The deployment of relays has been regarded as an effective means to improve the performance of the conventional wireless networks. The achievable performance generally depends on the availability of channel state information (CSI) at the relay and the destination nodes. The requirement of the dual-hop CSIs at the destination node, however, results in high computational complexity and unrealistic assumption for mobile relay networks, especially when the source-to-relay channel fluctuates rapidly due to the mobility of the source node. In this paper, we design an amplify-and-forward (AF) mobile relay network in which the instantaneous CSI of the source-to-relay link is unknown to the destination node. A composite hypothesis testing problem is formulated to derive the optimal detector. Unlike the existing approaches, the designed mobile relay network does not require excessive signalling overhead for obtaining the instantaneous CSI of the source-to-relay link at the destination while offering a significant performance improvement over the conventional wireless networks without the help from relays. The obtained performance even approaches that of the relay networks with full CSIs. When considering both implementation complexity issues and performance enhancement, the proposed detection scheme provides an alternative way of developing a low-complexity mobile relay networks.