Asymptotically Optimal Aperiodic Doppler Resilient Complementary Sequence Sets Via Generalized Quasi-Florentine Rectangles
Zheng Wang, Zhiye Yang, Yang Yang, Avik Ranjan Adhikary, Keqin Feng
TL;DR
This work tackles the design of Doppler-resilient aperiodic DRCS sets for high-mobility channels by introducing generalized quasi-Florentine rectangles, a broader combinatorial framework that extends Florentine and quasi-Florentine structures. It pairs these rectangles with Butson-type Hadamard matrices to construct DRCS sets that achieve asymptotic optimality with respect to established lower bounds on the aperiodic ambiguity function, formalized through the optimality factor $\hat{\rho}$ and the bound $\hat{\theta}_{\max} \ge \sqrt{MN \left( 1 - 2 \sqrt{M/(3KZ_y)} \right)}$. The paper provides rigorous construction theorems showing DRCS sets with parameters $(K,N,L,N,\Pi)$ where $\Pi = (-L,L) \times (-L,L)$, and demonstrates that for certain $N$ the sets are exactly optimal, while in general they are asymptotically optimal as $N$ grows. The results extend the parameter flexibility and set sizes beyond prior work, with explicit corollaries and comparisons that highlight practical gains for ISAC and high-Doppler applications.
Abstract
Doppler-resilient complementary sequence (DRCS) sets play a vital role in modern communication and sensing systems, particularly in high-mobility environments. This work makes two primary contributions. First, we refine the definition of quasi-Florentine rectangles to a more general form,termed generalized quasi-Florentine rectangles, and propose a systematic method for their construction. Second, we propose several sets of aperiodic DRCS based on generalized quasi Florentine rectangles and Butson-type Hadamard matrices. The proposed aperiodic DRCS sets are shown to be asymptotically optimal with respect to the lower bound of aperiodic DRCS sets.