A GAN-Based Method for Cognitive Covert Communication UAV Jamming-Assistance Under Fully Labeled Sample Conditions

Abstract

This paper addresses the optimization problem for mobile jamming assistance schemes in cognitive covert communication (CR-CC), where cognitive users adopt the underlying mode for spectrum access, while an unmanned aerial vehicle (UAV) transmits the same-frequency noise signals to interfere with eavesdroppers. Leveraging the inherent dynamic game-theoretic characteristics of covert communication (CC) systems, we propose a novel covert communication optimization algorithm based on generative adversarial networks (GAN-CCs) to achieve system-wide optimization under the constraint of maximum detection error probability. In GAN-CC, the generator simulates legitimate users to generate UAV interference assistance schemes, while the discriminator simulates the optimal signal detection of eavesdroppers. Through the alternating iterative optimization of these two components, the dynamic game process in CC is simulated, ultimately achieving the Nash equilibrium. The numerical results show that, compared with the commonly used multi-objective optimization algorithm or nonlinear programming algorithm at present, this algorithm exhibits faster and more stable convergence, enabling the derivation of optimal mobile interference assistance schemes for cognitive CC systems.

1. Introduction

The scarcity and underutilization of spectrum resources have driven the emergence of cognitive radio (CR) technology [1]. However, with the development of technology, its transmission security faces the same threats and challenges. Current encryption methods and physical layer security technologies have problems that make it difficult to meet current electromagnetic security needs [2,3,4,5,6]. Consequently, CC—a low-detection, low-interception secure communication paradigm—has garnered substantial attention [7].

The theoretical evolution of CC spans three key stages, as follows: Lee et al. propose that CC means the user’s communication is not perceived by any users other than the communication object [8]. Shahzad et al. believe that the eavesdropper’s detection probability of the user’s communication satisfies the given concealment constraints, namely CC [9]. Bash et al. define CC as low-detection/low-interception communications for information security, aiming both to protect data security and to ensure that the communication behavior is not detected [10]. Based on the above concepts, this paper further defines CR-CC as a secure communication method that achieves low detection and low interception by concealing communication elements such as transmission information, transmission mechanism, transmission channel, and transmission protocol.

Based on the theoretical basis, Bash et al. studied the CC over additive white Gaussian noise (AWGN) channels and defined the fundamental boundary of CC as the root mean square criterion [11]. He et al. further studied the fundamental bounds of CC networks with noise uncertainty (CNU) and verified that the maximum achievable rate of CC is positive [12]. Che et al. and Wang et al. studied CC over binary symmetric channels (BSC) and discrete memoryless channels (DMCs), respectively, and further verified the bounds of the root-mean-square criterion [13,14].

However, at the same time, for the complex CR system, approximate optimization and linear regression optimization methods are difficult to handle with such a problem. Intelligent CR-CC refers to the application of deep learning (DL) techniques to conventional CR networks to achieve CC, using its unique training mechanism and model construction method to overcome many difficulties and shortcomings of conventional CC.

Deep learning techniques have achieved certain application results in the field of radio communication (RC), such as physical layer authentication security [15,16,17], radio frequency (RF) fingerprinting of wireless devices [18,19], and detection of user simulation attacks [20,21]. In particular, deep learning technology integrated with game theory has developed and been applied rapidly in the field of CC, and has achieved certain research results in aspects such as dataset support [22], CC parameter analysis [23], and efficiency [24]. GAN can analyze sample features and extract label information based on limited data to train the optimal generator. Its “adversarial” method is similar to the dynamic game between users and eavesdroppers in CC systems. This method has broad development and application prospects in the field of CC.

The main contributions of this paper are as follows:

• Modeling and analysis of a UAV-assisted CR-CC system with multi-objective optimization.
• Formulation of CC dynamics as a GAN-based adversarial game.
• Proposal of the GAN-CC algorithm, including network design and training procedures.
• Comprehensive performance validation through simulations.

