### Related Work
The optimization goal is to maximize the SL's EE while guaranteeing the PL's minimum required rate. For the overlay mode, two algorithms were proposed: one solves a sequence of more accessible FP to fulfill the first-order optimality conditions of the original problem; the other enjoys a weaker optimality claim but with even lower computational complexity. In [15], researchers addressed spectrum scarcity and energy limitations in cognitive radio networks. They proposed a joint optimization of transmission time allocation and power control for radio frequency energy harvesting systems. They converted the non-convex EE maximization to a convex problem via the proposed approximate convex policy for the co-frequency interference (CO-ACP) scheme. Then, they used Frank-Wolfe (FW) with one-dimensional linear programming to achieve the optimal solution. The numerical results indicated that the CO-ACP can achieve a tight lower-bound optimum solution. Since EE focuses on the entire system performance, taking EE as the objective function as resource allocation problems will not indicate each user's priority. Weighted sum energy efficiency (WSEE), defined as the weighted sum of users' EE, considers individual users' EE and overall system EE. It is suitable for heterogeneous networks with diverse EE requirements for different users. For this reason, more and more studies have adopted WSEE rather than EE as the objective function for systems such as D2D communications and cognitive radio networks. For example, the authors in [16] investigated D2D communications overlaying cellular networks with spectrum-power trading. In their system, D2D users act as cellular users' (CUs') relays, exchanging their transmit power for the opportunities to access the licensed bands. The proposed spectrum-power trading schemes analyze two scenarios: public-interested and self-interested D2D users. The optimization objectives include maximizing WSEE via relay selection, spectrum allocation, and power control. Nevertheless, EE and WSEE maximization problems are challenging due to their non-convex form. Specifically, EE maximization results in a single-ratio FP problem, while the latter involves multiple-ratio FP problems [23]. Conventional approaches like Charnes-Cooper transformation (CCT) and Dinkelbach's algorithm effectively solve single-ratio FP problems. However, they struggle with multiple-ratio FP cases. Quadratic transform is able to handle multiple-ratio FP problems but a series of prerequisites must be satisfied [24]. Overall, these methods have already established a very mature solution framework. However, significant computational complexity is required within this framework to obtain a near-optimal solution. In addition, when jointly optimizing spectrum allocation and power control for EE or WSEE maximization, the resulting mixed-integer fractional programming (MIFP) problems will be more challenging. In recent years, cellular networks have rapidly evolved toward being ultra-dense and heterogeneous, raising increasingly higher requirements for wireless resource management [25]. With this trend, artificial intelligence (AI) technology deeply integrates with wireless communication networks and plays a crucial role in spectrum allocation and power control [26]. With the aid of neural networks (NNs), machine learning (ML) methods such as supervised learning, unsupervised learning, and reinforcement learning (RL) have overcome the difficulties mentioned above to a certain extent when dealing with EE or WSEE maximization problems. For example, the authors in [27] proposed a resource allocation strategy based on deep learning (DL) for underlay cognitive radio networks with multiple-input-single-output (MISO) interference channels. The proposed scheme optimizes SUs' transmit power and beamforming vector to maximize their sum EE while ensuring the QoS requirements for both PUs and SUs. The authors designed a deep neural network (DNN) architecture with three interconnected units.