Hidden true show false anti-interception transmission method based on true and false frequency multiplexing

Abstract

The application discloses a true-false frequency multiplexing-based hidden true and false anti-interception transmission method, which is applied to a multi-source cooperative anti-interception transmission system, and the corresponding method comprises the following steps: a plurality of cooperative users send a plurality of frequency bands of real signals and decoy signals; a legal receiver calculates the signal-to-noise ratio of the received real signal; an interceptor calculates the signal-to-noise ratio of the intercepted real signal and the signal-to-noise ratio of the deceived signal; a first target optimization problem is constructed according to the signal-to-noise ratio of the received real signal, the signal-to-noise ratio of the intercepted real signal and the signal-to-noise ratio of the deceived signal; a two-stage alternating double-domain optimization method is used to solve the first target optimization problem, and a group of optimal solutions is obtained; a second target optimization problem about a frequency multiplexing factor is constructed according to the group of optimal solutions, and the Newton method is used to solve the second target optimization problem, and the frequency multiplexing factor is obtained. The application realizes the purpose of maximizing the safety transmission rate of the real signal and deceiving the interceptor.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of information security and communication countermeasure, and particularly relates to a true-false frequency multiplexing-based anti-interception transmission method. BACKGROUND

[0002] In the field of wireless communication, especially in the case where communication signals are easily intercepted by non-cooperative parties, the security of information transmission is of great importance. In military applications, secure communication is crucial for preventing adversaries from intercepting strategic information. In industrial environments, it is essential for protecting sensitive data from espionage. For civilian applications, secure communication ensures the protection of personal data and privacy. With the continuous development of technologies such as Internet of Things (IoT) and smart cities, strong security measures are essential for mitigating potential threats and vulnerabilities in these non-cooperative environments. In the fields of military and industrial protection, addressing passive threats such as interception and eavesdropping, and conducting research on secure transmission in the context of electronic reconnaissance and electromagnetic countermeasure scenarios, are major challenges, and are also areas that academic research urgently needs to break through.

[0003] Existing secure transmission technologies mainly focus on physical layer security and covert communication. Physical layer security methods mainly focus on improving the secrecy capacity through signal processing methods to ensure information security. Covert communication methods focus on the concealment of communication behavior, i.e., communication signals are difficult to detect, and most research is considered from a single perspective. Both physical layer security methods and covert communication methods belong to passive defense security strategies.

[0004] There are three main methods for physical layer security: beamforming, relay selection, and artificial noise. In the article B. Lyu, C. Zhou, S. Gong, D. T. Hoang, and Y.-C. Liang, “Robust secure transmission for active rls enabled symbiotic radio multicast communications,” IEEE Trans. Wireless Commun., vol. 22, no. 12, pp. 8766-8780, 2023. and the article Z. Yin, N. Cheng, Y. Hui, W. Wang, L. Zhao, K. Aldubaikhy, and A. Alqasir, “Multi-domain resource multiplexing based secure transmission for satellite-assisted lot: Ao-sca approach,” IEEE Trans. Wireless Commun., vol. 22, no. 11, pp. 7319-7330, 2023. the asymmetric characteristics of channel state information are used to achieve secure transmission through beamforming and relay selection. In addition, there is the artificial noise method, which actively transmits artificial noise in the null space of the main channel to reduce the signal reception quality of the eavesdropper. In the article J. Marin, M. Bernhardt, and T. Riihonen, “Full-duplex constant-envelope jamceiver and self-interference suppression by highpass filter: Experimental validation for wi-fi security,” IEEE J. Sel. Areas Commun., vol. 41, no. 9, pp. 2937-2950, 2023. the University of Tampere designed a full-duplex jamming transceiver that transmits a frequency-modulated continuous wave (FMCW) signal commonly found in low-cost radar systems to prevent eavesdroppers from being able to receive the same signal while correctly interpreting the wireless local area network (WLAN) signal.

[0005] Unlike traditional physical layer security methods, covert communication techniques focus more on anti-detection capability. Common methods include power control, interference injection, and relay selection. In the article L. Bai, J. Xu, and L. Zhou, “Covert communication for spatially sparse mmwave massive mimo channels,” IEEE Trans. Commun., vol. 71, no. 3, pp. 1615-1630, 2023, the Kullback-Leibler divergence and total variation distance are used as indicators of concealment. By optimizing the transmit power and interference power, low detection probability communication is achieved and the concealment rate under massive multiple-input multiple-output (MIMO) fading channels is analyzed. Relay selection and interference injection methods are also applicable to covert communication. In the article X. Wang, Z. Fei, P. Liu, J. A. Zhang, Q. Wu, and N. Wu, “Sensing aided covert communications: Turning interference into allies,” IEEE Trans. Wireless Commun., pp. 1-1, 2024, a method is proposed to jointly design radar waveforms and communication transmit beamforming vectors based on two channel state information (CSI) models. This effectively turns interference into allies in order to maximize the covert transmission rate while considering the maneuvering height of the enemy target.

[0006] Some studies also consider both the secrecy capability and concealment of signal transmission. In the article M. Forouzesh, F. Samsami Khodadad, P. Azmi, A. Kuhestani, and H. Ahmadi, “Simultaneous secure and covert transmissions against two attacks under practical assumptions,” IEEE Internet Things J., vol. 10, no. 12, pp. 10 160-10 171, 2023, a joint method of time slot selection and interference injection is proposed to maximize the secrecy capability under the constraint of concealment in order to simultaneously cope with non-cooperative data capture and communication detection.

[0007] However, the prior art considers the problem from a single angle: the physical layer security method can ensure high secure transmission capacity, but usually ignores concealment, and focuses on the security of the information layer; The concealment communication scheme emphasizes the anti-detection ability of the communication behavior itself, and provides high concealment, but usually the transmission rate of the signal is limited. And both the physical layer security and the concealment communication scheme belong to the passive defense strategy, without considering the security design of attack and defense integration. SUMMARY

[0008] In order to solve the above problems existing in the prior art, the present application provides a true-false frequency multiplexing-based anti-interception transmission method. The technical problem to be solved by the present application is solved by the following technical scheme:

[0009] The embodiment of the present application provides a true-false frequency multiplexing-based anti-interception transmission method, comprising:

[0010] The method is applied to a multi-source cooperative anti-interception transmission system, the system comprising a plurality of cooperative users, a legitimate receiver and an interceptor; the corresponding method comprising:

[0011] The plurality of cooperative users send a plurality of frequency bands of real signals and decoy signals; wherein the real signals and the decoy signals are mixed and transmitted in the frequency domain by a non-orthogonal frequency division multiplexing scheme in the transmission process;

[0012] The legitimate receiver receives the signals and calculates the signal-to-noise ratio of the received real signals according to the received signals;

