Biphase Sequence Generation with Low Sidelobe Autocorrelation Function

Since Barker-like sequences could not be found for sequence lengths greater than 13, radar system designers have been searching for biphase sequences with discrimination (ratio of the magnitude of the mainlobe to the magnitude of the peak sidelobe of the autocorrelation function of the sequence) greater than 13. We present new results on biphase Legendre sequences for all prime lengths. The results of the paper are as follows. 1) Two lemmas on the symmetric properties of the Legendre sequences are stated and using these lemmas and simple rules of modulo arithmetic, a method is suggested for generating long sequences which does not require multiplications and divisions. 2) From the properties of autocorrelation function of the cyclically shifted Legendre sequence (LS) for prime lengths, a computationally efficient method is evolved for carrying out systematic search for sequences with discrimination greater than 13. The proposed method reduces the computational load by a factor of approximately 16. Using these techniques, we generated codes up to length 1019. In each case we searched for the code which gives the maximum discrimination for that length.