Concealed communication method for confronting full-duplex eavesdropper based on probability transmission in symbiotic radio

Abstract

A hidden communication method for confronting a full-duplex eavesdropper based on probability transmission in symbiotic radio comprises the following steps: constructing a system model which comprises a main transmitter Alice, a main receiver Bob, an auxiliary transmitter BD and a full-duplex eavesdropper Willie; the main transmitter Alice selectively transmits information according to a link channel state with the main receiver Bob; when the channel gain # imgabs0 # of a legal link is greater than a preset threshold value delta, the information is transmitted; otherwise, the information is not transmitted; the auxiliary transmitter BD secretly sends confidential information to the main receiver Bob through a reflection link by using the transmission behavior of the main transmitter Alice, and the full-duplex eavesdropper Willie works in a full-duplex mode and simultaneously sends artificial noise to interfere legal communication and eavesdrop. The technical problem to be solved by the invention is to provide the hidden communication method for confronting the full-duplex eavesdropper based on probability transmission in the symbiotic radio, the strong eavesdropper is confronted by using the uncertainty of link information, and the detection performance and the concealment performance of the eavesdropper are comprehensively analyzed.

Description

Technical Field

[0001] The present invention relates to the technical field of symbiotic radio, in particular to a covert communication method based on probability transmission in symbiotic radio to counter full-duplex eavesdroppers. Background Art

[0002] With the rapid development of modern wireless communication technologies, wireless communications are becoming increasingly integrated into our daily lives. The widespread adoption of 5G and the Internet of Things (IoT) is driving increasing demand for spectrum and energy, leading to increasingly scarce spectrum resources. Therefore, new communication technologies are needed to improve the spectrum utilization and energy efficiency of future wireless communication networks. Symbiotic radio (SR) technology is considered a promising solution to address spectrum scarcity and energy challenges in the IoT. SR combines the advantages of cognitive radio (CR) and ambient backscatter communication (AmBC), enabling efficient spectrum and energy utilization. It is expected to become a new communication paradigm for the future development of passive IoT. At the same time, due to the open and broadcast nature of wireless channels, wireless transmission faces serious security challenges.

[0003] While encryption and physical layer security technologies effectively prevent information interception and decryption, they are still far from sufficient in the face of increasingly powerful adversaries, especially in scenarios with high security requirements. To address these issues, covert communication, by protecting communication behavior, has effectively improved security protection and has been successfully applied in various scenarios, including IoT networks, CR networks, SR networks, and Internet of Vehicles networks.

[0004] Currently, there have been some inventions that study covert communication in symbiotic radio.

[0005] Patent 1: CN119364390A, a secure transmission system and method based on a STAR-RIS-assisted symbiotic radio system. This invention incorporates a reconfigurable intelligent surface for both transmission and reflection, achieving full spatial coverage through signal reflection and transmission, enhancing device deployment flexibility. While meeting system communication requirements and power constraints, it can significantly increase the minimum communication security rate for secondary users.

[0006] Patent 2: CN117915338A, a collaborative interference-assisted secure communication method for symbiotic radio. This method optimizes the beamforming vectors of the primary user's base station and the reflection coefficient matrices of two smart reflective surfaces to maximize the primary user's information transmission security. This invention enables secure information transmission in the presence of eavesdroppers.

[0007] Patent 3: CN119316847A, a design and optimization method for a symbiotic radio system based on a smart reflective surface. By utilizing the smart reflective surface and controlling the reflective unit switches through on-off keying, the system minimizes the error probability of scattered transmission, achieving a higher primary transmission rate and a lower secondary transmission bit error rate.

[0008] The above patents are only covert measures taken against passive eavesdroppers. With the development of wireless communications, the capabilities of eavesdroppers are constantly improving. Moreover, during SR long-distance communication, continuous information transmission may not only lead to transmission interruption, but also cause energy waste, especially under poor channel conditions. Summary of the Invention

[0009] The technical problem to be solved by the present invention is to provide a covert communication method based on probabilistic transmission in symbiotic radio to combat full-duplex eavesdroppers, utilize the uncertainty of link information to combat powerful eavesdroppers, and comprehensively analyze the detection performance and concealment performance of eavesdroppers; enhance the concealment performance while also being able to resist active attacks from powerful eavesdroppers.

