# Quantum PSO-Based Optimization of Secured IRS-Assisted Wireless-Powered IoT Networks
## 2 System Model and Problem Formulation
### Information Transmission  
After the EH phase, the UDs utilize the harvested energy to transmit information on uplink. A complex baseband signal, represented as \(x_{k}\), is sent by every \(k_{th}\) user. We assume that in order to transfer the information signal to the H-AP, \(u_{k}\) uses all the energy captured during the downlink phase [47; 48]. As a result, the average power at the \(k_{th}\) user's transmitter, represented by \(P_{k}\)[42], is written as follows:  
\[P_{k}=\frac{E_{k}}{t_{k}}=\frac{\xi_{k}t_{0}P_{t}\Big{|}(\mathbf{h}_{iu_{k}}^{H }\mathbf{\Phi}_{0}\mathbf{g}_{ai})\Big{|}^{2}}{t_{k}},\quad\forall k. \tag{5}\]  
The signal received at the H-AP, transmitted by the \(k_{th}\) user during the \(k_{th}\) uplink slot [49], is expressed as follows:  
\[y_{a}=(\mathbf{h}_{iu_{k}}^{H}\mathbf{\Phi}_{1}\mathbf{g}_{ai})x_{k}+z_{a} \tag{6}\]  
where \(x_{k}=\sqrt{p_{k}}s_{k}\) represents the information signal transmitted on uplink, and \(z_{a}\) denotes the noise at the H-AP, modeled as a complex Gaussian distributed random variable with zero mean and variance \(\sigma^{2}\). Additionally, the IRS phase-shift matrix for the uplink phase is represented as \(\mathbf{\Phi}_{1}=\text{diag}(\beta_{1}e^{i\omega_{1}},\beta_{2}e^{i\omega_{2}}, \dots,\beta_{N}e^{i\omega_{N}})\), where each diagonal element corresponds to the IRS phase-shift matrix. Here, the phase-shift and amplitude reflection coefficients, respectively, for each IRS element are denoted by \(\omega_{n}\in[0,2\pi]\) and \(\beta_{n}\in[0,1]\). The amplitude reflection coefficient is adjusted to \(\beta_{n}=1\forall n\) in order to achieve maximal signal reflection from the IRS. The achievable uplink throughput for the \(k_{th}\) user in the \(k_{th}\) time slot is expressed as:  
\[R_{k}=t_{k}\log_{2}\!\left(1+\frac{P_{k}|(\mathbf{h}_{iu_{k}}^{H}\mathbf{\Phi}_{1 }\mathbf{g}_{ai})|^{2}}{\sigma^{2}}\right),\quad\forall k \tag{7}\]  
where \(t_{k}\) is the time slot for uplink information transmission and \(P_{k}\) is the available transmit power on uplink for the \(k_{th}\) user. As in [50], the signal received at the eavesdropper is  
\[y_{\epsilon}=(\mathbf{h}_{iu_{k}}^{H}\mathbf{\Phi}_{1}\mathbf{h}_{i\epsilon}+ \mathbf{h}_{eu_{k}})x_{k}+(\mathbf{h}_{ij}^{H}\mathbf{\Phi}_{1}\mathbf{h}_{i \epsilon}+\mathbf{h}_{j\epsilon})x_{j}+z_{\epsilon} \tag{8}\]  
where \(x_{k}\) and \(x_{j}\) represent the signals from the \(k_{th}\) user and the jammer, respectively. Hence, the achievable rate (in bits per second per hertz) for the eavesdropper in the \(k_{th}\) slot can be calculated as  
\[R_{E}=t_{k}\log_{2}\!\left(1+\frac{P_{k}|(\mathbf{h}_{iu_{k}}^{H}\mathbf{\Phi}_{1 }\mathbf{h}_{i\epsilon}+\mathbf{h}_{eu_{k}})|^{2}}{P_{j}|\mathbf{h}_{ij}^{H} \mathbf{\Phi}_{1}\mathbf{h}_{i\epsilon}+\mathbf{h}_{j\epsilon}|^{2}+\sigma_{ \epsilon}^{2}}\right) \tag{9}\]  
In this paper, we enhance the sum secrecy throughput by efficiently designing and leveraging the resources in an IRS-assisted secure WPIN. Note that increasing the downlinktime allocation enhances harvested energy; however, this reduces the time for wireless devices to transmit information, degrading network throughput. Therefore, to maintain secrecy rates above a predefined threshold while managing transmit power, determining the optimal allocation of time between the downlink and uplink phases is crucial. Additionally, the IRS reflecting elements can be adjusted to constructively align beams in the desired direction, further improving network performance.