Essentially, this paper is organized as follows: Section 2 establishes the model of the UAV mobile interference-assisted CC system, analyzes the relevant parameters, and derives the multi-objective optimization system equation. Section 3 introduces the GAN-CC UAV interference-assistance optimization algorithm, presents the algorithm framework and network structure, and formulates the algorithm training process. Section 4 conducts the verification of the algorithm simulation results and the discussion of parameters. Section 5 summarizes and presents the future prospects of this research.

2. Materials and Methods

This section first establishes the UAV mobile interference-assisted CC system model, quantifies the behaviors of each user within the CC system, analyzes the relevant parameters, and finally derives the multi-objective optimization system equation for subsequent research.

2.1. System Model

Figure 1 illustrates a CR network CC system consisting of the following communication nodes: the primary user transmitter and receiver (PT, PR), the authorized cognitive user transmitter and receiver (AT, AR), and the auxiliary jammer UAV and eavesdropper, Eve. Among them, the cognitive user’s communication uses an underlay approach for co-channel access, while the UAV assists the CR user’s CC by emitting noise to interfere with the eavesdropper.

According to the problem setting, UAV is able to obtain the location information of PT, PR, AT, and AR, but considering Eve’s passive reception mode and secret eavesdropping characteristics, its accurate location information cannot be obtained, so it is assumed that Eve is located in the reference plane and the UAV’s position error parameter for Eve is expressed as a Gaussian distribution with variance of ${\epsilon }_{E\mathrm{ve}}^2$.

Each communication node in the system is assumed to transmit with a single antenna, and the effects of antenna polarization are not considered. In the underlay mode CC, each legal user communication and UAV noise are transmitting on the same frequency, that is, there will be mutual interference of signals. In addition to the antenna propagation gain, it is also necessary to consider the path propagation loss problem in communication. The wireless electromagnetic wave enters the receiver after propagating through multiple non-visible paths, and its signal strength obeys the Rayleigh distribution [25]. Thus, the transmission gain of each communication link channel is expressed based on Rayleigh fading, and the channel gain corresponding to the $\left(n\in \left\{\mathrm{1,2},\dots ,N\right\}\right)$ time slot is expressed as follows:

$$h_{a,b}(n)=A_d(\frac{c}{4\pi f_c{d}_{a,b}\left(n\right)}{)}^{d_e}{\alpha }_e^{a,b},a,b\in \{\mathit{PT},\mathit{PR},\mathit{AT},\mathit{AR},\mathit{UAV},\mathit{Eve}\}$$

(1)

Among them, $A_d$ represents antenna gain, $f_c$ represents carrier frequency, $d_{a,b}(n)=\sqrt{(x_{a-n}-x_{b-n}{)}^2+(y_{a-n}-y_{b-n}{)}^2+(z_{a-n}-z_{b-n}{)}^2}$ represents the space distance of the node $a,b$ in the system with the n time slot, $d_e$ represents the path decay index, $c=3\times 10^8 \mathrm{m}/\mathrm{s}$, and ${\alpha }_e^{a,b}$ represents the fading parameter and obeys the Rayleigh distribution [26].

It is worth noting that in the CC system, the parameters ${\alpha }_e^{PT,PR}$, ${\alpha }_e^{PT,AR}$, ${\alpha }_e^{AT,PR}$, ${\alpha }_e^{AT,AR}$, ${\alpha }_e^{UAV,PR}$, and ${\alpha }_e^{UAV,AR}$ obey the frequency-free-selectivity standard Rayleigh fading with mean 0 and variance 1, while the parameter distribution patterns of ${\alpha }_e^{UAV,Eve}$ and ${\alpha }_e^{AT,Eve}$ are related to the actual sample data. Similarly, the UAV can obtain $PR$, $AR$ noise variance, while the parameters of noise variance at Eve are also related to the sample data.