[0010] To solve the above technical problems, the technical solution adopted by the present invention is: a covert communication method based on probabilistic transmission in symbiotic radio to resist full-duplex eavesdroppers, comprising the following steps: Build a system model, including the main transmitter Alice, the main receiver Bob, the auxiliary transmitter BD and the full-duplex eavesdropper Willie; The primary transmitter Alice selectively transmits information based on the link channel state with the primary receiver Bob: when the channel gain of the legitimate link is > Transmit information when the preset threshold δ is reached, otherwise do not transmit; The auxiliary transmitter BD uses the transmission behavior of the main transmitter Alice to secretly send confidential information to the main receiver Bob through the reflection link. The full-duplex eavesdropper Willie works in full-duplex mode and sends artificial noise to interfere with legitimate communications and eavesdrop.

[0011] Preferably, the probability that Alice transmits hidden information in a single time slot is ; in represents the channel gain from Alice to Bob, which is expressed as ,|hab|² The mean of is exponentially distributed. is the preset threshold at Bob.

[0012] Preferably, the signal received by the main receiver Bob is expressed as ; in and denote the transmission power of Alice and Willie respectively, represents the reflection coefficient of BD, 、 and are the channel gains from Willie to Bob, Alice to BD, and BD to Bob, respectively. 、 and express; 、 and are the signals generated by Alice, Willie and BD respectively, where is the index used by each channel, is the total number of channels used, satisfying is the local noise at Bob, expressed as .

[0013] Preferably, the main signal is demodulated first, and Bob's signal-to-interference-plus-noise ratio (SINR) can be expressed as ; The denominator represents the main signal, and the numerator represents the noise, which includes the hidden signal 、 The interference signal sent by Willie and local noise , represents the reflection coefficient of BD, and denote the transmission power of Alice and Willie respectively, and denote the channel gains from Alice to Bob and BD respectively, and denote BD and the channel gain from Willie to Bob respectively.

[0014] Assuming that the main signal can be perfectly removed from the received signal by perfect successive interference cancellation (SIC), the SINR of the concealed signal is: ; The denominator represents the covert signal, and the numerator represents the noise, which includes the interference signal sent by Willie and local noise , represents the reflection coefficient of BD, and denote the transmission power of Alice and Willie respectively, represents the channel gain from Alice to BD, and denote BD and the channel gain from Willie to Bob respectively.

[0015] Finally, the hidden signal is decoded. Using Shannon's formula theorem, Bob's hidden rate is as follows: ; Where p is the probability that Alice transmits covert information in a single time slot, The signal-to-noise ratio (SINR) of the concealed signal.

[0016] Preferably, Bob's concealment rate is optimized to maximize the reception rate at Bob. The optimization is defined as follows:

[0017] in, represents the hidden constraint, represents the range of reflection coefficient, represents the reliability constraint, is an arbitrarily small positive integer, is the target rate threshold.

[0018] Preferably, Willie determines whether Alice transmits information by a likelihood ratio test, and the average power of the received signal is: ; in and denote the channels from Willie and BD to Willie respectively, is the Willie self-interference coefficient; is the local noise of Willie, express, Indicates that no transmission has been made. Indicates transmission.

[0019] Preferably, according to the Newman-Pearson criterion, Willie minimizes the probability of detection error through a likelihood ratio test; for a given transmission time slot, the average received power received by Willie is determined as follows: ; in It means Willie judges that Alice has transmitted hidden information. Indicates that Willie judges that Alice has not transmitted any hidden information is the detection error threshold; when the average power received by Willie is greater than , Willie judges that Alice has transmitted hidden information; if it is less than , then it is determined that Alice did not transmit hidden information.

[0020] Preferably, Willie's false detection probability , where the false alarm probability , missed detection probability , by discussing the detection threshold in sections The relationship with channel parameters is solved.

