## 2 Related Works
### Optimal Power Allocation  
Power allocation plays a crucial role in enhancing both the reliability and security of communications in relay networks. [PERSON] et al. proposed and analyzed two power allocation schemes, optimal adaptive power allocation (OAPA) and suboptimal fixed power allocation (SFPA), to enhance physical layer security in MISO systems with unknown eavesdroppers, demonstrating that SFPA achieves comparable secrecy outage performance to OAPA with lower complexity [28]. [PERSON] et al. proposed a secure communication model for satellite communications using interference relay collaboration at the physical layer, deriving theoretical relay selection standards and optimizing power allocation to minimize secrecy outage probability and presenting performance analyses for various relay selection criteria and power allocation schemes [29]. In [30], a joint power allocation and aerial jamming scheme for a UAV-enabled NOMA system were proposed for enhancing reliability and security against eavesdropping, and analytical expressions and numerical results were derived to demonstrate the scheme's superiority and identify the optimal UAV height for maximizing effective secrecy throughput. Ref. [31] proposed a joint power and sub-channel allocation algorithm to maximize secrecy capacity in non-orthogonal multiple access (NOMA)-based uplink massive machine type communication (mMTC) networks, demonstrating its superiority over other algorithms and orthogonal multiple access schemes in enhancing secrecy capacity. This paper builds upon these foundational studies by integrating LF relaying and cooperative jamming in a diamond network with untrusted relays. Our contribution lies in optimizing power allocation to maximize the RSP, thus ensuring both secure and reliable communications. By comparing our results with existing methods, we highlight the novelty and effectiveness of our proposed scheme in enhancing physical layer security. We need to highlight that this work stands out from prior research in the following ways:  
* This work addresses the optimization of security and reliability in a diamond network configuration involving two untrusted relays, specifically focusing on the physical layer. The study introduces a cooperative jamming technique to enhance the secure transmission of data while ensuring that the source message remains confidential from untrusted relays. The integration of lossy DF relaying at the untrusted relays helps maintain data confidentiality by allowing for controlled decoding errors, thus minimizing the risk of eavesdropping by the relays. * A novel analytical framework is proposed that explores the optimal power allocation between the source, the relays, and the destination to maximize the RSP. This framework incorporates the impact of cooperative jamming on the overall network performance and provides a comprehensive analysis of the power distribution needed to achieve the highest possible RSP, ensuring both reliability and security in the communication system. * The paper also introduces an RSP metric to evaluate the performance of the proposed system. This metric quantifies the likelihood that the destination successfully decodesthe original information while the untrusted relays fail to do so. Numerical results demonstrate that optimizing the power allocation between the source and the relays is critical for achieving the best possible balance between reliability and security in the network. In modern communication systems, secure and reliable data transmission is critical, particularly in scenarios where sensitive information is transmitted over potentially compromised channels. One specific application scenario for the proposed framework is in military and government communication networks, where the confidentiality and integrity of data are paramount. These networks often operate in environments with a high risk of eavesdropping or unauthorized access, making robust physical layer security essential.