Anti-covert communication design method based on artificial noise assisted interference

Abstract

The invention discloses an anti-covert communication design method based on artificial noise assisted interference, and relates to the technical field of wireless communication. The method comprises the following steps: constructing an anti-covert communication system model with a full-duplex receiver; selecting an illegal information transmitter (Alice), an illegal information receiver (Bob) and a monitor (Willie) as entity research objects of the anti-covert communication system model; constructing two optimization problems: converting an anti-covert communication system model into constructing a listener optimal detection error probability optimization problem and an optimal artificial noise setting optimization problem; the optimization problem is simplified; solving an optimization problem; according to the design method, artificial noise (AN) is emitted in Alice and Bob communication environments to realize anti-covert communication, the optimal detection error probability optimization problem and the optimal artificial noise setting optimization problem are realized, the detection error probability at Willie is reduced, and relatively low noise emission power is used.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication, and particularly relates to a design method for anti-covert communication based on artificial noise assisted interference. Background Art

[0002] Physical layer secure communication utilizes the uncertainty and unpredictability of the wireless channel to minimize the acquisition of information by unauthorized eavesdroppers. However, in situations where users not only value the privacy and integrity of their information but also wish to avoid being monitored and hide their communication activities, traditional physical layer security may be insufficient. In some communication scenarios, the exposure of communication activities can bring unpredictable risks and losses. Covert wireless communication, with its advantage of hiding communication activities, has attracted extensive research interest and activities.

[0003] Traditional physical layer security technologies and covert wireless communication both aim to ensure communication security. Physical layer security focuses on protecting private communication content, while covert wireless communication focuses on protecting more fundamental and broader legitimate communication activities. In these studies, the focus is often on how to design from the perspective of Alice (illegal information transmitter) to ensure that Bob (illegal information receiver) can correctly receive information while avoiding detection by the eavesdropper (Willie). However, in practice, the role of the eavesdropper (Willie) is equally crucial. In many cases, we need to study from the perspective of the monitor how to effectively detect and identify the existence of covert communication, that is, attempt to detect or discover the existence of covert communication. For example, in the military and security fields, the need to detect illegal covert communication is equally crucial. However, research on "detecting" covert communication is still scarce, and most of the literature focuses on the design and optimization of transmitters.

[0004] Based on the above research, the present invention focuses on studying anti-covert communication technology from the perspective of the eavesdropper (Willie). The present invention realizes anti-covert communication by transmitting artificial noise (AN) in the communication environment of Alice (illegal information transmitter) and Bob (illegal information receiver), and designs a method for optimizing the optimal detection error probability problem and the optimal artificial noise setting optimization problem. The invention reduces the detection error probability at the eavesdropper (Willie) and uses a lower noise transmission power. Summary of the Invention

[0005] The purpose of the present invention is to provide a design method for anti-covert communication based on artificial noise assisted interference to solve the problem that there is little research on "detecting" covert communication in the prior art in the above background art, and most of the literature focuses on the design and optimization of transmitters.

[0006] To achieve the above object, the present invention is implemented by the following technical solutions:

[0007] An anti-covert communication design method assisted by artificial noise (AN) interference, comprising the following steps:

[0008] S1. Construct an anti-covert communication system model with a full-duplex receiver: Select an illegal information transmitter (Alice), an illegal information receiver (Bob), and a monitor (Willie) as the entity research objects of the anti-covert communication system model;

[0009] S2. Construct two optimization problems: Transform the anti-covert communication system model into an optimization problem for optimizing the optimal detection error probability of the monitor (Willie) and an optimization problem for setting the optimal artificial noise (AN);

[0010] S3. Simplify the optimization problems: Transform the optimization problem of the optimal detection error probability in S2 into solving the optimal P bmax , and transform the optimization problem of setting the optimal artificial noise (AN) in S2 into solving the optimal where P bmax represents the optimal noise power generated by the illegal information receiver (Bob), represents the minimum optimal noise power transmitted by the monitor (Willie);

[0011] S4. Solve the optimization problems: For the optimization problem of the optimal detection error probability, obtain the optimal P bmax by solving through a two-dimensional search method, and obtain the optimal For the optimization problem of setting the optimal artificial noise (AN), use the solved P bmax and to solve for P w ; where, represents the optimal detection error probability that can satisfy its own constraints, and P w represents the noise power transmitted by the monitor (Willie);

[0012] S5. Convergence and complexity analysis: Analyze the convergence and complexity of the anti-covert communication system model.

