Generalized Sarwate bounds on the periodic correlation of complex roots of unity sequences

In this paper, a general periodic correlation bound named generalized Sarwate bound for complex roots of unity sequence set with zero or low correlation zone (ZCZ/LCZ), with respect to family size, sequence length, maximum autocorrelation sidelobe, maximum crosscorrelation value and the zero or low correlation zone, are derived. It is shown that all the previous periodic binary sequence bounds, such as Sarwate bound, Welch bound, Tang-Fan bound and Peng-Fan bound, are only special cases of the generalized Sarwate bound.