CN115665729A - Hidden transmission method under multi-eavesdropper joint detection environment - Google Patents

Hidden transmission method under multi-eavesdropper joint detection environment Download PDF

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CN115665729A
CN115665729A CN202211272563.7A CN202211272563A CN115665729A CN 115665729 A CN115665729 A CN 115665729A CN 202211272563 A CN202211272563 A CN 202211272563A CN 115665729 A CN115665729 A CN 115665729A
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alice
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朱媛姝
钱玉文
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Nanjing University of Science and Technology
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Abstract

The invention discloses a hidden transmission method under a multi-eavesdropper joint detection environment, which comprises the following steps: establishing a wireless covert communication network model; the eavesdropping node detects whether the sending node sends the message or not and calculates the minimum detection error probability of the eavesdropping node; the target node sends an interference signal to resist the eavesdropping node; under the condition of meeting given concealment constraint and minimizing the detection error probability of the eavesdropping node, maximizing the concealment transmission rate of the system by power distribution and selecting the most appropriate transmission power of the interference node to obtain the optimal concealment transmission rate of the system; and the target node comprehensively considers the concealment and reliability constraints of the system and solves the maximum effective rate of the sending node. The invention improves the detection performance, effectively resists the situation of cooperative detection of double detectors and obviously improves the hidden transmission rate.

Description

Hidden transmission method under multi-eavesdropper joint detection environment
Technical Field
The invention belongs to the technical field of covert communication, and particularly relates to a covert transmission method under a multi-eavesdropper joint detection environment.
Background
With the rapid development of mobile communication technologies represented by 5G and the extension of human activities to space and deep sea, modern wireless communication technologies using electromagnetic waves, acoustic waves, light, and the like as information transmission media have become the main communication methods in various scenes. Among them, radio communication is currently the most widely used communication method. Due to the openness of the radio medium, the communication signal is easily intercepted and intercepted by a third party, and further, the leakage of the communication content or the exposure of the communication intention is caused. Ensuring the security of information transmitted over wireless links is therefore crucial for consumer, industrial and military applications.
Data transmitted in wireless networks typically use various encryption schemes and key exchange protocols to prevent the transmitted data from being intercepted by an eavesdropper. Although the traditional cryptography-based encryption method promises to ensure the integrity of any transmitted information, the security of the traditional cryptography-based encryption method depends on the difficulty of some number theory problems, quantum computing can effectively solve the complex mathematical problems which are difficult to solve by the traditional computers by virtue of the powerful computing power of the quantum computing method, so that most public key systems are cracked, and modern communication is in danger. With the continuous progress of research, physical layer security has become an emerging technology which supplements and significantly improves the security of wireless network communication, and provides a reliable alternative. However, both the encryption technology and the physical layer security technology focus on preventing information from being stolen, and cannot completely solve the privacy problem, and the wireless transmission process itself may expose the source location information of the user or be used for reverse attack by an eavesdropper, which is very fatal in military countermeasures. To this end, we need covert communication to prevent transmission detection first, and covert communication (also called low detection probability communication, LPD) is becoming a new technology to achieve strong security and privacy in wireless communication. The covert communication aims at realizing the transmission of hidden information of two communication parties, and besides protecting the content of the communication, the covert communication emphasizes that a non-cooperative eavesdropping party is difficult to detect the transmission behavior, namely the transmission process is not easy to attract the attention of an eavesdropping person.
In the field of covert communications, uncertainties are often introduced through artificial noise, making it impossible for a detector/eavesdropper to determine whether covert transmissions exist. In many existing covert communication networks, only one detector exists, but in practical situations, an eavesdropper is everywhere. Therefore, the uniform distribution of the eavesdroppers is considered under the plane condition, and two eavesdroppers are considered in the scene for detection.
Disclosure of Invention
The invention aims to provide a hidden transmission method under a multi-eavesdropper joint detection environment.
The technical solution for realizing the purpose of the invention is as follows: a hidden transmission method under a multi-eavesdropper joint detection environment comprises the following specific steps:
(10) Establishing a wireless covert communication network model, wherein the wireless covert communication network model comprises a sending node, a legal receiving destination node and two eavesdropping nodes, the sending node carries out covert transmission to the destination node, namely the sending node generates a random signal with a certain probability and sends the random signal to the destination node;
(20) The eavesdropping node detects whether the sending node sends the message or not and calculates the minimum detection error probability of the eavesdropping node;
(30) The target node sends an interference signal to resist the eavesdropping node;
(40) Under the condition of meeting given concealment constraint and minimizing the detection error probability of the eavesdropping node, maximizing the concealment transmission rate of the system by power distribution and selecting the most appropriate transmission power of the interference node to obtain the optimal concealment transmission rate of the system;
(50) And the target node comprehensively considers the concealment and reliability constraints of the system and solves the maximum effective rate of the sending node.