[0013] Preferably, the illegal information transmitter (Alice) has 1 information transmission antenna;

[0014] Both the illegal information receiver (Bob) and the monitor (Willie) have 2 antennas, namely an information receiving antenna and an information transmitting antenna;

[0015] In the anti-covert communication system model, the channel is a quasi-static Rayleigh fading channel, and the eavesdropper (Willie) fully knows any transmitted carrier frequency, the relevant antennas, and the distances between all nodes.

[0016] Preferably, the S1 specifically includes the following content:

[0017] S101. Calculate the signals received at the illegal information receiver (Bob) and the signals received at the eavesdropper (Willie):

[0018] Let the channels from the illegal information transmitter (Alice) to the illegal information receiver (Bob), from the illegal information transmitter (Alice) to the eavesdropper (Willie), and from the illegal information receiver (Bob) to the eavesdropper (Willie) be represented by h ab 、h aw and h bw respectively. The signal received at the illegal information receiver (Bob) is:

[0019]

[0020] where h wb represents the channel from the eavesdropper (Willie) to the illegal information receiver (Bob), and h bb represents the channel from the illegal information receiver (Bob) to itself; x a 、x b represent the signals transmitted by the illegal information transmitter (Alice) and the illegal information receiver (Bob) respectively, satisfying where i = 1,..., n represents the symbol index;

[0021] Similarly, the signal received at the eavesdropper (Willie) is:

[0022]

[0023] where, n b and n w are both complex additive white Gaussian noises, represented by and respectively;

[0024] S102. In the anti-covert communication system model, the eavesdropper (Willie) faces a binary hypothesis problem. The null hypothesis H0 means that the illegal information transmitter (Alice) does not transmit, while the alternative hypothesis H1 means that the illegal information transmitter (Alice) transmits and sends covert information to the illegal information receiver (Bob); Use 1 / 2 to represent the prior probabilities of the hypotheses H0 and H1. Based on this, the detection error probability is given by:

[0025]

[0026] where is the probability that the eavesdropper (Willie) makes a decision in favor of H1 when H0 is true; is the probability that the eavesdropper (Willie) makes a decision in favor of H0 when H1 is true;

[0027] After the operation, the detector threshold at the eavesdropper (Willie) becomes:

[0028]

[0029] Meanwhile, the minimum detection error probability at the eavesdropper (Willie) is expressed as:

[0030]

[0031] where φ is the self-interference coefficient at the illegal information receiver (Bob); P a is the transmission power of the illegal information transmitter (Alice);

[0032] S103. Calculate the transmission outage probability from the illegal information transmitter (Alice) to the illegal information receiver (Bob); When the illegal information transmitter (Alice) is transmitting, the signal-to-interference-plus-noise ratio at the illegal information receiver (Bob) is:

[0033]

[0034] Assume that there is a predetermined rate from the illegal information transmitter (Alice) to the illegal information receiver (Bob), denoted by R ab ; When C ab ≤R ab , the transmission from the illegal information transmitter (Alice) to the illegal information receiver (Bob) is interrupted, where C ab is the channel capacity from the illegal information transmitter (Alice) to the illegal information receiver (Bob); The transmission outage probability from the illegal information transmitter (Alice) to the illegal information receiver (Bob) is:

[0035]

[0036] where |hij| 2 The average value in different communication time slots is denoted by 1 / λ ij , where the subscript ij is ab ,,aw , bw or bb ;

[0037] S104. Solve the expected detection error probability of the eavesdropper (Willie) and analyze the new optimization problem:

[0038] Use the detection error probability at the eavesdropper (Willie) as a measure of the concealment. The expected detection error probability of the eavesdropper (Willie) is:

[0039]

[0040] where

[0041] Preferably, the S2 specifically includes the following content:

[0042] Under the condition of the detection error probability constraint ε, solve the optimal minimum artificial noise (AN) power. The functional representations of the optimal detection error probability optimization problem and the optimal artificial noise (AN) setting optimization problem are as follows:

[0043]

[0044] subject to π 1 R ab (1 - δ ab ) ≥ τ, (1.9)

[0045] P bmin + P bmax ≤ 2P avg , (1.10)

[0046]

