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-pth 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.