Design of Matched and Mismatched Filters Based on Peak Sidelobe Level Minimization

Abstract

‎This paper focuses on the design of matched filters with low peak sidelobe level as well as mismatched‎ ‎filters with low loss in processing gain and peak sidelobe level‎, ‎for phase codes‎. ‎We propose an algorithm ‎which employs the least-p-th norm minimax based on the genetic algorithm‎, ‎and a method based on the‎ ‎semidefinite programming to deal respectively with the resulting matched and mismatched optimization problems‎. A framework is also presented to design mismatched filters that are robust to Doppler shifts. ‎Simulation results show that using the proposed methods for finding matched filters leads to better peak sidelobe‎ ‎level and integrated sidelobe level for binary and polyphase codes compared to previous works‎. ‎In addition‎, ‎the mismatched filters designed by the proposed methods have very low peak sidelobe level in‎ ‎the binary and polyphase cases‎.