[0047] The maximum noise power P w at the eavesdropper (Willie) satisfies the transmission outage probability condition to ensure effective communication. Thus, the upper limit criterion of P w is obtained as follows:

[0048]

[0049] P w The proof is as follows: In the case where the illegal information receiver (Bob) does not emit noise, P w satisfies: The transmission outage probability that makes the channel capacity C ab is less than the preset rate R ab , and its functional representation is:

[0050]

[0051] Meanwhile, δ ab (P w ) satisfies:

[0052] R ab (1 - δ ab (P w )) ≥ τ·(1.14)

[0053] Simplifying (1.14) gives:

[0054]

[0055] where R ab is the preset transmission rate between the illegal information transmitter (Alice) and the illegal information receiver (Bob); τ is the given effective covert rate requirement.

[0056] Preferably, the specific content of S3 is as follows:

[0057] The expected detection error probability at the eavesdropper (Willie) is:

[0058]

[0059] where

[0060] Preferably, the solution of the optimization problem in S4 specifically refers to: solving the optimization problem P1 and finding the optimal solution by using a step - by - step solution method

[0061] By solving the formulas (1.9) and (1.11), their solutions are respectively and Thus, solving The specific function is expressed as:

[0062]

[0063] Preferably, the specific content of S4 is as follows:

[0064] S401. Give the proposition: The optimal is obtained by the search method; Transforming (1.9) and (1.11) gives:

[0065]

[0066] S402. Given the initial values ∈ = 0.4, R ab = 1, φ = 0.01, τ = 0.01:0.5;

[0067] S403. Let the given initial values be substituted into Equation (1.18), and obtain through the gradient descent method in S401

[0068]

[0069] S404. Then substitute each initial value into (1.12) to obtain the upper limit of P under the fixed τ value, and search within the range of P w until w until

[0070] S405. Repeat the steps of S404 until the end to obtain the optimal and

[0071] The above formula (1.17) is the solution of formula (1.9) and formula (1.11) respectively. Change the value of P w until At this time, P w is the noise power of the optimal minimum listener (Willie).

[0072] Preferably, the complexity analysis described in S5 specifically includes the following content:

[0073] Based on the calculation of the number of multiplications, the complexity analysis is as follows:

[0074] According to Equation (1.18), (1.19) and the solution process of in S401, in terms of floating-point operations, record the computational complexity of as while the computational complexity of

[0075]

[0076] Therefore, the total complexity of the anti-covert communication system model is:

[0077]

[0078] where t, p, q represent the number of iterations.

[0079] Compared with the prior art, the beneficial effects of the present invention are:

[0080] (1) The present invention contemplates a covert communication system in which both the receiver and the supervisor operate in full-duplex mode. In this system, the role of the warden is to interfere with the communication between the illegal information transmitter (Alice) and the illegal information receiver (Bob) by actively generating artificial noise (AN), thereby reducing the communication quality. This forces the communicators to make two choices: abandon the communication or reduce the interference noise power transmitted by the illegal information receiver (Bob) to improve the communication quality. With the above design, anti-covert communication is achieved. For the above system, the present invention first proposes the concept of anti-covert communication and studies the impact of the interference noise power transmitted by Willie on the performance of covert communication.

[0081] (2) Considering the uncertainty of the interference noise (transmitted by the illegal information receiver (Bob)) and the artificial noise (AN) (transmitted by the monitor (Willie)), the optimization problem of the minimum artificial noise (AN) power at the monitor (Willie) under the constraint of the expected detection error probability is analyzed. The present invention proposes an algorithm for minimizing the detection error probability. The numerical results show that the anti-covert communication performance under artificial noise interference is superior, which can reduce the performance of covert communication and achieve anti-covert communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 It is a schematic flow chart of the anti-covert communication design method based on artificial noise-assisted interference in the present invention;

[0083] Figure 2 It is a model diagram of the anti-covert communication system in the anti-covert communication design method based on artificial noise-assisted interference in the present invention;

[0084] Figure 3 It is a schematic diagram of the relationship between τ and in the anti-covert communication design method based on artificial noise-assisted interference in Embodiment 1 of the present invention;

[0085] Figure 4 It is a schematic diagram of the relationship between τ and in the anti-covert communication design method based on artificial noise-assisted interference in Embodiment 1 of the present invention;

[0086] Figure 5 It is a schematic diagram of the relationship between P w and P e in the anti-covert communication design method based on artificial noise-assisted interference in Embodiment 1 of the present invention; DETAILED DESCRIPTION OF THE INVENTION

