Energy-efficient transmission (EET) has become a very important problem in wireless communication. Optimal power allocation (OPA) is one of the general methods to achieve EET. But when OPA is only considered in EET, it maybe cannot analyze EET problems accurately. This paper aims at analyzing energy-efficient bidirectional direct and relay transmission (RT) through joint optimization of transmit power (TP) and transmit time (TT) allocation. In RT, direct links (DLs) are existed. The EET problems are given with three optimization cases: (i) maximizing sum throughput (ST) to maximize energy efficiency (EE), in such case, optimal TT (OTT), optimal relay position (ORP), and outage probability analysis are given; (ii) minimizing total energy consumption (TEC) to maximize EE, in such case, optimal TP (OTP), OTT with gradient-descent algorithm, and influences of asymmetry and asymmetry transmission tasks are given; and (iii) maximizing ST and minimizing TEC simultaneously to maximize EE, in such case, Dinkelbach’s algorithm and one-by-one optimal algorithm are given. Simulation results are presented to validate theoretical analysis. Results reveal that relay technique and DLs in RT can improve system’s EE.

节能传输（EET）已成为无线通信中非常重要的问题。最佳功率分配（OPA）是实现EET的常规方法之一。但是，仅在EET中考虑OPA时，它可能无法准确地分析EET问题。本文旨在通过联合优化发射功率（TP）和发射时间（TT）分配来分析节能双向直接传输和中继传输（RT）。在RT中，存在直接链接（DL）。在三种优化情况下给出了EET问题：（i）最大化总吞吐量（ST）以最大化能源效率（EE），在这种情况下，给出了最佳TT（OTT），最佳中继位置（ORP）和停电概率分析; （ii）最小化总能耗（TEC）以最大程度提高EE，在这种情况下为最佳TP（OTP），采用梯度下降算法的OTT，给出了不对称和不对称传输任务的影响；（iii）同时最大化ST和最小化TEC以最大化EE，在这种情况下，给出了Dinkelbach算法和一对一最佳算法。给出仿真结果以验证理论分析。结果表明，中继技术和RT中的DL可以提高系统的EE。