###### Abstract  
As the popularity of smartphones, wearable devices, intelligent vehicles, and countless other devices continues to rise, the surging demand for mobile data traffic has resulted in an increasingly crowded electromagnetic spectrum. Spectrum sharing serves as a solution to optimize the utilization of wireless communication channels, allowing various types of users to share the same frequency band securely. This paper investigates spectrum allocation and power control problems in overlay spectrum sharing, with a focus on promoting green communication. Maximizing weighted sum energy efficiency (WSEE) requires solving complex multiple-ratio fractional programming (FP) problems. In contrast, weighted sum power (WSP) minimization offers a more straightforward approach. Moreover, because WSP is directly related to users' power consumption, we can dynamically adjust their weights to balance their residual energy. We prioritize WSP minimization over the more common WSEE maximization. This choice not only simplifies computation but also maintains users' quality of service (QoS) requirements. The joint optimization for multiple primary users (PUs) and secondary users (SUs) can be decomposed into two components: a weighted bipartite matching problem and a series of convex resource allocation problems. Utilizing [PERSON]'s method, our system-level simulation results show that the proposed scheme achieves optimal performance with minimal computational time. We explore strategies to accelerate the proposed scheme by refining the selection of initial values for [PERSON]'s method. g 2025 15 4290 11 April 2025 13 April 2025 13 April 2025 13 April 2025 13 April  
over Long-Term Evolution (LTE) carriers. It can be foreseen that spectrum sharing will continue to be a vital research frontier in next-generation wireless networks [3]. Cognitive radio (CR) [4] has played a significant role in motivating the development of spectrum sharing. It enables a secondary user (SU) to access a PU's licensed band, typically through either underlay, overlay, or interweave mode, thereby enhancing system spectrum efficiency (SE). Specifically, in the underlay mode, SUs can operate simultaneously on PUs' licensed bands under the interference temperature limits. As a result, the SUs must carefully manage spectrum access and power control. In the overlay mode, SUs opportunistically access idle licensed bands through spectrum sensing. This approach guarantees no interference to PUs. The interweave mode is similar to the overlay mode. This mode also allows users to access the licensed spectrum bands opportunistically. Differently, it dilutes the concepts of PUs and SUs. Ongoing users are considered PUs, while incoming users are considered SUs [5]. Beyond the three typical methods, cooperative spectrum sharing--a form of overlay sharing that uses relaying techniques--provides a critical supplement [6]. It essentially belongs to overlay spectrum sharing. In this mode, SUs act as relays, helping PUs with poor channel conditions communicate. After the PUs complete their data transmission, the SUs can access the corresponding licensed bands. By dedicating part of their energy budget to relay PU transmissions, SUs gain temporary access to licensed bands. This creates a win-win scenario where both user types benefit [7]. In the abovementioned modes, spectrum allocation and power control play a significant role in enhancing overall system performance while ensuring the QoS of different priority levels for heterogeneous users. On the one hand, spectrum allocation involves strategically assigning frequency bands to different users to optimize bandwidth usage and minimize interference [8]; on the other hand, power control refers to managing transmission power levels across different devices, which can enhance the corresponding received signal-to-noise ratio (SNR) levels while reducing overall energy consumption [9]. Effective spectrum allocation and precise power control facilitate seamless communication and ensure the required QoS for all users.