Intelligent Reception of Frequency Hopping Signals Based on CVDP

Abstract

The frequency hopping communication systems have been widely used in anti-jamming communication due to their anti-interception and anti-interference capabilities. With the increasingly complex electromagnetic environment, the transmitter of the frequency hopping communication system adopts more flexible frequency hopping patterns to cope with interference. Therefore, to address the problem of traditional frequency hopping receiver systems being unable to receive properly due to intelligent frequency hopping sequence decisions made at the transmitter, we design a CVDP (CNN_VIT_Dual Multi-head Probsparse Self-attention) network based on a convolutional neural network (CNN) module and Transformer Encoder module to realize the intelligent reception of frequency hopping signals. The designed CNN module extracts the global features and spatial information of the time-frequency spectrograms and serves as the input of the VIT (Vision Transformer) network, which not only solves the problem that the VIT network is difficult to converge on small data sets but also improves the stability and robustness of the VIT network. In the Transformer Encoder module of the VIT network, a dual multi-head self-attention mechanism is used to extract critical time-frequency features and a $Probsparse$ self-attention idea is introduced to reduce the computational complexity. Simulation results on hopping frequency estimation and received BER(Bit Error Rate) of CVDP networks in different interference and channel environments show that when a hopping sequence is unknown, CVDP-based intelligent hopping receiver systems can achieve nearly the same receiver performance as conventional reception systems in which a hopping sequence is known.

1. Introduction

With the increasingly complex electromagnetic interference environment, the anti-interference capability of communication systems must meet higher and more stringent requirements to ensure the reliable transmission of information [1]. While traditional frequency hopping communication has strong anti-interference and anti-interception capabilities, complex electromagnetic interference and intelligent interference have a significant impact on its information transmission performance. Therefore, an intelligent anti-interference frequency hopping communication system is needed to cope with complex and changing interference environments and ensure normal communication between the two parties. By dynamically changing parameters such as frequency hopping sequence, hopping speed, and signals bandwidth through learning and intelligent decision-making, the transmitter achieves intelligent anti-interference based on full awareness of the electromagnetic environment. An intelligent anti-interference decision algorithm based on a Deep Q-Network with priority experience replay based on Pareto sample (PPER-DQN) for bivariate frequency hopping mode has been proposed to intelligently generate high-performance frequency hopping patterns of the frequency hopping communication system [2]. However, due to the intelligent frequency hopping decision of the transmitter, the receiver does not know the hopping pattern and cannot guarantee the proper reception of the message. Therefore, the study of intelligent reception of frequency-hopping communication holds significant theoretical significance and application value.

The current research on intelligent communication reception has primarily focused on each processing module of conventional communication reception systems by using deep learning techniques to improve the performance of the communication system. In terms of channel estimation, in [3] neural networks were employed to learn the channel structure from a significant amount of training data in a large-scale Multiple-Input Multiple-Output (MIMO) system. In [4], a channel estimator utilizing deep learning was initially trained offline via simulated data, after which it was dynamically adjusted online to enhance its generalization capabilities. In [5] a deep learning-based channel estimation method was proposed under time-varying Rayleigh fading channels, which outperformed traditional methods in terms of mean square error (MSE) performance. Several studies have investigated the use of deep learning methods to address the challenges associated with channel estimation in orthogonal frequency division multiplexing (OFDM) systems [6,7,8]. Regarding channel equalization, an equalizer based on Multi-Layer Perceptron (MLP) networks was introduced [9], which demonstrates better error performance than traditional equalization methods. Concerning signal demodulation, convolutional neural networks were used [10] to demodulate binary phase-shift keying signals with transmission rates faster than the Nyquist rate. Furthermore, deep confidence networks and stacked self-encoders were employed [11] to implement signals demodulation for near-range multipath channels. The long short-term memory (LSTM) unit-aided intelligent DNN(Deep Neural Networks)-based deep learning (DL) demodulator for orthogonal frequency division multiplexing-aided differential chaos shift keying (OFDM-DCSK) systems was proposed [12]. In terms of channel decoding, Recurrent Neural Networks (RNNs) were utilized as decoders for convolutional codes under correlated noise [13]. It extracts sequence information of convolutional codes using a bidirectional Gate Recurrent Unit (GRU) network and calculates decoding results by a fully connected neural network. Although this approach outperforms traditional algorithms, it is not suitable for storing convolutional codes of long length. Another study [14] proposed a minimum-sum decoding algorithm based on a Back Propagation (BP) network, which reduces the computational complexity of the BP algorithm and improves decoding speed.

