Decimation Generator of Zadoff-Chu Sequences

Abstract

A compact expression for Zadoff-Chu sequences is introduced and used to show that all sequences of a given odd prime length are permutations of two seed sequences. In addition, it helps us derive a decimation formula and demonstrate that when two pre-calculated seed sequences and stored in the memory, any desired Zadoff-Chu sequence of odd prime length can be generated, sample-by-sample, simply by incrementing the read index by a corresponding step value. In this manner no calculation of sequence elements is required. That is, this algorithm does not require any additions, multiplications, or trigonometric calculations to generate sequences in real-time. Furthermore, the proposed table-lookup requires storing only a single sequence pair for each desired Zadoff-Chu sequence family of odd prime length.