## 4 Numerical Results and Discussion  
Unless otherwise specified, we set \(d_{SR}=d_{RD}=2\) km, \(d_{JU}=d_{UD}=1\) km [21], \(g_{S}=g_{I}=5.88\), \(b_{S}=b_{I}=0.4472\)[33], and \(\varepsilon=2.5\)[21]. In the following simulations, we employed Monte Carlo methods, conducting a total of \(10^{8}\) simulation iterations. Figure 2 shows the impact of malicious jamming probability on the ABER in BPSK modulation. It can be seen that the ABER declines with an increase in the SJR, and conversely, it escalates with a higher probability of jamming events. At a high SJR, the probability of jamming occurrence has a greater influence on the ABER. For example, when SJR = 10 dB, \(\rho=0.01\); SJR = 10 dB, \(\rho=0.5\); SJR = 40 dB, \(\rho=0.01\); and SJR = 40 dB, \(\rho=0.5\), the ABER is \(2.8\times 10^{-7}\), \(1.5\times 10^{-3}\), \(1.6\times 10^{-24}\), and \(7.1\times 10^{-17}\), respectively. As the jamming probability increases, the ABER correspondingly rises. Since detecting random jamming is more challenging compared to continuous jamming, it is more suitable for practical jamming scenarios. Therefore, we propose that our jamming probability model is more effective for real-world applications than the model presented by [24]. From Figure 2, it is observable that the simulation outcomes are in close alignment with the outcomes derived from theoretical analysis. Figures 3 and 4 analyze the effect of the location of the RIS on the system performance in the case when the jamming probability is one. As \(d_{SR}\) decreases, the ABER decreases accordingly; meanwhile, as \(d_{JU}\) decreases, the ABER increases accordingly. This indicates that the closer the RIS is to the transmitter, the better the performance of the system, since the stronger the jamming signal, the higher the ABER. Therefore, the farther the jamming RIS is from the jammer, the better the ABER performance. This is because the closer it is to the transmitter, the more it can effectively collect and transmit signals. Additionally, from Figure 4, it can be observed that as the SJR increases, the position of the jamming RIS has a more significant impact on the ABER. For instance, when the SJR = 20 dB, the ABER at \(d_{JU}=1\) km and \(d_{JU}=0.1\) km are 0.05 and 0.41, respectively, differing by one order of magnitude. When the SJR = 40 dB, the ABER values are \(3.94\times 10^{-9}\) and 0.02, respectively, differing by seven orders of magnitude. Figure 2: ABER versus SJR (dB) curves for a wireless system with a varying \(\rho\). We analyzed the influence of diverse channel environments on the ABER using \(g_{S}\) and \(g_{J}\), as shown in Figure 5. \(g_{S}\) and \(g_{J}\) represent the degree of fluctuation in the received signal power. A larger shape parameter indicates less power fluctuation and a more stable channel condition. By analyzing Figure 5, it can be observed that as the values of \(g_{S}\) and \(g_{J}\) increase, the ABER decreases accordingly. At the same time, it can be found that when the values of \(g_{S}\) and \(g_{J}\) are greater than five, the improvement in the ABER at a high SJR is relatively significant. The ABER for BPSK modulation was observed to be as low as \(10^{-5}\), whereas under poor channel conditions, the ABER increased to \(10^{-2}\). This is because the channel condition is better and the signal intensity fluctuation is smaller. However, when the values of \(g_{S}\) and \(g_{J}\) are around one, the ABER performance is poorer, which is because the channel condition is worse and the signal fluctuation is larger now. Figure 4: ABER versus SJR (dB) curves for a wireless system with a varying \(d_{JU}\). Figure 3: ABER versus SJR (dB) curves for a wireless system with a varying \(d_{SR}\). Similarly, Figure 6 also analyzes the effect of the jamming parameter \(b_{J}\) on the ABER of the system. Both \(b_{S}\) and \(b_{J}\) represent the average power or intensity of the received signal. A larger scale parameter indicates a higher average power of the signal.