A generation method of an orthogonal set of real-valued periodic orthogonal sequences from Huffman sequences

Abstract

This paper presents a generation method of an orthogonal set of real-valued periodic orthogonal sequences which has fast correlation algorithm. The periodic orthogonal sequence has the periodic autocorrelation function with zero sidelobes, and its orthogonal set is the set of the sequences whose periodic crosscorrelation function of the zero shift is zero. The real-valued periodic orthogonal sequence of period N = 2 n with positive integer n is derived from a real-valued Huffman sequences of length M = 2 ν + 1 with positive integer ν and ν ≥ n which has the aperiodic autocorrelation function with zero sidelobes except at left and right shift-ends. The set of realvalued periodic orthogonal sequences can be sufficiently applied to various systems, such as synchronous CDMA systems and digital watermarkings.