Preferably, the specific method for detecting whether the sending node sends the message by the eavesdropping node is as follows:
the two eavesdropping nodes respectively adopt radiometers to carry out energy detection on the received signals and judge whether transmission signals exist or not;
whether a sending node sends a message is detected by adopting a joint judgment scheme, wherein the joint judgment scheme comprises two schemes, and the two schemes are shown in the following table:
Figure BDA0003895648260000021
the first scheme is as follows: if any eavesdropping node detects that the transmission exists, the eavesdropping node judges that the sending node sends the confidential information; scheme(s)II, secondly: only when two eavesdropping nodes detect that the transmission exists, the sending node is judged to send the confidential message; y is 0 Indicating that the transmitting node has not transmitted information, Y 1 Indicating that it is determined that the transmitting node transmitted the information,
Figure BDA0003895648260000022
indicating that the transmitting node has not transmitted information, Y 1 (i) I =1,2, indicating that the transmitting node has transmitted information.
Preferably, the method for the two eavesdropping nodes to respectively judge whether the transmission signal exists is as follows:
Figure BDA0003895648260000031
in the formula (I), the compound is shown in the specification,
Figure BDA0003895648260000032
indicating eavesdropping node w i Average received power of τ i Is w i The decision threshold of (2) is set,
Figure BDA0003895648260000033
indicating that the transmitting node has not transmitted information, Y 1 (i) Indicating that it is determined that the transmitting node has transmitted information.
Preferably, the minimum detection error probability of the eavesdropping node is calculated by:
the undetected rate and the false detection rate of the detector are respectively expressed as follows:
Figure BDA0003895648260000034
Figure BDA0003895648260000035
i is 1 for scheme one and 2 for scheme two;
suppose a sending node sends a guaranteeThe probability of secret information is Pr { H 1 }＝Pr{H 0 =1/2, the detection error probability ξ of the eavesdropping node is:
Figure BDA0003895648260000036
calculating the error probability according to the first scheme:
when the scheme is adopted, the undetected rate and the false rate of the eavesdropping node are as follows:
Figure BDA0003895648260000037
Figure BDA0003895648260000038
when the system is satisfied
Figure BDA0003895648260000039
(where subscript a denotes Alice, subscript b denotes Bob, and subscript w i An index i of w is 1 to represent the eavesdropping node 1, and is 2 to represent the eavesdropping node 2; p a Sending signal power for a sending node Alice;
Figure BDA00038956482600000310
is P b A maximum transmit power;
Figure BDA00038956482600000311
are the channel coefficients of Alice to Willie (i),
Figure BDA00038956482600000312
channel coefficients for Bob to the eavesdropping node Willie (i); l. capillary 2 Represents the square of the modulus;
Figure BDA00038956482600000313
representing the path loss coefficient from the sending node Alice to the eavesdropping node Willie (i);
Figure BDA00038956482600000314
represents the path loss coefficient of the destination node Bob to Willie (i), and w 1 And w 2 The optimal decision thresholds are respectively
Figure BDA00038956482600000315
And
Figure BDA00038956482600000316
wherein
Figure BDA00038956482600000317
Is P b A maximum transmit power;
Figure BDA00038956482600000318
channel coefficients Bob to Willie (i); l. capillary 2 Represents the square of the modulus;
Figure BDA00038956482600000319
represents the path loss coefficient from Bob to Willie (i);
Figure BDA00038956482600000320
minimum probability of detection error obtained for Gaussian white noise power
Figure BDA0003895648260000041
Comprises the following steps:
Figure BDA0003895648260000042
wherein subscript a denotes Alice, subscript b denotes Bob, and subscript w i Denotes Willie (i), the subscript i of w is 1 for Willie1, 2 for Willie2; p a Transmitting signal power for a transmitting node Alice;
Figure BDA0003895648260000043
is P b A maximum transmit power;
Figure BDA0003895648260000044
for the channel coefficients of Alice to Willie (i), the channel coefficients, similarly,
Figure BDA0003895648260000045
channel coefficients from Bob to Willie (i); l. capillary 2 Represents the square of the modulus;
Figure BDA0003895648260000046
represents the path loss coefficient from Alice to Willie (i);
Figure BDA0003895648260000047
represents the path loss coefficient from Bob to Willie (i);
when the scheme two is adopted, the undetected rate and the false rate of the eavesdropping node are as follows:
Figure BDA0003895648260000048
Figure BDA0003895648260000049
when the system is satisfied
Figure BDA00038956482600000410
(where subscript a denotes Alice, subscript b denotes Bob, and subscript w denotes i Denotes Willie (i), the subscript i of w is 1 for Willie1 and 2 for Willie2; p a Transmitting signal power for a transmitting node Alice;
Figure BDA00038956482600000411
is P b A maximum transmit power;
Figure BDA00038956482600000412
the channel coefficients for Alice to Willie (i), and, similarly,
Figure BDA00038956482600000413
channel coefficients from Bob to Willie (i); l. capillary 2 Representing the square of the modulus；
Figure BDA00038956482600000414
Represents the path loss coefficient from Alice to Willie (i);
Figure BDA00038956482600000415
represents the pathloss coefficient from Bob to Willie (i), and w 1 And w 2 Respectively as the optimal decision threshold
Figure BDA00038956482600000416
And
Figure BDA00038956482600000417
wherein P is a Transmitting signal power for a transmitting node Alice;
Figure BDA00038956482600000418
channel coefficients for Alice to Willie (i); l. capillary 2 Represents the square of the modulus;
Figure BDA00038956482600000419
represents the path loss coefficient from Alice to Willie (i);
Figure BDA00038956482600000420
minimum probability of detection error obtained for Gaussian white noise power
Figure BDA00038956482600000421
Comprises the following steps:
Figure BDA00038956482600000422
wherein subscript a denotes Alice, subscript b denotes Bob, and subscript w i Denotes Willie (i), the subscript i of w is 1 for Willie1, 2 for Willie2; p is a Transmitting signal power for a transmitting node Alice;
Figure BDA00038956482600000423
is P b Maximum transmission power；
Figure BDA00038956482600000424
The channel coefficients for Alice to Willie (i), and, similarly,
Figure BDA00038956482600000425
channel coefficients from Bob to Willie (i); l. capillary 2 Represents the square of the modulus;
Figure BDA00038956482600000426
represents the path loss coefficient from Alice to Willie (i);
Figure BDA00038956482600000427
represents the path loss coefficient from Bob to Willie (i).