In addition to optimizing individual processing modules of the receiver with deep learning, several studies utilized deep learning to optimize multiple modules simultaneously. In [15], a fully connected network was employed to simultaneously perform equalization and decoding in multipath channels. However, its performance is worse than the minimum MSE method with known channel statistics. In [16], DNN (Deep Neural Networks) network structure was utilized to implement channel equalization and symbol detection in OFDM (Orthogonal Frequency Division Multiplexing) receivers, and experimental results demonstrate its superiority over traditional methods. To achieve end-to-end optimization of wireless communication systems, [17,18] have investigated the use of deep learning to optimize the entire communication system, excluding RF (Radio Frequency) A/D and D/A. Additionally, an end-to-end wireless communication system using DNN was developed [19] and a conditional generative adversarial network (GAN) was used to represent channel effects and to implement key functions such as encoding, decoding, modulation, and demodulation. In [20] a deep receiver was proposed that optimally implements the entire information recovery process for conventional reception using deep neural networks, and the BER (Bit Error Rate) of the proposed deep receiver outperforms that of the conventional receiver in the presence of various factors, such as noise, power amplifier nonlinear distortion, frequency bias, multipath fading, co-channel interference, and dynamic environment.

All of the above studies are related to conventional communication reception systems. In the detection of frequency hopping signals, in [21], a threshold selection method based on K-means clustering was proposed to achieve fast detection of frequency hopping signals under low signal-to-noise ratio conditions. In [22,23], the CNN networks are used to determine the presence of frequency hopping signals. However, they cannot estimate the specific hopping frequencies. In [24], the Radial Basis Function (RBF) neural network is employed to facilitate the nonlinear prediction of Frequency Hopping (FH) sequences and to enable the discrimination of multiple FH sequence signals. In [25,26], the LSTM networks are employed to predict frequency hopping sequences, but most of these sequences are generated using m-sequences, which are pseudo-random sequences with certain regularities. In contrast, the hopping sequences in this paper are intelligently generated by the transmitter based on different interference environments, and the deep reinforcement learning method utilized ensures that the hopping sequences are completely random. As a result, it is not possible to identify patterns from existing frequency hopping sequences for prediction. There is less research on intelligent reception of frequency hopping communication. In [27], a convolutional neural network-gated recurrent unit (CNN-GRU) network was designed to estimate multi-time slot frequency hopping sequences, and the simulation results demonstrated the network’s good generalization ability and robustness. However, this method suffers from a long delay in estimating frequency hopping sequences. So we will study the estimation of the frequency point of frequency hopping communication in a one-time slot.

In summary, the main contributions of this paper are as follows.

• We design a CVDP network that exhibits robust generalization performance for the estimation of hopping frequency during the one-time slot. This network reduces the delay and overcomes the difficulty of training due to few features and a small data set of frequency hopping signals in the one-time slot.
• The CVDP network combines the inductive bias property of CNN networks with the global inductive modeling capability of VIT networks [28] to solve the problem of poor convergence of VIT networks on small data sets and to improve the stability and robustness of VIT networks. A dual multi-head self-attention mechanism is proposed for extracting the time-frequency features of different low-dimensional subspaces to improve the network performance. Meanwhile, the idea of $Probsparse$ self-attention [29] is introduced to calculate only the self-attention of key points to reduce the computational complexity.
• Extensive simulation experiments have been conducted to evaluate the performance of the CVDP network in various scenarios, including multi-tone interference, single-band interference, multi-band interference, swept frequency interference, mixed interference, and channel fading, encompassing both frequency-flat Rayleigh fading and frequency-selective Rayleigh fading. The simulation results indicate that the CVDP network exhibits a high level of generalization performance across all of these environments. Moreover, the intelligent receiver system, which incorporates the CVDP network, performs remarkably close to an ideal receiver when dealing with an unknown frequency hopping sequence.

2. CVDP Network Design

Figure 1 presents the block diagram of an intelligent anti-interference system designed for frequency hopping communication in a complex electromagnetic environment.