[0013] The interceptor intercepts the signals and calculates the signal-to-noise ratio of the intercepted real signals and the signal-to-noise ratio of the decoy signals deceived by the decoy signals according to the intercepted signals;

[0014] According to the signal-to-noise ratio of the real signals received by the legitimate receiver, and the signal-to-noise ratio of the real signals intercepted by the interceptor and the signal-to-noise ratio of the decoy signals deceived by the decoy signals, a first target optimization problem of maximizing the real signal secret rate is constructed, and the received decoy signals of the interceptor are constrained to be stronger than the real signals;

[0015] A double-stage alternating dual-domain optimization method is used to solve the first target optimization problem to obtain a set of optimal solutions;

[0016] According to the set of optimal solutions, a second target optimization problem about a frequency multiplexing factor is constructed, and the Newton method is used to solve the second target optimization problem to obtain the frequency multiplexing factor, so as to realize the mixing process in the frequency domain by the non-orthogonal frequency division multiplexing scheme in the transmission process through the frequency multiplexing factor.

[0017] The present application has the following beneficial effects:

[0018] The true frequency multiplexing-based hidden true and false anti-interception transmission method provided by the application is different from the security transmission scheme researched from the defense angle only, and has the characteristics of attack and defense integration. Through multi-source user cooperation, a non-orthogonal frequency division multiplexing scheme is adopted to transmit the real signal and the decoy signal carrying confidential information on different frequencies, so as to produce overlap in the frequency domain, hide the real signal in the decoy signal by true and false frequency multiplexing to hide the real information, and at the same time, use the decoy signal to decoy the non-cooperative interceptor. Specifically, the hidden true and false problem is modeled as an optimization problem of maximizing the real signal secrecy rate, the user power allocation and the frequency multiplexing factor are jointly optimized to maximize the real signal secrecy rate, and the received decoy signal of the interceptor is stronger than the real signal, and a two-stage alternating dual-domain optimization method and Newton method are used to solve the optimization problem, the non-convex optimization problem is converted into a convex optimization problem, the calculation efficiency of the algorithm is improved, and the solution accuracy is improved. In general, the method hides the real information, and also ensures that the decoy signal misleads the interceptor, realizes the purpose of maximizing the security transmission rate of the real signal and deceiving the interceptor.

[0019] The application will be further described in detail below with reference to the accompanying drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 is a flowchart of a true and false frequency multiplexing-based hidden true and false anti-interception transmission method provided by an embodiment of the application;

[0021] Figure 2 is a CTSF anti-interception transmission framework diagram based on T / F frequency multiplexing provided by an embodiment of the application;

[0022] Figure 3 is a true signal secrecy rate comparison result diagram under different threshold conditions calculated by using the equal power allocation method and the BADO power allocation method respectively provided by an embodiment of the application;

[0023] Figure 4 is a total transmit power influence on the real signal secrecy rate comparison result diagram under different threshold conditions calculated by using the equal power allocation method and the BADO power allocation method respectively provided by an embodiment of the application;

[0024] Figure 5 is a total transmit power influence on the real signal SINR and the decoy signal SINR intercepted by the interceptor comparison result diagram under different threshold conditions calculated by using the equal power allocation method and the BADO power allocation method respectively provided by an embodiment of the application; ​​​

[0025] Figure 6 is the threshold value calculated by the equal power allocation method and the BADO power allocation method respectively provided by the embodiment of the present application The impact comparison result schematic diagram of the total transmission power on the real signal interception probability and the deception probability under the condition that

[0026] Figure 7 is the threshold value calculated by the equal power allocation method and the BADO power allocation method respectively provided by the embodiment of the present application The impact comparison result schematic diagram of the total transmission power on the real signal interception probability and the deception probability under the condition that

[0027] Figure 8 is the threshold value calculated by the equal power allocation method and the BADO power allocation method respectively provided by the embodiment of the present application The impact comparison result schematic diagram of the total transmission power on the real signal interception probability and the deception probability under the condition that DETAILED DESCRIPTION

[0028] The present application will be further described in detail below in combination with specific embodiments, but the embodiments of the present application are not limited thereto.

[0029] The method provided by the present application is applied to a multi-source cooperative anti-interception transmission system, the system comprising a plurality of cooperative users, a legal receiver and an interceptor, and the plurality of cooperative users in the system synchronously transmit real information and false information using different frequency bands. In the present application, the frequency band allocation of the signal adopts a non-orthogonal frequency division multiplexing scheme, which is different from the conventional wireless communication that usually uses OFDM (Orthogonal Frequency Division Multiplexing) to realize signal mutual non-interference. The non-orthogonal frequency division multiplexing scheme mixes the transmission of real signals and false signals in the frequency domain, and the transmission framework is as shown in Figure 1 The false signal can be used as a decoy signal to confuse the interceptor Eve. In this way, the real signal can be hidden in the false signal, and the false signal can be used to deceive the non-cooperative interceptor Eve, so as to achieve the goal of hiding the real and showing the false. In addition, the present application also considers K cooperative users and a legal receiver Bob, and assumes that the interceptor Eve has the same working mode as the legal receiver Bob and can intercept all the signals transmitted by the cooperative users, and the channel model adopts a Rician (Rice) fading channel.

[0030] Based on the transmission framework shown in Figure 1 Please refer to Figure 2 The embodiment of the present application provides an anti-interception transmission method for hiding the real and showing the false based on real and false frequency multiplexing, and specifically comprises the following steps:

[0031] S10, multiple cooperative users send multiple frequency bands of real signals and decoy signals; wherein, the real signals and the decoy signals are mixed and transmitted in the frequency domain through a non-orthogonal frequency division multiplexing scheme in the transmission process.

[0032] In the embodiment of the application, each cooperative user in the multiple cooperative users can send real signals or decoy signals, the number of the total frequency bands is K, the set of the frequency bands for transmitting the real signals is denoted as The set of the frequency bands for transmitting the decoy signals is denoted as In the transmission process of the multiple cooperative users and the legal receiver and the interceptor, the real signals and the decoy signals are mixed and transmitted in the frequency domain through a non-orthogonal frequency division multiplexing scheme, and the frequency multiplexing factor adopted in the non-orthogonal frequency division multiplexing scheme is denoted as α.

[0033] S20, the legal receiver receives signals and calculates the signal-to-noise ratio of the received real signals according to the received signals.