Preferably, when the destination node sends an interference signal to counter the eavesdropping node, the capacity expression and the hidden transmission rate expression are determined, and the specific process is as follows:
in a multi-eavesdropping node network, a sending node carries out hidden transmission; the received signal at the legal receiving destination node is:
Figure BDA0003895648260000051
wherein, P a Is the transmit power of the transmitting node; p b Receiving the noise emission power of the destination node for legal purpose;
Figure BDA0003895648260000052
representing the path loss coefficient from Alice to Bob; h is a total of a,b Channel coefficients from Alice to Bob; h is b,b Channel coefficients between Bob transmit antennas and Bob receive antennas; x is the number of a (k) A covert signal sent for Alice; x is a radical of a fluorine atom b (k) For the artificial noise at Bob, satisfy E [ | x b (k)| 2 ]＝1；n b (k) Is the noise at Bob, satisfies
Figure BDA0003895648260000053
Phi (0 < phi < 1) is interference cancellation coefficient(ii) a k =1,2, \8230;, n denotes the kth symbol in the slot;
P b compliance
Figure BDA0003895648260000054
The uniformity of the distribution of the water content in the water,
Figure BDA0003895648260000055
is P b Maximum transmit power, probability density function
Figure BDA0003895648260000056
Comprises the following steps:
Figure BDA0003895648260000057
receiving the signal-to-interference-and-noise ratio gamma at the destination node b Comprises the following steps:
Figure BDA0003895648260000058
wherein P is a Is the transmit power of the transmitting node; p is b Receiving the noise emission power of the destination node for legal purpose;
Figure BDA0003895648260000059
representing the path loss coefficient from Alice to Bob; h is a total of a,b Channel coefficients for Alice to Bob; h is b,b Channel coefficients between Bob transmit antennas and Bob receive antennas; l. capillary 2 Represents the square of the modulus; phi (phi is more than 0 and less than or equal to 1) is an interference cancellation coefficient;
transmission rate formula, capacity expression C a,b Comprises the following steps:
C a,b ＝log 2 (1+γ b )
given a system target transmission rate of R s Probability of system outage P out Comprises the following steps:
P out ＝Pr{C a,b ＜R s }＝Pr{log 2 (1+γ b )＜R s }
probability of connection O a,b ＝1-P out The system concealing transmission rate is
Figure BDA00038956482600000510
π 1 Probability of sending concealed messages for Alice, assuming Alice sends equal probability
Figure BDA00038956482600000511
Preferably, under the condition of meeting the given concealment constraint and minimizing the detection error probability of the eavesdropping node, the method maximizes the concealment transmission rate of the system by power allocation and selecting the most suitable transmission power of the interfering node, and the specific process of obtaining the optimal concealment transmission rate of the system is as follows:
(41) Setting a required detection error probability threshold value epsilon;
(42) Establishing a constraint condition: in combination with a minimum detection error probability of the system, it is required that the error probability of the eavesdropping node cannot be lower than a set error threshold, i.e. it is required that
Figure BDA0003895648260000061
(43) And (3) forming optimized content: the capacity expression is combined with the constraint condition to obtain optimized content, and the hidden transmission rate R is required to meet the given constraint condition when the detection error probability of the eavesdropping node meets the requirement c Maximum:
Figure BDA0003895648260000062
Figure BDA0003895648260000063
preferably, the specific method for solving the maximum effective rate of the sending node is as follows:
the total transmitting power of the system is P, and the transmitting power of a transmitting node and the transmitting power of a target node are made
Figure BDA0003895648260000064
Solving the total transmission power P of the system, wherein when the hidden condition constraint is met, the value range of P is as follows:
Figure BDA0003895648260000065
due to R c The optimal transmitting power of the system is obtained according to the value range of P as the increasing function of P:
Figure BDA0003895648260000066
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003895648260000067
Figure BDA0003895648260000068
wherein
Figure BDA0003895648260000069
Are the channel coefficients of Alice to Willie (i),
Figure BDA00038956482600000610
channel coefficients Bob to Willie (i); l. capillary 2 Represents the square of the modulus;
Figure BDA00038956482600000611
represents the path loss coefficient from Alice to Willie (i);
Figure BDA00038956482600000612
represents the path loss coefficient from Bob to Willie (i).
