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.

Abstract-Matched and mismatched filters are considered important parts of a radar signal processing unit. In this paper, we present an approach to optimize the matched filters and mismatched filters in short range pulse radars. For radar, the matched filter coefficients are the complex conjugates of transmitted code. We used binary phase codes as transmitted pulse. The disadvantage of binary phase codes is having high sidelobe levels in the output of correlation function. Thus, we decided to use optimization algorithms for finding binary phase codes with minimum peak sidelobe levels (MPS). After that, we succeeded in producing mismatched filter coefficients (Mis-co) for each code using floating point genetic algorithm (FGA) and we could generate and test the filter coefficients with maximum peak to sidelobe level ratio (PSR). For testing the filter, we plotted ambiguity function for each set of coefficients and tested the filter with Doppler shift.