## 4 Numerical Results  
In this section, we present numerical results to compare the performance of the proposed algorithm with four benchmark scenarios. WSSR is a crucial performance metric for PLS. Next, we discuss the impact of various variables on the performance of WSSR. The three-dimensional (3D) simulation setup is illustrated in Figure 2, where BS and STAR-RIS are positioned at \((0,0,5)\) and \((145,0,0)\) meters, respectively. Bob\({}_{l}\) and Eve\({}_{l}\) are randomly distributed along a semicircle centered on STAR-RIS with a radius of \(d_{T}=d_{R}=5\) m. The STAR-RIS is located at the center of this semicircle. In the simulations conducted, the narrow-band quasi-static fading channels extending from the BS to the STAR-RIS are characterized as Rician fading channels in the ensuing manner [29]. \[\mathbf{h}_{BS}=\sqrt{\frac{\rho_{0}}{d_{BS}^{R_{BS}}}}(\sqrt{\frac{K_{BS}}{K_ {BS}+1}}\mathbf{h}_{BS}^{LOS}+\sqrt{\frac{1}{K_{BS}+1}}\mathbf{h}_{BS}^{NLOS}) \tag{21}\]  
where \(K_{BS}\) is the Rician factor set as 5 dB, \(\alpha_{BS}=2.2\) denotes the corresponding path loss exponents, \(d_{BS}\) denotes the distances between the BS and the STAR-RIS, \(\rho_{0}=1\) representsthe path loss at a reference distance of 1 m, \(\mathbf{h}_{BS}^{LOS}=\mathbf{a}\mathbf{b}^{H}\) is the normalized line-of-sight (LoS) component, with \(\mathbf{a}=[a_{1},\cdots,a_{N}]^{T}\) and \(\mathbf{b}=[b_{1},\cdots,b_{M}]^{T}\) denote the steering vectors, and \(\mathbf{h}_{BS}^{NLOS}\) is the Rayleigh fading representing the non-line-of-sight (NLOS) component, the other indirect link channels are modeled similarly. It is assumed that the direct channel between the BS and Bob\({}_{t}\), Eve\({}_{t}\) is Rayleigh channel with the distance-dependent path loss which all direct links set \(\alpha=3.6\). The path loss factor for direct links is higher than that for indirect links, which allows for a more accurate simulation and validation of the benefits of STAR-RIS in enhancing communication performance. The STAR-RIS is a uniform rectangular array (URA) whose size is \(M=X\times Y\), where \(X\) is the element of the x-axis (vertical) and \(Y\) is the element of the y-axis (horizontal). We set \(M=30\). The BS is a large uniform linear array (ULA), which is comprised of \(N\) elements. The number of antennas is set to \(N=4\) and the noise power is set to \(\sigma^{2}=-80\) dBm. \(P_{t}=0\) dBm is the transmit power budget and the minimum rate requirement of legitimate users is set to \(\Gamma_{min}=-5\) dBm. The weight parameter and the algorithm convergence factor are set to \(\phi_{t}=0.5,\forall l\). and \(\kappa=10^{-3}\), respectively. For the parameters of the PDD method, we set \(c=0.1\), \(\eta=10^{-3}\). The initial value of \(\rho=0.1\). Moreover, each result is averaged over 150 independent Monte-Carlo trials. Figure 3 depicts the convergence performance of the proposed algorithm with different \(M\) and \(N\). From this figure, we observe that the WSSR stabilizes within approximately 5 iterations. An intuitive explanation for this result is that the direct link offers improved initial channel conditions, allowing the optimization algorithm to identify a superior solution more quickly during the initial stage, which accelerates the overall convergence process. Additionally, the reasonable setting of channel parameters and the low computational complexity of the proposed algorithm further enhance its rapid convergence. It is discerned that the WSSR exhibits a monotonic augmentation concomitant with the iterative process and culminates in equilibrated solutions after a finite number of iterations, and the iterative process converges more quickly. In addition, larger \(M\), \(N\) achieves a higher WSSR at the cost of slower convergence speed, since more variables need to be optimized. Due to coupling constraints, the WSSR with independent phase shift is slightly larger than the WSSR with coupled phase shift. Next, we consider the following benchmark scenarios for performance comparison, i.e., (1) IP scheme. (2) CP scheme.