In contrast to the traditional frequency hopping communication system, the intelligent anti-interference system of frequency hopping communication involves intelligent changes of the frequency hopping pattern by the sender. These changes are made through intelligent decision-making based on the electromagnetic interference environment to ensure uninterrupted communication. Instead of transmitting frequency hopping signals according to a predefined pattern, the sender adapts the pattern dynamically to avoid interferences. On the receiver side, a CVDP network estimates the frequency hopping sequence and achieves intelligent reception of the frequency hopping signals. The problem of predicting hopping frequency in the one-time slot is treated as a multiclassification problem. The CNN-GRU network designed in [27] assumes that both communicating parties have specified parameters, such as the frequency hopping period and channel bandwidth (excluding the frequency hopping sequence), and achieves estimation of multi-time slot frequency hopping sequences. However, this method has a delay for multiple time slots. In contrast, this paper primarily focuses on the estimation of frequency hopping frequency points for a one-time slot, where only the one-time slot is delayed. Furthermore, the module of the CVDP network in this paper is only used to estimate the frequency hopping frequency points. Even if the adversary employs this technology to estimate our frequency, it is difficult to effectively intercept the hopping signal without knowledge of other parameters of the unknown hopping signal.

2.1. Signal Models

In general, a single-frequency hopping signal can be expressed as Equation (1):

$$s\left(t\right)=\sqrt{2E}m\left(t\right)cos(2\pi f_{i}t+{\varphi }_i),i{T}_{FH}\le t<(i+1)T_{FH}.$$

(1)

where i is an integer; E denotes the signal’s power; $m\left(t\right)$ denotes the original information; $T_{FH}$ denotes the hopping period; $f_i$ denotes the hopping frequency; and ${\varphi }_i$ is a random phase.

Since the frequency hopping signal is non-steady, the received signal $r\left(t\right)$ is pre-processed using Short Time Fourier Transform (STFT), and the time-frequency spectrograms in the one-time slot are used as the input of the neural network. The mathematical expression of the Short Time Fourier Transform is Equation (2):

$$\left\{\begin{array}{c}STF{T}_r(t,\omega )={\int }_{-\infty }^{+\infty }r\left(\tau \right)Y^{\ast }(\tau -t)exp(-j\omega \tau )d\tau \hfill \\ r\left(t\right)=h(t,\tau )\ast s\left(t\right)+v\left(t\right)\hfill \\ h(t,\tau )={\displaystyle \sum _{j=0}^J}g(t,{\tau }_j)\delta (t-{\tau }_j)\hfill \end{array}\right..$$

(2)

where $Y^{\ast }\left(t\right)$ denotes the conjugate form of the window function, $r\left(t\right)$ denotes the received signals, $h(t,\tau )$ denotes the impulse response of the wireless channel, J is the number of channel paths, $g(t,{\tau }_j)$ is the j-th path channel gain coefficient, and ${\tau }_j$ is the j-th path channel transmission delay, $v\left(t\right)$ denotes the interference and noise encountered during transmission.

2.2. Network Structure

Figure 2 depicts the architecture of the CVDP network, which comprises two distinct modules, namely CNN, and VIT, where the VIT module consists of Embedding, Transformer Encoder, and MLP(Multi-Layer Perception) Head. The CNN module plays a vital role in reducing the dimensions of the input time-frequency spectrograms and extracting additional inductive bias information. The Embedding module is responsible for converting the CNN output feature map into a one-dimensional vector through linear mapping and introducing a learnable class vector to represent the global features of the encoded image. Additionally, the Embedding module preserves the spatial information between the feature maps through positional encoding. The Transformer Encoder module employs a self-attention mechanism to calculate the self-attention of key points and extract the time-frequency features of frequency hopping signals. Finally, the MLP Head module transforms the output dimensions into classification quantities, thereby enabling efficient classification.

2.2.1. CNN Module

In [30], combining CNN with self-attention modules has been proposed to improve the network performance.VIT network introduces a self-attention mechanism and pays more attention to the location of frequency hopping signals, which has excellent feature extraction ability, but it needs a large amount of data for training to converge. To address this limitation, we modify the VIT network, replacing the image segmentation module with a CNN network. The CNN module processes the time-frequency spectrograms and outputs the corresponding feature maps, which can reduce the size of the time-frequency spectrograms and improve the inductive bias of the network, enabling it to converge quickly even when trained on small data sets. Specifically, the CNN module’s structure, as presented in

Table 1. CNN network structure.

