Exact pairwise error probability of distributed space-time coding in wireless relays networks

In this paper, we analyze the pairwise error probability (PEP) of distributed space-time codes employing Alamouti scheme. We restrict our attention to the space-time code construction for Protocol III in the work of Nabar et al. (2004). In particular, we derive two exact closed-form expressions for PEP when the relay is either close to the source or destination. 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.