Asymptotically Optimal Sequence Sets With Low/Zero Ambiguity Zone Properties

TL;DR

This work tackles the design of unimodular sequence sets with low/zero ambiguity in delay-Doppler channels, addressing Doppler resilience in high-mobility communications and radar. It offers two analytical ZAZ constructions (A and B) inspired by modulating ZCZ sequences and a comb-like spectral design, plus a LAZ construction (C) based on novel mapping functions, all with proven cyclic distinctness and asymptotic optimality against established bounds. The results provide explicit, structure-based sequence families with provable delay-Doppler performance, suitable for QS-CDMA, V2X, and radar systems in dynamic environments. Collectively, these constructions advance practical, analytically tractable tools for achieving robust delay-Doppler estimation under spectral and Doppler constraints.

Abstract

Sequences with low/zero ambiguity zone (LAZ/ZAZ) properties are useful in modern communication and radar systems operating over mobile environments. This paper first presents a new family of ZAZ sequence sets motivated by the ``modulating'' zero correlation zone (ZCZ) sequences which were first proposed by Popovic and Mauritz. We then introduce a second family of ZAZ sequence sets with comb-like spectrum, whereby the local Doppler resilience is guaranteed by their inherent spectral nulls in the frequency domain. Finally, LAZ sequence sets are obtained by exploiting their connection with a novel class of mapping functions. These proposed unimodular ZAZ and LAZ sequence sets are cyclically distinct and asymptotically optimal with respect to the existing theoretical bounds on ambiguity functions.

Figures (4)

• Figure 1: The ambiguity magnitudes of ${\bm{s}}_0$ and ${\bm{s}_1}$ in $\mathcal{S}$ from Example 1.
• Figure 2: The magnitudes of the frequency-domain dual ${\bm{d}_n}$ corresponding to ${\bm{s}_n}$ in Example 2, $0\leq n\leq 4$.
• Figure 3: The ambiguity magnitudes of ${\bm{s}}_0$ and ${\bm{s}_1}$ in $\mathcal{S}$ from Example 2.
• Figure 4: The ambiguity magnitudes of ${\bm{s}}_0$ and ${\bm{s}_1}$ in $\mathcal{S}$ from Example 3.