The pairwise error probability and precoder design for amplify-and-forward half-duplex cooperative system

In this paper, we derive the exact asymptotic pairwise error probability (PEP) of an AF half-duplex cooperative system in which the maximum likelihood detector is used. Based on our analysis and observations, we propose a unitary precoder design to improve the system performance. We first design a precoder to achieve the full diversity gain function. Then for the case of a 4-QAM signal being transmitted, we further optimize the coding gain, and arrived at a closed-form optimum precoder. Simulations indicate that our proposed precoder design greatly improves the performance of the system