Wireless Pers Commun (2009) 51:231–244 DOI 10.1007/s11277-008-9640-9 Pairwise Error Probability of Distributed Space–Time Coding Employing Alamouti Scheme in Wireless Relays Networks Trung Q. Duong · Ngoc-Tien Nguyen · Trang Hoang · Viet-Kinh Nguyen Published online: 13 November 2008 © Springer Science+Business Media, LLC. 2008 Abstract In this paper, we analyze the pairwise error probability (PEP) of distributed space–time codes, in which the source and the relay generate Alamouti space–time code in a distributed fashion. We restrict our attention to the space–time code construction for Proto- col III in Nabar et al. (IEEE Journal on Selected Areas Communications 22(6): 1099–1109, 2004). In particular, we derive two closed-form approximations for PEP when the relay is either close to the destination or source and an upper bound for any position of the relay. Using the alternative definition of Q-function, we can express these PEPs in terms of finite integral whose integrand is composed of trigonometric functions. We further show that with only one relay assisted source-destination link, system still achieves diversity order of two, assuming single-antenna terminals. We also perform Monte-Carlo simulations to verify the analysis. Keywords Distributed space–time codes · Relay channels · Pairwise error probability (PEP) This paper was presented in part at the 7th International Symposium on Communications and Information Technologies, Sydney, Australia, Oct., 2007. T. Q. Duong (B ) Blekinge Institute of Technology, Ronneby 372 25, Sweden e-mail: quang.trung.duong@bth.se N.-T. Nguyen Ministry of Posts and Telematics (MPT), Hanoi, Vietnam e-mail: nntien@mpt.gov.vn T. Hoang Heterogeneous Silicon Integration Department, CEA/LETI, Grenoble, France e-mail: trang.hoang@cea.fr V.-K. Nguyen University of Technology-Hanoi National University, Hanoi, Vietnam e-mail: kinhnv@vnu.edu.vn 123