[0087] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0088] Compared with the traditional research on covert communication, in this work, the present invention first introduces the concept of anti-covert communication and proposes to use artificial noise (AN) to achieve anti-covert communication. Specifically, the eavesdropper (Willie) transmits artificial noise to affect the covert communication between the illegal information transmitter (Alice) and the illegal information receiver (Bob). Although the use of artificial noise and interference signals to enhance physical layer security has been widely discussed in the literature, there are still many problems in practical applications. However, no researcher has stood from the perspective of the eavesdropper (Willie) to use artificial noise (AN) to enhance its eavesdropping ability and prevent dangerous communication behaviors (such as spies stealing information and spreading it outside). The following describes the anti-covert communication design method based on artificial noise-assisted interference proposed by the present invention in conjunction with the relevant drawings, and the specific content is as follows.

[0089] Embodiment 1:

[0090] Please refer to Figure 1-2 , the anti-covert communication design method based on artificial noise-assisted interference includes the following steps:

[0091] S1. Construct an anti-covert communication system model with a full-duplex receiver: Select the illegal information transmitter (Alice), the illegal information receiver (Bob), and the eavesdropper (Willie) as the entity research objects of the anti-covert communication system model;

[0092] The illegal information transmitter (Alice) has 1 information transmission antenna;

[0093] Both the illegal information receiver (Bob) and the eavesdropper (Willie) have 2 antennas, namely an information receiving antenna and an information transmission antenna;

[0094] The channel in the anti-covert communication system model is a quasi-static Rayleigh fading channel, and the eavesdropper (Willie) fully understands any transmitted carrier frequency, the relevant antennas, and the distances between all nodes.

[0095] S1 specifically includes the following content:

[0096] S101. Calculate the signals received at the illegal information receiver (Bob) and the signals received at the eavesdropper (Willie);

[0097] The channels from the illegal information transmitter (Alice) to the illegal information receiver (Bob), from the illegal information transmitter (Alice) to the eavesdropper (Willie), and from the illegal information receiver (Bob) to the eavesdropper (Willie) are denoted by h ab , h aw and h bw respectively. The signal received at the illegal information receiver (Bob) is:

[0098]

[0099] Similarly, the signal received at the eavesdropper (Willie) is:

[0100]

[0101] n b and n w are both additive white Gaussian noise (AWGN), denoted by and respectively.

[0102] S102. In the anti-covert communication system model, the eavesdropper (Willie) faces a binary hypothesis problem. The null hypothesis H0 means that the illegal information transmitter (Alice) does not transmit, while the alternative hypothesis H1 means that the illegal information transmitter (Alice) transmits and sends covert information to the illegal information receiver (Bob). In the present invention, the prior probabilities of the hypotheses H0 and H1 are represented by 1 / 2. Based on this, the detection error probability is given by the following formula:

[0103]

[0104] where is the probability that the eavesdropper (Willie) makes a decision in favor of H1 when H0 is true. is the probability that the eavesdropper (Willie) makes a decision in favor of H0 while H1 is true.

[0105] After calculation, the detector threshold at the eavesdropper (Willie) becomes:

[0106]

[0107] Meanwhile, the minimum detection error probability at the eavesdropper (Willie) is expressed as:

[0108]

[0109] where φ is the self-interference coefficient at the illegal information receiver (Bob), where Pa The transmit power of the illegal information transmitter (Alice);

[0110] S103. Calculate the transmission outage probability from the illegal information transmitter (Alice) to the illegal information receiver (Bob); When the illegal information transmitter (Alice) is transmitting, the signal-to-interference-plus-noise ratio (SINR) at the illegal information receiver (Bob) is:

[0111]

[0112] Assume that there is a predetermined rate from the illegal information transmitter (Alice) to the illegal information receiver (Bob), denoted by R ab When C ab ≤R ab the transmission from the illegal information transmitter (Alice) to the illegal information receiver (Bob) is interrupted, where C ab is the channel capacity from the illegal information transmitter (Alice) to the illegal information receiver (Bob); The transmission outage probability from the illegal information transmitter (Alice) to the illegal information receiver (Bob) is:

[0113]

[0114] where

[0115] S104. Solve the expected detection error probability of the eavesdropper (Willie) and analyze the new optimization problem:

