# Anti-Jamming Power Control Algorithm for Wireless Communication Systems Based on MPC
## 2 System Description and Modeling Approach  
As illustrated in Figure 1, the wireless communication system comprises a transmitter and a receiver with the capacity to adaptively adjust the transmit power, with a maximum transmit power within a specified constraint. The transmission channel between the transmitter and the receiver is within the interference range of the jammer, which is capable of completely covering the receiver. Wireless communication systems are susceptible to sudden and unidentified malicious interference during the transmission phase, which can have a significant impact on the reliability of the transmission. As shown in Figure 2, the wireless communication transmission link and its feedback link can be configured to form a control loop. The system is modeled as a continuous-time control system, with model predictive control introduced into the setup. The RF (radio frequency front-end) monitors in real time through the receiver; its objective is to perform signal processing and estimate the SJNR, while the transmitter uses the feedback data to adjust the transmission power through MPC, ensuring the bit error rate at the receiver remains below the predefined target [13]. Assuming the transmission power of the transmitter is \(P_{\mathrm{s}}(t)\), the transmission channel is assumed to be an AWGN (Additive white Gaussian noise) channel. Assuming that free-space propagation loss is not considered, the jamming-plus-noise power within the channel is denoted by \(P_{\mathrm{I}}(t)\). Both the transmission power of the transmitter and the jamming-plus-noise power are expressed in dBm. At time t, the SJNR at the receiver can be approximated as \(\mathrm{SJNR}=P_{\mathrm{s}}(t)-P_{\mathrm{I}}(t)\). The system's bit error rate curve under a specific modulation  
Figure 1: Jamming attack model diagram. Figure 2: Anti-jamming control feedback link for wireless communication systems. scheme and a particular LDPC code is shown in Figure 3. According to reference [14], the waterfall region of the curve can be approximated as a straight line, as shown in Figure 3.  
\[y(t)=Cx(t)+D \tag{1}\]  
where in \(C\) and \(D\) are constants designated as the sensing coefficient and direct term, respectively. \(y(t)\) denotes the BER. The transmission power \(P_{s}(t)\) is selected as the control input \(u(t)\) and the state variable \(x(t)\) is selected as SJNR. Accordingly, the wireless communication system can be represented by a state equation of the following form, wherein \(A\) and \(B\) are constants designated as the dynamic characteristic coefficient and control coefficient, respectively. \[\left\{ \begin{array}{l}\mathrm{d}x(t)/\mathrm{d}t=Ax(t)+Bu(t)\\ y(t)=Cx(t)+D\end{array} \right. \tag{2}\]  
According to reference [14], the state equation can be formulated as:  
\[\left\{ \begin{array}{l}\mathrm{d}x(t)/\mathrm{d}t=Ax(t)+Bu_{1}(t)\\ y_{1}(t)=Cx(t)\end{array} \right. \tag{3}\]  
To facilitate the calculations below, the relationships involving \(u_{1}(t)\) and \(y_{1}(t)\) are given as follows:  
\[y_{1}(t)=y(t)-D \tag{4}\]  
\[u_{1}(t)=u(t)-P_{\mathrm{J}}(t) \tag{5}\]  
Upon applying the Laplace transform to both sides of the Equation (3), the following result is obtained:  
\[\left\{ \begin{array}{l}sX(s)=AX(s)+BU_{1}(s)\\ Y_{1}(s)=CX(s)\end{array} \right. \tag{6}\]  
The closed-loop transfer function is denoted as \(P(s)=Y_{1}(s)/U_{1}(s)=BC/(s-A)\). Given that the system's closed-loop transfer function possesses poles situated within the left half-plane, it can be concluded that the system is theoretically stable. The continuous-time system model effectively describes the system's dynamic behavior; however, it can lead to numerical instability and error accumulation in computations. Therefore, the system must be discretized to enable stable and accurate prediction and opti  
Figure 3: BER curves for a certain modulation and a certain LDPC code. mization within each sampling period.