Therefore, the respective co-channel signals received by the $i(i\in \{\mathrm{1,2},\dots ,M\left\}\right)$ channel of the AR node at the $n(n\in \{\mathrm{1,2},\dots ,N\left\}\right)$ time slot can be expressed as follows:

$$r_i^{AR}\left(n\right)=\sqrt{P_{AT}}{h}_{AT,AR}{s}_i^{AT}\left(n\right)+\sqrt{P_{PT}}{h}_{PT,AR}{s}_i^{PT}\left(n\right)+\sqrt{P_{UAV}\left(n\right)}{h}_{UAV,AR}\left(n\right)s_i^{UAV}\left(n\right)+n_i^{AR}\left(n\right)$$

(2)

Among them, $P_{AT}$ and $P_{PT}$ represent the signal transmit power of AT and PT nodes, and their values remain constant in the system duration T. $P_{UAV}\left(n\right)$ represent the signal transmit power of the UAV with artificial noise in the $n\mathrm{th}$s lot, $s_i^{AT}\left(n\right)$, $s_i^{PT}\left(n\right)$ and $s_i^{UAV}\left(n\right)$ correspond to the signals of AT, PT, and UAV in the $n\mathrm{th}$ slot, respectively. In order to be close to the actual non-ideal situation, we introduce $n_i^{AR}\left(n\right)$ as the additive white Gaussian noise (AWGN) parameter of AR nodes [27].

2.2. Communication Parameter Analysis

In the underlay CC, the cognitive user follows the principle that it cannot affect the normal communication of the primary user; the transmission rate of the $i\mathrm{th}$ channel at the $n\mathrm{th}$ slot of the PR needs to satisfy the following conditions:

$$R^{PR}\left(n\right)={\displaystyle \frac{1}{P}}\sum _{i=1}^P{R}_i^{PR}\left(n\right)={\mathit{log}}_2(1+{\displaystyle \frac{P_{PT}{\left|h_{PT, PR}\right|}^2}{P_{AT}{\left|h_{AT, PR}\right|}^2+P_{UAV}\left(n\right){\left|h_{UAV, PR}\left(n\right)\right|}^2+{\sigma }_{PR}^2}})\ge R_{min}^{PR}$$

(3)

where $R_{min}^{PR}$ is the minimum transmission rate constraint of the primary user, and ${\sigma }_{PR}^2$ is the variance of the AWGN at the PR node. Based on this, the CC rate of the AR in the $n\mathrm{th}$ time slot can be expressed as follows:

$$R^{AR, C}\left(n\right)={\displaystyle \frac{1}{M}}\sum _{i=1}^M{R}_i^{AR, C}\left(n\right)={\mathit{log}}_2(1+{\displaystyle \frac{P_{AT}{\left|h_{AT, AR}\right|}^2}{P_{PT}{\left|h_{PT, AR}\right|}^2+P_{UAV}\left(n\right){\left|h_{UAV, AR}\left(n\right)\right|}^2+{\sigma }_{AR}^2}})$$

(4)

And Eve determines the communication behavior by detecting whether information is transmitted between AT and AR, corresponding to the existence of CC. The received signal of Eve’s first channel at the $n\mathrm{th}$ time slot is as follows:

$$r_i^{Eve}\left(n\right)=\left\{\begin{array}{c}\sqrt{P_{UAV}\left(n\right)}{h}_{\mathit{UAV},Eve}\left(n\right)s_i^{\mathit{UAV}}\left(n\right)+\sqrt{P_{AT}}{h}_{AT,Eve}\left(n\right)s_i^{AT}\left(n\right)+n_i^{Eve}\left(n\right), H_1\\ \sqrt{P_{UAV}\left(n\right)}{h}_{\mathit{UAV},Eve}\left(n\right)s_i^{\mathit{UAV}}\left(n\right)+n_i^{Eve}\left(n\right), H_0\end{array}\right.$$

(5)

where $H_1$ and $H_0$ correspond to whether the cognitive user performs CC or not, and $n_i^{Eve}\left(n\right)$ denotes Eve’s AWGN with a variance of ${\sigma }_{Eve}^2$.