Index	Layers	Structure	Structural Parameters (Kernel Size, Stride)	Output Dimension
1	Input	-	-	3 × 256 × 128
2	Conv1	Conv-BN-ReLU	7 × 7 × 64.2	64 × 128 × 64
3	M	Maxpool	3 × 3 × 64.2	64 × 64 × 32
4	Res1	Conv-BN-ReLU Conv-BN-ReLU	3 × 3 × 64.0 3 × 3 × 64.2	64 × 64 × 32
5	Res2	Conv-BN-ReLU Conv-BN-ReLU	3 × 3 × 128.0 3 × 3 × 128.2	128 × 32 × 16
6	Res3	Conv-BN-ReLU Conv-BN-ReLU	3 × 3 × 256.0 3 × 3 × 256.2	256 × 16 × 8

Note: Conv stands for Convolutional layer (Conv); BN stands for Batch Normalization (BN); ReLU stands for Activation function ReLU; Res stands for Residual blocks.

, where the dimension of the time-frequency spectrograms is 256 × 128. The input to the network is a four-dimensional tensor with a size of 64 × 3 × 256 × 128 and a batch size of 64.

2.2.2. Transformer Encoder Module

The structure of the Transformer Encoder module consists of parallel dual Multi-head $Probsparse$ Self-attention (MPS) layers and the Multi-layer Perceptron block (MLP), which applies Residual Connection (Residual Connection) and Layer Normalization (Layer Norm) before each layer.

To learn more about different subtle features, the Transformer Encoder in this paper uses parallel dual multi-headed self-attention modules with different sizes. h denotes the number of heads in the multi-headed self-attention layer. Let the total dimension of each multi-headed self-attention layer be 256, one multi-head self-attention layer was set to $h1$, and the other multi-head self-attention layer was set to $h2$. Specifically, the time-frequency features are extracted in the low dimensional subspaces with the $256/h1$-dimension and $256/h2$-dimension, respectively, to improve the network performance.

The self-attention mechanism is to extract the feature with attention as shown in Equation (3).

$$A(\mathbf{Q},\mathbf{K},\mathbf{V})=softmax\left(\frac{\mathbf{Q}{\mathbf{K}}^T}{\sqrt{d}}\right)\mathbf{V}.$$

(3)

where $\mathbf{K}$, $\mathbf{Q}$ and $\mathbf{V}$ are the key matrices, query matrices, and value matrices of the self-attention module, which are obtained from the input sample sequence by spatial transformation, and d is the dimension of the input. Let the input sample sequence be $\mathbf{x}={\mathbb{R}}^{L\times d}$ and L be the length of the sequence, then define $\mathbf{K}=\mathbf{x}·{\mathbf{W}}^K\in {\mathbb{R}}^{L\times d}$, $\mathbf{Q}=\mathbf{x}·{\mathbf{W}}^Q\in {\mathbb{R}}^{L\times d}$, $\mathbf{V}=\mathbf{x}·{\mathbf{W}}^V\in {\mathbb{R}}^{L\times d}$. ${\mathbf{W}}^K$, ${\mathbf{W}}^Q$ and ${\mathbf{W}}^V$ are the fully connected layer learnable parameter matrices. Let ${\mathbf{q}}_i$, ${\mathbf{k}}_i$, ${\mathbf{v}}_i$ stand for the i-th row in $\mathbf{K}$, $\mathbf{Q}$, $\mathbf{V}$ respectively.

Since the traditional self-attention mechanism requires dot product operations on all $\mathbf{K}$ and $\mathbf{Q}$ values to calculate the correlation, a dual multi-headed self-attention layer will increase the computational amount, so the $Probsparse$ self-attention idea is introduced to reduce the computational amount. The distribution of self-attention probability has potential sparsity, only part of the dot product contributes to the main attention, and the other dot products can be ignored. The attention weight of the i-th component ${\mathbf{q}}_i$ of $\mathbf{Q}$ to all $\mathbf{K}$ can be viewed as a probability distribution $p\left({\mathbf{k}}_j\right|{\mathbf{q}}_i)$ shown in Equation (4), where $c({\mathbf{q}}_i,{\mathbf{k}}_j)$ is the correlation between ${\mathbf{q}}_i$ and ${\mathbf{k}}_j$ as shown in Equation (5), and let $\beta \left({\mathbf{k}}_j\right|{\mathbf{q}}_i)$ be uniformly distributed as shown in Equation (6). If a ${\mathbf{q}}_i$ contributes significantly to attention, its $p\left({\mathbf{k}}_j\right|{\mathbf{q}}_i)$ will deviate from the uniform distribution; conversely if it does not contribute to attention, its $p\left({\mathbf{k}}_j\right|{\mathbf{q}}_i)$ will approach the uniform distribution.