[0021] Preferably, Willie uses two antennas in full-duplex mode to transmit artificial noise and eavesdrop simultaneously. The local noise adopts a bounded uncertainty model with a probability density function of: ; in is the standard noise power, is a parameter that quantifies the size of the noise uncertainty.

[0022] Preferably, all links are modeled as Rayleigh fading channels.

[0023] The present invention provides a covert communication method based on probability transmission in symbiotic radio to counter full-duplex eavesdroppers, which has the following beneficial effects: 1. This invention utilizes the probabilistic uncertainty of link information for research. Alice intelligently selects the timing and method of transmission to reduce the probability of being detected by eavesdroppers. Due to the dynamic and random nature of the link from Alice to Bob, uncertainty exists in the signal transmission process, making it difficult to accurately predict the signal transmission characteristics. This method uses a predetermined threshold to detect the quality of the channel. At the same time, the backscatter device also adjusts its reflection coefficient based on environmental information to maximize the probability of concealed information transmission, thereby combating eavesdropping and interference by full-duplex eavesdroppers. 2. This paper derives the closed-form expression of Wiley's minimum detection error probability (DEP) and the corresponding optimal threshold, and analyzes the concealment performance including average DEP, concealment rate and concealment energy efficiency (CEE); 3. The present invention proposes an optimization scheme to obtain the optimal prior transmission probability; at the same time, the optimal reflection coefficient is solved by utilizing a hybrid grid gradient optimization algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The present invention will be further described below with reference to the accompanying drawings and examples: Figure 1 This is a model diagram of the covert transmission strategy system of the present invention; Figure 2are different reflection coefficients Under the condition of the threshold, the theoretical and simulation values of Willie's average minimum false detection probability increase with the threshold Experimental diagram of changes; Figure 3 At different thresholds Under the condition of noise parameter Experimental diagram of changes; Figure 4 At different reflection coefficients Below is an experimental diagram showing the theoretical and simulated values of Bob's concealed outage probability COP as the signal-to-interference-plus-noise ratio (SINR) changes.

[0025] Figure 5 is the relationship between Bob's concealment rate and concealment energy efficiency (CEE) and the reflection coefficient in the case of probabilistic transmission and deterministic transmission. relationship. DETAILED DESCRIPTION

[0026] As shown in Figure 1, there is a primary transmitter (Alice), a primary receiver (Bob), a secondary transmitter (BD), and a powerful eavesdropper (Willie). In this invention, Alice selectively initiates information transmission based on the link information between her and Bob. Meanwhile, BD attempts to exploit Alice's transmission behavior under Willie's surveillance to secretly transmit confidential information to Bob. Willie transmits artificial noise to interfere with legitimate communications while simultaneously eavesdropping. Furthermore, all links are modeled as Rayleigh fading, with all channels remaining constant within a given time slot and varying independently between different time slots. Furthermore, it is assumed that all nodes except Willie are equipped with a single antenna and operate in half-duplex mode, while Willie uses two antennas in full-duplex mode.

[0027] From Alice to BD, Bob and Willie, The channel coefficients to Bob and Willie are expressed as ,in , Since all channels are modeled as independent Rayleigh block fading channels, It follows an exponential distribution with a mean of .

[0028] In this invention, because Alice's transmission behavior to Bob is known to both parties, Bob carefully designs a detection threshold based on the signal sent from Willie. When the legitimate link is greater than the given threshold, it means that the channel state is good and can resist the interference from Willie, allowing the receiver to achieve a higher covert transmission rate. At this time, Alice sends information, otherwise she does not send. Therefore, the probability that Alice transmits covert information in a single time slot is expressed as ;(1) in represents the channel gain from Alice to Bob, which is expressed as ,|hab|² The mean of is exponentially distributed. is the preset threshold at Bob.

[0029] Assuming that BD sends covert information and Willie continuously sends artificial noise, the signal received by Bob can be expressed as follows: ;(2) in and denote the transmission power of Alice and Willie respectively. represents the reflection coefficient of BD. 、 and are the channel gains from Willie to Bob, Alice to BD, and BD to Bob, respectively. 、 and express. 、 and are the signals generated by Alice, Willie and BD respectively, where is the index used by each channel, is the total number of channels used, satisfying is the local noise at Bob, expressed as .

