In this thesis, the achievable rate at low SNR is established for Amplify-and-Forward (AF) cooperative system with a source node, a destination node and a relay node. To characterize the effect of relay locations, an aggregate channel model which consists of both long-term path loss and short-term path loss fading is used. To consider the effect of channel information at the relay, average and instantaneous power constraints are applied respectively when evaluating the achievable rate. As analytic solutions to the achievable rate seem difficult to obtain, approximations for the achievable rate, the optimal power loadings, the optimal amplification coefficients for both types of power constraints are derived in this thesis.