Covert transmission method based on user fairness in cognitive radio network

Abstract

The application discloses a hidden transmission method based on user fairness in a cognitive radio network. Step 1: a cognitive radio network with multiple secondary users is established; Step 2: in the cognitive radio network, a primary user source node transmits information to a primary user receiving node, and multiple secondary user transmitting nodes transmit hidden information to secondary user destination nodes; a suitable transmitting node is selected from the multiple secondary user transmitting nodes to transmit hidden information, and a suitable interference node is selected to transmit artificial noise; an illegal user detects whether the secondary user transmitting node transmits hidden information; and Step 3: under the constraints of hidden transmission and the maximum interference allowed by the primary user, the optimal transmitting power of the secondary user transmitting node and the interference node is obtained; and a fairness node selection method is provided. The application can effectively reduce the detection performance of the illegal user, and significantly improve the fairness of information transmission between users and the hidden transmission rate of the system.

Description

User-fairness-based covert transmission methods in cognitive radio networks Technical Field

[0001] This invention belongs to the field of wireless covert communication technology, specifically relating to a covert transmission method based on user fairness in cognitive radio networks. Background Technology

[0002] Due to the broadcast nature of wireless channels, information is vulnerable to eavesdropping and attacks by unauthorized users during transmission, making information transmission security an increasingly important concern. Traditional encryption algorithms use methods such as key encryption to ensure secure information transmission, but they can only guarantee that the information is not correctly decoded by unauthorized users to a certain extent; they cannot protect the information transmission process itself. Covert communication technology aims to enable wireless transmission between two users while ensuring that the transmission process remains concealed from unauthorized users, and is considered a promising security technology.

[0003] In cognitive radio networks, there are primary users and secondary users. Secondary users need to use the primary user's spectrum to transmit information. In Underlay mode, when the primary user's source node transmits information to the primary user's receiving node, the secondary user's transmitting node uses the primary user's spectrum to transmit information to the secondary user's destination node, but the secondary user's transmit power must be less than the primary user's interference threshold.

[0004] In this network environment, when multiple secondary user transmitting nodes need to send information to a single secondary user destination node, selecting a suitable node for transmission can effectively improve the system transmission rate. However, in the field of covert communication, it is necessary to consider not only the transmission rate of the legitimate channel but also the covertness of the transmission process. Furthermore, due to differences in location and environment, some users have better transmission channel conditions than others. If the selection process solely considers current transmission or covert performance, it can lead to significant differences in the chances of being selected for transmission, ultimately resulting in unfairness among users. Summary of the Invention

[0005] The purpose of this invention is to provide a covert transmission method based on user fairness in cognitive radio networks, which solves the problem of unfair information transmission between users caused by channel differences between users in the prior art.

[0006] The technical solution adopted in this invention is:

[0007] The covert transmission method based on user fairness in cognitive radio networks is carried out according to the following steps:

[0008] Step 1: Establish a cognitive radio network with multiple secondary users; the cognitive radio network includes one primary user source node T, one primary user receiver node R, and K secondary user transmitter nodes S1, S2, ... S K A secondary user destination node D, and an illegal user W;

[0009] Step 2: In a cognitive radio network, information is transmitted from the primary user source node to the primary user receiver node, and multiple secondary user transmitter nodes transmit covertly to the secondary user destination node; a suitable transmitter node is selected from among the multiple secondary user transmitter nodes to send covert information, and a suitable jamming node is selected to send artificial noise; unauthorized users detect whether the secondary user transmitter nodes are sending covert information.

[0010] Step 3: Under the constraints of concealment and the maximum interference allowed by the primary user, the optimal transmission power of the secondary user transmitting node and the interfering node is obtained; a fair node selection method is proposed.