[0034] In the embodiment of the application, the legal receiver receives the kth frequency band signal sent by the cooperative user, and calculates the received signal in the kth frequency band, which is expressed by a formula as follows:

[0035]

[0036] wherein, y k represents the signal received by the legal receiver in the kth frequency band, represents the set of the frequency bands for transmitting the real signals, represents the set of the frequency bands for transmitting the decoy signals, K represents the total number of the frequency bands sent by all the cooperative users, and here K and The sum of the frequency bands in the sets is K, represents the ith frequency band signal belonging to the set , which is a real signal, represents the ith frequency band signal belonging to the set , which is a decoy signal, p i represents the transmission power of the ith frequency band signal, represents the channel response of the legal receiver when receiving the ith frequency band signal, wherein the mean value is and the variance is n k represents the noise signal received by the legal receiver when receiving the kth frequency band signal, represents the power of the noise signal received by the legal receiver when receiving the kth frequency band signal, α represents the frequency multiplexing factor, p k represents the transmission power of the kth frequency band signal, h k represents the channel response of the legal receiver when receiving the kth frequency band signal, x k , denotes that k belongs to The kth frequency band signal in the middle, which is a real signal.

[0037] Since the decoy signal is intentionally set in advance, it is assumed that the legitimate receiver knows them and can eliminate the interference caused by these signals, so that y k It can be rewritten as:

[0038]

[0039] According to formula (2), the signal-to-noise ratio of the real signal received by the legitimate receiver can be calculated, and the formula is expressed as:

[0040]

[0041] Wherein, denotes that k belongs to the frequency band set used to transmit the real signal γ k denotes the signal-to-noise ratio of the received real signal calculated by the legitimate receiver after receiving the kth frequency band signal, p k denotes the transmission power of the kth frequency band signal, h k denotes the channel response of the legitimate receiver when receiving the kth frequency band signal, p i denotes the transmission power of the ith frequency band signal, h i denotes the channel response of the legitimate receiver when receiving the ith frequency band signal, c i,k denotes the correlation coefficient between the ith frequency band signal and the kth frequency band signal, denotes the power of the noise signal received by the legitimate receiver when receiving the kth frequency band signal, and K denotes the total number of frequency bands transmitted by all cooperative users.

[0042] The correlation coefficient c i,k between the ith frequency band signal and the kth frequency band signal in formula (3) can be calculated, and the calculation formula can be expressed as:

[0043]

[0044] S30, the interceptor intercepts the signal and calculates the signal-to-noise ratio of the intercepted real signal and the signal-to-noise ratio of the decoy signal according to the signal intercepted by it.

[0045] In the interception end of the embodiment of the application, in order to achieve the purpose of deception, the signal intercepted by the interceptor is expected to be a decoy signal, and the formula of the signal intercepted by the interceptor is expressed as:

[0046]

[0047] According to formula (5), the signal-to-noise ratio of the real signal intercepted by the interceptor can be calculated, and the formula is expressed as:

[0048]

[0049] wherein, denotes that k belongs to the set of frequency bands used to transmit the real signal γ e,k denotes the signal-to-noise ratio of the intercepted real signal calculated by the interceptor after receiving the kth frequency band signal, p k denotes the transmission power of the kth frequency band signal, h e,k denotes the channel response of the interceptor when receiving the kth frequency band signal, p i denotes the transmission power of the ith frequency band signal, h e,i denotes the channel response of the interceptor when receiving the ith frequency band signal, c i,k denotes the correlation coefficient between the ith frequency band signal and the kth frequency band signal, denotes the power of the noise signal received by the interceptor simultaneously when receiving the kth frequency band signal, K denotes the number of frequency bands sent by all cooperating users;

[0050] At the same time, the signal-to-noise ratio of the decoy signal deception to which the interceptor is deceived can be calculated, and the formula is expressed as:

[0051]

[0052] wherein, denotes that n belongs to the set of frequency bands used to transmit the decoy signal denotes the signal-to-noise ratio of the decoy signal deception calculated by the interceptor after receiving the nth frequency band signal, p n denotes the transmission power of the nth frequency band signal, h e,n denotes the channel response of the interceptor when receiving the nth frequency band signal, p j denotes the transmission power of the jth frequency band signal, c j,n denotes the correlation coefficient between the jth frequency band signal and the nth frequency band signal, denotes the power of the noise signal received by the interceptor simultaneously when receiving the nth frequency band signal.

[0053] The correlation coefficient c j,n between the jth frequency band signal and the nth frequency band signal in formula (7) can be calculated, and the calculation formula can be expressed as:

[0054]

[0055] S40, according to the signal-to-noise ratio of the real signal received by the legal receiver, and the signal-to-noise ratio of the real signal intercepted by the interceptor, the signal-to-noise ratio of the decoy signal deception, a first target optimization problem of maximizing the real signal secret rate is constructed, and the decoy signal received by the interceptor is stronger than the real signal.

[0056] In order to achieve the purpose of deception, it is necessary to ensure that the decoy signal is received as the main demodulation signal at the non-cooperative receiver, i.e. the interceptor, which requires the condition Specifically:

[0057] Let f k = p k || h e,k | 2 , f n = p n || h e,n | 2 , Then we have And is a monotonically increasing function, so we can get p n || h e,n | 2 ≥ p k || h e,k | 2 , which indicates that the strength of the decoy signal received by the interceptor should be greater than the strength of the intercepted real signal.

[0058] Define the probability that the interceptor intercepts the real signal as: This means that the SINR of the real signal received by the interceptor exceeds a certain SINR threshold where Pr represents the probability calculation function. Similarly, the probability that the interceptor is deceived by the decoy signal is defined as:

[0059]

[0060] Formula (9) shows that in the case where the decoy signal is dominant, the SINR of the decoy signal received by the interceptor must exceed a certain threshold. Comparing formula (3) and formula (6), it can be seen that multi-user cooperation can eliminate the interference caused by the decoy signal at the legitimate receiver, so that its SINR is only reduced by the noise and co-channel interference of other real signals in different frequency bands, while the SINR received by the interceptor will be interfered by all signals transmitted in the full spectrum.

[0061] Through the above analysis, in order to realize the anti-interception transmission of hiding the true and showing the false, an embodiment of the present application designs a transmission mode, which offsets the interception probability by the maximum safe rate, so as to achieve the purpose of hiding the truth. At the same time, the signal quality of the decoy signal received by the interceptor is also guaranteed, and the deception probability is improved, so as to achieve the purpose of showing the false. Therefore, according to the signal-to-noise ratio of the real signal received by the legal receiver, and the signal-to-noise ratio of the real signal intercepted by the interceptor and the signal-to-noise ratio of the decoy signal deception, an embodiment of the present application constructs a first target optimization problem of maximizing the real signal secrecy rate, which is expressed by the formula:

[0062]

[0063] Wherein, R s,k represents the secrecy rate of the k frequency bands. The first target optimization problem in formula (10) is a target function of maximizing the sum of the secrecy rates of the real signals, and the constraint conditions are: the first constraint condition is to ensure that the interceptor can be effectively deceived, wherein is a pre-set SINR threshold; the second constraint condition is to ensure that the decoy signal is dominant; and the third constraint condition is to limit the maximum transmission power of transmitting such real and false signals, P s represents a total transmission power threshold.

