## 2 System Model and Problem Formulation
Each frame starts with a preprocessing stage that includes pilot transmission, channel state information (CSI) reporting, and wireless resource allocation, followed by ten spectrum-sharing subframes. The PTs and the STs first send pilots. Then, the PR and the SRs estimate the channel gains and report CSI. With the CSI, the resource allocation can be determined. The details of spectrum sharing between one matched PL and SL pair are described as follows. When \(\rho_{m}\) matches with \(\beta_{n}\), where \(m\in\{1,\ldots,M\}\) and \(n\in\{1,\ldots,N\}\), each corresponding spectrum-sharing subframe is split into two phases. In phase one, PT \(m\) transmits its data to the PR using power \(p_{\rho,mn}\) while ST \(n\) remains silent. In phase two, when PT \(m\) has completed its uplink transmission, ST \(n\) can fulfill its data transmission to its corresponding SR using power \(p_{s,mn}\) on the RB of PT \(m\). If we denote the duration of phase one as \(\theta_{mn}\) of an RB in the time domain, phase two will last \(1-\theta_{mn}\) of an RB, where \(\theta_{mn}\) denotes the spectrum-sharing factor and \(\theta_{mn}\in(0,1)\). Discrete power levels are widely used in current wireless communication standards, such as LTE-A and 5G [32]. This approach is particularly beneficial for transmitters with limited capabilities due to hardware constraints, as seen in machine-type communications. Thus, this paper chooses the values of \(p_{\rho,mn}\) and \(p_{s,mn}\) from \(\{p_{min},p_{min}\Delta p,p_{min}(\Delta p)^{2},\ldots,p_{max}\}\), where \(\Delta p\) is the granularity of the power levels. Furthermore, we assume that the spectrum-sharing factor levels are also discrete. \(\theta_{mn}\) chooses its value from \(\{\Delta\theta,2\Delta\theta,\ldots,1-\Delta\theta\}\). The achievable SEs of \(\rho_{m}\) and \(\beta_{n}\) within one subframe are given as follows:  
\[S_{\rho,mn}=\theta_{mn}log_{2}(1+p_{\rho,mn}g_{\rho,m}/n_{0}), \tag{1}\]  
\[S_{s,mn}=(1-\theta_{mn})log_{2}(1+p_{s,mn}g_{s,n}/n_{0}), \tag{2}\]  
where \(n_{0}\) is the additive white Gaussian noise power density; \(g_{\rho,m}\) and \(g_{s,n}\) denote the channel gains between PT \(m\) and PR \(m\) or ST \(n\) and SR \(n\), respectively. The channel characteristics include both path loss and multipath fading. We use a block fading model, where all channel gains change independently from one frame to the next. This means that within a single frame, all channel gains are considered to be constant. The transmit power consumption of \(\rho_{m}\) and \(\beta_{n}\) within the corresponding subframe can be expressed as outlined below:  
\[P_{\rho,mn}=\theta_{mn}p_{\rho,mn}, \tag{3}\]  
\[P_{s,mn}=(1-\theta_{mn})p_{s,mn}. \tag{4}\]  
Green communication focuses on minimizing network energy consumption while meeting the QoS requirements. This strategy also supports sustainability goals, including carbon footprint reduction and environmental health preservation. As mentioned in the introduction, EE is the most critical performance metric in line with green communication. It focuses more on system performance but neglects users' priority. WSEE balances system-level EE and user fairness. This metric is particularly effective for networks with diverse user priorities. Network operators can leverage predefined weights to tailor their performance more effectively. Nevertheless, a WSEE maximization problem is often challenging since it belongs to multiple-ratio FP. If any ratio of the sum does not follow a concave-convex form, or its feasible region is non-convex, its optimization will be extremely complex. In this instance, standard global optimization algorithms will face limitations in practice, often exhibiting exponential complexity. When it comes to joint spectrum allocation and power control, the resulting MIFP will be even more difficult to solve. In the upcoming 6G era, the energy consumption of network infrastructure and connected terminals will further increase with the activation of the high-frequency spectrum.