Compared with the prior art, the invention has the following remarkable advantages:
the invention adopts the joint detection of the two detectors to reduce the detection error probability of the detectors, and can improve the detection performance by the joint detection, effectively resist the cooperative detection condition of the two detectors and obviously improve the hidden transmission rate.
The invention is described in further detail below with reference to the following figures and detailed description.
Drawings
Fig. 1 is a model diagram of a covert transmission method under a multi-eavesdropper joint detection environment according to the present invention.
Fig. 2 is a flow diagram of a method of covert communications against multiple eavesdroppers.
Fig. 3 is a performance comparison graph of two joint detections and a single detector, i.e., an eavesdropping node missed detection rate comparison graph, of the hidden transmission method in a multi-eavesdropping joint detection environment.
FIG. 4 is a comparison graph of performance of two joint detections and a single detector, namely, an eavesdropping node false detection rate, in the hidden transmission method under the multi-eavesdropper joint detection environment.
Detailed Description
A hidden transmission method under the environment of multi-eavesdropper joint detection provides a system model containing two eavesdroppers, and under the condition that the two eavesdroppers carry out joint detection, the minimum detection error probability and the optimum hidden transmission rate of the system are given by reasonably carrying out optimum power distribution on a sending node and artificial noise power, and the specific steps are as follows:
(10) Establishing a wireless covert communication network model of multiple eavesdroppers: the system comprises a sending node Alice, a legal receiving destination node Bob and two interception nodes Willie1 and Willie2. SendingBoth the party and the eavesdropping party are provided with an antenna, a legal receiving node is provided with two omnidirectional antennas, one is used for receiving signals, and the other is used for transmitting artificial noise. Sending node Alice sends hidden signal x to receiving node randomly a (k) And k = 1.. N, the receiving node sends artificial interference noise to the outside world to interfere the detection of the eavesdropping node. The sending node Alice codes the hidden information, n symbols are transmitted in each time slot, and the signal satisfies the condition that the mean power value is 1, namely E [ | x a (k)| 2 ]And =1. Using h as channel fading coefficient from any node x to another node y x,y Is represented by h x,y Satisfies the mean value of 0 and the variance of g x,y Circularly symmetric Gaussian distribution of (i.e.
Figure BDA0003895648260000081
All the receiving end noises are independent zero-mean additive white Gaussian noises with the power of
Figure BDA0003895648260000082
(20) The eavesdropping node detects whether the sending node sends the message:
H 0 the fact that the sending node Alice does not communicate with the receiving node Bob is shown, and the signal received by the eavesdropping node Willie (1, 2) only contains artificial noise and Gaussian noise; h 1 Indicating that the transmitting node Alice transmits a signal to the receiving node Bob, the signal received by the eavesdropping node Willie (1, 2) includes the signal from the transmitting node Alice and the remaining noise.
(21) The eavesdropping node eavesdrops the signal of the transmitting node and the eavesdropped signal
Figure BDA0003895648260000083
In particular to
Figure BDA0003895648260000084
Subscript a denotes Alice, subscript b denotes Bob, and subscript w i Denotes Willie (i), W has a subscript i of 1 representing Willie1, 2 for Willie2; n is wi Representing the noise at Willie (i); p a Transmitting signal power for a transmitting node Alice; p b Sending artificial noise power to a destination node Bob; x is the number of a (k) A sending signal of a sending node Alice; x is a radical of a fluorine atom b (k) An artificial noise signal for the destination node Bob;
Figure BDA0003895648260000085
representing the path loss coefficient from node x to node y.
Two eavesdropping nodes respectively detect: and the two eavesdropping nodes respectively adopt the radiometers to carry out energy detection on the received signals and judge whether the transmission signals exist or not. And the two eavesdropping nodes judge the covert communication condition respectively. Eavesdropping node w 1 ,w 2 The sending condition of the secret information is judged through a Neyman-Pearson criterion, and the judgment formula is as follows:
Figure BDA0003895648260000086
in the formula, i represents 1 or 2,T wi Indicating eavesdropping node w i Average received power of τ i Is w i The decision threshold of (1).
Figure BDA0003895648260000087
And
Figure BDA0003895648260000088
for eavesdropping on node w i The judgment result of the information transmission condition is as follows:
Figure BDA0003895648260000089
indicating that it is determined that the transmitting node has not transmitted information,
Figure BDA00038956482600000810
indicating that it is determined that the transmitting node has transmitted the information.
