Complementary code pairs that share the same bandwidth via symmetrical linear FM chips

Golay complementary code pairs have the advantage of being biphase, available at a variety of lengths as long as desired, with complete sidelobe cancellation. But, they have the disadvantage of requiring two frequencies/channels with the possibility of inexact sidelobe cancellation due to frequency selective fading. In this paper, the complementary code pair are transmitted at the same frequency band, while maintaining exact sidelobe cancellation by using linear frequency modulated (LFM) chips with mirror image symmetry. One code uses a LFM chip with rising frequency sweep, while the other uses its mirror image with decreasing frequency sweep. These two LFM chips have identical autocorrelations due to their mirror image symmetry. Therefore, addition of the matched filter outputs of the two codes results in exact sidelobe cancellation. These LFM chips are quasi-orthogonal in the convolution sense due to their symmetry. This results in small cross-correlation sidelobes outside the zero-sidelobe region. Since the complementary code pair share the same bandwidth and are symmetric, frequency selective fading does not change the symmetry property and therefore, does not affect sidelobe cancellation.