# Deep-Learning-Based Recovery of Frequency-Hopping Sequences for Anti-Jamming Applications
## 1 Introduction
[22] proposed an intelligent fast frequency-hopping algorithm based on improved Q-learning with the goal of maximizing the information transmission rate and minimizing the frequency-hopping overhead simultaneously. Their simulation results showed that the proposed scheme can rapidly learn frequency-hopping strategies with faster convergence. [PERSON] et al. [23] constructed a long short-term memory (LSTM) neural network model for the frequency prediction of the frequency-hopping system with the intercepted massive frequency-hopping signal data. Their simulation results showed that parameter estimation methods could accurately estimate the frequency in the presence of a certain amount of noise. As a further study, a kind of robust long-term spectrum prediction scheme with missing values and sparse anomalies based on tensor completion was proposed in [24]. Due to the variation in the electromagnetic environment, the transmitter of the intelligent anti-jamming communication makes intelligent decisions on the frequency-hopping sequence, and the receiver cannot know the frequency-hopping sequence used by the transmitter in advance, which undoubtedly increases the difficulty of the receiver's information recovery. At present, the research of intelligent anti-jamming of frequency-hopping communication mainly focuses on the transmitter. Although there are some efforts on the detection and parameter estimation of FH signals [25; 26; 27; 28] at the receiver side, these methods need to store frequency-hopping signals with a certain length of time for analysis and processing, which cannot be applied in real-time communication reception. In order to solve the problems in the complex electromagnetic jamming environment, in this paper, an intelligent anti-jamming frequency-hopping communication system model is established, and the intelligent recovery of frequency-hopping sequences using deep learning is proposed. In the proposed method, a convolutional neural network (CNN) was used to extract the high-dimensional features of time-frequency diagrams of frequency-hopping signals, and a gated recurrent unit (GRU) was used to learn the time correlation between the signals in the presence of jamming. Then, simulations were conducted to analyze the performance of the proposed method. Specifically, the main objectives and contributions of the paper are mainly as follows:  
1. We propose a deep-learning-based recovery method of frequency-hopping sequences. In the proposed method, we used the short-time Fourier transform (STFT) diagram of the received frequency-hopping signal as the input of the network. We designed a hybrid CNN and GRU network architecture for learning and adaptation to variant signal input length. The combination of the two networks ensured the accuracy of frequency-hopping sequence estimation under a complex electromagnetic environment. Simulation results showed that in both the single and mixed jamming scenarios, the proposed method achieved high accuracy in estimating the frequency-hopping sequences. 2. We used transfer learning to deal with new frequency-hopping systems with different frequency-hopping sets. We changed the last fully connected layer of the network so as to make the size of its output dimension correspond to the number of frequency points of the new frequency-hopping system. The simulation results showed that with transfer learning, the number of training samples could be reduced to a large extent. 3. We analyzed the BER performance of the frequency-hopping system. Our results showed that the BER performance of the proposed hybrid network was close to that of the frequency-hopping receiving system under ideal conditions, in both the single and mixed jamming environments. The rest of the paper is organized as follows: In Section 2, we introduce the intelligent anti-jamming frequency-hopping communication system model. Section 3 presents the details of the proposed method. In Section 4, extensive simulation experiments are conducted to verify the performance of the algorithm. Section 5 summarizes the paper.