Orthogonal and ZCZ Sets of Real-Valued Periodic Orthogonal Sequences from Huffman Sequences

Abstract

This paper presents a method of generating sets of orthogonal and zero-correlation zone (ZCZ) periodic real-valued sequences of period 2n, n ≥ 1. The sequences admit a fast correlation algorithm and the sets of sequences achieve the upper bound on family size. A periodic orthogonal sequence has the periodic autocorrelation function with zero sidelobes, and a set with orthogonal sequences whose mutual periodic crosscorrelation function at zero shift is zero. Similarly, a ZCZ set is the set of the sequences with zero-correlation zone. In this paper, we derive the real-valued periodic orthogonal sequences of period 2n from a real-valued Huffman sequence of length 2ν + 1, ν being a positive integer and ν ≥ n, whose aperiodic autocorrelation function has zero sidelobes except possibly at the left and right shift-ends. The orthogonal and ZCZ sets of real-valued periodic orthogonal sequences are useful in various systems, such as synchronous code division multiple access (CDMA) systems, quasi-synchronous CDMA systems and digital watermarkings.