$$p\left({\mathbf{k}}_j\right|{\mathbf{q}}_i)=\frac{c({\mathbf{q}}_i,{\mathbf{k}}_j)}{{\sum }_{l}c({\mathbf{q}}_i,{\mathbf{k}}_l)}\mathbf{V},$$

(4)

$$c({\mathbf{q}}_i,{\mathbf{k}}_j)=exp\left(\frac{{\mathbf{q}}_i{\mathbf{k}}_j^T}{\sqrt{d}}\right),$$

(5)

$$\beta \left({\mathbf{k}}_j\right|{\mathbf{q}}_i)=\frac{1}{L}.$$

(6)

The difference between the $p\left({\mathbf{k}}_j\right|{\mathbf{q}}_i)$ and the uniform distribution is measured using the Kullback-Leibler divergence, as shown in Equation (7).

$$\begin{array}{c}KL\left(\beta \right|\left|p\right)=-{\displaystyle \sum _{j=1}^L}\beta \left({\mathbf{k}}_j\right|{\mathbf{q}}_i)ln\left(\frac{p\left({\mathbf{k}}_j\right|{\mathbf{q}}_i)}{\beta \left({\mathbf{k}}_j\right|{\mathbf{q}}_i)}\right)\hfill \\ ={\displaystyle \sum _{j=1}^L}\beta \left({\mathbf{k}}_j\right|{\mathbf{q}}_i)ln\left(\beta \left({\mathbf{k}}_j\right|{\mathbf{q}}_i)\right)-{\displaystyle \sum _{j=1}^L}\beta \left({\mathbf{k}}_j\right|{\mathbf{q}}_i)ln\left(p\left({\mathbf{k}}_j\right|{\mathbf{q}}_i)\right)\hfill \end{array}.$$

(7)

Substituting Equation (4) and Equation (6), we get

$$\begin{array}{c}KL\left(\beta \right|\left|p\right)=ln{\displaystyle \sum _{l=1}^L}exp\left(\frac{{\mathbf{q}}_i{\mathbf{k}}_l^T}{\sqrt{d}}\right)-\frac{1}{L}{\displaystyle \sum _{j=1}^L}\frac{{\mathbf{q}}_i{\mathbf{k}}_j^T}{\sqrt{d}}-lnL\end{array}.$$

(8)

After removing the constant term $lnL$, the sparsity measure is obtained, as shown in Equation (9).

$$\begin{array}{c}M({\mathbf{q}}_i,\mathbf{K})=ln{\displaystyle \sum _{j=1}^L}exp\left(\frac{{\mathbf{q}}_i{\mathbf{k}}_j^T}{\sqrt{d}}\right)-\frac{1}{L}{\displaystyle \sum _{j=1}^L}\frac{{\mathbf{q}}_i{\mathbf{k}}_j^T}{\sqrt{d}}\end{array}.$$

(9)

where the first term is an LSE (Log-Sum-Exp) calculation and the second term is an arithmetic mean. However, in calculation $M({\mathbf{q}}_i,\mathbf{K})$, it is still necessary to calculate the dot product of each ${\mathbf{q}}_i$ for all ${\mathbf{k}}_j$, whose computation complexity is $O\left(L^2\right)$, and the LSE calculation suffers from numerical instability, so the approximation calculation method of the sparsity measure as shown in Equation (10) is used, and $\widehat{M}({\mathbf{q}}_i,\mathbf{K})⩾M({\mathbf{q}}_i,\mathbf{K})$ is proved in the [29].

$$\begin{array}{c}\widehat{M}({\mathbf{q}}_i,\mathbf{K})=\underset{j}{max}\left\{\frac{{\mathbf{q}}_i{\mathbf{k}}_j^T}{\sqrt{d}}\right\}-\frac{1}{L}{\displaystyle \sum _{j=1}^L}\frac{{\mathbf{q}}_i{\mathbf{k}}_j^T}{\sqrt{d}}\end{array}.$$

(10)

With the above equations, the original LSE operation is replaced by the maximum operation, which makes the value more stable. In the calculation of the $\widehat{M}({\mathbf{q}}_i,\mathbf{K})$, there are only sample dot-product pairs with $U=L\ln L$, other pairs filling with zero.

