## 1 Introduction
With the characteristics of SWIPT and CRN, introducing SWIPT into CRN, named SWIPT-enabled CRN, presents a promising solution for achieving energy-efficient and high-performance transmission, while improving the spectrum utilization [20]. Except for the SWIPT, optimal power allocation (OPA) is an effective method to improve the network SE and achieve energy-efficient transmission. For example, ref. [23] integrates the bidirectional relay, full-duplex, and SWIPT techniques, and investigates an alternating optimization algorithm to deal with the EE maximization problems, thus improving the network's SE, maximizing the network's EE, and prolonging the network's lifetime. Ref. [24] proposes a multi-user time-power resource allocation algorithm, thus improving the network throughout. Ref. [25] uses SWIPT-PS protocol to investigate a joint resource allocation problem under power control, thus maximizing the minimum transmission rate for the SUs. To provide an overview of the above studies, we can find that the BMR technique can reduce power consumption and improve the network SE. However, the traditional BMR selection algorithms usually fail to consider the SNR and global channel gain, simultaneously. The global channel gain means the channels between the relay node and the two receive nodes, rather than one of the receive nodes. At the same time, these relay selection algorithms mostly focus on using the relay link to achieve a bidirectional relay transmission (BRT). This means that they neglect the DL, which may be better to achieve a bidirectional direct transmission (BDT). Thus, they miss the chance to achieve an adaptive transmission with considering the relay link and DL, simultaneously. With the adaptive transmission, the network can switch between the BRT and BDT modes to achieve a higher transmission rate. Both of these two reasons will decrease the network SE with BMR transmission. In addition, with the combination of the BMR technique and CWN to construct a CRN, we can alleviate the issue of spectrum scarcity and further improve the network SE. But the existing studies usually focus more on improving the network SE, while relatively less attention is put on the energy-constrained relay nodes and the network EE. Furthermore, SWIPT is an effective method to solve the energy-constrained problem to extend the network lifetime and improve the network EE. What is more, the OPA also can effectively improve the network SE and EE. Based on the above literature review and analyses, in this paper, in order to effectively improve the SE and EE of the wireless network, and also to tackle the insufficiency of spectrum resources and the issues of energy-constrained nodes with the consideration of the above reasons, we design an energy-efficient adaptive bidirectional transmission strategy in the SWIPT-enabled CRN. At the same time, different from the mentioned studies, our designed strategy considers the BMR, the DL, the CWN, the SWIPT, and the OPA simultaneously. To better elucidate the distinctions between our work and related studies, a detailed comparison is provided in Table 1. With Table 1, the main contributions of this paper can be further summarized as follows. * To improve the network SE with BMR transmission, we propose to select an energy-constrained best relay node according to the received SNR of the relay node and the global channel gain from the relay node to SUs simultaneously to achieve a better BRT. * To further improve the network SE with BMR transmission, we propose to consider both the relay link and DL and design a total transmit power threshold (TTPT) determining algorithm to find the TTPT, which lets the transmission rates of the BRT be equal to the BDT. Through the TTPT, the network can switch between the BRT and BDT modes and achieve an adaptive transmission to achieve a higher transmission rate.