Quadriphase sequences for spread- spectrum multiple-access communication

Abstract

This paper studies constructions for quadriphase sequences that are suitable for use as signature sequences in quadriphase spread-spectrum multiple-access communications. Quadriphase sequences are closely related to biphase (i.e., binary) sequences, and many of the properties of the former can be expressed in terms of properties of the latter. Methods of construction are presented which obtain sets of quadriphase sequences from sets of biphase sequences. Methods of construction of quadriphase sequences are provided based upon the properties of the multiplicative characters of the finite field GF <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(q)</tex> where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q \equiv 1 \mod 4</tex> . These methods use codewords from low-rate Reed-Solomon codes, which are mapped onto the fourth roots of unity. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2q + 2</tex> sequences of period <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q - 1</tex> are constructed, for which the maximum magnitudes of the periodic cross correlation and the periodic out-of-phase autocorrelation are bounded by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3 \sqrt{q} + 5</tex> .