Eve determines the received signal by setting the detection threshold value $\tau$. The detection error probability in the $n\mathrm{th}$ slot is as follows:

$$\rho \left(n\right)=p\left(H_0\right)p\left(D_1|H_0\right)\left(n\right)+p\left(H_1\right)p\left(D_0\right|H_1\left)\right(n)$$

(6)

where $p\left(D_1\right|H_0\left)\right(n)$ and $p\left(D_0\right|H_1\left)\right(n)$ denote the probabilities of error-triggering and missed detection of Eve at the $n\mathrm{th}$ slot, and $p\left(H_1\right)$ and $p\left(H_0\right)$ denote the probability of whether the AT actually performs CC, $p\left(H_1\right)+p\left(H_0\right)=1$.

2.3. System Equation Derivation

According to the system model, the problem under study is essentially a comprehensive optimization of the UAV flight trajectory and transmission power to maximize the user CC rate and Eve’s detection error probability, aiming to achieve optimal system efficiency while preserving information security.

Based on the above derivation, we describe such a multi-objective non-convex optimization problem for a UAV interference-assisted CR-CC system as follows:

$$\begin{gathered} \left(p1\right)\begin{array}{c}max\\ \left(x_{\mathit{UAV}-n},y_{\mathit{UAV}-n},z_{\mathit{UAV}-n},P_{\mathit{UAV}}\left(n\right)\right)\end{array}{R}^{AR,C}\left(n\right) \\ \left(p2\right)\begin{array}{c}max\\ \left(x_{\mathit{UAV}-n},y_{\mathit{UAV}-n},z_{\mathit{UAV}-n},P_{\mathit{UAV}}\left(n\right)\right)\end{array}\rho (n) \end{gathered}$$

(7)

Subject to

$$0\le P_{UAV}\left(n\right)\le P_{UAV}^{max},n\in (\mathrm{1,2},\dots ,N)$$

(8)

$$R_{pr}\ge R_{pr}^{min}$$

(9)

$$V_{UAV}\le V_{max}·\delta ,n\in (\mathrm{1,2},\dots ,N-1)$$

(10)

To solve this problem, the current research adopts the approximate convex optimization (ACO) method and the block coordinate descent (BCD) method. However, these methods often need to reduce the dimension of system problems by simplifying the system problems through idealized hypotheses or by fixing one of the problems, which has many problems. Therefore, this paper proposes a GAN-based optimization algorithm for UAV interference-assisted schemes, i.e., the GAN-CC algorithm, using a deep learning approach.

3. Algorithm Design

In this section, the optimization process is transformed into a dynamic game problem between the UAV and Eve based on the system model, and the GAN-CC UAV interference-assistance optimization algorithm is proposed. In particular, we first introduce the algorithm framework and the network structure, and then develop the training process of the network model.

3.1. Principles of Counter CC

According to the analysis of the system model and optimization process in Part 2, the objectives of the optimization problem correspond to the metrics of the UAV jamming-assistance CR-CC system model, respectively.

Figure 2 shows the framework of the GAN-CC algorithm, which mainly consists of two subnetworks, namely, the generator and discriminator. The generator $w_g$ simulates the CC of legitimate users, and the discriminator $w_d$ simulates Eve’s eavesdropping behavior. Environment parameters include electromagnetic environment, communication state, and parameters of each node in the communication system. According to the system model, the environmental state parameters obtained by the generator include $h_{PT,PR}\left(n\right)$, $h_{AT,PR}\left(n\right)$, $h_{UAV,PR}\left(n\right)$, $h_{PT,AR}\left(n\right)$, $h_{AT,AR}\left(n\right)$, $h_{UAV,AR}\left(n\right)$, ${\sigma }_{PR}^2$, ${\sigma }_{PR}^2$, and ${\sigma }_{Eve}^2$. Meanwhile, the constraints in $w_g$ include the minimum communication rate constraint of the main user, $R_{min}^{PR}$, the maximum flight speed constraint of the UAV, $V_{max}$, and the maximum noise emission power constraint, $P_{UAV}^{max}$, while the condition in the discriminator is the initial detection threshold value, ${\tau }_0$.

