Good code sets from complementary pairs via symmetrical/antisymmetrical chips

Golay complementary code pairs have the advantage of being biphase codes, available at a variety of lengths, with exact sidelobe cancellation. However, they require transmission at two frequencies or channels. At the receiver, the two codes require reception in their own matched filters. The two matched filter outputs are then added, resulting in complete sidelobe cancellation. However, frequency- or channel-selective fading could result in inexact sidelobe cancellation. This paper introduces a new code constructed from the complementary code pair (A, B) by concatenating them with a gap in between, using one frequency band or one channel. 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 having the chips used for A and B satisfy the following two conditions: The two chips are symmetrical/antisymmetrical mirror images of each other and the cross-correlation between them is small-i.e., they are quasiorthogonal in the convolution sense. The symmetry/antisymmetry property results in the zero-sidelobe region, while the quasiorthogonality makes the adjacent region of cross-correlation sidelobes small. Linear frequency-modulated (LFM) and piecewise LFM chips satisfy both the symmetry/ antisymmetry and quasiorthogonality conditions. The symmetry/antisymmetry property is shown to be invariant under frequency-selective fading; therefore, sidelobe cancellation is also fading invariant. Any good code set that satisfies the symmetry/antisymmetry condition could be used as chips with the same Golay 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 generated by varying the slope of the LFM and piecewise LFM chips.