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IMA Journal of Mathematical Control and Information Advance Access published online on August 9, 2006
IMA Journal of Mathematical Control and Information, doi:10.1093/imamci/dnl020
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Article

Statistical solution to the capacity problem in direct-sequence code-division multiple-access communication systems

Nobuoki Eshima 1 *, Tohru Kohda 2, and Minoru Tabata 3

1 Department of Statistics, Oita University, 1-1 Idaiga-Oka, Hasama, Oita 879-5593, Japan
2 Department of Computer Science and Communication Engineering, Kyushu University, Fukuoka 812-8581, Japan
3 Department of Mathematical Sciences, Osaka Prefecture University, Osaka 599-8531, Japan

* To whom correspondence should be addressed.
Nobuoki Eshima, E-mail: eshima{at}med.oita-u.ac.jp


  Abstract

Capacity in the direct-sequence code-division multiple-access (DS/CDMA) communication system was considered according to the code acquisition performance with the conventional serial-search method, because code acquisition needs a difficult operation. Since capacity in DS/CDMA systems is defined by the maximum number of users that can simultaneously transmit their signals with the same carrier frequencies, assuring a larger capacity is very important in DS/CDMA systems with respect to the economy of frequency source. This paper reconsiders the capacity problem through a statistical approach to code acquisition. First, a DS/CDMA system model is reviewed. Second, properties of the counting method for code acquisition are discussed. It is proved that the method can acquire the target user's code under any number of interference users that simultaneously transmit their signals, and that the method can guarantee a considerable precision in code acquisition. Third, an observation time necessary for code acquisition is given from a statistical discussion, and the original counting method is modified into a simpler one. It is concluded that the capacity of the DS/CDMA communication system can be set by the ‘bit error-rate-based capacity or signal-to-noise ratio-based capacity’, i.e. ‘post-acquisition-based criterion’, rather than the ‘acquisition-based capacity’.

Keywords: acquisition-based capacity; bit error-rate-based capacity; code acquisition; DS/CDMA system; statistical decision theory.
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