# Resource Allocation of Multiple Base Stations for Throughput Enhancement in UAV Relay Networks
## 2 System Model
### Signal-to-Interference-Plus-Noise Ratio (SINR)  
Simultaneous transmissions from mBS and sBS can guarantee a seamless relay transmission to \(U_{o}\) and maximize the throughput of the UE in the URN, with the placement of UAV in a region where the UAV can receive signals from both mBS and sBS. Therefore, the SINR of a wireless backhaul link can be improved for a reliable relay transmission. Due to the non-orthogonal transmission in the power domain, mBS uses the transmit power of \(P_{mBS}\), where \(P_{mBS,U_{m}}^{1^{st}}\) and \(P_{mBS,UAV}^{1^{st}}\) are transmit powers allocated to the mBS-to-\(U_{m}\) link and mBS-to-UAV link in the first time slot, respectively. On the other hand, sBS transmits a signal with a maximum power of \(P_{sBS}\) to a scheduled node (e.g., UAV).  
If the relay transmission originates from mBS, both \(U_{m}\) and the UAV receive a superposition-coded signal, but \(U_{m}\) can remove the interference from the BS-UAV link by using the successive interference cancellation [32]. This is due to the channel condition that the BS-to-\(U_{m}\) link has a better channel condition than the BS-to-UAV link. On the other hand, the UAV receives interference from the BS-to-\(U_{m}\) link. Since sBS acts as an interference source to the relay transmission, both \(U_{m}\) and UAV receive interference from it. In another case, where relay transmission originates from sBS, the UAV receives forwarding data from sBS and interference from mBS. In summary, the received SINRs at the UAV for mBS-to-UAV and sBS-to-UAV links and the received SINR at \(U_{m}\) in the first time slot are given by  
\[SINR_{mBS,UAV}^{1^{st}} =\frac{P_{mBS,UAV}^{1^{st}}S_{mBS,UAV}}{P_{sBS}S_{sBS,UAV}+P_{mBS, U_{m}}^{1^{st}}S_{mBS,UAV}+\sigma_{UAV}^{2}}, \tag{1}\] \[SINR_{sBS,UAV}^{1^{st}} =\frac{P_{sBS}^{1^{st}}S_{sBS,UAV}}{(P_{mBS,U_{m}}^{1^{st}}+P_{mBS,UAV}^{1^{st}})S_{mBS,UAV}+\sigma_{UAV}^{2}}=\frac{P_{sBS}^{s}S_{sBS,UAV}}{P_{ mBS}S_{mBS,UAV}+\sigma_{UAV}^{2}},\] (2) \[SINR_{mBS,U_{m}}^{1^{st}} =\frac{P_{sBS,U_{m}}^{1^{st}}S_{mBS,U_{m}}}{P_{sBS}S_{sBS,U_{m}}+ \sigma_{U_{m}}^{2}}, \tag{3}\]  
where \(g_{tx,rx}\triangleq h_{tx,rx}\cdot l_{tx,rx}\) denotes the channel gain, \(h_{tx,rx}\) denotes the small-scale fading coefficient, \(l_{tx,rx}=d_{tx,rx}^{-pathloss}\) denotes the path loss-dependent large-scale fading coefficient, and \(d_{tx,rx}\) denotes the distance between the transmitter (tx) and receiver (rx), respectively. \(\sigma_{i}^{2}\) denotes the variance of the additive white Gaussian noise (AWGN) at node \(i\). Note that \(U_{m}\) receives its own data from mBS; hence, (3) is consistent, regardless of the relay transmission source.  
In the second time slot, the UAV forwards the received signal from mBS or sBS in the first time slot to \(U_{o}\) with a transmit power of \(P_{UAV}\), and \(U_{m}\) receives a signal with the  
Figure 2: Time slot allocation by the adaptive parameter of \(\lambda\).  
power of \(P_{mBS,U_{m}}^{2 nd}(=P_{mBS})\) from mBS. Both \(U_{o}\) and \(U_{m}\) receive interference from sBS. The received SINRs at \(U_{o}\) and \(U_{m}\) in the second time slot are expressed as follows:  
\[SINR_{UAV,U_{o}}^{2 nd} = \frac{P_{UAV}S_{UAV,U_{o}}}{P_{mBS,U_{m}}^{2 nd}S_{mBS,U_{o}}+P_{sBS }S_{sBS,U_{t}}+\sigma_{U_{o}}^{2}}, \tag{4}\] \[SINR_{mBS,U_{m}}^{2 nd} = \frac{P_{mBS,U_{m}}^{2 nd}S_{mBS,U_{m}}}{P_{sBS}S_{sBS,U_{m}}+P_{ UAV}S_{UAV,U_{m}}+\sigma_{U_{m}}^{2}}. \tag{5}\]