A New Improved Multi-Sequence Frequency-Hopping Communication Anti-Jamming System

Abstract

In order to address the challenge posed by existing anti-jamming methods (including intelligent anti-jamming techniques) that struggle to counter high-speed reactive jamming in complex jamming environments, we have developed a novel approach that involves leveraging intelligent jamming in such environments rather than merely attempting to evade jamming. Unlike existing anti-jamming techniques that extract energy from jamming signals as a power source, our proposed method can use intelligent reactive jamming signals as a positive factor in frequency detection. To be precise, we have designed an intelligent multi-sequence frequency hopping communication framework (IMSFH), which includes two stages: communication and training. Firstly, during the synchronous sequence transmission, supervised learning is used in the training stage to obtain the rules of reactive jamming through neural networks. In the communication stage, IMSFH using narrowband reception utilizes reactive jamming rules to improve the frequency-detection capability during actual payload transmission. The simulation results show that this method not only improves communication performance with the increase in jamming signal power and stronger anti-jamming ability when combating high-speed reactive jamming, but also better utilizes reactive jamming to improve communication performance in complex jamming environments.

1. Introduction

Wireless communication’s openness and shared nature provide users with easy access and connectivity benefits. Nevertheless, these advantages also expose communication networks to the wireless environment, making them more susceptible to jamming attacks compared to wired networks [1]. Jamming attacks represent a significant threat to wireless communication security, primarily through the emission of electromagnetic signals that disrupt and degrade the reception of user signals, severely affecting communication performance [2]. Particularly with the integration of communication countermeasures and artificial intelligence, wireless jamming techniques and capabilities have evolved. They have progressed from traditional conventional jamming to cognitive jamming, which includes environmental awareness and learning abilities. Eventually, they developed into intelligent jamming, capable of perception, learning, reasoning, and decision-making [3]. For instance, malicious attackers can detect and analyze legitimate users’ signal waveforms, using a Universal Software Radio Peripherals (USRP) device to transmit targeted jamming. Facing complex external jamming environments and evolving jamming patterns, users find it challenging to combat these new threats. Simultaneously, as technologies like unmanned aerial vehicles (UAVs), 5G cellular networks, and vehicle-to-everything communications (V2X) become widespread in daily life, the cost of building intelligent jamming devices has significantly decreased. This development makes the jamming environment increasingly complex. Therefore, to ensure the security of wireless communications, this paper studies how to counteract intelligent reactive jamming in more challenging environments.

Traditional anti-jamming techniques such as adaptive technologies [4], frequency hopping [5], and antenna mode switching [6] have been widely applied in wireless communication. In traditional frequency hopping (FH) communication systems, such as FH/BFSK, user data are initially modulated using Binary Frequency Shift Keying (BFSK), and then transmitted over frequency channels selected pseudorandomly based on a predefined hopping pattern. However, the performance of FH/BFSK systems significantly declines when facing intelligent reactive jamming [7]. Traditional anti-jamming methods lack the learning ability necessary to adapt to the dynamic and complex spectrum environments introduced by intelligent jamming [8]. To address this issue, reference [9,10] introduces game theory to simulate the adversarial relationship between legitimate users and malicious jammers. However, these studies typically assume that legitimate users can obtain the jammer’s Channel State Information (CSI), which is unrealistic in adversarial environments.

Considering the challenges in acquiring intelligence on the states of intelligent jammers, Reinforcement Learning (RL) and Deep Reinforcement Learning (DRL) [11,12,13,14] have been introduced to address the issue of anti-intelligent jamming. In [12], the authors propose a rapid anti-jamming algorithm based on generating similarity samples using Deep Reinforcement Learning. Reference [13] introduces a Sequential Deep Reinforcement Learning Algorithm (SDRLA) that operates without prior information, utilizing a spectral waterfall as input. In reference [14], a method based on Deep Double Q-learning is proposed to learn an effective communication strategy. Although these studies are capable of effectively avoiding slow-reactive jamming, they exhibit certain limitations when dealing with fast-reactive jamming. Fast-reactive jamming can change channels almost synchronously with the user, thus diminishing the effectiveness of these algorithms against such rapid changes. Although the aforementioned methods address reactive jamming through intelligent learning, they remain passive anti-jamming strategies. In more complex jamming environments, where fast and intelligent reactive jamming is encountered, this avoidance-based approach struggles to achieve effective anti-jamming communication.

In the context of complex jamming environments characterized by fast-reactive jamming, reference [15,16,17] has already explored novel approaches that exploit jamming rather than merely evading it. In [15], the authors introduce an anti-jamming scheme based on wireless energy harvesting, referred to as Multistic IA and OIA, which optimizes transmission rates by harnessing energy from jamming signals to aid communication. Furthermore, reference [16] proposes an anti-jamming strategy that combines neural network architectures with environmental backscatter communication techniques. The core of this strategy involves reflecting data sent through jamming signals back to the receiver, while simultaneously harvesting energy from these jamming signals to support communication needs. Additionally, building on [16], reference [17] introduces an intelligent deception strategy that actively transmits false signals to induce jamming, while also harvesting energy from these signals, thereby significantly improving the efficiency of jamming utilization. However, the methods proposed in [15,16,17] experience relatively low jamming utilization efficiency due to channel losses in wireless transmission, and the deep learning-based detector introduced in [17] requires high-quality training data. To enhance jamming utilization efficiency, ref. [18] proposes a method that uses jamming signals to transmit user information, employing user signals as a stimulus for guiding the decision on jamming signals. This method, however, relies on the separation of signal source estimation and is only applicable when user signals and jamming signals are uncorrelated. While [19] can address certain fast and complex reactive jamming, in highly complex jamming environments, the bit error rate increases, adversely affecting anti-jamming performance. To ensure the universal applicability of jamming utilization methods, increase the efficiency of jamming utilization, and enhance the resilience of communication systems, further in-depth research is required.

