New Bounds and Optimal Binary Signature Sets—Part I: Periodic Total Squared Correlation

Author

Ganapathy, Harish ; Pados, Dimitris A. ; Karystinos, George N.

Author_Institution

Dept. of Electr. Eng., State Univ. of New York at Buffalo, Buffalo, NY, USA

Volume

59

Issue

4

fYear

2011

fDate

4/1/2011 12:00:00 AM

Firstpage

1123

Lastpage

1132

Abstract

We derive new bounds on the periodic (cyclic) total squared correlation (PTSC) of binary antipodal signature sets for any number of signatures K and any signature length L. Optimal designs that achieve the new bounds are then developed for several (K,L) cases. As an example, it is seen that complete (K = L + 2) Gold sets are PTSC optimal, but not, necessarily, Gold subsets of K <; L + 2 signatures. In contrast, arguably against common expectation, the widely used Kasami sets are not PTSC optimal in general. The optimal sets provided herein are in this sense better suited for asynchronous and/or multipath code-division multiplexing applications.

Keywords

Gold codes; binary sequences; code division multiplexing; correlation methods; Gold sets; asynchronous code division multiplexing; binary antipodal signature sets; multipath code division multiplexing; optimal binary signature sets; periodic total squared correlation; Code division multiplexing; Correlation; Error correction; Error correction codes; Gold; Linear matrix inequalities; Measurement; Binary sequences; Gold sequences; Karystinos-Pados bounds; Kasami sequences; Welch bound; code-division multiple access (CDMA); cyclic correlation; periodic correlation; signature design; total squared correlation;

fLanguage

English

Journal_Title

Communications, IEEE Transactions on

Publisher

ieee

ISSN

0090-6778

Type

jour

DOI

10.1109/TCOMM.2011.020411.090404

Filename

5715836