than previous bounds.

Proposed sequences asymptotically meet the bound.

Sequences have small alphabets and are suitable for mobile environments.

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.