This system adopts a neural network-based approach to learn the rule of reactive jamming and utilize it. Specifically, we design an Intelligent Multi-Sequence Frequency Hopping (IMSFH) communication framework, which consists of two stages: the training stage and the communication stage. In the training stage, the transmitter sends a fixed, known frequency-hopping signal, learning the variations in reactive jamming signals as they adapt to changes in user signals. This enables the capture of the dynamic characteristics of reactive jamming. During the communication stage, the extracted reactive jamming patterns are utilized, combined with the neural network model, to enhance frequency-detection performance. Simulation results indicate that, compared to existing methods, this approach can effectively utilize reactive jamming signals in complex jamming environments, thereby improving communication performance. To highlight the distinctions between our work and previous studies, we summarize the primary contributions of this paper as follows:

• We optimize an intelligent learning-based jamming exploitation method, allowing for the preferable utilization of reactive jamming signals in complex jamming environments. This method improves model performance by optimizing the neural network, enabling better extraction of correlations between reactive jamming signals and user signals. This correlation is then leveraged to assist users in frequency detection. Since this approach directly extracts information from the jamming waveforms collected in real-time, it eliminates the need to predefine the spectral shape and response time of the jamming, making it effective in handling various types of jamming signals;
• We propose a reactive jamming utilization scheme based on a Multi-Sequence Frequency Hopping communication framework (MSFH), referred to as IMSFH, which exhibits enhanced anti-jamming performance as reactive jamming power increases. This scheme streamlines the processing of communication signals in complex jamming environments, thereby ensuring real-time communication for users. It effectively harnesses intelligent reactive jamming in scenarios where multiple types of jamming coexist, making it applicable to more complex environments.
• The proposed communication framework was compared with MPFH, FH, and WGMPFH in terms of communication performance against intelligent reactive jamming. Simulation results indicate that the proposed framework achieves significantly better bit error rate (BER) performance compared to MPFH, FH, and WGMPFH when countering intelligent reactive jamming. Additionally, the proposed framework was compared with IDFH in complex jamming environments. The simulation results demonstrate that the proposed communication framework outperforms IDFH significantly under such conditions.

The remainder of this paper is organized as follows. In Section 2, we review the related work. Section 3 presents the system model and problem formulation. Furthermore, Section 4 provides a detailed description of the jamming exploitation method based on IMSFH, and Section 5 discusses the simulation results and performance analysis. Finally, conclusions are provided in Section 6.

2. Related Work

2.1. Jamming Utilization

Reactive jamming can quickly learn communication decisions between users and implement tracking at a fast speed. In the face of complex and fast reactive jamming, traditional anti-jamming methods such as the use of a spread spectrum and frequency hopping are difficult to achieve ideal anti-jamming effects with. In [20], the author explored the development ideas of communication anti-jamming based on anti-brittleness. The concept of anti-brittleness communication has had a profound impact on the field of communication anti-jamming: the traditional “jamming suppression” anti-jamming communication mode is gradually shifting towards the “jamming utilization” anti-jamming communication mode. The research on jamming utilization can be mainly divided into the following directions: jamming information utilization, jamming energy collection, jamming-assisted positioning, jamming waveform utilization, and jamming utilization based on deep learning. In terms of utilizing jamming signals, reference [21] proposed an active anti-jamming (AAJ) scheme, in which the transmitting node remodulates the jamming signal with its own transmitted information to achieve anti-jamming communication. Reference [22] proposed using the reaction time of a reactive jammer to transmit information. Reference [23] attempted to describe jamming and determine the active utilization of jamming signals to improve the efficiency of wireless networks. We also utilize jamming signals to improve wireless networks and address potential issues that may arise in wireless networks. In terms of jamming energy harvesting, reference [16] proposed an anti-jamming scheme that combines neural network structure with environmental backscatter communication technology. The core of this scheme is to reflect the transmitted data back to the receiving end through jamming signals, and at the same time collect the energy of these jamming signals to support its communication needs. Based on references [16,17], an intelligent deception strategy is proposed, which induces jamming by actively transmitting false signals to the jammer, while collecting energy from these jamming signals, effectively improving the efficiency of jamming utilization. In terms of jamming waveform utilization, in order to solve the problem of low jamming utilization efficiency caused by wireless channel transmission loss in references [16,17], reference [18] proposes a method of using jamming waveforms to transmit user signals, utilizing the correlation between reactive jamming and user signals, and driving high-power jamming signals with low power to transmit the currently required user information. In terms of jamming-assisted positioning, reference [24] proposed a JAM-ME algorithm that uses jamming signals to assist positioning. This algorithm determines the position of the jamming machine through jamming signals, thereby establishing an autonomous jamming assisted navigation system. In terms of jamming utilization based on intelligent learning, ref. [19] proposed an intelligent differential frequency hopping communication framework (IDFH), which learns reactive jamming rules through neural networks to achieve anti-jamming communication. However, this method is only applicable to situations where only reactive jamming exists in the environment and still has certain limitations. Inspired by its jamming utilization concept, this paper proposes an intelligent multi-sequence frequency hopping communication framework that can improve communication performance in complex jamming environments by utilizing reactive jamming.