(23) The interception node joint detection scheme comprises the following steps: according to the detection results of the two parties, whether the hidden transmission is obtained or not is obtained by adopting a joint judgment schemeThe result of the detection of presence. Two decision schemes are proposed here: in the first scheme, if any eavesdropping node detects that the transmission exists, the eavesdropping node judges that the sending node sends the confidential information; in the second scheme, the sending node is judged to send the secret message only when two bit eavesdropping nodes detect that the transmission exists. Y is 0 And Y 1 Joint judgment results of information transmission conditions for two eavesdropping nodes: y is 0 Indicating that the transmitting node has not transmitted information, Y 1 Indicating that the transmitting node has determined to transmit the information.
TABLE 1 Joint detection decision scheme for eavesdropping nodes
Figure BDA0003895648260000091
(24) And calculating the detection error probability of the eavesdropping node. When the eavesdropping node detects the hidden transmission behavior, the detection result has two detection errors, namely detection omission and false detection. Wherein the omission is defined as when the transmitting node transmits the secret information (H) 1 Case), the eavesdropping node judges that the transmitting node has not transmitted the secret information. False detection is defined as when the sending node has not sent secret information (H) 0 Case), the eavesdropping node determines that the transmitting node transmitted the confidential information. According to the definitions of the missed detection and the false detection, the missed detection rate and the false detection rate of the detector are respectively expressed as that i is 1 to represent a scheme I, and 2 to represent a scheme II:
Figure BDA0003895648260000092
suppose the probability of sending secret information by the sending node is Pr { H 1 }＝Pr{H 0 =1/2, the detection error probability ξ of the eavesdropping node is:
Figure BDA0003895648260000093
(241) Calculating error probability according to the scheme I in the table
When the scheme is adopted, the undetected rate and the false rate of the eavesdropping node are as follows:
Figure BDA0003895648260000094
Figure BDA0003895648260000095
when the system is satisfied
Figure BDA0003895648260000096
(where subscript a denotes Alice, subscript b denotes Bob, and subscript w i Denotes Willie (i), the subscript i of w is 1 for Willie1, 2 for Willie2; p a Sending signal power for a sending node Alice;
Figure BDA0003895648260000097
is P b A maximum transmit power;
Figure BDA0003895648260000098
for the channel coefficients of Alice to Willie (i), the channel coefficients, similarly,
Figure BDA0003895648260000099
channel coefficients from Bob to Willie (i); l |, the hollow 2 Represents the square of the modulus;
Figure BDA00038956482600000910
represents the path loss coefficient from Alice to Willie (i);
Figure BDA00038956482600000911
represents the pathloss coefficient from Bob to Willie (i) and w 1 And w 2 The optimal decision thresholds are respectively
Figure BDA0003895648260000101
And
Figure BDA0003895648260000102
(wherein
Figure BDA0003895648260000103
Is P b A maximum transmit power;
Figure BDA0003895648260000104
channel coefficients from Bob to Willie (i); l |, the hollow 2 Represents the square of the modulus;
Figure BDA0003895648260000105
represents the path loss coefficient from Bob to Willie (i);
Figure BDA0003895648260000106
white gaussian noise power) the minimum probability of verification error that can be achieved by the system at this time
Figure BDA0003895648260000107
Comprises the following steps:
Figure BDA0003895648260000108
wherein subscript a denotes Alice, subscript b denotes Bob, and subscript w i Denotes Willie (i), the subscript i of w is 1 for Willie1 and 2 for Willie2; p a Transmitting signal power for a transmitting node Alice;
Figure BDA0003895648260000109
is P b A maximum transmit power;
Figure BDA00038956482600001010
the channel coefficients for Alice to Willie (i), and, similarly,
Figure BDA00038956482600001011
channel coefficients Bob to Willie (i); l. capillary 2 Represents the square of the modulus;
Figure BDA00038956482600001012
represents the path loss coefficient from Alice to Willie (i);
Figure BDA00038956482600001013
represents the path loss coefficient from Bob to Willie (i);
(242) The second scheme is adopted: the undetected rate and the false rate of the eavesdropping node are as follows:
Figure BDA00038956482600001014
Figure BDA00038956482600001015
when the system is satisfied
Figure BDA00038956482600001016
(where subscript a denotes Alice, subscript b denotes Bob, and subscript w i Denotes Willie (i), the subscript i of w is 1 for Willie1, 2 for Willie2; p a Sending signal power for a sending node Alice;
Figure BDA00038956482600001017
is P b A maximum transmit power;
Figure BDA00038956482600001018
for the channel coefficients of Alice to Willie (i), the channel coefficients, similarly,
Figure BDA00038956482600001019
channel coefficients from Bob to Willie (i); l. capillary 2 Represents the square of the modulus;
Figure BDA00038956482600001020
represents the path loss coefficient from Alice to Willie (i);
Figure BDA00038956482600001021
represents the pathloss coefficient from Bob to Willie (i) and w 1 And w 2 Respectively, of the optimal decision thresholdIs composed of
Figure BDA00038956482600001022
And
Figure BDA00038956482600001023
(wherein P is a Transmitting signal power for a transmitting node Alice;