The final $Probsparse$ self-attention is calculated as shown in Equation (11).

$$\begin{array}{c}A(\mathbf{Q},\mathbf{K},\mathbf{V})=softmax\left(\frac{\widehat{\mathbf{Q}}{\mathbf{K}}^T}{\sqrt{d}}\right)\mathbf{V}\end{array}.$$

(11)

where $\widehat{\mathbf{Q}}\in {\mathbb{R}}^{u\times d}$ is a sparse matrix and it only contains the Top-u $\mathbf{q}$ under the sparsity measurement $\widehat{M}(\mathbf{q},\mathbf{K})$, $u=c\ln L$, c is the sampling coefficient. In summary, $Probsparse$ self-attention requires only the calculation of the dot product of some $\mathbf{q}$ to $\mathbf{K}$, where the number of $\mathbf{q}$ is u, and its computational complexity is $O\left(L\ln L\right)$. Traditional self-attention requires computing the dot product of each $\mathbf{q}$ to $\mathbf{K}$, and its computational complexity is $O\left(L^2\right)$. So $Probsparse$ self-attention can significantly reduce the computational amount.

2.3. Loss Function

This network is mainly used to accurately predict the hopping frequency in the one-time slot, and this problem can be regarded as a multi-classification problem. In this paper, the received frequency hopping signal in one hopping time slot is first transformed into a time-frequency spectrogram X and then fed into the network whose mapping function is denoted by $\Lambda (:\Omega )$, where $\Omega$ is the parameters of the network model, and then the network output is fed into a classifier with N classes. And finally, the hopping frequency in the one-time slot is estimated, and the cross entropy is chosen as the loss function as follows:

$$\begin{array}{c}\begin{array}{c}{\mathbf{p}}_i=\Lambda (X:\Omega )\hfill \\ \xi =-\frac{1}{B}{\displaystyle \sum _{i=1}^B}{\displaystyle \sum _{n=1}^N}{a}_{in}log\left(p_{in}\right)\hfill \end{array}\end{array}.$$

(12)

where ${\mathbf{p}}_i=[p_{i1},p_{i2},\dots ,p_{iN}]$ is the output probability of the i-th sample on the classifier; B is the number of samples per training batch; N is the number of categories; $p_{in}$ is the output probability of the i-th sample in class n on the classifier; $a_{in}$ is the n-th label corresponding to the i-th sample. And One-hot is used to encode the sample labels.

3. Algorithm Simulation and Performance Analysis

3.1. Data Set Generation and Hyperparameter Setting

The set of frequency hopping frequencies is used for training the network, the frequency set is in (10 MHz, 20 MHz) with 25 KHz interval, the number of frequencies sets is 400, and the hopping frequency is selected randomly when generating samples, and the hopping speed is 2000 hop/s. The training data set contains two kinds of hopping signals’ time-frequency spectrograms. The one kind is the hopping signals under Gaussian white noise background with SNR (Signal-Noise Ratio) ranging from −10 dB to 10 dB at 2 dB intervals, generating a total of 13,200 sets of signals. The other kind is the frequency hopping signals under four different interferences, which are multi-tone interference, single-band interference, multi-band interference, and swept frequency interference with SIR (Signal-Interference Ratio) ranging from −10 dB to 10 dB at 2 dB intervals, and 1200 sets of hopping signals are generated in each SIR, resulting in a total of 52,800 sets of signals. A signal is processed by STFT with a window length of 1024 points and is corresponding to a hopping frequency. A training dataset containing 66,000 samples of time-frequency spectrograms is obtained.

The test data set contains the hopping signals under different interference and Rayleigh fading channels. The interference of the above four interfering signals superimposed is called mixed interference signals. SIR ranges from −16 dB to 2 dB at 2 dB intervals, and 500 sets of hopping signals under each of five kinds of interferences are generated in each SIR, resulting in a total of 25,000 sets of signals. Frequency hopping signals under frequency flat Rayleigh fading channels and frequency selective Rayleigh fading channels are generated with SNR ranging from −16 dB to 2 dB at 2 dB intervals, and the number of signal sets per SNR is 500. So the total sample size of time-frequency spectrograms of the test data set is 35,000.

