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This paper deals with a wireless relay system consisting of one source node, a number of relay nodes and one destination node. The relay nodes amplify and then encode their received signals using a distributed space-time code. Under a non-restrictive asymptotic assumption, we prove some upper bounds on the pairwise error probability for different transmission scenarios. These bounds suggest that significant diversity gains can be achieved in such cooperative systems. Moreover, they can be used to optimize the allocation of transmit powers to the nodes. In wireless sensor networks, however, the energy consumption associated with the hardware cannot be neglected. Therefore, we introduce a simple but realistic hardware model to numerically evaluate the overall energy-efficiency of the analyzed space-time coded cooperative relaying scheme. The numerical results show that, for a large range of path losses between the source and destination, direct transmission provides the best performance in terms of the overall energy consumption.