New Lower Bounds on Aperiodic Ambiguity Function of Unimodular Sequences

This paper presents new aperiodic ambiguity function (AF) lower bounds of unimodular sequences under certain low ambiguity zone. Our key idea, motivated by the Levenshtein correlation bound, is to introduce two weight vectors associated to the delay and Doppler shifts, respectively, and then exploit the upper and lower bounds on the Frobenius norm of the weighted auto- and cross-AF matrices to derive these bounds. Furthermore, the inherent structure properties of aperiodic AF are also utilized in our derivation. The derived bounds are useful design guidelines for optimal AF shaping in modern communication and radar systems.

Flag Sequence Set Design for Low-Complexity Delay-Doppler Estimation

This paper studies Flag sequences for lowcomplexity delay-Doppler estimation by exploiting their distinctive peak-curtain ambiguity functions (AFs). Unlike the existing Flag sequence designs that are limited to prime lengths and periodic auto-AFs, we aim to design Flag sequence sets of arbitrary lengths and with low (nontrivial) periodic/aperiodic auto- and cross-AFs. Since every Flag sequence consists of a Curtain sequence and a Peak sequence, we first investigate the algebraic design of zone-based Curtain sequence sets of arbitrary lengths. Our proposed design gives rise to novel Curtain sequence sets with ideal curtain auto-AFs and low/zero cross-AFs within the delay-Doppler zone of interest. Leveraging these Curtain sequence sets, two optimization problems are formulated to minimize the summed customized weighted integrated sidelobe level (SCWISL) of the Flag sequence set. Accelerated Parallel Partially Majorization-Minimization Algorithms are proposed to jointly optimize the transmit Flag sequences and matched/mismatched reference sequences stored in the receiver. Simulations demonstrate that our proposed Flag sequences lead to improved SCWISL and customized peak-to-max-sidelobe ratio compared with the existing Flag sequences. Additionally, our Flag sequences under Flag method exhibit Mean Squared Errors that approach the Cramer-Rao Lower Bound and the Sampling Bound at high signal-to-noise power ratios.