## 4 Simulation and Discussion  
Simulations are conducted to evaluate the effectiveness of the proposed security optimization (denoted as 'Proposed') algorithm for the GDSM system. During the simulations, we set \(N_{t}=4\), \(N_{t}=3\), \(N_{u}=2\), \(N_{e}=2\) and \(P_{t}=N_{r}\). The angles of [PERSON]'s distributed receivers are \(\Theta_{b}=(30^{\circ},50^{\circ},70^{\circ})\), and the angles of [PERSON]'s distributed receivers are \(\Theta_{e}=(20^{\circ},45^{\circ})\). Quadrature Phase Shift Keying (QPSK) is employed for APM realization, and each simulated secrecy rate is obtained through \(10^{4}\) Monte Carlo realizations. When executing the proposed algorithm, we set \(d_{max}=20\), \(\zeta_{0}=0.8\), \(\varepsilon=10^{-4}\), \(\delta=0.5\), \(\delta_{min}=10^{-4}\), and \(t_{max}=50\). We assume identical noise power at both Bob and Eve, and the SNR is defined as \(1/\sigma_{b}^{2}\). The channel data are generated based on the models provided in Equation (2), which defines the channel matrices for Bob and Eve, respectively. Both mobile and stationary UAV scenarios are considered, corresponding to cases with and without processing delay. When there is no processing delay, the angles of Bob and Eve used for the joint design of precoding and power-control factors at the UAV are accurate. Conversely, in the presence of processing delay, the angles of Bob and Eve at the UAV are obtained from the previous time step, leading to deviations from the current angle values. In addition, conventional zero-forcing (ZF) precoding [22] (\(\mathbf{P}=\mathbf{H}(\Theta_{b})(\mathbf{H}(\Theta_{b})\mathbf{H}^{H}( \Theta_{b}))^{-1}\), denoted as 'ZF') and the precoding method (\(\mathbf{P}=\mathbf{H}(\Theta_{b})/N_{t}\), denoted as 'Maxbeam') that maximize the power in [PERSON]'s direction [20], combined with different power control factors \(\zeta\), are used as benchmarks. Figures 2 and 3 present the system's secrecy rate, and Figures 4 and 5 present the achievable rates at [PERSON] and [PERSON], under various precoding and power-control factors. The secrecy rate is defined as the difference between [PERSON]'s and [PERSON]'s achievable rates. Although maximizing this relative difference is critical, minimizing [PERSON]'s absolute achievable rate is equally important. By reducing [PERSON]'s achievable rate to the greatest extent possible, we can fundamentally restrict its ability to intercept information, even when [PERSON]'s rate remains constant or decreases slightly. In addition, we show the secrecy rate when \(N_{e}=1\) and \(\Theta_{e}=25^{\circ}\) in Figures 2 and 3. Figure 3: The secrecy rate of AN-GSDM under different precoding and power-control factors. Figure 2: The secrecy rate of AN-GSDM under different precoding and power-control factors. The results in Figures 2-5 demonstrate that the proposed optimization algorithm significantly outperforms the benchmarks in terms of the secrecy rate. Unlike the benchmarks, which fail to consider [PERSON]'s location when controlling multiple beams and do not jointly optimize the precoding matrix and power-control factor, the proposed algorithm successfully mitigates information leakage. By employing a joint design approach, the algorithm balances the trade-off between maintaining [PERSON]'s achievable rate and suppressing [PERSON]'s interception  
Figure 4: The achievable rates at Bob and Eve under different precoding and power-control factors for AN-GSDM. Figure 5: The achievable rates at Bob and Eve under different precoding and power-control factors for AN-GSDM. capabilities. As the number of eavesdroppers increases, the secrecy rate decreases under low SNR conditions due to enhanced interference from multiple eavesdroppers. However, this decline is more pronounced in the low-SNR regime, where the number of eavesdroppers has a larger relative impact due to weaker signal strength. At this stage, the system faces higher interference from [PERSON], and further optimizations may be needed to counteract the increased noise levels.