[0064] S50, a two-stage alternating dual-domain optimization method is used to solve the first target optimization problem, and a set of optimal solutions is obtained.

[0065] Since formula (10) is a non-convex optimization problem, in order to solve the non-convex optimization problem, an embodiment of the present application first simplifies the first target optimization problem in formula (10) by using formula (3), formula (6) and formula (7) as follows:

[0066]

[0067] Let ξ i = p i c i,k , be an intermediate variable, and the variable replacement is performed on formula (12) to re-describe the first target optimization problem as a first target optimization problem which is expressed by the formula:

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074] in, Indicates a frequency band set The number of elements in γ k It represents the signal-to-noise ratio of the real signal received by the legitimate receiver after receiving the k-th frequency band signal, γ e,k It represents the signal-to-noise ratio of the intercepted real signal calculated by the interceptor after receiving the k-th frequency band signal, ξ i ,ξ t ,ξ n ,τ,μ k Both represent intermediate variables, ξ i =p i c i,k , p i represents the transmission power of the signal in the i-th frequency band, c i,k represents the correlation coefficient between the i-th frequency band signal and the k-th frequency band signal, ξ j =p j c j,n , p j represents the transmission power of the jth frequency band signal, c j,n represents the correlation coefficient between the jth frequency band signal and the nth frequency band signal, ξ n =p n c n,k , c n,k represents the correlation coefficient between the nth frequency band signal and the kth frequency band signal, p n represents the transmission power of the nth frequency band signal, ξ t =p t c t,k , c t,k represents the correlation coefficient between the t-th frequency band signal and the k-th frequency band signal, p t represents the transmission power of the t-th frequency band signal, h i represents the channel response of the legitimate receiver when receiving the signal in the i-th frequency band, h e,i represents the channel response of the interceptor when receiving the signal in the i-th frequency band, represents the SINR threshold, h e,j represents the channel response of the interceptor when receiving the j-th frequency band signal, h e,n It represents the channel response of the interceptor when receiving the nth frequency band signal, P s represents the total transmit power threshold, and K represents the number of frequency bands transmitted by all cooperating users.

[0075] Due to the existence of iτ, μ k In the first target optimization problem is multiplied together, so the first target optimization problem is still a non-convex optimization problem. However, it meets the mathematical structure of multivariate biconvex optimization, so the embodiments of the present application propose to solve this problem by using the two-stage alternating dual-domain optimization idea. Specifically:

[0076] The embodiments of the present application use the two-stage alternating dual-domain optimization method to solve the first target optimization problem, and obtain a set of optimal solutions, including:

[0077] Given the initial intermediate variables i = 0 ~ K-1, the first target optimization problem is re-expressed as the first sub-target optimization problem, and the MOSEK Solver tool is used to solve the first sub-target optimization problem to obtain the intermediate variable τ°, the intermediate variable

[0078] According to the intermediate variable τ°, the intermediate variable , the first target optimization problem is re-expressed as the second sub-target optimization problem, and the MOSEK Solver tool is used to solve the second sub-target optimization problem to update the intermediate variable The updated intermediate variable is taken as a set of optimal solutions. Specifically:

[0079] In the first stage, the embodiments of the present application give the initial intermediate variables i = 0 ~ K-1, find the introduced intermediate variables τ, μ from the first target optimization problem k , and re-construct the first target optimization problem as the first sub-target optimization problem, which is expressed as:

[0080]

[0081] Wherein,

[0082] By using the MOSEK Solver tool to solve the first sub-target optimization problem , the intermediate variable τ°, the intermediate variable

[0083] In the second stage, based on the intermediate variables τ°, the intermediate variables obtained by solving the first stage, find the introduced intermediate variable ξ i from the first target optimization problem , and re-construct the first target optimization problem Reconstructing as a second sub-target optimization problem, the formula is expressed as:

[0084]

[0085] Solving the second sub-target optimization problem by using the MOSEK Solver tool Updating the intermediate variable Updating the intermediate variable As a set of optimal solutions, for subsequent calculation.

[0086] S60, according to a set of optimal solutions, construct a second target optimization problem about frequency multiplexing factor, and solve the second target optimization problem by using Newton method, obtain the frequency multiplexing factor, and realize the mixing process in the frequency domain by the non-orthogonal frequency division multiplexing scheme in the transmission process through the frequency multiplexing factor.

[0087] Further, in order to realize solving more accurate frequency multiplexing factor, the embodiment of the application constructs a second target optimization problem about frequency multiplexing factor according to a set of optimal solutions, including:

[0088] Initializing the frequency multiplexing factor; calculating the new transmission power of the corresponding frequency band according to the secrecy rate of each frequency band, the initialized frequency multiplexing factor, and the signal-to-noise ratio of the real signal received by the legitimate receiver and the signal-to-noise ratio of the real signal intercepted by the interceptor; wherein the secrecy rate of each frequency band is calculated in the process of the first target optimization problem; constructing a second target optimization problem about frequency multiplexing factor according to a set of optimal solutions and new transmission power. Specifically:

[0089] In the process of solving the first target optimization problem , the secrecy rate R of each frequency band can be calculated s,k ; the initialized frequency multiplexing factor is denoted as α0; the denominators of the signal-to-noise ratios γ k and γ k,e shown in formulas (3) and (6) are denoted as constants C k and C k,e , respectively, and the formula is expressed as:

[0090]

[0091] In the process of solving the first target optimization problem , the value of C k shown in formula (15) and the value of C k,e shown in formula (16) can be determined respectively, and the transmission power p k of the real signal is The new transmission power after the re-distribution can be calculated by the following equation:

[0092]

[0093] Meanwhile, the C value shown in equation (17) can also be determined during the solving process n,e of the first target optimization problem n , The new transmission power after the redistribution can be calculated by the following equation:

[0094]

[0095] During the transmission process, α k , α k,e and α n,e take the same value. Here, α k , α k,e and α n,e in equation (18) and equation (19) all take the value of α0.

[0096] The c i,k value can be calculated by c i = ξ i / p i,k (i = 0, …, K-1). Finally, a second target optimization problem about the frequency multiplexing factor can be constructed according to the set of optimal solutions and the new transmission power, which is expressed as:

[0097]

[0098] wherein α represents the frequency multiplexing factor, f(α) represents the second target optimization problem about the frequency multiplexing factor, represents the optimal solution corresponding to the i-th frequency band in the set of optimal solutions, represents k belonging to the frequency band set used for transmitting the real signal p i ' represents the new transmission power of the i-th frequency band, and K represents the total number of frequency bands sent by all cooperative users.