According to the dynamic game process of CC, the training expectation of the $w_g$ is to generate the best interference assistance scheme $\left\{G_T,G_P\right\}$ based on the existing environment state parameters and the Eve threshold $\tau$, while the training expectation of $w_d$ is to optimize the detection threshold based on the communication parameters and UAV results to achieve the best signal detection scheme. Therefore, the GAN-CC algorithm is essentially designed to design an optimal generator to achieve the maximum CC rate, while the discriminator cannot detect it correctly. The antagonistic process of the network is described as follows:

$$\begin{gathered} \left(p3.1\right)\begin{array}{c}V(G,D)\\ max-D\end{array}=E_{H_0~P_{data}}\left[\mathit{lg}\left(D\left(H_0\right)\right)\right]+E_{z~P_z}\left[\mathit{lg}\left(1-D\left(G\left(z\right)\right)\right)\right] \\ \left(p3.2\right)\begin{array}{c}V(G,D)\\ min-G\end{array}=E_{H_0~P_{data}}\left[lg\left(D\right(H_0\left)\right)\right]+E_{z~P_z}\left[lg(1-D(G\left(z\right)\left)\right)\right] \end{gathered}$$

(11)

where $H_0$ represents the UAV scheme without CC, subject to the sample data distribution $p_{data}$; z is the environmental state parameter, subject to a prior probability distribution $p_z$; $D\left(G\right(z\left)\right)$ and $D\left(H_0\right)$ represent the output of $w_d$ at inputs $G\left(z\right)$ and $H_0$, respectively, corresponding to the discriminator’s analog signal detection under the condition that $w_g$ generates the scheme, whether CC is taking place or not.

Thus, the goal of $w_d$ is to make $D\left(H_0\right)$ as close to 1 as possible and $D\left(G\right(z\left)\right)$ close to 0, that is, to maximize $\mathit{lg}(D\left(H_0\right))$ and $\mathit{lg}(1-D\left(G\right(z\left)\right))$, thus allowing Eve to avoid error detection. The goal of $w_g$ is to generate the best solution, even if the value of $D\left(G\right(z\left)\right)$ is as close to 1 as possible, and to minimize $\mathit{lg}(1-D\left(G\right(z\left)\right))$, so that Eve detects errors. The above dynamic game objectives correspond to Equation (11), respectively.

3.2. Introduction of Full-Label Sample Condition

Due to the complex parameters of the CR-CC system, this paper focuses on solving the adversarial CC problem while preventing the GAN from generating “fake data” or the optimization process from being affected by other non-critical factors. This paper introduces some reasonable assumptions, mainly analyzing the CC problem under the full-label sample condition. The full-label sample condition assumes that the transmitting power and channel state information (CSI) of the legitimate user are known, the channel distribution information (CDI) of Eve is known, and the detection threshold is unknown.

3.3. Design of Discriminator and Generator Network Structure

Figure 3a shows the network structure of D, which is composed of three layers of the neural network. The neurons in the input layer are $P_{AT}^0$, $P_{AT}^1$, $P_{UAV}$, which, respectively, represent the transmitted power of cognitive users in the absence of CC, the CC-transmitted power of cognitive users, and the transmitted power of the UAV received by Eve. According to the Kolmogorov theorem, the number of neurons d in the hidden layer of the discriminator is set as 7 [28]. According to the system equations $(p1, p2)$ and the game process $\left(p3.1\right)$, the discriminator training process is essential to optimize $\tau$ and achieve the optimal signal detection probability, that is, the output layer neuron is Eve’s signal detection parameter.

