Cross‐correlation functions for quadratic‐phase sequences with different periods

Abstract

AbstractThe author has previously proposed new polyphase periodic sequences with autocorrelation sidelobe 0 and minimum cross‐correlation peak value. the periods of the sequences are odd prime N; the number of sequences is N ‐ 1. the sidelobe of the autocorrelation function is 0 and the absolute value peak of the cross‐correlation function for arbitrary two sequences of the same period satisfies the mathematical lower bound 1/√. This paper shows that the crosscorrelation function for these sequences with different periods is 1/√ at every term, where N1 and N2 are the periods of these sequences (Ni is the odd prime, N1 ≠ N2). Thus these sequences of various periods are useful for spread spectrum multiple access system because the number of channels can be increased remarkably by assigning sequences with different periods to the same frequency band.