[0099] For the solution of equation (20), the embodiments of the present application propose to solve it based on the Newton method, which is an iterative technique for solving nonlinear equations or optimization problems. It uses the first and second derivatives of the objective function to quickly converge to the extreme point of the objective function. For single-parameter optimization problems, the core idea of the Newton method is to use Taylor series expansion to approximate the objective function and iteratively update the parameters to find the optimal solution. Therefore, the embodiments of the present application use the Newton method to solve the second target optimization problem to obtain the frequency multiplexing factor, which includes:

[0100] Initialize the frequency multiplexing factor and use it as the frequency multiplexing factor of the current iteration; for example, the frequency multiplexing factor α0 can be used as the initial value.

[0101] According to the frequency multiplexing factor of the current iteration, the first-order gradient value and the second-order gradient value of the second objective optimization problem are calculated; wherein, the formula for the first-order gradient value of the frequency multiplexing factor is expressed as:

[0102]

[0103] Regarding the second-order gradient value of the frequency multiplexing factor, that is, the Hessian value, the formula is expressed as:

[0104]

[0105] The frequency multiplexing factor α is used according to the current iteration t , first-order gradient value f′(α t ) and the second-order gradient value f″(α t ) Calculate the frequency multiplexing factor α for the next iteration t+1 , the formula is:

[0106]

[0107] Determine whether the frequency multiplexing factor of the next iteration meets the iteration stop condition, such as determining whether |f′(α t )|<ε1or|α t+1 -α t |<ε2 or the maximum number of iterations N max , ε1, ε2 and N max The threshold is set according to actual needs. If it is met, the frequency multiplexing factor of the next iteration is output. If it is not met, the frequency multiplexing factor of the next iteration is used as the frequency multiplexing factor of the current iteration, and the step of calculating the first-order gradient value and the second-order gradient value of the second objective optimization problem based on the frequency multiplexing factor of the current iteration is returned until the iteration stop condition is met, and the optimal frequency multiplexing factor α obtained by the iteration is output. The frequency multiplexing factor α is used to realize the mixing process in the frequency domain of the non-orthogonal frequency division multiplexing scheme during the transmission process.

[0108] Based on the above solution, the following theorem can be obtained from the embodiment of the present invention:

[0109] Theorem 1: As the transmission power p of the k-th frequency band signal k The increase of the confidentiality rate R of the k-th frequency band signal s,k It increases monotonically, but the growth rate decreases gradually.

[0110] Proof: In formula (3), γ kWith the p k This is because the molecular p k ||h k || 2 Increase while the denominator remains unchanged, considering that other power allocations are determined, γ in formula (6) e,k Also with p k increases with the increase of .

[0111] The logarithmic function log2(1+x) is a monotonically increasing function, but the rate of increase decreases as x increases. k and γ e,k All follow p k increases with the increase of log2(1+γ k ) and log2(1+γ k,e ) will also follow p k increases with the increase of log2(1+γ k ) and log2(1+γ k,e ) will increase with γ k and γ k,e Assume that where a k =||h k || 2 , a k,e =||h e,k || 2 , calculate R s,k Relative to p k The first derivative of :

[0112]

[0113] Where ln(2) represents the logarithm of e to base 2, and ln(2) is approximately equal to 0.693147. From formula (24), we can see that: That is R s,k With the p k Monotonically increasing, then calculate R s,k Relative to p k The second derivative of :

[0114]

[0115] From formula (25), we can see that the second-order derivative is negative, indicating that R s,k The growth rate of p k As the transmission power p of the kth user increases, it gradually decreases. k The increase of the confidentiality rate R of the kth user s,k It increases monotonically, but the growth rate decreases gradually.

[0116] To verify the effectiveness of the anti-interception transmission method based on true and false frequency multiplexing provided by the embodiment of the application, the following experiments are performed for verification.

[0117] 1. Experimental simulation parameters

[0118] The system involves four users, denoted as K=4. Among them, users 1 and 3 work at a real frequency and transmit real signals, while users 2 and 4 work at a false frequency and transmit decoy signals. The channel model includes a legal channel and an eavesdropping channel, and the Rician factor is set to 10 dB. Since the anti-interception scheme based on T / F frequency multiplexing proposed by us is a non-orthogonal frequency division multiplexing scheme, we choose the OFDM scheme as the experimental comparison benchmark. In addition, an equal power allocation scheme is also used as a comparison benchmark, and the power of the real signal is set to be equal to the power of the decoy signal. The OFDM scheme and the BADO (Bi-Stage Alternating Dual-Domain Optimization) power allocation implemented by the application are compared.

[0119] 2. Experimental part

[0120] I. In order to verify the influence of total transmit power on the security performance of real signals and the effectiveness of the CTSF (Conceal Truth while Show Fake) scheme and the BADO scheme proposed by the application, four experimental scenarios are set in the experiment of the application:

[0121] (1) The OFDM scheme is used to transmit signals, and no decoy signal is added. The security rate of the real signal under different total transmit powers is calculated;

[0122] (2) The CTSF scheme is used to send signals, but the BADO scheme proposed by the application is not used for power allocation optimization, but equal power transmission is used. The security rate of the real signal under different total transmit powers is calculated;

[0123] (3) The CTSF scheme is used to send signals and the BADO scheme proposed by the application is used to optimize multi-user power allocation and time / frequency correlation coefficients. The eavesdropping end threshold is set to 0.2, and the security rate of the real signal under different total transmit powers is calculated;

[0124] (4) The CTSF scheme is used to send signals and the BADO scheme proposed by the application is used to optimize multi-user power allocation and time / frequency correlation coefficients. The eavesdropping end threshold is set to 0, and the security rate of the real signal under different total transmit powers is calculated.

[0125] The experimental results are as followsFigure 3 As shown, Figure 3 The effect of total transmit power on the real signal confidentiality rate performance is shown. Figure 3 It can be clearly seen that the total confidentiality rate of the real signal increases with the total transmission power P s According to Theorem 1, as the total transmission power P s With the increase of , more transmission power can be allocated to the real signal to maximize the confidentiality rate, thereby improving the confidentiality rate performance. It can also be seen from Figure 3 that the CTSF scheme proposed in the present invention is combined with the BADO scheme, and its efficiency is better than the baseline scheme in both confidentiality and deception performance. Compared with the OFDM scheme, the CTSF scheme proposed in the present invention has non-orthogonal interference between the true and false signals, which effectively reduces the signal quality in the eavesdropping channel. When the power of the real signal and the decoy signal is the same, the equal power allocation method cannot always ensure that the constraint conditions are met, that is, n belongs to k belongs to In addition, as the total transmission power P s With the increase of , under given deception constraints, the power of the decoy signal may be wasted, thereby limiting the secure transmission performance of the real signal.