[0030] In addition, the uncertainty of Willie local noise is considered, which can be characterized by a bounded noise uncertainty model. Therefore, The probability density function (PDF) of is given by ;(3) in is the standard noise power, is a parameter that quantifies the size of the noise uncertainty.

[0031] From equation (2), we can see that by first demodulating the main signal, Bob’s signal-to-interference-plus-noise ratio (SINR) can be expressed as ;(4) Assuming that the main signal can be perfectly removed from the received signal by perfect successive interference cancellation (SIC), the SINR of the concealed signal is: ;(5) Finally, the hidden signal is decoded and, using Shannon's theorem, Bob's hidden rate is given by ;(6) Optimization goal of the present invention The goal of this invention is to optimize the preset fixed energy under the concealment constraint to maximize the reception rate at Bob. Therefore, the optimization problem is defined as follows: ;(7) ; (7a) ; (7b) ; (7c) Where (7a) represents the concealment constraint, (7b) represents the range constraint of the reflection coefficient, and (7c) represents the reliability constraint. The details will be explained below.

[0032] 1) Concealment Constraint: During the transmission process, Willie uses hypothesis testing based on the collected information to determine whether Alice has transmitted covert information. To achieve covert transmission, the concealment constraint must be satisfied. This means that the average minimum probability of Willie making an error during the detection process must be greater than or equal to a given requirement. This paper uses Willie's average minimum error probability (DEP) to evaluate the average minimum probability of Willie making an error during the detection process. Therefore, to obtain the concealment constraint, Willie's average minimum DEP must be calculated.

[0033] consider Indicates that Alice did not transmit any hidden information. This means Alice has transmitted hidden information. Assume that Willie’s received signal are independent and identically distributed (iid), and Under the two assumptions, the average power received by Willie is as follows: ;(8) in and are the transmission powers of Alice and Willie respectively, represents the reflection coefficient of BD. represents the channel gain from Alice to Willie, and denote the channel gains from Willie and BD to Willie respectively, is the Willie's self-interference coefficient. is the local noise of Willie, express.

[0034] According to the Newman-Pearson criterion, Willie minimizes the probability of detection error through the likelihood ratio test. For a given transmission time slot, the average received power received by Willie is determined as follows: ;(9) in It means Willie judges that Alice has transmitted hidden information. Indicates that Willie judges that Alice has not transmitted any hidden information is the detection error threshold. When the average power received by Willie is greater than , Willie judges that Alice has transmitted hidden information; if it is less than , then it is determined that Alice did not transmit hidden information.

[0035] According to the definition of DEP, DEP consists of false alarm probability and missed detection probability, that is, ,in , Willie's false detection probability is further divided into two cases and expressed as follows: (1) , ;(10) in is the transmission probability of a single time slot at Alice, ; ; ; ; ; ; (2) ; ;(11) in is the transmission probability of a single time slot at Alice, ; ; ; ; ; By performing derivative operations on each case, Willie's optimal detection threshold and minimum false detection probability are expressed as ;(12) in is the standard noise power, is a parameter that quantifies the size of the noise uncertainty, ; ;(13) in is the transmission probability of a single time slot at Alice, is the standard noise power, is a parameter that quantifies the size of the noise uncertainty, ; Furthermore, based on formula (13), Willie's average minimum false detection probability is ;(14) in is a linearly independent solution of the modified Bessel equation describing exponential decay type behavior, where the variables involved are expressed as follows G1 and G2 are solved using the Gauss Chebyshev method, where ; ; From formula (14), we can see that The value of The size of , that is, the transmission energy value preset in the transmission strategy of the present invention and the reflection strategy at BD will affect Willie's judgment. This means that by adjusting the preset transmission energy value and reflection coefficient, the ideal concealment effect can be achieved. Combined with equation (6), the concealment constraints of the present invention are (7a)-(7c).

[0036] This invention primarily considers concealment performance while satisfying concealment constraints. Due to the complexity of the problem, this invention prioritizes probabilistic transmission over reflection coefficient. Within the constraints, the two-dimensional optimization problem is converted to a one-dimensional optimization. The optimal probabilistic transmission threshold and reflection coefficient are then searched for to maximize the concealed transmission rate at Bob.

