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.