Minimum PSL Discrete-Phase Waveform Design with Length-Change Mismatched Filter

This paper considers the joint design of the Multiphase Shift Key (MPSK) waveform and its mismatched filter to achieve an excellent autocorrelation function. More specifically, a general optimization model that accounts for the minimization of Peak Sidelobe Level (PSL) of autocorrelation in the presence of the SNR, discrete phase, and constant modulus constraints, as well as the filter length requirement, is developed. In order to handle the resultant NP-hard problem, the Primal-dual Type (PDT) algorithm is introduced along with each iteration step required to solve four subproblems with closed-form solutions. Finally, the simulation examples are provided to evaluate the proposed optimization model and the effectiveness iteration procedure. The numerical results highlight that the devised waveform and filter can attain a lower PSL than the other design strategy while possessing low SNR loss.