[0037] Now combined with the attached Figure 1 The specific embodiments of the present invention are described as follows: Figure 1 An example of a covert transmission system against full-duplex eavesdroppers in symbiotic radio is given. The distribution function parameter of each link is set to 1, the noise of Alice and Bob is 1, and the noise parameter of Willie is is 1, the self-interference coefficient is 0.5, hidden constraint is 0.1.

[0038] like Figure 2 As shown, at different reflection coefficients The theoretical and simulation values of Willie's average minimum false detection probability and the threshold . It can be observed that the theoretical and simulated values are consistent: the minimum DEP first increases and then decreases, and there exists an optimal threshold that maximizes the Willie expected minimum DEP. Furthermore, the DEP decreases with increasing reflection coefficient, and when the threshold is sufficiently large, the DEPs converge. Therefore, it can be concluded that the prior transmission probability, compared to the reflection coefficient, dominates the DEP.

[0039] like Figure 3 As shown, at different thresholds The theoretical and simulated values of Willie's average minimum false detection probability and noise parameters We found that along with increases with the increase of =5 tends to be stable, which means that the greater the noise uncertainty, the greater the probability of being detected. However, when the noise uncertainty reaches a certain value, the signal-to-noise ratio is already very low, and the signal is submerged in the noise. Even if the noise increases, the distinguishability between the signal and the noise is close to the limit, and the probability of false detection tends to be stable. For different transmission probabilities, the closer ,The larger the DEP is, the more uncertain the noise is. Therefore, when the noise uncertainty is large, the transmission probability should be increased to be close to the threshold to improve the Willie error detection probability.

[0040] Figure 4The figure shows the relationship between the concealed outage probability (COP) and the signal-to-interference-plus-noise ratio (SINR) for different reflection coefficients. The results show that the COP gradually decreases and approaches zero as the SINR increases. This is because a larger SINR results in more transmitted signals and a smaller probability of information outage. When the SINR approaches a certain value, the signal completely dominates, and the outage probability is zero. At the same SINR, a smaller reflection coefficient and a smaller reflected signal increase the probability of an outage. Therefore, the outage probability can be reduced by increasing the SINR and adjusting the reflection coefficient.

[0041] like Figure 5 Figure 2 shows the relationship between the concealment rate and CEE as a function of the reflection coefficient for both probabilistic and deterministic transmission. The results show that both the concealment rate and CEE increase with increasing reflection coefficients and concealment constraints. Furthermore, the concealment rate and CEE of the probabilistic transmission scheme are significantly higher than those of the deterministic transmission scheme, demonstrating the superiority of the proposed scheme. Therefore, it can be concluded that the probabilistic transmission scheme is indeed effective in resisting active attacks from adversaries, especially exhibiting significant performance improvements under energy-constrained conditions.

[0042] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The scope of protection of the present invention shall be the technical solutions set forth in the claims, including equivalent alternatives to the technical features of the technical solutions set forth in the claims. In other words, equivalent alternatives and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A covert communication method based on probabilistic transmission in symbiotic radio to counter full-duplex eavesdroppers, characterized in that: The following steps are involved: Build a system model, including the main transmitter Alice, the main receiver Bob, the auxiliary transmitter BD and the full-duplex eavesdropper Willie; The primary transmitter Alice selectively transmits information based on the link channel state with the primary receiver Bob: when the channel gain of the legitimate link is > Transmit information when the preset threshold δ is reached, otherwise do not transmit; The auxiliary transmitter BD uses the transmission behavior of the main transmitter Alice to secretly send confidential information to the main receiver Bob through the reflection link. The full-duplex eavesdropper Willie works in full-duplex mode and sends artificial noise to interfere with legitimate communications and eavesdrop.

2. According to claim 1, a covert communication method for resisting full-duplex eavesdroppers based on probabilistic transmission in symbiotic radio, characterized in that: The probability that Alice transmits hidden information in a single time slot is ； in represents the channel gain from Alice to Bob, which is expressed as ,|hab|² The mean of is exponentially distributed. is the preset threshold at Bob.

