Tighter Lower Bounds on Aperiodic Ambiguity Function and Their Asymptotic Achievability

This paper presents tighter lower bounds on the maximum aperiodic ambiguity function (AF) magnitude of unimodular sequences under certain delay-Doppler low ambiguity zones (LAZ). These bounds are derived by exploiting the upper and lower bounds on the Frobenius norm of the weighted auto- and cross-AF matrices, with the introduction of two weight vectors associated with the delay and Doppler shifts, respectively. As a second major contribution, we demonstrate that our derived lower bounds are asymptotically achievable with selected Chu sequence sets by analyzing their maximum auto- and cross- AF magnitudes within certain LAZ.