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Cooperative communication (CC) exploits space diversity through allowing multiple nodes cooperatively relay signals to the receiver so that the combined signal at the receiver can be correctly decoded. Since CC can reduce the transmission power and extend the transmission coverage, it has been considered in topology control protocols , . However, prior research on topology control with CC only focuses on maintaining the network connectivity, minimizing the transmission power of each node, whereas ignores the energy efficiency of paths in constructed topologies. This may cause inefficient routes and hurt the overall network performance in cooperative ad hoc networks. In this paper, to address this problem, we introduce a new topology control problem: energy-efficient topology control problem with cooperative communication, and propose two topology control algorithms to build cooperative energy spanners in which the energy efficiency of individual paths are guaranteed. Both proposed algorithms can be performed in distributed and localized fashion while maintaining the globally efficient paths. Simulation results confirm the nice performance of all proposed algorithms.