2.2. Multi-Sequence Frequency Hopping

References [25,26,27,28,29,30] studied multi-sequence frequency hopping. Reference [25] proposed a multi-mode frequency hopping communication framework (MPFH), which was further enhanced through convolutional encoding and maximum-likelihood decoding. Based on the MPFH communication framework in [25], reference [26] proposed a wide-gap multi-pattern frequency hopping communication method (WGMPFH) to resist reactive jamming, in which the transmitted signal induces reactive jamming to target the data channel, while the complementary channel uses a wide-interval frequency pattern to stay away from reactive jamming. Reference [27] proposed that the anti-jamming advantage of dual-sequence frequency hopping communication is applied to meet the anti-jamming requirements of space-tracking telemetry command receivers under a low signal-to-noise ratio. A multi-sequence frequency hopping communication framework (MSFH) represents messages through channels and has a strong anti-jamming ability. Compared with differential frequency hopping (DFH), it has a better anti-jamming effect in the face of partial frequency band jamming [28]. Reference [29] mentions that DFH has good anti-tracking jamming performance, but it points out that the DFH receiver does not have prior knowledge of channel selection and generally adopts broadband reception for the entire operating frequency band. Broadband reception brings problems such as high hardware overhead and difficult networking. Without considering coding, its performance is not as good as conventional frequency hopping when facing non-tracking jamming such as sweep jamming and multi-tone jamming. Compared with DFH, MSFH can adopt narrowband reception, which has a better anti-jamming effect when facing complex jamming [30]. In order to maximize coding gain, narrowband filtering is generally not performed. In a complex jamming environment, there is not only reactive jamming, but there are also other types of random non-intelligent jamming, such as multi-tone jamming and sweep frequency jamming. Although there have been some research achievements in using anti-jamming methods to deal with certain fast and complex reactive jamming [19], in complex jamming environments, the error rate increases, which affects the anti-jamming performance. Studying the performance of MSFH in complex jamming environments is of great significance for evaluating its emergency communication performance. This paper proposes an intelligent multi-sequence frequency hopping communication framework that effectively addresses jamming in complex jamming environments by utilizing reactive jamming.

Although some studies have improved the anti-jamming performance of multi-sequence frequency hopping, they have only actively avoided reactive jamming and have not changed its passive anti-jamming nature. For example, reference [25] only analyzed the system performance of multi-sequence frequency hopping communication systems under reactive jamming, without pointing out ways to deal with reactive jamming. Reference [26] only use a wide-interval frequency mode to keep complementary channels away from reactive jamming. Inspired by the idea of jamming utilization in [19], in order to make the jamming utilization method universal, improve the efficiency of reactive jamming utilization, and enhance the anti-brittleness of communication systems, more in-depth research is needed for existing analysis models [25] that ignore the impact of environmental noise on the system. This article proposes an intelligent multi-sequence frequency hopping communication framework that effectively improves communication performance by utilizing reactive jamming. Frequency hopping (MSFH) represents messages through channels and has strong resistance to tracking jamming. Compared with differential frequency hopping (DFH), it has a better anti-jamming effect in the face of partial frequency band jamming. In complex jamming environments, there is not only reactive jamming, but there are also other types of non-intelligent jamming, such as multi-tone jamming and sweep frequency jamming. DFH can avoid some sweep jamming through frequency hopping, but due to the fixed frequency hopping pattern of DFH, sweep jamming may still cover the frequency used by the target signal under certain conditions.

3. System Model and Problem Formulation

3.1. System Model

The system model of this paper is illustrated in Figure 1. We consider a wireless communication scenario in a complex jamming environment, involving multiple jammers and a user pair (receiver and transmitter). The user pair counters various types of jammers, including intelligent jammers capable of emitting reactive jamming and non-intelligent jammers that emit sweeping jamming, multi-tone jamming, and other types. Both receivers and intelligent jammers are capable of spectrum sensing and obtaining channel state information. The user employs Multi-Sequence Frequency-Hopping (MSFH) technology for communication. Unlike conventional frequency-hopping communication, MSFH encodes information through channel representation and the hopping points associated with the frequency-hopping sequence. The receiver, using two complementary frequency-hopping sequences, can obtain prior knowledge of the next hop channel selection. It only needs to detect the frequency in each time slot and compare it with the two complementary frequency-hopping sequences to retrieve the corresponding bit information.