To facilitate the quantification of the results, the output neurons are approximated as multivariate classifiers, so the SoftMax function is chosen for the activation function [29], while the weight optimization process of the implicit layer needs to fit the data, so the ReLU function is chosen [30].

Figure 3b shows the network structure of G, which is composed of three layers of neural networks. The input layer neuron parameters are $h_{PT,PR}\left(n\right)$, $h_{AT,PR}\left(n\right)$, $h_{UAV,PR}\left(n\right)$, $h_{PT,AR}\left(n\right)$, $h_{AT,AR}\left(n\right)$, $h_{UAV,AR}\left(n\right)$, ${\sigma }_{AR}^2$, ${\sigma }_{PR}^2$, and ${\sigma }_{Eve}^2$. The number of neurons in the hidden layer $g$ is set to 19. According to the system equations $(p1, p2)$ and the game process $\left(p3.2\right)$, the goal of the generator is to maximize the CC rate, that is, to generate the optimal UAV flight path and transmission power scheme. The output layer neurons of the generator correspond to $G1$ and $G2$.

The ReLU function is selected for the implicit layer in line with D to enhance the accuracy of the weight update and improve the fit to the data, while the activation function of each neuron in the output layer is selected as the ReLU for the convenience of outputting a non-approximate UAV scheme.

3.4. GAN-CC Network Model Training

Algorithm 1 describes the algorithm training process. The overall idea of the GAN-CC algorithm training is based on pre-training, alternating iterative training of G and D. The iterative optimization process is controlled by the changes in the corresponding loss functions of G and D to achieve the Nash Equilibrium of the system. The final result of G is the best CC scheme that can cope with all possible eavesdropping behaviors. The weights are updated using gradient descent training, and according to the game equations ($p3.1,p3.2$), the loss functions for constructing the discriminator and generator, respectively, are constructed as follows:

$$L_D={\mathit{\nabla }}_{{\omega }_d}\left(\mathit{lg}(D\right(x\left)\right)+\mathit{lg}(1-D\left(G\right(z\left)\right)\left)\right)$$

(12)

$$L_G={\mathit{\nabla }}_{{\omega }_g}(\mathit{lg}(1-D(G\left(z\right)\left)\right))$$

(13)

Specifically, taking D as an example, the output of the implied layer is $H_d$, the output of the output layer is $C_d$, and the value of the loss function is $L_d$. The update of the weights from the implied layer to the output layer ${\omega }_d^2$ and the update of the weights from the input layer to the implied layer ${\omega }_d^1$ are:

$${\omega }_d^2={\omega }_d^2+{\lambda }_d^{\prime }{\displaystyle \frac{\partial L_d}{\partial C_d}}{\displaystyle \frac{\partial C_d}{\partial {\omega }_d^2}}$$

(14)

$${\omega }_d^1={\omega }_d^1+{\lambda }_d^{\prime }{\displaystyle \frac{\partial L_d}{\partial C_d}}{\displaystyle \frac{\partial C_d}{\partial H_d}}{\displaystyle \frac{\partial H_d}{\partial {\omega }_d^1}}$$

(15)

where ${\lambda }_d^{\prime }$ denotes the training learning rate of D; ${\lambda }_d^{\prime }$ and ${\lambda }_g^{\prime }$ can be updated according to the loss functions $L_d$ and $L_g$ during the adversarial training, serving as adaptive learning rates [31].