MATLAB software was used to generate the training and test datasets. The experimental environment and configuration are shown in

Table 2. Experimental environment and configuration.

Experimental Environment	Environment Configuration
Operating System	Win 10
CPU	Intel Core i5-12400F
GPU	NVIDIA RTX3060
Memory	16 GB
Programming Languages	Python 3.9
Deep Learning Framework	PyTorch 1.12

.

To ensure the network training effect while speeding up the training speed, let the initial learning rate be 0.001 and the total of rounds be $\lambda =6$. After each round of learning, the learning rate decreases by $0.1^{\lambda }$. Adam is chosen for the optimizer and the training batch size is 64.

3.2. Estimation Performance of Hopping Frequency

The accuracy of the CVDP network’s hopping frequency estimation in the one-time slot determines its performance.

3.2.1. Experiment 1

Estimation of hopping frequency in the one-time slot by CVDP network under multiple interference environments. To analyze the role of each module, four comparison networks are built based on the network model in this paper (as shown in Figure 2). CNN network only retains the CNN module of CVDP, and the global pooling layer and the fully connected layer are added later. CNN-VIT0 network is that the dual multi-head $Probsparse$ self-attention mechanism of CVDP is replaced by the original self-attention mechanism. CNN-VIT1 network is that the dual multi-head $Probsparse$ self-attention mechanism of CVDP is replaced by the dual multi-head self-attention mechanism. CNN-VIT2 network is that the dual multi-head $Probsparse$ self-attention mechanism of CVDP is replaced by the single multi-head $Probsparse$ self-attention mechanism. The above four networks, the CNN-GRU network [25], and the CVDP network of this paper were trained under the same training set with the same hyperparameter settings. Under five interference environments including multi-tone interference, single-band interference, multi-band interference, swept frequency interference, and mixed interference, the generalization ability of the six networks for hopping frequency estimation in the one-time slot is tested respectively. To further investigate the optimal setting for parameter h, the performance of CVDP networks with different values of h was tested under mixed interference environments. To more audiovisual demonstrate the difference between the interfering signals and the frequency hopping signals, Figure 3 shows the time-frequency spectrograms in 20-time slots under five interfering environments. The accuracy of hopping frequency estimation is shown in Figure 4 when time-frequency spectrograms in the one-time slot are input to the network.

As seen in Figure 4, the four improved VIT networks (CNN-VIT0, CNN-VIT1, CNN-VIT2, and CVDP) have better network performance than CNN networks and CNN-GRU networks, this is because after combining the inductive bias characteristics of CNN networks and the global inductive modeling capability of VIT networks, the VIT networks demonstrate approximately 15 to 20% improvement in convergence, stability, and robustness on small datasets. Moreover, the self-attention mechanism of the VIT network makes the network focus on the frequency hopping signals region and minimizes the influence of interfering signals. The CNN network and CNN-GRU network cause serious performance degradation because they do not accurately extract the differences between frequency hopping signals and interfering signals in terms of time-frequency characteristics. Among the four improved VIT networks, the CNN-VIT1 network and the CVDP network have better performance, this is because the CNN-VIT1 and CVDP, through a dual multi-head self-attention mechanism, can better extract the positional features of frequency hopping signals in the entire spectrum, capturing global dependencies. The CNN-GRU network is suitable for extracting joint features of multiple time slots, but they are not included in the one-time slot. So its performance deteriorates due to the inability to extract joint features. Therefore, CNN-VIT1 and CVDP networks are more suitable for solving the task of a one-time slot frequency hopping frequency estimation. In addition, the accuracy of the hopping frequency estimation of the CVDP network is only slightly lower than that of the CNN-VIT1 network, indicating that the $Probsparse$ self-attention mechanism can achieve the purpose of reducing the computation while not affecting the network performance. Furthermore, it was found that the h should not be too large or too small. Therefore, in the case of a total dimension of 256, the h of one multi-head self-attention layer is set to 8 heads, while the h of the other multi-head self-attention layer is set to 16 heads, as this combination achieves the best performance.

3.2.2. Experiment 2

Estimation performance of hopping frequency in the one-time slot by CVDP network under the influence of fading channels. The propagation of signals can be influenced by various factors such as terrain and obstacles, which may lead to multipath fading in the received signals. Additionally, the relative motion between the transmitter and receiver can cause a Doppler shift, as demonstrated in Equation (13)

$$\Delta f=\frac{fvcos\theta }{v_c}.$$

(13)

where f is the frequency of the hopping signals, v is the relative speed between the transmitter and receiver, $\theta$ represents the angle between the direction of hopping signals motion and the incident direction, and $v_c$ is the speed of light.

