# Anti-Jamming Power Control Algorithm for Wireless Communication Systems Based on MPC
## 1 Introduction  
Since electromagnetic waves are the carriers of information transmission, wireless communication channels are inherently open, making it easier for jammers to inject malicious signals into the target transmission channel. This jamming reduces the signal-to-jamming-and-noise ratio at the receiver, complicating the correct demodulation of transmitted data, which degrades transmission quality and may even lead to complete transmission failure [1, 2]. To ensure reliable transmission under malicious jamming while minimizing energy consumption, adaptive power adjustment techniques are required [3]. These techniques dynamically adjust the transmission power of the wireless communication system to adapt to varying electromagnetic environments, thereby enhancing system reliability and conserving power [4]. Conventional adaptive power control methodologies often fail to respond promptly or make optimal power adjustments in the face of rapidly time-varying malicious jamming, thereby compromising system performance. In contrast, reinforcement learning is capable of attaining adaptive immunity to unknown and dynamic environments. This is achieved by enabling intelligences to engage in continuous trial and error, thereby facilitating learning and optimization of strategies within the environment [5]. For example, Reference [6] tackles the challenge of interference in dynamic wireless communication environments by proposing a fast reinforcement learning-based strategy. Specifically, it introduces the Win or Learn Fast Policy Hill Climbing (WolLF-PHC) method to rapidly converge to optimal interference avoidance strategies, outperforming traditional methods in performance and convergence speed. Reference [7] addresses the problem of mitigating reactive jamming in wireless networks. It proposes a deception-based anti-jamming strategy using reinforcement learning to deceive the jammer into attacking a victim channel while maintaining communication in safe channels, thereby improving communication resource usage andmitigating jamming effects. However, reinforcement learning in wireless communication anti-jamming is limited by its reliance on high computational requirements and extensive training data. Additionally, it faces challenges in hyperparameter sensitivity and vulnerability to adversarial attacks in dynamic communication environments. Control theory, as a scientific discipline that examines the dynamic behavior of systems and the methodologies employed to regulate them, offers a robust methodology for addressing the challenge of BER stability in wireless communication systems. So, scholars have proposed anti-jamming techniques for communication systems based on stability control theory [8]. In reference [9], a state feedback controller with an integrator is introduced to rapidly stabilize the bit error rate (BER) under sudden malicious jamming. Reference [10] addresses malicious jamming in multi-parameter adaptive wireless systems by proposing a stability control algorithm using multiple Lyapunov functions to maintain BER within acceptable limits during jamming. However, in more complex electromagnetic environments, basic state feedback controllers may lack sufficient stability and convergence speed [11]. Ensuring BER stability in such environments is critical for reliable wireless communication. This paper presents a novel power control approach for wireless communication systems, designed to resist jamming based on model predictive control principles [12]. Suddenly, unanticipated malicious jamming often delays the adaptive power adjustment process in wireless communication systems, leading to an increased bit error rate. To address this issue, the proposed method analyzes the BER stability of wireless communication systems using MPC-based power control. To enhance BER stability, the power controller uses the current system state and constraints to predict future system states and transmission power over a specified time horizon, calculating an optimal power control sequence [13].