# Generalized cross-correlation properties of Chu sequences

Jae Won Kang, Younghoon Whang, Byung Hoon Ko, Kwang Soon Kim

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)

## Abstract

In this paper, detailed cross-correlation properties for Chu sequences are investigated. All possible values of the cross-correlation function of Chu sequences are derived for any given sequence length and lag, and the maximum magnitude distribution function $\rho -{N}(x)$, which is defined as the number of all Chu sequence pairs with length-$N$ whose maximum magnitude of the cross-correlation function is ${\sqrt {Nx}}$, is obtained. Also, good lower and upper bounds on the maximum number of available Chu sequences and a construction algorithm for the corresponding partial Chu sequence set are proposed when the maximum magnitude of the cross-correlation among the sequences is constrained. Numerical examples show that the proposed bounds are quite tight and the proposed construction algorithm is near-optimal up to fairly large value of $N$.

Original language English 6003788 438-444 7 IEEE Transactions on Information Theory 58 1 https://doi.org/10.1109/TIT.2011.2166244 Published - 2012 Jan

### Bibliographical note

Funding Information:
Manuscript received January 13, 2011; revised August 03, 2011; accepted August 15, 2011. Date of publication August 30, 2011; date of current version January 06, 2012. This work was supported by the MKE (The Ministry of Knowledge Economy), Korea, under the ITRC (Information Technology Research Center) support program supervised by the NIPA (National IT Industry Promotion Agency) (NIPA-2011-C1090-1121-0007).

## All Science Journal Classification (ASJC) codes

• Information Systems
• Computer Science Applications
• Library and Information Sciences