## 4 Simulation Results and Analysis  
The performance of the HPTR learning algorithm was evaluated and analyzed through simulation experiments. In the experiment, the equipment was placed 0.5 m below the water surface. The transmitter, located at coordinates (0,0), sent signals to the receiver while selecting the appropriate transmission power. The power setting ranged from 1 to 10 W and was quantized into five discrete levels. The system operated with a center frequency of 20 kHz and a bandwidth of 2 kHz. The transmitter utilized the relay node to assist it in forwarding information. Upon receiving the trigger signal from the transmitter, the relay, positioned at (0.5,1.1), forwarded the signal to the receiver at a fixed transmission power, thereby enhancing the reliability of information delivery. The receiver, located at (1.9,0.3), decoded the received messages using a selection combination approach and evaluated BER and the signal-to-noise ratio (SNR) of the received signals to provide this feedback to the transmitter and relay. Meanwhile, an intelligent jammer at (0.5,\(-\)0.2) employed software-defined radio equipment to monitor the channel's transmission state and estimate the quality of the transmitted signals. Using a reinforcement learning algorithm, the jammer dynamically selected its interference power, which ranged from 1 to 10 W, and was quantized into five levels to maximize its long-term discounted utility. Based on the chosen interference power, the jammer transmits interference signals targeting the receiver and relay. The transmitter power cost coefficient was set to 0.03, the interference power cost coefficient was 0.02, and the noise power was fixed at 0.1. The anti-jamming performance of the proposed HPTR algorithm was compared with that of two benchmark algorithms commonly used in UACNs. * QPR: An anti-jamming power allocation algorithm based on Q-learning, similar to the approach described in Ref. [10]. Among the algorithms discussed in Refs. [10; 11; 12], the one in Ref. [12] is the most comparable to the proposed HPTR algorithm and is thus selected for performance comparison. * PTR: A reinforcement learning algorithm based on hybrid strategies [13]. This algorithm introduces decision randomness to create uncertainty and deceive jammers and enhance robustness against interference. In the anti-interference attack and defense scenario of UACNs, whether the agent can quickly reach the Nash equilibrium solution is an important indicator for evaluating the convergence of the algorithm. Figure 1 shows the convergence of the HPTR algorithm in terms of utility. The results show that both the transmitter and the jammer can converge quickly, where the utility of the transmitter gradually increases over time, while the utility of the jammer gradually decreases over time, which verifies the effectiveness of the proposed model. Figure 2 illustrates the convergence of the HPTR algorithm in terms of utility. The transmitter and the jammer converged quickly, and the transmitter's utility increased over time, while the jammer's utility decreased. The results validated the effectiveness of the proposed scheme model. As shown in Figure 3, the _SINR_ and transmitter utility of the proposed scheme were improved over time, while the message BER decreased. Specifically, from the initial stage to 1000 time slots, the message error rate of HPTR was reduced from 0.63 to 0.60, the  
Figure 1: Utility convergence curve. Figure 2: Transmitter anti-jamming communication performance: (**a**) transmitter utility, (**b**) bit error rate, and (**c**) SINR. _SINR_ increased from 0.24 to 0.275 (increased by 14.5%), and the transmitter utility was increased by 125%. In comparison to QPR, the proposed scheme exhibited a higher _SINR_, improved transmitter utility, and a lower BER. For instance, at 1000 time slots, the HPTR scheme improved the transmitter utility by 12.5% and the SNR by 3.77% and reduced the bit error rate by 1.6%, compared with those of QPR.