# Deep-Learning-Based Recovery of Frequency-Hopping Sequences for Anti-Jamming Applications
## 1 Introduction  
With the increasingly complex electromagnetic environment, intentional jamming has brought great challenges to the normal operation of wireless communication systems [1], so it is urgent to improve the anti-jamming capability. Traditional anti-jamming methods, such as filtering [2], direct sequence spread spectrum [3], and adaptive antenna [4], lack flexibility and have poor adaptability to the complex and changeable electromagnetic environment. Frequency-hopping communication [5] is widely used in common anti-jamming communications due to its strong anti-interference ability, ease of multi-access networking, and superior security. The frequency-hopping (FH) mechanism plays an important role in anti-jamming frequency-hopping communication, and the frequency-hopping sequence is the key to controlling frequency hopping. At present, the frequency-hopping sequence detection is mainly realized by the Bayesian detection algorithm [6], sequence prediction based on probability distribution algorithms [7], chaotic frequency-hopping sequence detection based on neural network algorithms [8], and frequency-hopping synchronous capture strategy based on subsequence search [9]. However, most of the sequence detection methods only consider the white Gaussian noise channel without jamming and also need prior information such as the frequency-hopping time and frequency-hopping set. In practicalapplications, frequency-hopping signals are usually accompanied by strong interference signals, and the above-mentioned methods will have limitations in this circumstance. Artificial intelligence algorithms have been widely used in various fields of wireless communications at present, and intelligent anti-jamming communication systems based on artificial intelligence algorithms have also become a new research issue [10; 11]. Intelligent decision making is used as the key technology in intelligent anti-jamming communication systems, which take into account the selection of parameters such as power [12] and frequency [13] and use the domain knowledge of pattern recognition [14] and multi-agent decision making [15] to adaptively search for the optimal solution of the objective function in a solution space to achieve efficient and reliable communication. For example, in NC-OFDM communication systems, radial basis function neural network algorithms [16], Q-learning algorithms [17], and BP neural network algorithms [18] are used to realize an intelligent decision-making process for communication parameters. In frequency-hopping systems, a double-deep Q-network (DDQN)-based anti-jamming scheme was proposed to solve anti-jamming communication [19]. In the proposed algorithm, the interactions between a radio transmitter and a follower jammer were formulated as a Markov decision process (MDP). The jammer was adjusted to improve the interference performance, and the radio terminal fed the state feedback information into the algorithm's input parameters and then selected the transmit power and hopping rate according to the output of the policy network. [PERSON] et al. [20] proposed a dynamic epsilon-DQN intelligent decision-making method to solve the problem of intelligent anti-jamming decision making in frequency-hopping communication systems. The proposed algorithm introduced experience replay and dynamic epsilon mechanism based on PHC under the framework of the DQN algorithm. [PERSON] et al. [21] designed a multi-agent fuzzy deep reinforcement learning algorithm based on centralized training and decentralized execution (MFDRL-CTDE) to improve the anti-jamming performance of frequency-hopping asynchronous networks in complex electromagnetic environments. Their simulation results showed that the algorithm has a great advantage in convergence speed and has good adaptability to a changeable complex electromagnetic environment. [PERSON] et al.