[0116] The detection error probability at the eavesdropper (Willie) can be used as a measure of the concealment level. The expected detection error probability of the eavesdropper (Willie) is:

[0117]

[0118] where

[0119] S2. Construct two optimization problems. To reduce the detection error probability of traditional covert communication, a design method for anti-covert communication based on artificial noise assisted interference is proposed, which specifically includes the following: Under the constraint of the detection error probability ε, solve for the optimal minimum AN noise power; The two optimization problems are to construct the optimal detection error probability optimization problem 1 for the eavesdropper and the optimal artificial noise setting optimization problem 2, which specifically include the following:

[0120] The new optimization problems are as follows:

[0121]

[0122] subject to π 1 R ab (1 - δ ab ) ≥ τ, (1.50)

[0123] P bmin +P bmax ≤ 2P avg , (1.51)

[0124]

[0125] The maximum noise power P at the eavesdropper (Willie) w should satisfy the transmission outage probability condition to ensure effective communication; thus, we can obtain the upper bound criterion of P w as follows:

[0126]

[0127] P w The proof is as follows: In the case where the illegal information receiver (Bob) does not emit noise, P w should satisfy such that the transmission outage probability of the channel capacity C ab is less than the preset rate R ab :

[0128]

[0129] Meanwhile, δ ab (P w ) should satisfy:

[0130] R ab (1 - δ ab (P w )) ≥ τ. (1.55)

[0131] Simplifying (1.55) gives:

[0132]

[0133] S3. Simplify the optimization problem: Transform the optimal detection error probability optimization problem in S2 into solving the optimal P bmax and transform the optimal artificial noise setting optimization problem in S2 into solving the optimal Specifically, it includes the following content:

[0134] The expected detection error probability at the eavesdropper (Willie) can be obtained as:

[0135]

[0136] where

[0137] Then the P1 optimization problem becomes as follows:

[0138]

[0139] subject to π 1 R ab (1 - δ ab ) ≥ τ, (1.58)

[0140] P bmin + P bmax ≤ 2P avg , (1.59)

[0141]

[0142] S4. Solve the optimization problem: For the optimal detection error probability optimization problem, the optimal P is obtained by the two-dimensional search method bmax , and the optimal For the optimal artificial noise setting optimization problem, use the solved P bmax and to solve for P w ;

[0143] S4 specifically includes the following content:

[0144]

[0145] The above formula (1.61) is the solution of equations (1.58) and (1.60) respectively. Change the value of P w until The P at this time w is the noise power of the optimal minimum listener (Willie).

[0146] S401. Give a proposition that the optimal is obtained by the search method; Transforming equation (1.58) gives:

[0147]

[0148] S402. Given the initial values ε = 0.4, R ab = 1R ab = 1,

[0149] φ = 0.01, τ = 0.01:0.5;

[0150] S403. Let the given initial values be substituted into equation (1.62), and the

[0151] S404. Then, substituting each initial value into Equation (1.53), the upper limit of P under the fixed τ value can be obtained. At this time, we can search within the range of P w until w is reached.

[0152] S405. Repeat step S404 until the end to obtain the optimal and

[0153] S5. Complexity analysis: Based on the optimization problem in S4, an analysis of the convergence and complexity of its algorithm is proposed. This algorithm can converge and obtain the optimal solution. Based on the calculation of the number of multiplications, the complexity of this algorithm is relatively low, which specifically includes the following:

[0154] S501. Complexity analysis: Based on the calculation of the number of multiplications, the complexity analysis is as follows:

[0155] According to Equations (1.62), (1.63) and the solution process of in S401, in terms of floating-point operations, the computational complexity of is while the computational complexity of

[0156] Therefore, the total complexity of the anti-covert communication system model is:

[0157]

[0158] where t, p, and q are the number of iterations.

[0159] Compared with the traditional covert communication scheme, the complexity of the traditional covert communication scheme is usually higher than that of the proposed scheme. Therefore, the complexity of the artificial noise assisted interference scheme proposed in the present invention is lower than that of the traditional covert communication scheme.

