In this paper, to improve communication system's energy-efficiency (EE), multi-case optimization of two new transmission strategies is investigated. Firstly, with amplify-and-forward relaying and full-duplex technique, two new transmission strategies are designed. The designed transmission strategies consider direct links and non-ideal transmission conditions. At the same time, detailed capacity and energy consumption analyses of the designed transmission strategies are given. In addition, EE optimization and analysis of the designed transmission strategies are studied. It is the first case of EE optimization and it is achieved by joint optimization of transmit time (TT) and transmit power (TP). Furthermore, the second and third cases of EE optimization with respectively optimizing TT and TP are given. Simulations reveal that the designed transmission strategies can effectively improve the communication system's EE.