Figure BDA00038956482600001024
channel coefficients for Alice to Willie (i); l. capillary 2 Represents the square of the modulus;
Figure BDA00038956482600001025
represents the path loss coefficient from Alice to Willie (i);
Figure BDA00038956482600001026
gaussian white noise power) the minimum probability of verification error that the system can achieve at this time
Figure BDA00038956482600001027
Comprises the following steps:
Figure BDA00038956482600001028
wherein subscript a denotes Alice, subscript b denotes Bob, and subscript w i Denotes Willie (i), the subscript i of w is 1 for Willie1 and 2 for Willie2; p is a Transmitting signal power for a transmitting node Alice;
Figure BDA0003895648260000111
is P b A maximum transmit power;
Figure BDA0003895648260000112
for the channel coefficients of Alice to Willie (i), the channel coefficients, similarly,
Figure BDA0003895648260000113
channel coefficients from Bob to Willie (i); l |, the hollow 2 Represents the square of the modulus;
Figure BDA0003895648260000114
represents the path loss coefficient from Alice to Willie (i);
Figure BDA0003895648260000115
represents the path loss coefficient from Bob to Willie (i);
it can be seen that when the system satisfies covert communication implementation conditions, although the two decision schemes are not the same, the minimum probability of detection error for the two schemes is equal when the probability of sending and not sending secret information is equal. And when the system does not meet the conditions for realizing covert communication, the detection error probability is 0, and the legal node can not carry out covert transmission of information.
When in use
Figure BDA0003895648260000116
The minimum detection error probability of the system is
Figure BDA0003895648260000117
This corresponds to a situation where the eavesdropping node randomly guesses the covert transmission.
(30) At a destination node, the full-duplex receiver Bob transmits an interference signal to resist the eavesdropping node so as to reduce the detection performance of the eavesdropping node. And self-interference elimination technology is adopted at Bob, namely AN has no influence on Bob.
In a multi-eavesdropping node network, a sending node Alice carries out hidden transmission; the received signal at the legitimate receiver Bob is
Figure BDA0003895648260000118
Wherein, P a Is the transmit power of the transmitting node; p b Receiving the noise emission power of the destination node for legal purpose;
Figure BDA0003895648260000119
representing the path loss coefficient from Alice to Bob; h is a total of a,b Channel coefficients for Alice to Bob; h is b,b Channel coefficients between Bob transmit antennas and Bob receive antennas; x is a radical of a fluorine atom a (k) A covert signal sent for Alice; x is the number of b (k) For the artificial noise at Bob, satisfy E [ | x b (k)| 2 ]＝1；n b (k) Is the noise at Bob, satisfies
Figure BDA00038956482600001110
Phi (phi is more than 0 and less than or equal to 1) is an interference cancellation coefficient; k =1,2, \8230;, n denotes the kth symbol in the slot.
P b Compliance
Figure BDA00038956482600001111
The uniformity of the distribution of the pressure in the chamber,
Figure BDA00038956482600001112
is P b Maximum transmission power, probability density function thereof
Figure BDA00038956482600001113
Is composed of
Figure BDA00038956482600001114
The signal to interference and noise ratio gamma at Bob b Is composed of
Figure BDA00038956482600001115
Wherein P is a Is the transmit power of the transmitting node; p is b Receiving the noise emission power of the destination node for legal purpose;
Figure BDA0003895648260000121
representing the path loss coefficient from Alice to Bob; h is a,b Channel coefficients for Alice to Bob; h is a total of b,b Channel coefficients between Bob transmit antennas and Bob receive antennas; l. capillary 2 Represents the square of the modulus; phi (0 < phi)Less than or equal to 1) is an interference cancellation coefficient.
Transmission rate formula capacity expression C a,b Comprises the following steps: c a,b ＝log 2 (1+γ b ) In (14) get
Figure BDA0003895648260000122
System concealment transmission rate: given a system target transmission rate of R s Probability of system outage P out Comprises the following steps: p is out ＝Pr{C a,b ＜R s Is brought into (15)
Figure BDA0003895648260000123
Wherein g is b,b Is h b,b A channel variance; phi (phi is more than 0 and less than or equal to 1) is an interference cancellation coefficient;
Figure BDA0003895648260000124
is P b A maximum transmit power;
Figure BDA0003895648260000125
is the variance of the noise;
Figure BDA0003895648260000126
g a,b is h a,b A channel variance; p is a Is the transmit power of the transmitting node;
Figure BDA0003895648260000127
representing the path loss coefficient from Alice to Bob.
Probability of connection O a,b ＝1-P out Is brought into (16) to
Figure BDA0003895648260000128
System covert transmission rate of
Figure BDA0003895648260000129
Brought into (17) to
Figure BDA00038956482600001210
Wherein pi 1 Probability of sending concealed messages for Alice, assuming Alice sends equal probability
Figure BDA00038956482600001211
(40) Establishing an optimization problem: under the condition of meeting given concealment constraint and minimizing the detection error probability of an eavesdropper, power distribution is carried out on the transmitting power and the noise power to maximize the concealment transmission rate of the system, and the optimal concealment transmission rate of the system is obtained.