[0011] The invention is further characterized by;

[0012] Step 1 is as follows:

[0013] In a cognitive radio network, each node is equipped with only a single antenna and operates in half-duplex mode. Each transmission cycle contains M time slots, and only one node is allowed to transmit covert messages within each time slot. It is assumed that the channel between any two nodes is a quasi-static Rayleigh fading channel, meaning the channel fading coefficient remains constant within the same transmission time slot but changes independently and randomly in different time slots. The connections between nodes T and R, T and D, and S are described. k (k = 1, 2, ..., K) to D, S k To R, S k The channel fading coefficients to W are respectively represented by h tr h td h kd h kr h kw In other words, assuming h tr h td h kd h kr h kw They respectively follow a mean of zero and a variance of λ. tr , λ td , λ kd , λ kr , λ kw The noise is a cyclic symmetric complex Gaussian distribution; it is assumed that all receiver noise is independent zero-mean additive white Gaussian noise with a noise power of N0.

[0014] In step 2, the unauthorized user detects whether the secondary user's transmitting node sends covert information and uses the Neyman-Pearson criterion to determine whether covert transmission exists.

[0015] Step 2 is as follows:

[0016] Step 2.1: The primary user source node sends information to the primary user receiving node. The information received by the primary user receiving node is as follows (1):

[0017]

[0018] Among them, P t and x t (m) represent the transmit power and transmitted signal of the primary user source node T, respectively, and satisfy E[|x t (m)| 2 ] = 1, P i and x i (m) Selected secondary user transmitter node S i The transmit power and the transmitted signal, and satisfying E[|x i (m)| 2 ] = 1; P j and x j (m) represent the selected interference node S. j The transmit power and transmitted artificial noise, and satisfying E[|x j (m)| 2 ] = 1, P j Obey [0, P] J The uniform distribution of n r (m) is the white noise at the primary user receiving node R;

[0019] Step 2.2: The selected secondary user transmitting node is denoted as S. i Simultaneously, a suitable node is selected to send artificial noise; the selected interfering node is denoted as S. j Assume S j The secondary user destination node cooperates with the secondary user destination node to eliminate artificial noise. H0 and H1 represent the cases where the secondary user transmitting node does not send information and when it sends information, respectively. The information received by the secondary user destination node is as follows (2):

[0020]

[0021] Where m = 1, ..., M, represents the m-th transmission time slot, and n d (m) represents the white noise at point D;

[0022] Under H1, the information transmission rate from the secondary user transmitting node to the secondary user destination node is as follows (3):

[0023]

[0024] According to the definition of the probability of a system security interruption, the probability of a system security interruption is as follows (4):

[0025] P out =Pr{C sd <R c} (4);

[0026] Among them, R c Substituting formula (3) into formula (4) for the system's target transmission rate, the system's security interruption probability is given by formula (5):

[0027]

[0028] Based on the definition of covert transmission rate, the covert transmission rate of the system is obtained as follows (6):

[0029] R sd =R c (1-P out (6);

[0030] Substituting formula (5) into formula (6), we further obtain the formula for the system's covert transmission rate as follows (7):

[0031] R sd =R c {1-Pr(P i |h id | 2 <α)} (7);

[0032] in,

[0033] Step 2.3: When an unauthorized user detects whether a secondary user's transmitting node is sending covert information, the information it receives is as follows (8):

[0034]

[0035] Where, n w (m) represents the noise at point W;

[0036] To determine whether a secondary user's transmitting node sends covert information to the secondary user's destination node, an unauthorized user uses the Neyman-Pearson criterion to judge the transmission status of the secondary user's covert information. The judgment formula is as follows (9):

[0037]

[0038] Among them, T w Let T be the average received power of the illegal user, and τ be the decision threshold for the illegal user. w When the threshold is >τ, the unauthorized user believes that the secondary user's transmitting node has sent covert information; the judgment result at this time is represented by D1. Meanwhile, T... w When <τ, the illegal user believes that the secondary user's transmitting node does not send covert information, and the judgment result is represented by D0.

