Designing Sequence Set and Mismatched Filter Bank with Diagonal-Ridge-Type Doppler Tolerance via Relative Level Optimization

To detect high-speed moving targets using multiple-transmitter systems, the transmit sequence set should possess Doppler tolerance performance similar to that of linear frequency modulated signal, characterized by a diagonal-ridge-type auto-ambiguity function (AF). Although they provide space and waveform diversities to enhance sensing performance compared to single-transmitter systems, the cross-AFs introduced by the multiple transmit sequences decrease the degrees-of-freedom (DOFs), and thus the sidelobe levels of both the auto- and cross-AFs are not sufficiently low. In this paper, we first establish the relative level (between AF sidelobe and mainlobe) -based fractional models to jointly design the transmit sequence set and mismatched filter bank with diagonal-ridge-type Doppler tolerance and low sidelobe AFs. Moreover, a novel similarity constraint between the sequence and mismatched filter is devised to flexibly adjust the receiver output loss. Together with the relative-level scheme, it also reduces the DOF loss incurred by the cross AFs. Furthermore, the resultant challenging sum-of-fraction formulations with nonlinear and nonconvex constraints are effectively tackled via fraction separation and decoupling. Finally, we extend our design to solve the joint design problem of sequence set and mismatched filter bank with low sidelobe level in correlation function. Numerical results demonstrate the excellent performance of the proposed methods.