A novel method for constructing almost perfect polyphase sequences

Abstract

This paper proposes a novel method of constructing almost perfect polyphase sequences based on the shift sequence associated with a primitive polynomial f(x) of degree 2J over finite field GF(p) (p odd prime, J = 1,2, ⋯) and a pair of almost perfect sequences completely orthogonal. Almost perfect polyphase sequences of length 2(pJ + 1) are constructed with phases as any positive even number. New families of almost perfect polyphase sequences in other lengths are also provided. In particular, several new families of almost perfect quadriphase sequences of lengths m(pJ + 1) are attained, where m = 4 or 8, and pJ -1 = 0 (mod m). © Springer-Verlag Berlin Heidelberg 2006.