### 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 |
---|---|

Article number | 6003788 |

Pages (from-to) | 438-444 |

Number of pages | 7 |

Journal | IEEE Transactions on Information Theory |

Volume | 58 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 Jan 1 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*IEEE Transactions on Information Theory*,

*58*(1), 438-444. [6003788]. https://doi.org/10.1109/TIT.2011.2166244

}

*IEEE Transactions on Information Theory*, vol. 58, no. 1, 6003788, pp. 438-444. https://doi.org/10.1109/TIT.2011.2166244

**Generalized cross-correlation properties of Chu sequences.** / Kang, Jae Won; Whang, Younghoon; Ko, Byung Hoon; Kim, Kwang Soon.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Generalized cross-correlation properties of Chu sequences

AU - Kang, Jae Won

AU - Whang, Younghoon

AU - Ko, Byung Hoon

AU - Kim, Kwang Soon

PY - 2012/1/1

Y1 - 2012/1/1

N2 - 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 $N$.

AB - 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 $N$.

UR - http://www.scopus.com/inward/record.url?scp=84862956458&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862956458&partnerID=8YFLogxK

U2 - 10.1109/TIT.2011.2166244

DO - 10.1109/TIT.2011.2166244

M3 - Article

AN - SCOPUS:84862956458

VL - 58

SP - 438

EP - 444

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 1

M1 - 6003788

ER -