[0126] 2. To verify the threshold To investigate the impact of the real signal confidentiality rate and the effectiveness of the BADO scheme, four experimental scenarios were set up in the experiment of this invention:

[0127] (1) Using equal power allocation and total transmission power P s Set to 15dB;

[0128] (2) Using equal power allocation and total transmission power P s Set to 10dB;

[0129] (3) The two-stage alternating dual-domain optimization method (BADO) proposed in this invention is used to optimize power allocation, and the total transmission power P s Set to 15dB;

[0130] (4) The two-stage alternating dual-domain optimization method (BADO) proposed in this invention is used to optimize power allocation, and the total transmission power p S Set to 10dB.

[0131] The experimental results are as follows Figure 4 As shown, Figure 4 Threshold value is shown The impact of constraints on the confidentiality of real signals. Figure 4 It can be seen that as the threshold As the interception threshold increases, the total confidentiality rate of the real signal first increases and then decreases. In addition, compared with the equal power allocation scheme, the CSTF scheme containing the BADO scheme proposed in this invention shows excellent confidentiality rate performance. According to formula (7), as the interception threshold As the threshold increases, a higher transmission power needs to be allocated to the decoy signal to achieve the desired deception, which will result in a reduction in the transmission power allocated to the real signal. When the threshold is small, the interference caused by frequency reuse becomes the dominant factor. This interference seriously damages the interception capability of the eavesdropping channel, and the impact exceeds the reduction of the real signal transmission power. Therefore, at the threshold When the threshold is small, the total confidentiality rate increases. On the other hand, when the threshold When is large, in order to maintain the deception quality, the transmitter allocates more transmit power to the decoy signal, which results in less transmit power allocated to the real signal, thus leading to a significant drop in the confidentiality rate.

[0132] 3. To verify the effect of total transmit power on the SINR of the real signal and the SINR of the decoy signal intercepted by the interceptor, as well as the effectiveness of the BADO scheme, three experimental scenarios were set up in the experiment of the present invention:

[0133] 1. Interception threshold Set to 0.2 and adopt equal power allocation scheme, calculate the real signal SINR and decoy signal SINR intercepted by the interceptor under different total transmit power conditions;

[0134] 2. Interception threshold Set it to 0.2 and use the BADO scheme proposed in the present invention to optimize power allocation, and calculate the real signal SINR and decoy signal SINR intercepted by the interceptor under different total transmit power conditions;

[0135] 3. Interception threshold The value is set to 0 and the BADO scheme proposed in the present invention is used to optimize power allocation, and the SINR of the real signal and the SINR of the decoy signal intercepted by the interceptor are calculated under different total transmit power conditions.

[0136] The experimental results are as follows Figure 5 As shown, Figure 5 Shows the total transmit power P s Signal-to-noise ratio γ for interceptors e,k and The impact of γ is evaluated, and the signal-to-noise ratio of the real signal intercepted by the interceptor is e,k and the signal-to-noise ratio of the decoy signal received by the interceptor from Figure 5 It can be seen that when the threshold When , it shows that there is no deception constraint at this time, and the intercepted real signal SINR is significantly higher than the SINR of the received decoy signal. Figure 3 The results shown in this paper show that although a higher security rate can be achieved under these conditions, the purpose of deception is not achieved. When effective deception constraints are applied, the decoy signal dominates the interceptor's received signal, causing the SINR of the decoy signal to exceed the SINR of the intercepted true signal. This result is consistent with the modeling of the CTSF scheme proposed in this invention. In addition, as the total transmit power P s As increases, the SINR curve shows an upward trend, which confirms the analysis result in Theorem 1. In addition, after comparison, it can be concluded that the BADO scheme proposed in the present invention performs better than the equal power allocation strategy.

[0137] 4. To verify the threshold To investigate the impact of the real signal SINR and the decoy signal SINR intercepted by the interceptor and the effectiveness of the BADO scheme, two experimental scenarios were set up in the experiment of the present invention:

[0138] (1) Using equal power allocation scheme, calculate different thresholds The real signal SINR and decoy signal SINR intercepted by the interceptor under the conditions;

[0139] (2) Use the BADO scheme proposed in this invention to optimize power allocation and calculate different thresholds The real signal SINR and decoy signal SINR intercepted by the interceptor under certain conditions.

[0140] The experimental results are as follows Figure 6 As shown, Figure 6 Threshold value is shown The signal-to-noise ratio of the real signal intercepted by the interceptor is γ e,k and the signal-to-noise ratio of the decoy signal The impact of Figure 6 It can be seen that: with the threshold As the threshold increases, the SINR of the decoy signal received by the interceptor increases first and then decreases, while the SINR of the intercepted real signal decreases first and then increases. As the value of increases, more transmit power should be allocated to transmit the decoy signal to ensure the deception purpose and effectiveness, which in turn reduces the transmit power allocated to the real signal, resulting in a decrease in the SINR of the intercepted real signal. In addition to the interceptor power allocation, the T / F frequency multiplexing factor determines the degree of spectrum overlap between the real signal and the fake signal, affecting the interference level between them and thus the SINR at the interceptor end. Specifically, when the threshold When the power required to transmit the decoy signal increases within a certain range, it is relatively easy to meet the first constraint in formula (10), that is, n belongs to k belongs to The SINR of the decoy signal will increase with the threshold However, when the threshold When it continues to increase, not only does it need to give the decoy signal a higher transmission power, but it also has to reduce the interference between the real signal and the decoy signal. Despite the adjustment, it becomes challenging to meet the first constraint in formula (10), which leads to an increase in the SINR of intercepting the real signal.

[0141] 5. To verify the effect of total transmit power on the probability of intercepting a true signal and the probability of spoofing, as well as the effectiveness of the BADO scheme, three experimental scenarios were set up in the experiment of the present invention:

[0142] (1) Threshold Set to 0.2, use the equal power allocation method, and calculate the true signal interception probability and deception probability under different total transmit power conditions;

[0143] (2) Threshold Set to 0.2, use the BADO scheme proposed in this invention to optimize power allocation, and calculate the true signal interception probability and deception probability under different total transmit power conditions;

[0144] (3) Threshold Set to 0, use the BADO scheme proposed in the present invention to optimize power allocation, and calculate the true signal interception probability and deception probability under different total transmit power conditions.