[0160] Example 2:

[0161] Based on Example 1, but different in that the present invention further designs a simulation experiment to verify the correctness and effectiveness of the derivation results of the anti-covert communication design method based on artificial noise assisted interference proposed in the present invention. The specific simulation parameter settings are as follows:

[0162] Set the transmission power of the illegal information transmitter (Alice) to P a = -10 dB, the predetermined rate of the illegal information transmitted from the illegal information transmitter (Alice) to the illegal information receiver (Bob) is R ab = 1, and the receiver noise power of the illegal information receiver (Bob) and the eavesdropper (Willie) is The self - interference cancellation coefficient of the illegal information receiver (Bob) is φ = 0.01. The average power constraint of the artificial noise power of the illegal information receiver (Bob) is 40 dB, and the upper - bound constraint of the detection error probability at the eavesdropper (Willie) is ε = 0.4. For simplicity, the means of all fading channels are considered as

[0163] Figure 3 The results show that when the power of P a remains unchanged, the influence of φ on This is because In formula (1.62), all other variables are known and fixed; therefore, as φ increases, the function also decreases, resulting in a decrease in the value of P w Moreover, the present invention also finds that the value of increases as P a increases. This is because the value of increases as the value of P a increases, which is consistent with the changes described in the figure.

[0164] Figure 4 shows the influence of different P a power times and different self - interference coefficients φ on In the first half of the τ value, the values of P bmax and can satisfy the constraint condition Therefore, the previous value can reach the maximum value of the constraint condition, that is The value of P_{w}^{*} can no longer make satisfy the constraint condition, so will decrease, and as φ increases, the speed of reaching the break point will be faster and faster, which is consistent with the changes described in the figure.

[0165] Figure 5 shows the influence of different self - interference coefficients φ on the detection error probability P e of the eavesdropper (Willie) when the required secrecy rate is fixed at τ. The results are consistent with the figure.

[0166] As described above, it is only used to help understand the method of the present invention and its core essence. However, the protection scope of the present invention is not limited thereto. For those of ordinary skill in the art in the technical field of the present invention, any equivalent replacement or change made within the technical scope disclosed by the present invention according to the technical solution and inventive concept of the present invention should be covered within the protection scope of the present invention. In summary, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. Anti-covert communication design method based on artificial noise assisted interference, characterized in that: The following steps are involved: S1. Construct an anti-covert communication system model with a full-duplex receiver: select illegal information transmitters, illegal information receivers and eavesdroppers as the entity research objects of the anti-covert communication system model; S2. Construct two optimization problems: transform the anti-covert communication system model into the optimization problem of constructing the optimal detection error probability optimization problem of the listener and the optimization problem of the optimal artificial noise setting; S3, simplify the optimization problem: transform the optimal detection error probability optimization problem in S2 into solving the optimal P bmax , transforming the optimization problem of the optimal artificial noise setting in S2 into solving the optimal Among them, P bmax represents the optimal noise power generated by the illegal information receiver, represents the minimum optimal noise power emitted by the listener; S4. Solve the optimization problem: For the optimization problem of optimal detection error probability, the optimal P is obtained by two-dimensional search method. bmax , and obtain the optimal For the optimal artificial noise setting optimization problem, the solved P bmax and To solve P w ;in, It means that the detection error probability can satisfy the optimal detection error probability under its own constraints, P w It represents the noise power emitted by the listener; S5. Convergence and complexity analysis: Analyze the convergence and complexity of the anti-covert communication system model.

2. The anti-covert communication design method based on artificial noise assisted interference according to claim 1 is characterized in that: The illegal information transmitter has an information transmission antenna; The illegal information receiver and the eavesdropper each have two antennas, namely an information receiving antenna and an information transmitting antenna; The channel in the anti-covert communication system model is a quasi-static Rayleigh fading channel, and the listener is fully aware of any transmitted carrier frequency, related antennas and distances between all nodes.

