# Joint Beam-Forming Optimization for Active-RIS-Assisted Internet-of-Things Networks with SWIPT
## 4 Simulation Results and Discussion  
To validate the reliability of the proposed energy-harvesting sum maximization algorithm at the user end, this paper compares the proposed energy-harvesting sum maximization algorithm at the user end with three benchmark scenario algorithms, respectively, which are designed as follows: (1) A-RIS-assisted using average power splitting algorithm (\(\rho_{k}=0.5\)); (2) P-RIS-assisted algorithm; and (3) traditional RIS-assisted algorithm without RIS. The propagation loss model \(L(d)=C_{0}\left(\frac{d}{D_{0}}\right)^{-\kappa}\) is used in this paper, where \(C_{0}=-30\) dB denotes the propagation loss at \(D_{0}=1\) m, \(d\) denotes the link distance, and \(\kappa\) represents the propagation loss index. The propagation loss indices from the base station to the RIS and the user are assumed to be \(\kappa_{BI}=3\) and \(\kappa_{BU}=3\), respectively, and the propagation loss index from the RIS to the user is assumed to be \(\kappa_{IU}=2.2\). It is assumed thatall channels \(G\), \(h_{b,k}\), \(h_{r,k}\) undergo flat-terrain attenuation and maintain stability over time. The other parameters of the proposed energy-harvesting sum maximization algorithm at users are set as follows: the number of reflective units of the RIS \(N=12\); the number of base station input channels \(M=20\); the number of users \(K=4\); the maximum number of iterations \(L_{\text{max}}=200\); the minimum signal-to-dryness-noise ratio required for each user \(\gamma_{k}=10\) dB; the maximum radiant power of the A-RIS \(p_{\text{max}}=10\) mW; the maximum radiant power of the base station antennae \(P_{B}=20\) W; the noise power \(\sigma_{k}^{2}=-80\) dBm, \(\delta_{k}^{2}=-80\) dBm, \(\sigma_{p}^{2}=-80\) dBm; and the penalty factor \(\mu=5\times 10^{-7}\). Figure 3 illustrates the convergence curves of the proposed algorithm for maximizing the sum of energy harvesting at the user's location under different channel conditions. Channel 1 represents the BS-user K channel, channel 2 represents the BS-Passive RIS-user K channel, and channel 3 represents the BS-A-RIS-user K channel. From Figure 3, it can be observed that the proposed algorithm for maximizing the sum of energy harvesting at the user's location can reach a stable value relatively quickly after 2-3 iterations, demonstrating good convergence. The stable value of the proposed algorithm under Channel 1 conditions is 35.1% higher than that under Channel 2 conditions. This improvement is attributed to the A-RIS's ability to provide additional transmit power to enhance signal strength, overcoming the drawback of substantial signal degradation due to the passive RIS's inherent \"multiplicative fading\". As a result, the user receives more energy, leading to a larger sum of harvested energy at the user's location. Furthermore, the stable value of the proposed algorithm under Channel 2 conditions is 67.5% higher than that under Channel 3 conditions. This is because the P-RIS can adjust its reflection array phase to change the transmission beam direction of the base station antenna, thereby enhancing the transmission efficiency of the beam. As a result, the user receives more energy, and the proposed algorithm for maximizing the sum of energy harvesting at the user's location harvests more energy. Figure 4 illustrates the variation in total energy collected at the user's location under different transmission scenarios as the maximum allowable transmit power of the base station changes. This encompasses considerations for the number of reflecting elements  
Figure 3: Convergence of the proposed algorithm for maximizing energy harvesting at the user end. in the RIS and the number of antennae at the base station. The graph reveals that with an increase in the base station's maximum allowable transmit power, there is a corresponding rise in the total energy collected at the user's location for all algorithms.