## 3 System Model and Problem Formulation
To avoid this issue, the AP does not participate in the wireless energy supply during the uplink time. During the uplink information transmission time, UN \(i\) may select link \(L_{ij}\), if it exhibits a better link quality compared to that of link \(L_{iA}\). Otherwise, link \(L_{ij}\) is not active, and UN \(i\) may directly transmit information to the AP. Links that can potentially be activated for data offloading are termed feasible links, and \(L\) represents the set of these links. A binary variable \(B_{ij}\) is introduced to represent the status of the feasible links during the uplink transmission. If \(L_{ij}\) is activated for information transmission, \(B_{ij}\) equals 1. Otherwise, it is 0. Due to the unidirectional nature of the links, the following formula applies:  
\[1\ \geq\ B_{ji}{+}B_{ij},\ \forall\ L_{ij}\ \in\ L. \tag{2}\]  
In the uplink time, the energy consumption of UNs is mainly due to two actions: transmitting information and receiving information. The energy consumption for transmitting information also includes the energy required for offloading data and the non-ideal circuit. Here, \(Pc\) represents the power loss caused by the extra electronic device during the UN transmission time [22]. The transmission energy consumption of UN \(i\) is expressed as follows:  
\[E_{ii}=\sum\
olimits_{L_{ij}\in L}(P_{c}{+}P_{i})t_{ij},\ \forall\ i\ \in\ N, \tag{3}\]  
where \(P_{i}\) is the transmission power of UN \(i\), and its value is in the interval of [0, \(P_{max}\)]. In the receiving information phase, UNs need to consume energy for receiving data. The amount of information received by UN \(i\) through links \(L_{ii}\) is expressed as \(r_{ui}\). The total amount of information received by UN \(i\) is \(\sum\
olimits_{L_{uij}\in L}r_{ui}\). The energy consumption of the UNs to receive information is mainly attributed to the electronic devices that receive signals. The energy required to receive 1 bit of information is denoted as \(E_{dec}\) nl/bit. Therefore, the total energy consumption of UN \(i\) during the reception of information is expressed as follows [23]:  
\[E_{ri}{=}\ E_{dec}\sum\
olimits_{L_{ui\in L}}r_{ui},\ \forall i\ \in\ N. \tag{4}\]  
According to Equations (2)-(4), UNs must abide the energy constraint for self-sustaining operation in the entire time block. In other words, the total energy consumption of UN \(i\) should not exceed the harvested energy. This can be expressed using the following formula:  
\[E_{ri}{+}E_{ii}\ \leq\ E. \tag{5}\]  
The energy constraints ensure that the energy consumption of the UNs does not exceed the harvested energy. However, as the communication volume increases, the energy harvesting time and information transmission time in the solutions significantly increase. Under TDMA, the channel state of each active link depends only on its corresponding signal-to-noise ratio (SNR). Here, \(SNR_{ij}\) denotes the SNR of link \(L_{ij}\). Once the transmission power of UN \(i\) is determined, the capacity \(C_{ij}\) of link \(L_{ij}\) can be calculated using the following formula:  
\[C_{ij}{=}\ Wlog_{2}(1+SNR_{ij}), \tag{6}\]  
where \(SNR_{ij}=\frac{P_{i}S_{ij}}{W\eta}\), \(W\) represents the bandwidth, and \(\eta\) represents the spectral noise power. The amount of information transmitted by the UNs through link \(L_{ij}\) is affected by the limited link capacity, denoted by \(C_{ij}\).The amount of transmitted information is denoted by \(r_{ij}\) in the link \(L_{ij}\). Thus, the link capacity constraints are as follows:  
\[r_{ij}\;\leq\;C_{ij}t_{ij}. \tag{7}\]  
where \(t_{ij}\) is the active time of link \(L_{ij}\). After receiving data, each UN must transmit all the generated and forwarded data through its own output link. Let \(I_{i}\) denote the amount of data generated by UN \(i\). Then, the traffic constraint that UN \(i\) must satisfy is as follows:  
Figure 1:0  
After all UNs complete the information transmission, the AP needs to completely receive all of the information before the end of the time block. Otherwise, information may be lost.