Periodic Correlation Bounds of Binary Sequence Pairs

The periodic correlation bounds of binary sequence pairs are presented in this paper. Through the definition of sequence pair and its autocorrelation and cross-correlation function and by using the weighting method, we obtain the bounds of family size, sequence length, maximum periodic autocorrelation sidelobe value, maximum periodic cross-correlation value, and maximum periodic autocorrelation mainlobe value. The previous binary sequences bounds, such as Sarwate and Welch bounds can be considered as special cases of the bounds. The bounds present the theoretical foundation of designing binary sequence pairs set with good correlation properties.