3. The anti-covert communication design method based on artificial noise assisted interference according to claim 1 or 2, characterized in that: The S1 specifically includes the following contents: S101, calculating the signal received by the illegal information receiver and the signal received by the monitor: The channels from the illegal information transmitter to the illegal information receiver, from the illegal information transmitter to the monitor, and from the illegal information receiver to the monitor are represented by h ab 、h aw and h bw It means that the signal received at the illegal information receiver is: Among them, h wb represents the channel from the listener to the illegal information receiver, h bb represents the channel from illegal information receiver to illegal information receiver; x a 、x b Indicates the satisfied signals transmitted by the illegal information transmitter and the illegal information receiver respectively Where i=1,...,n represents the symbol index; Similarly, the signal received at the listener is: Among them, n b and n w are all complex white Gaussian noise, respectively. and express; S102. In the anti-covert communication system model, the listener faces a binary hypothesis problem. The null hypothesis H0 indicates that the illegal information transmitter did not transmit, while the alternative hypothesis H1 indicates that the illegal information transmitter did transmit and sent covert information to the illegal information receiver. 1 / 2 is used to represent the prior probability of hypothesis H0 and H1. Based on this, the probability of detection error is Given by: in, is the probability that the listener makes a decision in favor of H1 when H0 is true; is the probability that the listener makes a decision in favor of H0 when H1 is true; After calculation, the detector threshold at the listener becomes: At the same time, the minimum detection error probability at the listener is expressed as: Where φ is the self-interference coefficient at the illegal information receiver; P a The transmission power of illegal information transmitters; S103, calculating the transmission interruption probability from the illegal information transmitter to the illegal information receiver; in the case of transmission by the illegal information transmitter, the signal to interference noise ratio at the illegal information receiver is: Assume that there is a predetermined rate from the illegal information transmitter to the illegal information receiver, denoted by R ab Indicates; when C ab ≤R ab When the transmission from the illegal information transmitter to the illegal information receiver is interrupted, C ab is the channel capacity from the illegal information transmitter to the illegal information receiver; the transmission interruption probability from the illegal information transmitter to the illegal information receiver is: in, |hij| 2 The average value in different communication time slots is 1 / λ ij Indicates that the subscript ij for ab , aw , bw or bb ; S104. Solve the expected detection error probability of the listener and analyze the new optimization problem: The detection error probability at the listener is used as a measure of concealment, and the expected detection error probability of the listener is: in, 4. The anti-covert communication design method based on artificial noise assisted interference according to claim 3 is characterized in that: The S2 specifically includes the following contents: Under the condition of detection error probability constraint ε, the optimal minimum artificial noise power is solved; the function expression of the optimal detection error probability optimization problem and the optimal artificial noise setting optimization problem is as follows: subject top1R ab (1-d ab )≥τ, (1.9) P bmin +P bmax ≤2P avg , (1.10) The maximum noise power P at the listener w Satisfy the transmission interruption probability condition to ensure effective communication; thus, P w The upper limit criterion is as follows: P w The proof is as follows: When the illegal information receiver does not emit noise, P w Satisfy: Make the channel capacity C ab The transmission interruption probability is less than the preset rate R ab , whose function is expressed as: At the same time ab (P w )satisfy: R ab (1-d ab (P w ))≥t. (1.14) Simplifying (1.14) we get: Among them, R ab is the preset transmission rate between the illegal information transmitter and the illegal information receiver; τ is the given effective concealment rate requirement.

5. The anti-covert communication design method based on artificial noise assisted interference according to claim 4 is characterized in that: The S3 specifically includes the following contents: The expected detection error probability at the listener is: in, 6. The anti-covert communication design method based on artificial noise assisted interference according to claim 5 is characterized in that: Solving the optimization problem in S4 specifically refers to: solving the optimization problem P1, taking a step-by-step approach to find the optimal By solving formula (1.9) and formula (1.11), the solutions are and So as to solve The specific function is expressed as:

7. The anti-covert communication design method based on artificial noise assisted interference according to claim 6 is characterized in that: The S4 specifically includes the following contents: S401, given proposition: optimal Obtained by searching method; transforming (1.9) and (1.11) yields: S402, give initial value ∈=0.4,R ab =1, φ=0.01,τ=0.01:0.5; S403, let the given initial value be substituted into formula (1.18), and obtain it through the gradient descent method in S401 S404, then substitute the initial values ​​into (1.12) to obtain P under a fixed τ value w The upper limit of P w Search within the range until S405, repeat step S404 until the end, and obtain the optimal and The above formula (1.17) is the solution of formula (1.9) and formula (1.11), respectively. w until the value of At this time, P w That is the optimal and minimum noise power of the listener.

8. The anti-covert communication design method based on artificial noise assisted interference according to claim 7 is characterized in that: The complexity analysis described in S5 specifically includes the following contents: Based on the calculation of the number of multiplications, the complexity analysis is as follows: According to equations (1.18), (1.19) and S401 The solution process, in terms of floating-point operations, will The computational complexity of and The computational complexity is Therefore, the total complexity of the anti-covert communication system model is: Among them, t, p, and q represent the number of iterations.

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