中文摘要：

分析了无线传感器网络中端到端误码率给定情况下协作波束形成的能量效率，给出了不同路径损耗因子和传输距离下的最优协作发射节点个数。首先，综合考虑发射能耗和电路能耗，给出了接近实际情况的系统能耗模型，并推导出系统能耗与误码率之间的近似闭式关系。然后，基于该近似模型，给出了不同路径损耗因子和传输距离下使系统能耗最小的优化协作发射节点个数。理论分析和仿真结果表明：在系统调制方式和误码率给定的情况下，存在着一个临界距离使协作波束形成比非协作传输和协作空时编码都更节能；而且在不同路径损耗因子和传输距离下，存在不同的最优协作发射节点个数使系统能耗最小。

英文摘要：

The energy consumption of cooperative beamforming was studied under given requirements on the end-to-end bit error rate （BER）, and the optimal numbers of cooperative node were obtained for different propagation environments and transmission distances. Considering both transmit and circuit energies, a practical energy consumption model of cooperative beamforming in WSN was first proposed, and then its closed-form approximate solution was obtained. Based on this model, the energy consumption of cooperative beamforming was minimized by optimizing the numbers of cooperative nodes. Analysis and simulations show that over some distance ranges, cooperative beamforming can achieve energy savings compared with non-cooperative and STBC-based cooperative systems. Moreover, it is showed that there are the optimal numbers of cooperative nodes to minimize the total energy consumption for different propagation environments and transmission distances.