Good code sets from complementary pairs via polyphase chips

In this paper, a new code is constructed by concatenating a Golay complementary code pair (A, B) with a gap in between. The autocorrelation of this code contains a zero-sidelobe region on either side of the mainlobe and an adjacent region of small cross-correlation sidelobes. This is achieved by using a polyphase code pair as chips for A and B that satisfy two conditions: they have conjugate symmetry/anti-symmetry property and are quasi-orthogonal in the convolution sense. The conjugate symmetry/anti-symmetry property results in the zero-sidelobe region, while the quasi-orthogonality property makes the adjacent region of cross-correlation sidelobes small. The complementary code pair could also be interlaced in the time domain avoiding the above mentioned gap. However, the zero-sidelobes and the small cross-correlation sidelobes are also interlaced in its autocorrelation. Polyphase codes based on linear FM (LFM) and piecewise LFM (PLFM) waveforms are used as chips for the complementary code pair, since they satisfy both the conjugate symmetry/anti-symmetry and the quasi-orthogonality conditions. Any polyphase good code set that satisfies the conjugate symmetry/anti-symmetry condition could be used as chips with the same complementary code pair to generate a good code set with a zero-sidelobe region and an adjacent region of small cross-correlation sidelobes. Such sets are constructed using polyphase code sets based on LFM and PLFM waveforms as chips.