(41) Setting a required detection error probability threshold value: this value is designed according to the system requirements, e.g., if Wille requires 90% (i.e., 1-epsilon) probability not to hear Alice's communication with Bob, epsilon =0.1.
(42) Establishing a constraint condition: for a given (41) condition in combination with the minimum detection error probability (equation 11) of the system, it is required that the error probability of the eavesdropping node cannot be lower than a set error threshold, i.e. it is required that
Figure BDA0003895648260000131
(43) And (3) forming optimized content: and (4) combining the capacity expressions (18) and the constraint conditions set forth in the (42) to obtain optimized contents. Requiring a covert transmission rate R under the condition that the detection error probability of the eavesdropping node meets the given constraint condition c And max.
Figure BDA0003895648260000132
(50) The target node comprehensively considers the concealment and reliability constraints of the system and solves the maximum effective rate R of the sending node c 。
Let total power of system transmission be P, letTransmitting power of transmitting node and destination node
Figure BDA0003895648260000133
The influence R can be seen again from the formula (18) c The variable in size is only P, and R c Is an increasing function with respect to P. And (3) solving the P, wherein when the hidden condition constraint of the formula (19) is met, the value range of the P is as follows:
Figure BDA0003895648260000134
due to R c Is an increasing function of P, and the optimal transmitting power of the system is obtained according to the value range of P
Figure BDA0003895648260000135
Wherein
Figure BDA0003895648260000136
Figure BDA0003895648260000137
Wherein
Figure BDA0003895648260000138
For the channel coefficients of Alice to Willie (i), the channel coefficients, similarly,
Figure BDA0003895648260000139
channel coefficients from Bob to Willie (i); l. capillary 2 Represents the square of the modulus;
Figure BDA00038956482600001310
represents the path loss coefficient from Alice to Willie (i);
Figure BDA00038956482600001311
represents the path loss coefficient from Bob to Willie (i).
R obtained at this time c Is the optimal solution. It shows that the sending node can find an optimal transmission power, so that the hidden message can still be sent at a certain rate in the environment of multi-eavesdropper joint detection.

Claims (7)

1. A hidden transmission method under a multi-eavesdropper joint detection environment is characterized by comprising the following specific steps:
(10) Establishing a wireless covert communication network model, wherein the wireless covert communication network model comprises a sending node, a legal receiving destination node and two eavesdropping nodes, the sending node carries out covert transmission to the destination node, namely the sending node generates a random signal with a certain probability and sends the random signal to the destination node;
(20) The eavesdropping node detects whether the sending node sends the message or not and calculates the minimum detection error probability of the eavesdropping node;
(30) The target node sends an interference signal to resist the eavesdropping node;
(40) Under the condition of meeting given concealment constraint and minimizing the detection error probability of the eavesdropping node, maximizing the concealment transmission rate of the system by power distribution and selecting the most appropriate transmission power of the interference node to obtain the optimal concealment transmission rate of the system;
(50) And the target node comprehensively considers the concealment and reliability constraints of the system and solves the maximum effective rate of the sending node.
2. The hidden transmission method under the multi-eavesdropper joint detection environment according to claim 1, wherein the specific method for detecting whether the sending node sends the message by the eavesdropping node is as follows:
the two eavesdropping nodes respectively adopt the radiometers to carry out energy detection on the received signals and judge whether transmission signals exist or not;
whether a sending node sends a message is detected by adopting a joint judgment scheme, wherein the joint judgment scheme comprises two schemes, and the two schemes are shown in the following table:
Figure FDA0003895648250000011
the first scheme comprises the following steps: if any eavesdropping node detects that the transmission exists, the eavesdropping node judges that the sending node sends the confidential information; scheme II: only when two eavesdropping nodes detect that the transmission exists, the sending node is judged to send the confidential message; y is 0 Indicating that the transmitting node has not transmitted information, Y 1 Indicates that it is determined that the transmitting node has transmitted information, Y 0 (i) Indicating that the transmitting node has not transmitted information, Y 1 (i) I =1,2, which indicates that the transmitting node has transmitted the information.
3. The hidden transmission method under the environment of multi-eavesdropper joint detection according to claim 2, wherein the method for the two eavesdropping nodes to respectively judge whether the transmission signal exists is as follows:
Figure FDA0003895648250000021
in the formula (I), the compound is shown in the specification,
Figure FDA0003895648250000022
indicating eavesdropping node w i Average received power of τ i Is w i Threshold of decision of (Y) 0 (i) Indicating that the transmitting node has not transmitted information, Y 1 (i) Indicating that the transmitting node has transmitted the information.
