The multiple access broadcast (MABC) is an effective two phases transmission (2P) ANC protocol for the half-duplex (HD) communication mode. However, MABC does not make use of channel gain of the direct link (DL) no matter how strong it is. On the other hand, the time division broadcast (TDBC) is known as a three phases transmission (3P) protocol which enables transceivers to utilize DL and thus offers the possibility to achieve higher performance compared with the MABC at the expense of a reduced spectral efficiency due to the one extra transmission phase. In this paper, we investigate a joint single relay selection (SRS) and power allocation schemes for energy-efficient wireless
communication systems with analog network coding (ANC) for TDBC, where two-way relay channel with two end nodes and N parallel relay nodes is considered under an assumption of perfect channel-state information (CSI). Our objective is to minimize
the total system transmit power consumption under quality-of-service (QoS) constraints for TDBC protocol with joint single relay selection and nodes power allocation. In addition, a zero-forcing based relay signal combining technique that combines the signals received at the 1st and 2nd transmission phases, also known as zero-forcing relay power allocation (ZF-RPA), is investigated. Numerical simulation shows that the traditional
variable gain relay power allocation (VG-RPA) is more energy-efficient than the ZF-RPA scheme for TDBC in cases with and without utilizing DL.