3.2. Problem Statement

According to the system model description, the receiver must detect the communication frequency of the user signal at each time slot, which is actually to identify whether there is a user signal on each channel, where $f\in F$. Assuming that in time slot $\mathrm{k}$, the user selects frequency $f_k^U$ for communication, the power of the user’s communication signal can be expressed as $P_U={\int }_{-b_{u/2}}^{b_{u/2}}S(f)df$, where $b_U$ is the bandwidth of the user’s baseband signal, and $S\left(f\right)$ is the low-pass equivalent power spectral density (PSD) of the user’s bandpass signal. After the intelligent jammer perceives the user’s communication decision in time slot $\mathrm{k}$, it selects the jamming power $P_J$ and jamming frequency $f_k^J$ to interfere with the user’s reactive jamming signal. In order to ensure the effectiveness of jamming performance, the intelligent jammer will inevitably emit reactive jamming signals with a higher power than the user signal to the target frequency. Of course, a non-intelligent jammer will also emit non-intelligent jamming signals with a power $P_j$ and a jamming frequency $f_k^j$. Through the above settings, the instantaneous environmental state of time slot $\mathrm{k}$ can be represented as $s_k=(s_k^1,s_k^2,s_k^3,\dots ,s_k^m)$, where $s_k^m$ denotes the received power of a signal with a frequency of $m$ in the time slot $\mathrm{k}$; (1) refers to its specific form.

$$s_k^m=P_U{g}_U\delta (m=f_k^U)+P_J{g}_J\delta (m=f_k^J)+P_j{g}_j\delta (m=f_k^j)+n(f),$$

(1)

In Equation (1), $g_J$ and $g_{\mathrm{j}}$ represent the transfer function of intelligent reactive jamming signals and non-intelligent jamming signals from the jammer to the receiver, respectively, while $g_U$ represents the transfer function of the communication signal from the transmitter to the receiver. In addition, $n(f)$ is the PSD function of noise; $\delta (x)$ is the indicator function. When $x$ is a true value, $\delta (x)=1$, and vice versa; then, $\delta (x)=0$. Given the dynamic and uncertain nature of the environment, numerous unknown parameters, such as $g_J$ and $g_j$, make it impractical to directly determine the communication frequency based on $S_k$.

In order to utilize reactive jamming in complex jamming environments, although it is difficult to obtain intelligent jamming signal decisions, the decision of intelligent reactive jamming may be correlated with the frequency of the user’s signal [6]. So, we define the environmental state as $S_k=\{s_k,s_{k-1},\dots ,s_{k-l+1}\}$, where the backtracking time length is $l$. $S_k$ is a two-dimensional matrix of size $l\times M$. Its thermodynamic image is called a spectral waterfall plot, which includes both time-domain and frequency-domain information. As shown in Figure 2, we can see from the spectrum waterfall that there is a certain regularity between the frequency decision of reactive jamming and the user’s communication frequency.

Figure 2 illustrates the spectrum waterfall of a complete communication stream in a complex jamming environment. This communication stream includes intelligent reactive jamming, as well as non-intelligent frequency sweeping jamming and multi-tone jamming. The interval between each white line represents the communication time required for one hop. From Figure 2, we can observe that the intelligent jammer is capable of sensing the user’s communication frequency in each time slot and transmitting intelligent reactive jamming signals. When the reactive jamming signal synchronizes with the user signal, it can be assumed that each frequency hop encounters the same-frequency reactive jamming. In this scenario, the presence of reactive jamming increases the power of each hop signal, thereby enhancing frequency-detection performance based on energy detection. However, the channel state in real-world environments is constantly changing dynamically, and not all jamming signals overlap with the user signals at all times. As shown in Figure 2, reactive jamming at the same frequency in one time slot may shift to a different frequency jamming in the next, potentially causing frequency-detection errors. Due to the dynamic and unpredictable nature of reactive jamming signals, understanding their jamming rule is crucial. To address this, we designed the IMSFH framework, which leverages neural networks to learn the rule of reactive jamming within the spectrogram waterfall, thereby improving the performance of frequency detection.

The IMSFH communication framework designed in this paper is illustrated in Figure 3, and its structure is similar to the MSFH communication framework introduced in [25]. At the transmitter part, we select channels based on the bit information to synthesize a multi-sequence frequency hopping sequence. This sequence controls the frequency synthesizer to generate the transmission carrier frequency, and the end of the RF part produces the multi-sequence frequency-hopping signal. At the receiver part, we replace the filtering and non-coherent detection components from reference [25] with a frequency-detection network that has frequency-detection and intelligent learning capabilities. Finally, the communication frequencies identified by the frequency-detection network are assembled into a frequency sequence, which is then compared with the corresponding frequency positions in channel 0 and channel 1 to demodulate bit information.

4. Jamming Utilization Method Based on IMSFH

In Section 3.2, we discussed that implementing the utilization of reactive jamming requires learning its jamming patterns through neural network training. Therefore, we designed the IMSFH communication framework to meet this requirement. Similarly, the communication process is divided into a training stage and a communication stage. In this section, we will present a comprehensive overview of the reception process and the specific workings of the frequency-detection network.