[0145] The experimental results are as follows Figure 7 As shown, Figure 7 Evaluated the total transmit power P s The impact on the true signal interception probability and deception probability of the proposed CTSF scheme. Figure 7 It can be seen that as the total transmission power P s As the interception probability and deception probability of the real signal increase, the interception probability and deception probability of the real signal will increase. This is because when more transmit power is allocated to transmit false decoy signals, the quality constraint threshold of the decoy signal Easier to satisfy. For a given threshold The probability of deception increases obviously with the increase of the transmit power. Although the objective function of the present application simulates the maximization of the secure transmission rate of the real signal, the numerator in formula (6) also increases with the increase of the transmit power, which in turn increases the possibility of the real signal being intercepted. Compared with the equal power allocation scheme, the BADO scheme of the present application shows a higher probability of deception and a lower probability of interception of the real signal in the CTSF scheme. In addition, if the deception signal is not constrained, resulting in too low probability of deception and too high probability of interception of the real signal, the goal of CTSF cannot be achieved.

[0146] Six, in order to verify the threshold The influence of the probability of interception of the real signal and the probability of deception and the effectiveness of the BADO scheme, two experimental scenarios are set in the experiment of the present application:

[0147] (1) The equal power allocation method is used to calculate the probability of interception of the real signal and the probability of deception under different threshold conditions ;

[0148] (2) The two-stage alternating dual-domain optimization method (BADO) proposed in the present application is used to optimize the power allocation, and the probability of interception of the real signal and the probability of deception under different threshold conditions are calculated.

[0149] The experimental results are shown in Figure 8 , Figure 8 which show the influence of the deception constraint threshold on the probability of interception and the probability of deception. It can be seen from Figure 8 that: with the increase of the threshold , the probability of interception decreases rapidly. This is because more transmit power allocation and less interference are required to ensure the deception condition, which is consistent with the change of the SINR value analyzed in Figure 6 . In addition, compared with the equal power allocation scheme, the BADO scheme of the present application realizes a higher probability of deception and a lower probability of interception. Specifically: when the threshold is in a small range (threshold ), the probability of deception remains at 1, which indicates that the deception constraint condition can be fully met in this range. However, with the continuous increase of the threshold T h , it becomes challenging to meet the deception constraint condition, eventually leading to a decrease in the probability of deception.

[0150] In summary, the true-false frequency multiplexing-based anti-interception transmission method proposed in the embodiments of the present application is different from the security transmission scheme researched only from the defense angle, and has the characteristics of attack and defense integration, aiming at the interception threat in wireless communication. Through multi-source user cooperation, a non-orthogonal frequency division multiplexing scheme is adopted to make the real signal carrying confidential information and the decoy signal transmitted on different frequencies, so as to produce overlap in the frequency domain, hide the real signal in the decoy signal by true-false frequency multiplexing to hide the real information, and at the same time, use the decoy signal to decoy the non-cooperative interceptor. Specifically, the true-false problem is modeled as an optimization problem of maximizing the real signal secrecy rate, the user power allocation and the frequency multiplexing factor are jointly optimized to maximize the real signal secrecy rate, and the received decoy signal of the interceptor is constrained to be stronger than the real signal. A two-stage alternating dual-domain optimization method and Newton method are also proposed to solve the optimization problem, the non-convex optimization problem is converted into a convex optimization problem, and the calculation efficiency and solution accuracy are improved. In general, the method proposed in the present application hides the real information, and at the same time, ensures that the decoy signal misleads the interceptor, realizes the purpose of maximizing the security transmission rate of the real signal and deceiving the interceptor.

[0151] In the description of the present application, it should be understood that the terms "first", "second" are only for the purpose of description, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first", "second" can explicitly or implicitly include one or more of the features. In the description of the present application, the meaning of "multiple" is two or more, unless otherwise specifically limited.

[0152] Although the present application is described herein in conjunction with various embodiments, other variations of the disclosed embodiments can be understood and implemented by those skilled in the art with reference to the specification and drawings. In the specification, the word "comprising" does not exclude other components or steps, and "one" or "an" does not exclude multiple. Some measures are described in mutually different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0153] The above is a further detailed description of the present application in conjunction with specific preferred embodiments, and the specific implementation of the present application cannot be limited to these descriptions. For those skilled in the art to which the present application belongs, without departing from the concept of the present application, a number of simple deductions or substitutions can be made, which should be regarded as falling within the protection scope of the present application.

Claims

1. A method for anti-interception transmission based on true and false frequency multiplexing, characterized in that, The application is applied to a multi-source cooperative anti-interception transmission system, which comprises a plurality of cooperative users, a legal receiver and an interceptor; the corresponding method comprises: The plurality of cooperative users transmit real signals and decoy signals in a plurality of frequency bands; wherein the real signals and the decoy signals are mixed and transmitted in the frequency domain through a non-orthogonal frequency division multiplexing scheme in the transmission process; The legal receiver receives signals and calculates the signal-to-noise ratio of the received real signals according to the received signals; The interceptor intercepts signals and calculates the signal-to-noise ratio of the intercepted real signals and the signal-to-noise ratio of the decoy signals according to the intercepted signals; A first target optimization problem of maximizing the real signal secrecy rate is constructed according to the signal-to-noise ratio of the real signals received by the legal receiver and the signal-to-noise ratio of the real signals intercepted by the interceptor and the signal-to-noise ratio of the decoy signals, and the received decoy signals by the interceptor are stronger than the real signals; A two-stage alternating dual-domain optimization method is used to solve the first target optimization problem to obtain a set of optimal solutions; A second target optimization problem about the frequency multiplexing factor is constructed according to the set of optimal solutions, and the Newton method is used to solve the second target optimization problem to obtain the frequency multiplexing factor, so that the mixing process in the frequency domain through the non-orthogonal frequency division multiplexing scheme in the transmission process is realized through the frequency multiplexing factor.

2. The anti-interception transmission method based on true-false frequency multiplexing of claim 1, characterized in that, The signal-to-noise ratio of the received real signals calculated by the legal receiver is expressed by the formula: wherein represents k belongs to the set of frequency bands used for transmitting real signals γ k represents the signal-to-noise ratio of the received real signal calculated by the legitimate receiver after receiving the kth frequency band signal, p k represents the transmission power of the kth frequency band signal, h k represents the channel response of the legitimate receiver when receiving the kth frequency band signal, p i represents the transmission power of the ith frequency band signal, h i represents the channel response of the legitimate receiver when receiving the ith frequency band signal, c i,k represents the correlation coefficient between the ith frequency band signal and the kth frequency band signal, represents the power of the noise signal received by the legitimate receiver when receiving the kth frequency band signal, K represents the total number of frequency bands transmitted by all cooperative users.

