## 1 Introduction
As highlighted in [15; 16; 17], integrating AN with DM has the potential to improve the secrecy rate and overall security of the system by exploiting spatial diversity and effective interference management, thus offering stronger protection against eavesdropping. However, these approaches still face significant challenges in optimizing key system parameters, such as power control and beamforming design, to achieve an optimal balance between security enhancement and system efficiency. Moreover, transmission rates are often constrained, further complicating the implementation of these techniques in practical scenarios. To address these limitations, several advanced solutions have been proposed, with a particular focus on the utilization of cooperative receivers. Specifically, DM with cooperative receivers (DM-CR), introduced in [18], secures transmissions by utilizing cooperative receivers and incorporating a predefined distortion factor to ensure robust performance regardless of the eavesdropper's location. Building on this, spatial DM (SDM), as presented in [19], combined DM with spatial modulation (SM) to bolster resilience against distributed eavesdroppers and enhance transmission rates. To further improve transmission rates, generalized SDM (GSDM) [20] employed distributed receivers to encode information through signal indices, thereby reinforcing security. Additionally, the work in [21] proposed a DM with distributed receiver selection (DM-DRS) technique, which activated a specific subset of receivers to modulate information using receiver indices, complemented by a scrambling matrix to obstruct interception attempts. Furthermore, SDM integrated with AN [22] combined the strengths of SM, DM, and AN to achieve concurrent improvements in both security and transmission rates. Collectively, these advancements exploit the unique properties of wireless channels, significantly enhancing information security in UAV communication systems. Despite these achievements, existing research on DM and AN technologies predominantly focuses on static channel conditions, precoding schemes, or power allocation, often neglecting the benefits of joint optimization across multiple parameters, such as precoding matrices and power-control factors, in dynamic UAV scenarios. This oversimplification poses challenges, as it prevents the full utilization of potential security enhancements. Additionally, the non-convex nature of the associated optimization problems complicates the design of efficient algorithms. Therefore, overcoming these limitations is crucial for achieving optimal performance in UAV communications under practical deployment conditions. In this paper, we propose an AN-GSDM framework to enhance the security of downlink UAV communication systems. Specifically, we derive the secrecy rate expression for the AN-GSDM system and formulate a joint optimization problem. To address the non-convex nature of this problem, we develop an alternating iterative algorithm. The key contributions of this work are as follows: (1) We introduce artificial noise (AN) into the generalized spatial directional modulation (GSDM) system to further enhance its security. We analyze the impact of multiple parameters, including the precoding matrix and power-control factors, on the secrecy rate of the AN-GSDM system. (2) The proposed method jointly optimizes the precoding matrix and power-control factors to efficiently manage multi-beam transmissions and artificial noise. By leveraging approximation techniques and alternating optimization, we solve the non-convex joint optimization problem, making the approach more applicable to real-world systems. (3) Simulation results validate the superior security performance and robust convergence properties of the proposed approach. Moreover, the method demonstrates strong performance even under high dynamic conditions and with localization errors, highlighting its practical viability in real-world UAV communication scenarios.