4.1. IMSFH Receiver Framework

The IMSFH receiving process is illustrated in Figure 4. To address the dynamic variations of reactive jamming signals, a training stage is introduced to learn these change rule. Therefore, the reception of user signal is divided into two stages: a communication stage and training stage, both of which share the same multi-sequence frequency-hopping signal generation method. Similarly, the user signal is divided into communication signals and synchronization signals. We assume that the synchronization signal is known in advance, so it serves as the training sample for the network. The specifics of these two stages are as follows: a training stage is introduced to learn these changing patterns in order to cope with the dynamic changes in jamming signals. The user signal is divided into two stages:

• Training stage: During this stage, the synchronization signal is preprocessed and presented to the neural network in the form of a spectrum waterfall. Next, the neural network learns the reactive jamming rule in the spectrum waterfall using a supervised learning approach. Specifically, during the training stage, the frequency points of the user at each moment are clearly known. However, the received signal may consist of a composite signal that includes both the user signal and various jamming signals. The primary function of the neural network is to extract the features of reactive jamming from these composite signals and identify their correlation with the user’s signal frequency. These correlations encompass the reaction time needed for reactive jamming and the spectral characteristics of the reactive jamming signals. As the training continues to converge, in the communication stage, we will determine the user’s communication frequency based on the correlation between the reactive jamming signal features extracted during the training stage and the currently received composite signal, thereby achieving effective utilization of reactive jamming. Finally, the trained network is deployed during the communication stage;
• Communication stage: At this stage, the receiver feeds the received complete communication stream as a spectrum waterfall into the trained network for frequency detection. In the frequency-detection process, due to the fact that the frequency-detection network has already learned the reactive jamming rules in early training, and the reactive jamming signal is correlated with the user’s communication frequency, the frequency-detection network outputs the user’s communication frequency after using the spectrum waterfall as input. Therefore, reactive jamming signals can be used to improve the performance of frequency detection. Finally, the obtained frequency information is compared with two dual channels 0 and 1 to obtain bit information.

4.2. Data Preprocessing

It should be noted that since the signal being input into the network is in the form of a spectral waterfall, preprocessing of the signal is also required, as shown in processes (2), (3), and (4). Firstly, we obtain the spectral state $s_k^m$ at the $k$ frequency $m$ of the time slot in the form of the Discrete Fourier Transform (DFT), as shown in formula (2), where $N$ is the number of sampling points in the DFT, $f_s$ is the sampling frequency, and $m_{index}=m\cdot N/f_s$ is the index of $s_k^m$ in the DFT result. We superimpose and combine the DFT results of multiple consecutive time points to obtain a spectral waterfall. As shown in Formulas (3) and (4), after data preprocessing, we can use $S_k^m$ as the input of the network in the form of a thermodynamic diagram and train it.

$$s_k^m=x[m_{index}]={\displaystyle \sum _{n=0}^{N-1}}x[n]\cdot e^{-j{\displaystyle \frac{2\pi }{N}}{m}_{index}n},$$

(2)

$$s_k=(s_k^1,s_k^2,s_k^3,\dots ,s_k^m),$$

(3)

$$S_k=\left[\begin{array}{c}{s}_{k-1}\\ {\mathrm{s}}_{k-2}\\ ⋮\\ s_{k-L}\end{array}\right]=\left[\begin{array}{cccc}{s}_{k-1}^1& s_{k-1}^2& \dots & s_{k-1}^m\\ s_{k-2}^1& s_{k-2}^2& \dots & s_{k-2}^m\\ ⋮& ⋮& ⋮& ⋮\\ s_{k-L}^1& s_{k-L}^2& \dots & s_{k-L}^m\end{array}\right]$$

(4)

4.3. Frequency-Detection Network

With the development of artificial intelligence technology, pattern recognition has been widely applied in many fields, such as speech recognition and image classification. Pattern recognition involves processing collected information and classifying objects with similar characteristics based on specific rules using classifiers. In this paper, in order to effectively perform frequency detection, we utilized the time–frequency information of the environment, which is represented as a spectral waterfall. We input the spectral waterfall into a neural network to transform the frequency-detection problem into a supervised classification problem, which is a common method in the field of pattern recognition. Specifically, during the training stage, since we already know the synchronization signal and its frequency, we can use the spectral waterfall corresponding to different frequencies as different category labels for classification training through supervised learning methods. After the training stage is complete, during the communication stage, the network determines the current user’s communication frequency by analyzing the spectrum waterfall of the incoming complete communication stream. The core advantage of this method is that it allows the network to not only learn frequency characteristics, but also effectively utilize the reactive jamming rule learned during the training stage, thereby improving the accuracy and efficiency of communication. Through this approach, we can effectively utilize neural networks to complete frequency-detection tasks, enhancing our adaptability to dynamic communication environments.

4.3.1. Network Structure and Parameter Updates

The model structure is shown in

Table 1. Network structure.

Layer	Parameters
Input	Input Size: 150 × 150 × 3
Conv2D	8 filters (activation: ReLU), Kernel Size: 3 × 3 (stride: 1)
Pooling	Max Pooling, Kernel Size: 2 × 2 (stride: 2)
FC	128 (activation: ReLU)
Dropout	Probability: 0.2
FC	128 (activation: ReLU)
Dropout	Probability: 0.2
Output	32

. Since the input information in practical communication needs to be processed in real-time and the spectrum waterfall becomes more complex in a challenging jamming environment, we have referred to and improved the structure proposed in [31]. Specifically, we lowered the initial learning rate and introduced an early stopping mechanism during the model training. This not only reduces the network training time and ensures real-time communication, but also helps prevent overfitting, thus enabling the learning of reactive jamming rule in complex spectrum waterfalls. In pattern recognition, the frequency-detection problem is transformed into a multi-classification problem. Therefore, the loss function used in this paper is the Cross-Entropy loss function, whose expression is shown in (5).

$$Loss(\widehat{y},y)=-Min{\displaystyle \sum _{i=l}^M}{y}_i\log ({\widehat{y}}_i)$$

(5)