Algorithm 1 Training Procedure of GAN-CC

Initialization 1: Establish a frequency-free, selective, small-scale Rayleigh fading parameter distribution with mean 0 and variance 1, where the path-fading index ${\alpha }_e$ is chosen as 2.8 (${\alpha }_e^{a,b}=\left\{-\mathrm{1.0848,0.9039},-0.8941,-1.2015,-1.4296,-1.9746,-\mathrm{1.2852,0.0611,0.0076,0.1774}\right\}$) [32,33]; establish a Gaussian AWGN parameter distribution with mean 0 and variance 3 to simulate a real communication scenario ($AWGN=\{-0.6354,-\mathrm{2.1392,1.2825},-\mathrm{1.2110,3.1169},-\mathrm{3.2806,0.8905,2.8324,0.5696,4.4047}\}$) [34]; initialize the weights ${\omega }_d$ and ${\omega }_g$ of each layer of the discriminator and generator using Gaussian-distributed random data with mean 0 and a variance of ${\displaystyle \frac{2}{S_l}}$, where $S_l$ denotes the number of neurons in the layer $l$ of the neural network [35]. Pre-processing 2: Use sample data to pre-train D and G (numpy.random.normal (loc = 0.0, scale = 1.0, size = 10)). 3: While the loss function has not converged or the training number is less than the maximum iterations, do 4:  When the system reaches Nash equilibrium, end the model training, and obtain the best output solution based on the sample data. 5:  For k steps, do 6:   According to Equation (12), calculate the loss function of D and iteratively train it, updating the neural network weights along the direction of the rising gradient of the loss function. 7:  End for 8:  According to Equation (13), calculate the loss function of G and iteratively train it, updating the neural network weights along the direction of the gradient decrease of the loss function. 9: End while Output 10: Obtain the optimal CC jamming-assistance scheme.

4. Results and Discussion

In this section, the GAN-CC algorithm’s performance and parameter sensitivity are further evaluated by comparing different learning rate settings, validating numerical simulation results, and discussing parameters.

4.1. Convergence Performance Analysis

Figure 4 shows the effects of fixed and adaptive learning rates on the convergence of the algorithm. It can be seen that during the process of network training, the value of the loss function of D monotonically increases, while the loss function of G monotonically decreases. Finally, they reach a Nash equilibrium, where the value of the loss function tends to be stable, the overall convergence rate is faster, and the results are stable. At the same time, we can see that the convergence rate of the network is faster in the case of the adaptive learning rate, which makes the algorithm perform better in practice.

4.2. Covert Communication Performance Analysis

The CC performance of the GAN-CC algorithm is analyzed through comparative studies with the iterative optimization process of the BCD method. The BCD approach operates by fixing UAV positioning parameters under current configurations and transforming the system problem into a single-objective optimization task for transmission power iteration, aiming to maximize the CC rate. Consequently, its simulation results exhibit discrete distributions with high similarity between consecutive iterations. Comparative simulations reveal that the GAN-CC algorithm demonstrates superior capability in handling complex sample data and non-ideal multi-objective optimization scenarios, effectively mitigating excessive idealization assumptions inherent in conventional methods. Moreover, it maintains robust convergence and stability while achieving comparable or enhanced CC performance relative to traditional approaches, thereby demonstrating superior optimization characteristics.

4.3. Parameter Discussion

According to the changes in the minimum detection error probability, ${\rho }_{\min }$, and the maximum CC rate, $R_{\max }$, of the system under different parameter conditions in

Table 1. ${\rho }_{\min }$, $R_{\max }$ changes.

Parameter Setting	Minimum Detection Error Probability ${\mathit{\rho }}_{\mathit{min}}$	Maximum CC Rate ${\mathit{R}}_{\mathit{max}}$
Training learning rate $\lambda \prime$	(a)	(b)
Primary users’ minimum transmission rate $R_{\mathit{min}}^{\mathit{PR}}$	(c)	(d)
Cognitive users’ transmission power $P_{\mathit{AT}}$	(e)	(f)
UAV channel parameter $h_{\mathit{UAV}–\mathit{PR}}$	(g)	(h)