[0039] Assuming that the number of symbol transmissions tends to infinity within a communication phase, i.e. K→∞, the average power received by illegal users is given by the following formula (10);

[0040]

[0041] Let the false negative rate and false positive rate be expressed as P. MD =Pr{D0|H1} and P FA =Pr{D1|H0}; The sum of the false negative rate and the false positive rate gives the tester's error probability as follows (11):

[0042] ξ=P MD +P FA (11);

[0043] When the system satisfies P i |h iw | 2 ≤P J |h jw | 2 When the decision threshold is set to the optimal decision threshold τ, the decision threshold is then set. * =ρ3, the minimum test error probability of the system is given by the following formula (12):

[0044]

[0045] The mean of the minimum test error probability is obtained as shown in the following formula (13):

[0046]

[0047] Step 3 is as follows:

[0048] Step 3.1: To prevent unauthorized users from learning about the transmission process, the minimum probability of error for unauthorized users must satisfy the following formula (14):

[0049] ξ * ≥1-ε (14);

[0050] Where ε is the threshold of the concealment condition;

[0051] To ensure that the transmission power of secondary users is less than the interference threshold of primary users, their transmission power must meet the following condition (15):

[0052] P i |h ir | 2 +P J |h jr | 2 ≤I th (15);

[0053] I th This is the maximum interference threshold allowed by the main user;

[0054] Based on the constraints of formulas (14) and (15), the optimal transmit power of the secondary user transmitting node is obtained as follows: formula (16), and the optimal interference power of the interfering node is obtained as follows: formula (17).

[0055]

[0056]

[0057] Substituting formula (16) into formula (7) for the system's covert transmission rate, we further obtain the system's covert transmission rate as formula (18):

[0058]

[0059] in,

[0060] Step 3.2: From formula (18), the magnitude of the covert transmission rate is related to the channel conditions between users. Select... As an interference node, let choose As the transmitting node, a node selection scheme that balances transmission rate and fairness is proposed, with interfering node S... j and secondary user transmitter node S i The results are obtained using the following formulas (19) and (20):

[0061]

[0062] in, make

[0063]

[0064] in:

[0065]

[0066] Substituting formulas (19) and (20) into formula (18), we obtain the covert transmission rate of the system under this transmission scheme as formula (21):

[0067]

[0068] Further solving equation (21) yields the following expression for the system's covert transmission rate:

[0069]

[0070] in:

[0071] First of all, let Find the probability density function f for Z. Z (z) represents formula (23):

[0072]

[0073]

[0074] Secondly, let Find the probability density function f for T. T (t) is from formula (24):

[0075]

[0076] Finally, let Find the probability density function f for W. W (w) is from formula (25):

[0077]

[0078] Where Ei(·) is the exponential integral function,

[0079] The beneficial effects of this invention are that the covert transmission method based on user fairness in cognitive radio networks achieves fairness in information transmission among users and improves the covert transmission rate of the system through a fairness node selection scheme. It effectively improves the covert transmission rate of the system under the conditions of minimum detection error probability satisfying given covert constraints and maximum allowable interference constraints for the primary user, and provides the optimal transmission power for the secondary user transmitting node and interfering node. Furthermore, this method selects suitable secondary user transmitting nodes and interfering nodes based on the ratio of channel conditions between nodes to their mean, further improving the fairness of information transmission among users. Compared with existing methods, this invention can effectively reduce the detection performance of unauthorized users, significantly improve the fairness of information transmission among users and the covert transmission rate of the system, and has certain practical significance. Attached Figure Description

[0080] Figure 1 is a wireless transmission network model diagram of the covert transmission method based on user fairness in cognitive radio networks according to the present invention;

[0081] Figure 2 is a comparison of the covert transmission rate of the covert transmission method based on user fairness in the cognitive radio network of the present invention with that of the existing scheme under different numbers of nodes K.

[0082] Figure 3 is a comparison of the fairness of the covert transmission method based on user fairness in cognitive radio networks of the present invention with existing schemes under different numbers of nodes K. Detailed Implementation

[0083] The following detailed description of the covert transmission method based on user fairness in cognitive radio networks according to the present invention, with reference to the accompanying drawings and specific embodiments, is provided in detail.