In (5), $y$ represents the true frequency label value and $\widehat{y}$ denotes the predicted frequency value of the input spectrum waterfall $S_k$. $M$ is the total number of categories of the spectrum waterfalls. ${\widehat{y}}_i$ represents the predicted probability of the corresponding category $i$, while $y_i$ indicates the probability of the true label belonging to category $i$. According to [32], the optimization objective of this paper is expressed in (6). Additionally, the weight update used in this paper is shown in (7), where $w$ denotes the model parameters and $\eta$ represents the learning rate.

$$Min(Loss(\widehat{y},y))=-Min{\displaystyle \sum _{i=l}^M}{y}_i\log ({\widehat{y}}_i)$$

(6)

$${\mathrm{w}}_{\mathrm{t}+1}={\mathrm{w}}_{\mathrm{t}}-\eta {\displaystyle \frac{\partial (\mathrm{Loss})}{\partial ({\mathrm{w}}_{\mathrm{t}})}}$$

(7)

4.3.2. Training and Communication Process

Due to the dynamic changes in complex jamming communication environments, as shown in Figure 5, this paper adopts an online learning strategy to train the network in real-time during each communication cycle. This approach enables the network to adapt promptly to environmental changes, thereby learning the rule of reactive jamming more effectively. Similarly, according to our analysis, the weights of the convolutional layer remain relatively stable, as it primarily extracts the fundamental time–frequency characteristics between user signals and reactive jamming. As a result, we adopted the idea of transfer learning as referenced in [33], updating only the weights of the fully connected layer. This approach not only handles the dynamic characteristics of reactive jamming in complex jamming environments but also reduces the computational complexity of updating parameters. The GPU used in the experimental environment is the NVIDIA GeForce RTX 2080 Ti × 2, with a floating-point computing performance of $26.9\times {10}^{12}$ operations per second, while the FLOP of the model proposed in this paper is $63.3\times {10}^6$. Consequently, it is capable of meeting the real-time requirements of online learning during the communication process.

As outlined in the communication framework, the process begins with the generation of information bits and the corresponding frequency-hopping signals. Since the training signals and training hops are known, the training signals can be received. The signals are then processed into a spectrum waterfall through data preprocessing, which is subsequently divided into a test set and training set for network training. Through training, the dynamic rule of reactive jamming can be effectively learned. Given that the training duration is predetermined, the reception timing of the communication signal can be accurately inferred. Similarly, the trained network is employed to classify the spectrum waterfall of the communication signal, facilitating frequency detection and subsequently extracting bit information based on the identified frequency characteristics. In the end, to further analyze and validate the reactive jamming rule, the bit information is subjected to a Cyclic Redundancy Check (CRC). Upon successful CRC, the frequency detection result is confirmed as accurate and is subsequently employed as a training sample for future communication iterations. The specifics of the proposed algorithm are outlined in Algorithm 1.

Algorithm 1: Intelligent Multi-Sequence Frequency Hopping (IMSFH)

$\begin{array}{l}\mathrm{Notatio}:\\ S_{ts}:\mathrm{Training} \mathrm{signal} \mathrm{matrix}\\ S_{cs}:\mathrm{communication} \mathrm{signal} \mathrm{matrix}\\ H_t:\mathrm{The} \mathrm{hops} \mathrm{numbers} \mathrm{of} \mathrm{training}\\ H_c:\mathrm{The} \mathrm{hops} \mathrm{numbers} \mathrm{of} \mathrm{communication} \\ 1:\mathrm{Start} \mathrm{Communication}\\ 2:\hspace{1em}\mathrm{Generate} \mathrm{multi}-\mathrm{sequence} \mathrm{frequency} \mathrm{hopping} \mathrm{signal} \mathrm{and} \mathrm{two} \mathrm{dual} \mathrm{frequency} \mathrm{sequences}\\ 3:\hspace{1em}\mathrm{Start} \mathrm{training} \mathrm{stage}\\ 4:\hspace{1em} \mathrm{IF} \mathrm{hops} \le H_t\\ 5:\hspace{1em}\hspace{1em}\hspace{1em}{S}_{TS}=\mathrm{Receiving} \mathrm{signal} S_{ts}\\ 6:\hspace{1em}\mathrm{END}\\ {7:\hspace{1em} \mathrm{Spectrum} \mathrm{Waterfall}\left(\mathrm{SW}\right)=\mathrm{Preprocess} \mathrm{S}}_{ts}\\ 8: \hspace{1em}\mathrm{Start} \mathrm{Frequency} \mathrm{detection} \mathrm{network} \mathrm{training}\\ 9: \hspace{1em}\mathrm{End} \mathrm{Frequency} \mathrm{detection} \mathrm{network} \mathrm{training}\\ 10: \mathrm{End} \mathrm{training} \mathrm{stage}\\ 11: \mathrm{Start} \mathrm{communication} \mathrm{stage}\\ 12:\hspace{1em}\mathrm{IF} \mathrm{hops} \le H_c\\ 13:\hspace{1em}\hspace{1em}\hspace{1em}{S}_{CS}=\mathrm{Receiving} \mathrm{signal} S_{cs}\\ 14:\hspace{1em}\mathrm{END}\\ {15:\hspace{1em} \mathrm{Spectrum} \mathrm{Waterfall}\left(\mathrm{SW}\right)=\mathrm{Preprocess} \mathrm{S}}_{cs}\\ 16:\hspace{1em}\mathrm{Frequency} \mathrm{Sequence}=\mathrm{Frequency} \mathrm{detection} \mathrm{network} \mathrm{Classify}(\mathrm{SW})\\ 17:\hspace{1em} \mathrm{Communication} \mathrm{bit}=\mathrm{Comparison} \mathrm{between} \mathrm{Frequency} \mathrm{Sequence} \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{and} \mathrm{the} \mathrm{two} \mathrm{dual} \mathrm{frequency} \mathrm{sequences}\\ 18: \mathrm{End} \mathrm{communication} \mathrm{stage}\\ 19: \mathrm{CRC} \mathrm{check}s \mathrm{the} \mathrm{communication} \mathrm{bit}\\ 20: \mathrm{IF} \mathrm{CRC} \mathrm{check} \mathrm{is} \mathrm{pass}\\ 21:\hspace{1em}\hspace{1em} \mathrm{The} \mathrm{classify} \mathrm{results} \mathrm{are} \mathrm{added} \mathrm{to} \mathrm{the} \mathrm{training} \mathrm{set} \mathrm{for} \mathrm{the} \mathrm{next} \mathrm{communication}\\ 22: \mathrm{END}\\ 23:\mathrm{END} \mathrm{Communication}\end{array}$

