Good code sets from complementary pairs via sub-chip encoding

This dissertation introduces a new code, constructed by concatenating Golay complementary code pair (A, B) with a gap in between. The autocorrelation of this code has a zero-sidelobe region on either side of the mainlobe and an adjacent region of small cross-correlation sidelobes. This is achieved by replacing the sinusoidal chip in the complementary code pair with waveforms that satisfy two conditions: symmetry/anti-symmetry and quasi-orthogonality in the convolution sense. This will be referred to as sub-chip encoding. Symmetry/anti-symmetry property results in the zero-sidelobe region on either of the mainlobe, due to complete sidelobe cancellation of the complementary code pair. Quasi-orthogonality of the two chips keeps the adjacent region of cross-correlations small. Since the symmetry/anti-symmetry property is invariant to frequency selective fading, the zero-sidelobe region is also fading invariant. Linear FM (LFM) and Piecewise Linear LM (PLFM) waveforms satisfy both the symmetry/anti-symmetry and quasi-orthogonality conditions. The proposed codes are constructed using continuous frequency LFM and PLFM waveforms, discrete frequency LFM and PLFM waveforms and polyphase codes based on LFM and PLFM waveforms as chips for the complementary code pair. The complementary code pair could also be interlaced in the time domain avoiding gaps. In this case, the zero-sidelobe region and the small cross-correlation sidelobes are interlaced as well. It is also shown that transmitting a second concatenated/interlaced code constructed form the complementary code pair (-A, B) at another frequency band could result in cancellation of the small cross-correlation sidelobes. Although frequency selective fading between the two frequency bands could affect cancellation of the small cross-correlation sidelobes, the remaining non-zero sidelobes will be very small. Any quasi-orthogonal code set that satisfies the symmetry/anti-symmetry condition could be used as chips with the same complementary code pair to result in a good code set with a zero-sidelobe region. Several such good code sets are constructed by changing the chirp rate/slope of the LFM and PLFM waveforms.