[0084] As shown in Figure 1, the covert transmission method based on user fairness in cognitive radio networks of the present invention is implemented according to the following steps:

[0085] Step 1: Establish a cognitive radio network with multiple secondary users;

[0086] The cognitive radio network in step 1 includes one primary user source node T, one primary user receiver node R, and K secondary user transmitter nodes S1, S2, ... S K There is a secondary user destination node D and an unauthorized user W. Each node in the network is equipped with only a single antenna and operates in half-duplex mode. Each transmission cycle contains M time slots, and only one node is allowed to transmit covert messages within each time slot. It is assumed that the channel between any two nodes is a quasi-static Rayleigh fading channel, meaning the channel fading coefficient remains constant within the same transmission time slot but changes independently and randomly in different time slots. The connections between nodes T and R, T and D, and S are described. k(k = 1, 2, ..., K) to D, S k To R, S k The channel fading coefficients to W are respectively represented by h tr h td h kd h kr h kw In other words, assuming h tr h td h kd h kr h kw They respectively follow a mean of zero and a variance of λ. tr , λ td , λ kd , λ kr , λ kw The noise is a cyclic symmetric complex Gaussian distribution; it is assumed that all receiver noise is independent zero-mean additive white Gaussian noise with a noise power of N0.

[0087] Step 2: In this network, the primary user source node transmits information to the primary user receiving node. At the same time, multiple secondary user transmitting nodes have data to be covertly transmitted to the same secondary user destination node. To improve the reliability of the covert information transmission of secondary users and reduce the detection performance of unauthorized users, a suitable transmitting node needs to be selected from the multiple secondary user transmitting nodes to send the covert information, and a suitable interference node needs to be selected to send artificial noise. Unauthorized users detect whether the secondary user transmitting nodes send covert information.

[0088] The specific process of step 2 is as follows:

[0089] Step 2.1: The primary user source node transmits information to the primary user receiving node.

[0090] The primary user source node sends information to the primary user receiving node, and the information received by the primary user receiving node is as shown in formula (1):

[0091]

[0092] Among them, P t and x t (m) represent the transmit power and transmitted signal of the primary user source node T, respectively, and satisfy E[|x t (m)| 2 ] = 1. P i and x i (m) Selected secondary user transmitter node S i The transmit power and the transmitted signal, and satisfying E[|x i (m)| 2 ] = 1. P jand x j (m) represent the selected interference node S. j The transmit power and transmitted artificial noise, and satisfying E[|x j (m)| 2 ] = 1, P j Obey [0, P] J The uniform distribution of n r (m) is the white noise at the primary user receiving node R;

[0093] Step 2.2: Multiple secondary user transmitting nodes transmit covert information to secondary user destination nodes. To improve the reliability of covert information transmission between secondary users and reduce the detection performance of unauthorized users, a suitable transmitting node is selected from multiple secondary user transmitting nodes to send covert information, and a suitable interference node is selected to send artificial noise.

[0094] The specific process of step 2.2 is as follows:

[0095] Step 2.2.1: Multiple secondary user transmitting nodes wish to send covert information to the secondary user destination node. To improve the reliability of covert information transmission between secondary users and reduce the detection performance of unauthorized users, a suitable transmitting node is selected from the multiple secondary user transmitting nodes to send the covert information. The selected secondary user transmitting node is denoted as S. i Simultaneously, a suitable node is selected to send artificial noise; the selected interfering node is denoted as S. j Assume S j The secondary user destination node cooperates with the secondary user destination node to eliminate artificial noise. H0 and H1 represent the cases where the secondary user transmitting node does not send information and when it sends information, respectively. The information received by the secondary user destination node is given by formula (2):

[0096]

[0097] Where m = 1, ..., M, represents the m-th transmission time slot, and n d (m) represents the white noise at point D.