4.3.3. Algorithm Complexity Analysis

Considering the actual computing power scheduling situation, an algorithm complexity analysis was conducted on the network model. The network structure is shown in Table 1. The convolutional layer is responsible for extracting low-level features (such as edges, textures, etc.) from the spectral waterfall image, and scanning the input image through a filter to generate a feature map. The pooling layer is subsampled by the feature map through a max pooling operation, reducing computation and memory usage while preserving important feature information. The fully connected layer integrates and classifies the features extracted by the convolutional layer and pooling layer, and outputs the final classification result. The Dropout layer randomly discards a portion of the neurons to prevent overfitting and improve the model’s generalization ability. In this paper, hard decision is adopted, where each output layer generates decision values for each frequency category.

Based on the parameters in Table 1, the computational complexity of this network model is approximately $63.3\times {10}^6$ FLOPs.

5. Simulation Results and Analysis

5.1. Simulation Environment and Parameter Configuration

We validated the anti-jamming performance of the IMSFH system and compared its Bit Error Rate (BER) performance under reactive jamming with conventional FH/BSFK, the MPFH proposed in [25], and WGMPFH proposed in [26]. Additionally, we compared the BER performance of IMSFH and IDFH, proposed in [19], under complex jamming environments. There are two sets of M = 32 orthogonal hopping sequences with available frequency-hopping points. The bandwidth of the user signal at each frequency-hopping point is set to 0.6 MHz. The frequency hopping rate is 5000 times per second, with each hop transmitting 1 bit. In this setting, there are 2560 bits of training data and 15,360 bits of communication data, so the frequency hopping is used during the training stage 2560 times, while the frequency hopping is used during the communication stage 15,360 times. Setting up complex jamming environments includes reactive jamming, multi-tone jamming, and sweep frequency jamming. As mentioned earlier, IDFH shows a sharp decline in communication performance in complex jamming environments. We have also designed relevant simulation experiments to verify that IMSFH maintains good communication performance using reactive jamming in complex jamming environments.

5.2. Network Training Parameters

The training parameters of the model utilized in this paper are illustrated in

Table 2. Model training parameters.

Parameters	Value
Image Size	150 × 150 × 3
Total Number of Samples	2560
Test Sample Number	1280
Training Sample Number	1280
Loss Function	Categorical
Initial Learning Rate	0.03
Optimizer	Stochastic Gradient Descent
Batch Number	32

. To evaluate the effectiveness of the frequency recognition network in communication scenarios, the jamming-to-signal ratio (JSR) and signal-to-noise ratio (SNR) were both set to 0. The network’s training process is illustrated in Figure 6. The results demonstrate that, despite operating in a complex jamming environment and using a small-scale training sample size, the network achieves recognition accuracy that satisfies the requirements for reliable communication.

5.3. Simulation Result Analysis

Due to the decrease in the signal-to-noise ratio, the frequency point detection network can learn less information from the spectrum waterfall. Moreover, due to the presence of multiple instances of jamming in complex jamming environments, this paper utilizes intelligent reactive jamming. As the JSR increases, unused jamming can also affect system performance. Therefore, we first verified the bit error rate (BER) performance of IMSFH in different signal-to-noise ratio (SNR) environments. In the simulation, we set the power of non-utilized jamming and set three different reactive jamming values, with JSR = {0, 5, 10}, to achieve an SNR of {−10, −8, −6, −4, −2.0}. The simulation results are shown in Figure 7. From Figure 7, it can be seen that under the same JSR, the system error rate performance increases with the increase in SNR. This is because as the SNR increases, the noise decreases, making it easier for IMSFH to obtain reactive jamming from the spectrum waterfall, improving the efficiency of utilizing reactive jamming. We can also see from Figure 7 that under the same JSR, for every 2 dB increase in SNR, the bit error rate performance can be improved by 1.6 dB.

In addition, we can also see from Figure 7 that in the case of a low SNR, as the power of reactive jamming increases, the communication performance of IMSFH improves. Therefore, this paper also designed corresponding simulations to analyze and illustrate the performance. We analyzed the performance of SNR = {0, −5, −10} under different JSR = {11, 9, 7, 5, 3, 1, −3, −5} conditions, and the simulation results are shown in Figure 8.