3. The covert communication method for resisting full-duplex eavesdroppers based on probabilistic transmission in symbiotic radio according to claim 1, characterized in that: The signal received by the main receiver Bob is expressed as ； in and denote the transmission power of Alice and Willie respectively, represents the reflection coefficient of BD, 、 and are the channel gains from Willie to Bob, Alice to BD, and BD to Bob, respectively. 、 and express; 、 and are the signals generated by Alice, Willie and BD respectively, where is the index used by each channel, is the total number of channels used, satisfying is the local noise at Bob, expressed as .

4. The covert communication method for resisting full-duplex eavesdroppers based on probabilistic transmission in symbiotic radio according to claim 3, characterized in that: First, demodulate the main signal. Bob's signal interference noise can be expressed as ； The denominator represents the main signal, and the numerator represents the noise, which includes the hidden signal , the interference signal sent by Willie and local noise , represents the reflection coefficient of BD, and denote the transmission power of Alice and Willie respectively, and denote the channel gains from Alice to Bob and BD respectively, and denote the channel gains from BD and Willie to Bob respectively; Assuming that the main signal can be perfectly removed from the received signal by perfect continuous interference cancellation, the SINR of the concealed signal is: ； The denominator represents the covert signal, and the numerator represents the noise, which includes the interference signal sent by Willie and local noise , represents the reflection coefficient of BD, and denote the transmission power of Alice and Willie respectively, represents the channel gain from Alice to BD, and denote the channel gains from BD and Willie to Bob respectively; Finally, the hidden signal is decoded. Using Shannon's formula theorem, Bob's hidden rate is as follows: ； Where p is the probability that Alice transmits covert information in a single time slot, Signal-to-noise ratio of the covert signal.

5. The covert communication method for resisting full-duplex eavesdroppers based on probabilistic transmission in symbiotic radio according to claim 4, characterized in that: Optimize Bob's concealment rate to maximize the reception rate at Bob. The optimization is defined as follows: in, represents the hidden constraint, represents the range of reflection coefficient, represents the reliability constraint, is an arbitrarily small positive integer, is the target rate threshold.

6. The covert communication method for resisting full-duplex eavesdroppers based on probabilistic transmission in symbiotic radio according to claim 5, characterized in that: Willie uses the likelihood ratio test to determine whether Alice transmits information. The average power of the received signal is: ； in and denote the channels from Willie and BD to Willie respectively, is the Willie self-interference coefficient; is the local noise of Willie, express, Indicates that no transmission has been made. Indicates transmission.

7. The covert communication method for resisting full-duplex eavesdroppers based on probabilistic transmission in symbiotic radio according to claim 6, characterized in that: According to the Newman-Pearson criterion, Willie minimizes the probability of detection error through the likelihood ratio test. For a given transmission time slot, the average received power received by Willie is determined as follows: ； in It means Willie judges that Alice has transmitted hidden information. Indicates that Willie judges that Alice has not transmitted any hidden information is the detection error threshold; when the average power received by Willie is greater than , Willie judges that Alice has transmitted hidden information; if it is less than , then it is determined that Alice did not transmit hidden information.

8. The covert communication method for resisting full-duplex eavesdroppers based on probabilistic transmission in symbiotic radio according to claim 7, characterized in that: Willie's false detection probability , where the false alarm probability , missed detection probability , by discussing the detection threshold in sections The relationship with channel parameters is solved.

9. The covert communication method for resisting full-duplex eavesdroppers based on probabilistic transmission in symbiotic radio according to claim 1, characterized in that: Willie uses two antennas in full-duplex mode to transmit artificial noise and eavesdrop simultaneously. The local noise adopts a bounded uncertainty model with a probability density function of: ； in is the standard noise power, is a parameter that quantifies the size of the noise uncertainty.

10. The covert communication method for resisting full-duplex eavesdroppers based on probabilistic transmission in symbiotic radio according to claim 1, characterized in that: All links are modeled as Rayleigh fading channels.

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