[0098] Step 2.2.2: Under H1, the information transmission rate from the secondary user transmitting node to the secondary user destination node is as follows (3):

[0099]

[0100] According to the definition of the probability of a system security interruption, the probability of a system security interruption is given by formula (4):

[0101] P out =Pr{C sd<R c} (4);

[0102] Among them, R c Substituting formula (3) into formula (4) for the system's target transmission rate, the system's security interruption probability is given by formula (5):

[0103]

[0104] Based on the definition of covert transmission rate, the covert transmission rate of the system is obtained as formula (6):

[0105] R sd =R c (1-P out (6);

[0106] Substituting formula (5) into formula (6), we further obtain the formula for the system's covert transmission rate as (7):

[0107] R sd =R c {1-Pr(P i |h id | 2 <α)} (7);

[0108] in,

[0109] Step 2.3: Unauthorized users detect the communication status and use the Neyman-Pearson criterion to determine whether covert transmission exists.

[0110] The specific process of step 2.3 is as follows:

[0111] Step 2.3.1: When an unauthorized user detects whether a secondary user's transmitting node is sending covert information, the information it receives is as shown in formula (8):

[0112]

[0113] Where, n w (m) represents the noise at point W.

[0114] Step 2.3.2: Regarding whether the secondary user transmitting node sends covert information to the secondary user destination node, the unauthorized user judges the transmission status of the secondary user's covert information using the Neyman-Pearson criterion. The judgment formula is formula (9):

[0115]

[0116] Among them, T w Let T be the average received power of the illegal user, and τ be the decision threshold for the illegal user. w When the threshold is >τ, the unauthorized user believes that the secondary user's transmitting node has sent covert information; the judgment result at this time is represented by D1. Meanwhile, T... w When <τ, the illegal user believes that the secondary user's transmitting node does not send covert information, and the judgment result is represented by D0.

[0117] Assuming that the number of symbol transmissions tends to infinity within a communication phase, i.e. K→∞, the average power received by illegal users is given by formula (10);

[0118]

[0119] Step 2.3.3: Express the false negative rate and false positive rate as P. MD =Pr{D0|H1} and P FA =Pr{D1|H0}; The sum of the false negative rate and the false positive rate gives the tester's error probability as formula (11):

[0120] ξ=P MD +P FA (11);

[0121] Step 2.3.4: When the system satisfies P i |h iw | 2 ≤P J |h jw | 2 When the decision threshold is set to the optimal decision threshold τ, the decision threshold is then set. * =ρ3, the minimum test error probability of the system is given by formula (12):

[0122]

[0123] Step 2.3.5: The mean of the minimum test error probability is obtained as formula (13):

[0124]

[0125] Step 3: Under the constraints of concealment and the maximum interference allowed by the primary user, obtain the optimal transmission power of the secondary user transmitting node and the interference node; to ensure fairness among users, a fair node selection method is proposed.

[0126] The specific process of step 3 is as follows:

[0127] Step 3.1: Under the constraints of concealment and the maximum interference allowed by the primary user, obtain the optimal secondary user transmit power;

[0128] To prevent unauthorized users from learning about the transmission process, the minimum probability of error in the unauthorized user's test must satisfy the condition given by formula (14):

[0129] ξ * ≥1-ε(14);

[0130] Where ε is the threshold for the concealment condition.

[0131] To ensure that the transmission power of secondary users is less than the interference threshold of primary users, their transmission power must meet the condition specified in formula (15):

[0132] P i |h ir | 2 +P J |h jr | 2 ≤I th (15);

[0133] I th This is the maximum interference threshold allowed by the main user;

[0134] Using the constraints of formulas (14) and (15), the optimal transmit power of the secondary user transmitting node is obtained as formula (16), and the optimal interference power of the interfering node is obtained as formula (17):

[0135]

[0136]

[0137] Substituting formula (16) into formula (7) for the system's covert transmission rate, we further obtain the system's covert transmission rate as formula (18):

[0138]

[0139] in,

[0140] Step 3.2: To ensure fairness among users, a fairness node selection method is proposed.