From Figure 8, we can observe that under the same Signal-to-Noise Ratio (SNR) conditions, the system’s bit error rate (BER) performance increases with the increase in Jamming-to-Signal Ratio (JSR). This is because as the JSR increases, the characteristics of the reactive jamming signal become more prominent in the spectrum waterfall diagram. Consequently, the system is able to learn more reactive jamming information under the same SNR conditions. This increased information enhances the efficiency of leveraging reactive jamming, thereby improving the system’s communication performance.

As mentioned earlier, in the receiver section, we replace the filtering and non-coherent detection components from reference [25] with a frequency-detection network that has frequency-detection and intelligent learning capabilities. To further demonstrate the improvement of IMSFH in this area, we conducted corresponding experiments for performance validation. In addition, we also compared the performance of IMSFH with other MSFH schemes in experiments and analyzed the performance differences under the same jamming environment.

Figure 9 shows the accuracy of user frequency signals received by IMSFH, WGMPFH [26], and MPFH [25] system receivers in a communication environment using only intelligent reactive jamming. In this scenario, the SNRs for the WGMPFH and MPFH systems are set to 13.35 dB, while the SNR for the IMSFH system is 0 dB. From Figure 9, we can see that due to the decrease in SJR, the accuracy of the user signals received by each system receiver will also decrease, but the IMSH will slightly increase (greater than 99%). This is because as SJR decreases, the jamming power will increase, and the reactive jamming characteristics in the spectrum waterfall become more prominent. This enhances the ability of the frequency-detection network to effectively learn reactive jamming rules.

On the basis of the unchanged experimental conditions in Figure 9, we verified the impact of frequency mismatch on BER performance and added a demonstration of the BER performance of traditional FH/BPSK (SNR = 13.35 dB). The accuracy of IMSFH in Figure 9 has always been greater than 99%, and it can be seen from Figure 10 that its BER performance is also very excellent. Even under low SJR conditions and despite the IMSFH system having an SNR significantly lower than that of the other systems, it still demonstrates superior performance. This is because compared with the MPFH and WGMPFH proposed in references [25,26], we do not avoid jamming, but actively utilize reactive jamming to improve communication performance and achieve good anti-jamming effects.

As mentioned earlier, without considering encoding, DFH uses broadband reception and performs worse than MSFH using narrowband reception in the face of non-tracking jamming. Similarly, in this case, the anti-jamming performance of IDFH in reference [19] is also weaker than that of IMSFH. We have verified that in complex jamming environments (reactive jamming, multi-tone jamming, frequency sweeping jamming), multi-tone jamming and frequency sweeping jamming are non-tracking non-intelligent jamming. To demonstrate the superior performance of IMSFH, we conducted relevant experiments to compare IDFH with IMSFH and analyze their performance differences in the same complex jamming environment. From Figure 11, we can observe that under the same signal-to-noise ratio (SNR), when JSR = −3, the bit error rate gain of IMSFH is close to 3 dB compared to IDFH. Similarly, with the increase in JSRs, as other non-intelligent jamming powers increase, the reactive jamming power also increases. When the JSR is large, IMSFH can more effectively utilize reactive jamming to achieve anti-jamming communication. When the JSR = 5, the bit error rate gain of IMSFH is close to 9 dB. It can be seen that in a complex jamming environment, when the JSR is high, IMSH has a better utilization effect on reactive jamming than IDFH.

Through the analysis of simulation results, it can be seen that the signal-to-noise ratio has a significant impact on the IMSFH system. For IMSFH, FH/BFSK, WGMPFH, and MPFH, IMSFH is based on the idea of jamming utilization. The higher the reactive jamming power, the better the jamming utilization efficiency and anti-jamming performance. For IDFH and IMSFH, they are both based on the idea of using reactive jamming to improve communication performance. In complex jamming environments, except for reactive jamming, other forms of jamming are unfavorable factors for communication. By comparing the simulation results of IDFH and IMSFH, it can be seen that IMSFH performs better. Therefore, when anti-reactive jamming occurs in more complex jamming environments, IMSFH is a better choice.

6. Conclusions

This paper optimizes a reactive jamming utilization technique combined with deep learning and, on this basis, constructs the Intelligent Multi-Sequence Frequency Hopping (IMSFH) communication framework. Compared with existing jamming utilization methods, this framework analyzes training signals during the training stage to learn a reactive jamming rule from the spectrum waterfall and leverages this learned rule to improve frequency-detection performance during the communication stage, ultimately achieving effective utilization of reactive jamming. Finally, a simulation study of the IMSFH framework under different jamming parameters was conducted, and its performance was compared with IDFH communication frameworks. The simulation results demonstrate that as the reactive jamming power increases in complex jamming environments, the performance of IMSFH significantly improves. Compared with the MSFH communication framework and other improved MSFH frameworks, IMSFH exhibits superior performance. The IMSFH communication framework does not rely on specific preconditions, simplifying the communication signal processing flow and ensuring communication quality in low-SNR environments. Moreover, in complex jamming environments, IMSFH outperforms the IDFH communication framework by making better use of intelligent reactive jamming, demonstrating enhanced anti-jamming capabilities.