3. The true-with-false frequency multiplexed hidden true show false anti-interception transmission method according to claim 1, characterized in that, The signal-to-noise ratio of the intercepted real signals calculated by the interceptor is expressed by the formula: wherein, denotes that k belongs to the set of frequency bands used for transmitting real signals γ e,k denotes the signal-to-noise ratio of the intercepted real signal calculated by the interceptor after receiving the kth frequency band signal, p k denotes the transmission power of the kth frequency band signal, h e,k denotes the channel response of the interceptor when receiving the kth frequency band signal, p i denotes the transmission power of the ith frequency band signal, h e,i denotes the channel response of the interceptor when receiving the ith frequency band signal, c i,k denotes the correlation coefficient between the ith frequency band signal and the kth frequency band signal, denotes the power of the noise signal received by the interceptor simultaneously with the kth frequency band signal, K denotes the number of frequency bands transmitted by all cooperating users; The signal-to-noise ratio of the decoy signals calculated by the interceptor is expressed by the formula: wherein, denotes that n belongs to the set of frequency bands used for transmission of the decoy signal denotes the signal-to-noise ratio of the decoyed signal deception calculated by the interceptor after receiving the nth frequency band signal, p n denotes the transmit power of the nth frequency band signal, h e,n denotes the channel response of the interceptor at the time of receiving the nth frequency band signal, p j denotes the transmit power of the jth frequency band signal, c j,n denotes the correlation coefficient between the jth frequency band signal and the nth frequency band signal, denotes the power of the noise signal received by the interceptor simultaneously with the nth frequency band signal.

4. The true-with-false frequency multiplexed hidden true show false anti-interception transmission method according to claim 1, characterized in that, The first target optimization problem of maximizing the real signal secrecy rate constructed is expressed by the formula: wherein denotes that k belongs to the set of frequency bands used to transmit real signals denotes that n belongs to the set of frequency bands used to transmit decoy signals denotes the set of frequency bands denotes the number of elements in R s,k denotes the secrecy rate of the kth frequency band, γ k denotes the signal-to-noise ratio of the received real signal computed by the legitimate receiver after receiving the kth frequency band signal, γ e,k denotes the signal-to-noise ratio of the intercepted real signal computed by the interceptor after receiving the kth frequency band signal, ξ i , ξ t , ξ n , τ, μ k all denote intermediate variables, ξ i = p i c i,k , p i denotes the transmit power of the ith frequency band signal, c i,k denotes the correlation coefficient between the ith frequency band signal and the kth frequency band signal, ξ j = p j c j,n , p j denotes the transmit power of the jth frequency band signal, c j,n denotes the correlation coefficient between the jth frequency band signal and the nth frequency band signal, ξ n = p n c n,k , c n,k denotes the correlation coefficient between the nth frequency band signal and the kth frequency band signal, p n denotes the transmit power of the nth frequency band signal, ξ t = p t c t,k , c t,k denotes the correlation coefficient between the tth frequency band signal and the kth frequency band signal, p t denotes the transmit power of the tth frequency band signal, h i denotes the channel response of the legitimate receiver when receiving the ith frequency band signal, h e,i denotes the channel response of the interceptor when receiving the ith frequency band signal, denotes the SINR threshold, h e,j denotes the channel response of the interceptor when receiving the jth frequency band signal, h e,n denotes the channel response of the interceptor when receiving the nth frequency band signal, P s denotes the total transmit power threshold, K denotes the number of frequency bands sent by all cooperating users.

5. The true-false frequency multiplexing based hidden true-indicated false anti-interception transmission method according to claim 4, characterized in that, The two-stage alternating dual-domain optimization method is used to solve the first target optimization problem to obtain a set of optimal solutions, including: Given the initial intermediate variable i = 0 ~ K - 1, the first target optimization problem is re-expressed as a first sub-target optimization problem, and the first sub-target optimization problem is solved by using the MOSEK Solver tool to obtain the intermediate variable τ°, the intermediate variable According to the intermediate variable τ°, the intermediate variable The first target optimization problem is re-expressed as a second sub-target optimization problem, and the second sub-target optimization problem is solved by using the MOSEK Solver tool to update the intermediate variable The updated intermediate variable is taken as a set of optimal solutions.

6. The anti-interception transmission method based on true-false frequency multiplexing of claim 5, characterized in that, The first sub-target optimization problem constructed is expressed by the formula: wherein, 7. The anti-interception transmission method based on true-false frequency multiplexing of claim 5, characterized in that, The second sub-target optimization problem constructed is expressed by the formula:

8. The true-with-false frequency multiplexed hidden true show false anti-interception transmission method according to claim 1, characterized in that, The second target optimization problem about the frequency multiplexing factor is constructed according to the set of optimal solutions, including: The frequency multiplexing factor is initialized; According to the secrecy rate of each frequency band, the initialized frequency multiplexing factor, and the signal-to-noise ratio of the real signals received by the legal receiver and the signal-to-noise ratio of the real signals intercepted by the interceptor, the new transmission power of the corresponding frequency band is calculated; wherein the secrecy rate of each frequency band is calculated in the process of the first target optimization problem; The second target optimization problem about the frequency multiplexing factor is constructed according to the set of optimal solutions and the new transmission power.

9. The anti-interception transmission method based on true-false frequency multiplexing of claim 8, characterized in that, The second target optimization problem about the frequency multiplexing factor is constructed according to the set of optimal solutions and the new transmission power, which is expressed by the formula: wherein a denotes a frequency multiplexing factor, f(a) denotes a second target optimization problem with respect to the frequency multiplexing factor, denotes an optimal solution corresponding to the i-th frequency band in the set of optimal solutions, denotes that k belongs to the set of frequency bands used for transmitting the real signal p' i denotes a new transmit power of the i-th frequency band, and K denotes the total number of frequency bands transmitted by all cooperating users.

10. The true-with-false frequency multiplexed hidden true reveal false antijamming transmission method of claim 1, wherein, The Newton method is used to solve the second target optimization problem to obtain the frequency multiplexing factor, including: The frequency multiplexing factor is initialized and used as the frequency multiplexing factor of the current iteration; According to the frequency multiplexing factor of the current iteration, the first-order gradient value and the second-order gradient value of the second target optimization problem are calculated; According to the frequency multiplexing factor of the current iteration, the first-order gradient value and the second-order gradient value, the frequency multiplexing factor of the next iteration is calculated; determining whether the frequency multiplexing factor of the next iteration meets an iteration stop condition, if yes, outputting the frequency multiplexing factor of the next iteration, if not, taking the frequency multiplexing factor of the next iteration as the frequency multiplexing factor of the current iteration, and returning to the step of calculating the first-order gradient value and the second-order gradient value of the second target optimization problem according to the frequency multiplexing factor of the current iteration until the iteration stop condition is met.

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