, it can be seen that ${\rho }_{\min }$ always decreases monotonically with the increase in $P_{\mathrm{AT}}$, which is consistent with the actual situation—the greater the CC transmission power of the cognitive user, the greater the risk of being detected by an eavesdropper. Meanwhile, as shown in Figure (a) in Table 1, $\lambda \prime$ does not change the value of ${\rho }_{\min }$, but only changes the convergence speed of the model; thus, the larger the learning rate is within the preset range, the faster the model converges. And $R_{min}^{PR}$ and $h_{UAV-PR}$ affect the value of ${\rho }_{\min }$. As shown in Figure (c) in Table 1, with the increase in $R_{min}^{PR}$, the system imposes greater constraints on the UAV transmission power in the case of constant CC power, so the concealment performance of communication is affected, and ${\rho }_{\min }$ decreases monotonically. As shown in Figure (g) in Table 1, with the increase in $h_{UAV-PR}$, the signal interference of UAV to the primary user is stronger under the condition of constant noise power, so the constraint is stronger, which affects the CC performance, and ${\rho }_{\min }$ decreases monotonically.

In terms of the maximum CC rate, $R_{\max }$, of the system, it can be seen that $R_{\max }$ always increases monotonically with the increasing $P_{\mathrm{AT}}$. At the same time, it can be seen from Figure (b) in Table 1 that $\lambda \prime$ still only affects the model convergence rate and does not change the value of $R_{\max }$. And $R_{min}^{PR}$ and $h_{UAV-PR}$ have an effect on the value of $R_{\max }$. As shown in Figure (d) in Table 1, with the increase in $R_{min}^{PR}$, the system will generate greater constraints on both $P_{AT}$ and $P_{UAV}\left(n\right)$, resulting in the restriction of the CC rate, and $R_{\max }$ monotonically decreases. As shown in Figure (h) in Table 1, with the increase in $h_{UAV-PR}$, the UAV transmit power will decrease under the condition that $R_{min}^{PR}$ is constant, and more cognitive user power can be released to a certain extent, so $R_{\max }$ monotonically increases. The above two influencing factors have little influence when $P_{\mathrm{AT}}$ is small, and the data gap increases with the increase in $P_{\mathrm{AT}}$; subject to the constraint of the eavesdropping risk, $R_{\max }$ cannot keep increasing, and will tend to a stable value.

5. Conclusions

This study addresses the significant challenge of optimizing mobile jamming-assisted schemes for cognitive CC systems through the novel integration of GANs and game-theoretic principles. By formulating the CC process as a dynamic adversarial game between legitimate users and eavesdroppers, the GAN-CC algorithm can dynamically analyze the process of CC based on the generated datasets of legitimate users and eavesdroppers, jointly optimize the trajectory and transmission power of UAV to maximize the CC rate while minimizing the detection probability of eavesdroppers, thereby improving the efficiency of CC by approximately 60%. The main contributions include the following:

• System modeling: A comprehensive framework for UAV-assisted CR-CC that integrates underlay spectrum access, Rayleigh fading channels, and multi-objective optimization constraints.
• Algorithm design: A GAN-based adversarial training mechanism where the generator synthesizes optimal interference schemes and the discriminator emulates adaptive eavesdropper detection, achieving Nash equilibrium through iterative optimization.
• Performance validation: Numerical simulations demonstrate that GAN-CC outperforms conventional methods (e.g., block coordinate descent) in terms of convergence speed, stability, and CC rate maximization, particularly under non-ideal channel conditions.

The algorithm’s robustness stems from its ability to bypass idealized assumptions inherent in traditional optimization approaches and directly addresses the dynamics of non-convex and high-dimensional systems. Simulation results further reveal that the adaptive learning rate mechanism significantly accelerates convergence, while parameter sensitivity analyses highlight the trade-off between detection error probability (${\rho }_{\min }$) and CC rate ($R_{\max }$) under varying constraints.

These findings underscore the practical applicability of GAN-CC in CC networks, where dynamic interference management and eavesdropper evasion are critical. However, this study is mainly based on the full-label sample condition, introduces some assumptions, and does not consider the energy consumption, endurance of the UAV, or the dynamic and real-time performance of the CC system. Therefore, the parameter update model should be further added to support promotion and application. Future work will explore extensions to multi-UAV cooperative systems and heterogeneous channel environments to further enhance the scalability and adaptability of the framework.