Title :
A Constructive Representation for the Fourier Dual of the Zadoff–Chu Sequences
Author :
Li, Chih-Peng ; Huang, Wei-Chieh
Author_Institution :
Nat. Sun Yat-Sen Univ., Kaohsiung
Abstract :
In this paper, a complex matrix C consisting of a set of perfect sequences is studied. The matrix C is constructed by taking the inverse discrete Fourier transform (IDFT) of a diagonal matrix, in which the diagonal elements comprise an arbitrary periodically perfect sequence gamma. Properties of the matrix C are presented. In addition, the Fourier dual E of the matrix C is investigated. When gamma is a Zadoff-Chu sequence for the case of N even, M=1, and g=0, an explicit representation for the matrix E is derived.
Keywords :
binary sequences; discrete Fourier transforms; matrix algebra; Zadoff-Chu sequences; complex matrix; constructive representation; diagonal matrix; inverse discrete Fourier transform; periodically perfect sequence; Autocorrelation; Channel estimation; Chirp; Discrete Fourier transforms; Fourier transforms; Frequency synchronization; OFDM; Discrete Fourier transform (DFT); Fourier dual; Zadoff–Chu sequence; perfect sequence;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2007.907336