[0141] Observing formula (18), it can be found that the magnitude of the covert transmission rate is related to the channel conditions between users. To obtain the highest covert transmission rate for a single transmission, the following should be selected: As an interference node. Let Should be selected As the transmitting node, the selection process involves different users based on their location and environment. Some users have better transmission channel conditions than others. Simply considering the current transmission performance during the selection process would lead to significant differences in the chances of being selected for transmission, ultimately resulting in unfairness among users. Therefore, a node selection scheme that balances transmission rate and fairness is proposed, with interfering node S... j and secondary user transmitter node S i We obtain the results using formulas (19) and (20) respectively:

[0142]

[0143] in, make

[0144]

[0145] in,

[0146] Substituting formulas (19) and (20) into formula (18), we obtain the covert transmission rate of the system under this transmission scheme as formula (21):

[0147]

[0148] Solving equation (21) further yields the expression for the system's covert transmission rate, which is equation (22):

[0149]

[0150] in:

[0151] First of all, let Find the probability density function f for Z. Z (z) represents formula (23):

[0152]

[0153]

[0154] Secondly, let Find the probability density function f for T. T (t) is from formula (24):

[0155]

[0156] Finally, let Find the probability density function f for W. W (w) is from formula (25):

[0157]

[0158] Where Ei(·) is the exponential integral function,

[0159] The following detailed description of the covert transmission method based on user fairness in cognitive radio networks according to the present invention will be provided through specific embodiments.

[0160] Example;

[0161] This embodiment presents a covert transmission method based on user fairness in the Underlay mode of a cognitive radio network. First, a cognitive radio network with multiple secondary user transmitting nodes and multiple interfering nodes is established. This network includes one primary user source node T, one primary user receiver node R, and K secondary user transmitting nodes S1, S2, ... S... K There is a secondary user destination node D and an unauthorized user W. Each node in the network is equipped with only a single antenna and operates in half-duplex mode. Each transmission cycle contains M time slots, and only one node is allowed to transmit covert messages within each time slot. It is assumed that the channel between any two nodes is a quasi-static Rayleigh fading channel, meaning the channel fading coefficient remains constant within the same transmission time slot but changes independently and randomly in different time slots. The connections between nodes T and R, T and D, and S are described. k (k = 1, 2, ..., K) to D, S k To R, S k The channel fading coefficients to W are respectively represented by h tr h td h kd h kr h kw It means that h tr ~CN(0,λ) tr ), h td ~CN(0,λ) td ), h kd ~CN(0,λ) kd ), h kr ~CN(0,λ) kr ), h kw ~CN(0,λ) kw ), that is, h tr h td h kd h kr h kw They respectively follow a mean of zero and a variance of λ.tr , λ td , λ kd , λ kr , λ kw The noise is a cyclic symmetric complex Gaussian distribution; it is assumed that all receiver noise is independent zero-mean additive white Gaussian noise with a noise power of N0.

[0162] The method of this invention was tested using Monte Carlo simulation for 10... 5 The system performance was tested through more than one independent simulation. The test conditions were: the source node sending and not sending information had equal probability, and the target safe rate R... c =1bps / Hz, I th =15dB, P t =10dB, ε=0.1, the results are shown in Figure 2 and Figure 3.

[0163] Figure 2 shows a comparison between this invention and several existing methods, presenting curves illustrating the covert transmission rate as a function of the number of secondary user transmitting nodes K under different methods. It can be seen that the rate increases with the number of secondary user transmitting nodes. This is because a larger number of nodes increases the chance of being selected for information transmission, thus increasing the covert transmission rate. Specifically, the random interference node selection method involves selecting secondary user transmitting nodes each time based on the ratio of the channel conditions between secondary users to their mean. Channels between secondary users and primary users and illegal users are randomly selected, and interference nodes are also randomly selected. The random node selection method involves randomly selecting both secondary user transmitting nodes and interference nodes. Furthermore, two different scenarios are considered. The first scenario involves a total number of transmissions being limited, where the sum of the transmission counts of all nodes equals the total number of transmissions, indicating the end of information transmission. The second scenario, where the total power of each node is limited, refers to setting the same total transmission power for each node. Each time a node transmits, its remaining transmission power equals the total transmission power minus the power used in that transmission. If the remaining transmission power fails to support information transmission for three consecutive transmissions, the node is considered to be ceasing transmission. This process continues until all nodes cease transmission, at which point the transmission is considered complete. Figure 3 shows that the fairness method presented in this paper yields the highest covert transmission rate curve. The random node method, with almost equal selection probabilities for each node, has the lowest covert transmission rate. The random interference node selection method, due to the secondary user transmitting node being selected based on the ratio of the channel to the channel mean, and the random selection of channels between the secondary user and the primary user and illegal users, as well as the random selection of interference nodes, results in a higher covert transmission rate than the random node method. Figure 3 also shows that the covert transmission rate under the total number of transmissions limitation scenario is higher than that under the total power limitation scenario, because the total power limitation restricts the number of transmissions per node.

