Complementary Binary Code Design based on Mismatched Filter

Complementary code (CC) pairs have the interesting characteristic that the superposition of the two related autocorrelation functions (ACFs) has zero sidelobes in range direction. This is an important property for radar applications to avoid range sidelobes. However, CC pairs exist only for limited codeword lengths. Therefore, the general idea of CC design is extended here by applying a mismatched filter (MMF) procedure to the binary phase codeword pairs. There are two objectives considered. The first objective is to design MMF impulse responses to fulfill the zero sidelobe property. The second objective is to find binary phase codeword pairs in cooperation with the MMFs which have a high gain in signal-to-noise ratio (SNR). It is shown that for all codeword lengths (even where the classic CC pair does not exist) there exist binary phase codeword pairs and the related MMF impulse response coefficients which also have the zero sidelobe property. Furthermore, these codeword pairs have high gains in SNR which are nearly the same as for the classic matched filter technique.