Families Of Polyphase Sequences Research Articles

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Oct 1, 2022
Linyan Yu + 2

Open Access

A new family of polyphase sequences with low correlation

Cryptography and Communications
Aug 20, 2021
Zhi Gu + 3

A Family of Polyphase Sequences With Asymptotically Optimal Correlation

Sequences with low correlation have important applications in communications, radar, and cryptography. In this paper, a simple construction of polyphase sequences using additive and multiplicative characters over the finite field ${\mathrm {F}}_{q}$ is proposed. The construction works for any finite field ${\mathrm {F}}_{q}$ with $q>2$ and generates a family of $q-1$ sequences with period $q-1$ and maximum correlation $\sqrt {q}$ . This family is asymptotically optimal with respect to the well-known Welch bound. Most notably, the maximum autocorrelation magnitude of each sequence in this family is equal to 1, and every two distinct sequences are orthogonal to each other. The distribution of the correlation magnitudes of this family is also established.

IEEE Transactions on Information Theory
Apr 1, 2018
Zhengchun Zhou + 2

Merit Factor of Chu Sequences and Best Merit Factor of Polyphase Sequences

Chu sequences are a family of polyphase sequences that have perfect periodic autocorrelations and good aperiodic autocorrelations. It has previously been proved that the maximum offpeak (aperiodic) autocorrelation (in absolute value) of the Chu sequence of length n is asymptotically equal to 0.480261√n. It has also been empirically observed that the merit factor of Chu sequences appears to grow like a constant times √n. In this note, we provide an analytic proof that the merit factor of the Chu sequence of length n is bounded below by a constant multiple of √n for all n. To the author's knowledge, this is the first time a family of polyphase sequences of all lengths has been proved to have merit factor growing at least like order √n.

IEEE Transactions on Information Theory
Sep 1, 2013
Idris Mercer

The Extended FDH Sequences

A new construction method for polyphase sequences with two-valued periodic auto- and crosscorrelation functions is proposed. This method gives L families of polyphase sequences for each prime length L which is bigger than three. For each family of sequences, the out-of-phase auto- and crosscorrelation functions are proved to be constant and asymptotically reach the Sarwate bound. Furthermore, it is shown that sequences of each family are mutually orthogonal.