[0164] As shown in Figure 3, by comparing the curves of this invention and other methods with the number of transmitting nodes K for different secondary users, it can be seen that the random node method has the highest fairness because each node has an almost equal probability of being selected. The fairness of the method presented in this paper is second only to the random node method and higher than the random interference node method. This is because the method presented in this paper selects nodes each time according to the ratio of the channel to its mean, while the random interference node selection method only considers the channel fairness between secondary users, without considering the channel between secondary users and primary users or illegal users. Therefore, the fairness of the method presented in this paper is higher than that of the random interference node selection method. It can also be seen that the fairness under the total power limitation of each node is higher than that under the total transmission count limitation. This is because under the total transmission count limitation, there is no limit to the number of transmissions between each user. Due to channel differences, the number of transmissions for each user varies slightly, so the system fairness in this case is lower than that under the total power limitation of each node.

[0165] This invention presents a covert transmission method based on user fairness in cognitive radio networks. Through a fair node selection method, it achieves fairness in covert transmission among users and maximizes the system's covert transmission rate. The optimal transmission power of secondary user transmitting nodes and interfering nodes is obtained by satisfying the covert constraints with the minimum detection error probability and the maximum interference constraints allowed by the primary user. The selection of secondary user transmitting nodes and interfering nodes is performed through a fair node selection scheme, which not only ensures fairness among users but also improves the system's covert transmission rate, demonstrating its applicability.