The network’s ability to generalize over both frequency flat and frequency selective Rayleigh fading channels was tested due to the potential for severe signal distortion caused by various factors. The maximum Doppler shift was set to 10 Hz, and for frequency-selective Rayleigh fading, three paths were used with path delays of 0 s, 1.5 µs, and 90 µs, respectively, and the average path gains were 0 dB, −3 dB, and −6 dB. The accuracy of hopping frequency estimation in the one-time slot was measured in Figure 5, and the average running time required for training and testing the six networks was shown in Figure 6 and Figure 7 to comprehensively evaluate the network performance.

From Figure 5, it can be seen that the CVDP and CNN-VIT1 networks exhibit superior accuracy compared to other networks in frequency-flat Rayleigh fading channels, indicating excellent generalization capabilities. However, the network’s performance generally degrades in frequency-selective Rayleigh fading channels due to inter-symbol interference and signal fading. Despite this, the CVDP and CNN-VIT1 networks still exhibit the highest accuracy, and the performance gain is more significant than that observed in flat fading channels. Moreover, the CVDP network maintains a similar level of accuracy as the CNN-VIT1 network but requires less computational amount, leading to the best overall performance under both fading channels.

The running speed of the CVDP network, as shown in Figure 6 and Figure 7, is faster than that of the CNN-VIT1 network which utilizes only a dual multi-head self-attention mechanism. Additionally, the running time of the CVDP network is near to that of the CNN-VIT0 network. These results indicate that the incorporation of $Probsparse$ self-attention reduces computation complexity. CNN networks and CNN-GRU networks have simple structures and consequently exhibit the shortest running times.

In summary, the CVDP network in this paper has superior estimation accuracy and a shorter running time compared to other comparison networks.

3.3. Performance of Frequency Hopping Intelligent Reception

The CVDP network is applied to the frequency hopping reception system shown in Figure 1 to realize the intelligent reception when the frequency hopping sequence is unknown. A 100,000-bit (0,1) sequence is sent randomly to test the reception performance of the frequency hopping system separately under BPSK (Binary Phase-Shift Keying) modulation and QPSK (Quadrature Phase Shift Keying) modulation. The experiment was conducted in seven environments, namely multi-tone interference environment, single-band interference environment, multi-band interference environment, swept frequency interference environment, mixed interference environment, frequency flat Rayleigh fading channel, and frequency selective Rayleigh fading channel. The BER curves of the CVDP-based frequency hopping intelligent receiver system and the conventional receiver system are shown in Figure 8 and Figure 9.

Conventional reception refers to an ideal reception scenario in which a receiver is aware of the frequency hopping sequence transmitted from the transmitter. It can be seen from Figure 8 and Figure 9 that the intelligent reception system performs well under both BPSK modulation and QPSK modulation. The intelligent reception system exhibits remarkable reception performance in five different interference environments, and its BER is only slightly different from that of the conventional reception system when the SIR is low. Despite severe signal distortion caused by multipath fading and Doppler shift in two fading channel environments, the CVDP network ensures accurate hopping frequency estimation and enables the intelligent receiver system to attain the performance of a conventional receiver system.

When the transmitter of a frequency hopping system makes intelligent decisions according to an electromagnetic interference environment, the hopping sequence is no longer fixed [2]. Consequently, a conventional receiver is unable to predict the hopping sequence, and its BER may increase up to 50% or more, resulting in communication un normally. However, an intelligent reception system based on CVDP for hopping signals can achieve optimal reception performance when the hopping period and signal bandwidth are known, and it has better adaptability and interference immunity.

4. Conclusions

To solve the situation that the frequency hopping sequence of the receiver is unknown due to the intelligent decision of the transmitter of the frequency hopping system, a CVDP network by combining the CNN network and improved VIT network has been designed. It is used for the hopping frequency estimation of the frequency hopping receiver system to realize the intelligent reception of the frequency hopping system. The simulation results show that the comprehensive performance of the CVDP network designed is better than other comparative networks and has better adaptability to the interference environment. And the performance of the CVDP-based frequency hopping intelligent reception system is almost the same as that of the conventional reception system, even when the hopping sequence is unknown.