Claims

1. A covert transmission method based on user fairness in cognitive radio networks, characterized in that, The specific steps are as follows: Step 1: Establish a cognitive radio network with multiple secondary users; the cognitive radio network includes a primary user source node. A primary user receiving node ， Secondary user transmission nodes A secondary user destination node and an unauthorized user Step 1 specifically involves: Each node in the cognitive radio network is equipped with only a single antenna and operates in half-duplex mode. Each transmission cycle contains M time slots, and only one node is allowed to transmit covert messages within each time slot. It is assumed that the channel between any two nodes is a quasi-static Rayleigh fading channel, meaning the channel fading coefficient remains constant within the same transmission time slot but changes independently and randomly in different time slots. The connections between nodes T and R, and T and D are then established. To D, To R, The channel fading coefficients to W are respectively used as ， ， ， ， Indicates, assuming ， ， ， ， They respectively follow the pattern of having a mean of zero and a variance of . ， ， ， ， The noise follows a cyclic symmetric complex Gaussian distribution; assuming all receiver noise is independent zero-mean additive white Gaussian noise with a noise power of... ； Step 2: In a cognitive radio network, information is transmitted from the primary user source node to the primary user receiver node, and multiple secondary user transmitter nodes transmit covertly to the secondary user destination node. Select a suitable transmitting node from multiple secondary user transmitting nodes to send covert information, and at the same time select a suitable interference node to send artificial noise; the illegal user detects whether the secondary user transmitting node sends covert information; Step 2 is specifically as follows: Step 2.1, the main user source node sends information to the main user receiving node, and the information received by the main user receiving node is as shown in formula (1): (1); where, and These are the main user source nodes. The transmit power and the transmitted signal, and satisfy the following: ， and Selected secondary user launch node The transmit power and the transmitted signal, and satisfy the following: ； and These represent the selected interference nodes. The transmission power and the transmitted artificial noise, and meet the requirements. ， obey Uniform distribution It is the main user receiving node White noise at the location; Step 2.2, the selected secondary user transmitting node is denoted as Simultaneously, a suitable node is selected to send artificial noise; the selected interference node is denoted as... Assuming The secondary user destination node cooperates with the secondary user destination node to eliminate artificial noise. and These represent the cases where the secondary user transmitting node does not send information and the cases where it sends information, respectively. The information received by the secondary user destination node is shown in formula (2): (2); where, , indicating the first One transmission time slot, express White noise at the location; The information transmission rate from the secondary user transmitting node to the secondary user destination node is shown in formula (3): (3); According to the definition of the probability of a security interruption, the probability of a system security interruption is as shown in formula (4): (4); among which, Substituting formula (3) into formula (4) for the system's target transmission rate, the system's security interruption probability is shown in formula (5): (5); Based on the definition of covert transmission rate, the covert transmission rate of the system is obtained as shown in formula (6): (6); Substituting formula (5) into formula (6), we further obtain the formula for the system's covert transmission rate as shown in formula (7): (7); among which, Step 2.3: When an unauthorized user detects whether a secondary user's transmitting node is sending covert information, the information it receives is shown in formula (8): (8); among which, express Noise at the location; Regarding whether the secondary user transmitting node sends covert information to the secondary user destination node, the illegal user judges the transmission status of the secondary user's covert information by the Neyman-Pearson criterion, and the judgment formula is shown in formula (9): (9); among which, The average received power of unauthorized users. The threshold for sentencing unauthorized users, when At that time, the unauthorized user believed that the secondary user's transmitting node had sent covert information, and the judgment result was... Indicate; and At this time, if an unauthorized user believes that the secondary user's transmitting node is not sending covert information, the judgment result will be... This means that, assuming the number of symbol transmissions tends to infinity within a communication phase, that is... The average power received by illegal users is shown in formula (10): (10); Express the false negative rate and false positive rate as follows: and The sum of the false negative rate and the false positive rate yields the detector's error probability, as shown in formula (11): (11); When the system satisfies When this happens, the decision threshold is set to the optimal decision threshold. The minimum test error probability of the system is shown in formula (12): (12); The mean of the minimum test error probability is obtained as shown in formula (13): (13); Step 3: Under the concealment constraint and the maximum interference constraint allowed by the primary user, obtain the optimal transmission power of the secondary user transmitting node and the interference node; a fair node selection method is proposed; the specific steps of step 3 are: Step 3.1, in order to prevent the transmission process from being known by illegal users, the minimum detection error probability of illegal users is required to meet the condition shown in formula (14): (14); among which, The threshold for concealment conditions; to ensure that the transmission of secondary users is less than the interference threshold of primary users, their transmission power must meet the conditions shown in formula (15): （15）； This is the maximum interference threshold allowed by the primary user; through the constraints of formulas (14) and (15), the optimal transmission power of the secondary user transmitting node is obtained as formula (16), and the optimal interference power of the interfering node is shown in formula (17): （16）； (17); whereby, substituting formula (16) into the system's covert transmission rate in formula (7), the system's covert transmission rate is further obtained as shown in formula (18): (18); among which, Step 3.2: From formula (18), the magnitude of the covert transmission rate is related to the channel conditions between users. Select... As an interference node, let ,choose As the transmitting node, a node selection scheme that balances transmission rate and fairness is proposed, along with interference nodes. and secondary user launch nodes We obtain the results using formulas (19) and (20) respectively: (19); among which, ,make ； (20); where: Substituting formulas (19) and (20) into formula (18), the system's covert transmission rate is obtained as shown in formula (21): (21); Further solving formula (21) yields the expression for the system's covert transmission rate, as shown in formula (22): (22); where: first, let ,right Find its probability density function For formula (23): （23）； Secondly, let ,right Find its probability density function For formula (24): (24); Finally, let ,right Find its probability density function For formula (25): (25); among which, It is an exponential integral function. 。 2. The covert transmission method based on user fairness in cognitive radio networks according to claim 1, characterized in that, In step 2, the unauthorized user detects whether the secondary user's transmitting node sends covert information and uses the Neyman-Pearson criterion to determine whether covert transmission exists.

Images