4. The hidden transmission method under the environment of multi-eavesdropper joint detection according to claim 3, wherein the calculation method of the minimum detection error probability of the eavesdropping node is as follows:
the undetected rate and the false detection rate of the detector are respectively expressed as follows:
Figure FDA0003895648250000023
Figure FDA0003895648250000024
i is 1 for scheme one and 2 for scheme two;
suppose that the probability of sending secret information by a sending node is Pr { H 1 }＝Pr{H 0 =1/2, the detection error probability ξ of the eavesdropping node is:
Figure FDA0003895648250000025
calculating the error probability according to the first scheme:
when the scheme is adopted, the undetected rate and the false rate of the eavesdropping node are as follows:
Figure FDA0003895648250000026
Figure FDA0003895648250000027
when the system is satisfied
Figure FDA0003895648250000028
(where subscript a denotes Alice, subscript b denotes Bob, and subscript w denotes i The subscript i of w is 1 to represent the wiretap node 1, and is 2 to represent the wiretap node 2; p a Sending signal power for a sending node Alice;
Figure FDA0003895648250000029
is P b A maximum transmit power;
Figure FDA00038956482500000210
from Alice to Willie (i)The channel coefficients are then transmitted to the receiver,
Figure FDA00038956482500000211
channel coefficients for Bob to the eavesdropping node Willie (i); l. capillary 2 Represents the square of the modulus;
Figure FDA00038956482500000212
representing the path loss coefficient from the sending node Alice to the eavesdropping node Willie (i);
Figure FDA00038956482500000213
represents the path loss coefficient from the destination node Bob to Willie (i), and w 1 And w 2 The optimal decision thresholds are respectively
Figure FDA0003895648250000031
And
Figure FDA0003895648250000032
wherein P is b max Is P b A maximum transmit power;
Figure FDA0003895648250000033
channel coefficients from Bob to Willie (i); l |, the hollow 2 Represents the square of the modulus;
Figure FDA0003895648250000034
represents the path loss coefficient from Bob to Willie (i);
Figure FDA0003895648250000035
minimum probability of detection error obtained for Gaussian white noise power
Figure FDA0003895648250000036
Comprises the following steps:
Figure FDA0003895648250000037
wherein subscript a denotes Alice, subscript b denotes Bob, and subscript w i Denotes Willie (i), the subscript i of w is 1 for Willie1, 2 for Willie2; p is a Transmitting signal power for a transmitting node Alice;
Figure FDA0003895648250000038
is P b A maximum transmit power;
Figure FDA0003895648250000039
the channel coefficients for Alice to Willie (i), and, similarly,
Figure FDA00038956482500000310
channel coefficients Bob to Willie (i); l. capillary 2 Represents the square of the modulus;
Figure FDA00038956482500000311
represents the path loss coefficient from Alice to Willie (i);
Figure FDA00038956482500000312
represents the path loss coefficient from Bob to Willie (i);
when the scheme two is adopted, the undetected rate and the false rate of the eavesdropping node are as follows:
Figure FDA00038956482500000313
Figure FDA00038956482500000314
when the system is satisfied
Figure FDA00038956482500000315
(where subscript a denotes Alice, subscript b denotes Bob, and subscript w i Denotes Willie (i), w has a subscript i of 1 for Willie1 and 2 for Willie2；P a Transmitting signal power for a transmitting node Alice;
Figure FDA00038956482500000316
is P b A maximum transmit power;
Figure FDA00038956482500000317
the channel coefficients for Alice to Willie (i), and, similarly,
Figure FDA00038956482500000318
channel coefficients from Bob to Willie (i); l |, the hollow 2 Represents the square of the modulus;
Figure FDA00038956482500000319
represents the path loss coefficient from Alice to Willie (i);
Figure FDA00038956482500000320
represents the pathloss coefficient from Bob to Willie (i), and w 1 And w 2 The optimal decision thresholds are respectively
Figure FDA00038956482500000321
And
Figure FDA00038956482500000322
wherein P is a Transmitting signal power for a transmitting node Alice;
Figure FDA00038956482500000323
channel coefficients for Alice to Willie (i); l |, the hollow 2 Represents the square of the modulus;
Figure FDA00038956482500000324
represents the path loss coefficient from Alice to Willie (i);
Figure FDA00038956482500000325
for Gaussian white noise power, obtainedMinimum probability of detection error
Figure FDA00038956482500000326
Comprises the following steps:
Figure FDA0003895648250000041
wherein subscript a denotes Alice, subscript b denotes Bob, and subscript w i Denotes Willie (i), the subscript i of w is 1 for Willie1 and 2 for Willie2; p a Sending signal power for a sending node Alice;
Figure FDA0003895648250000042
is P b A maximum transmit power;
Figure FDA0003895648250000043
the channel coefficients for Alice to Willie (i), and, similarly,
Figure FDA0003895648250000044
channel coefficients from Bob to Willie (i); l |, the hollow 2 Represents the square of the modulus;
Figure FDA0003895648250000045
represents the path loss coefficient from Alice to Willie (i);
Figure FDA0003895648250000046
represents the path loss coefficient from Bob to Willie (i).
5. The hidden transmission method under the multi-eavesdropper joint detection environment according to claim 1, wherein when the target node sends an interference signal to combat the eavesdropping node, a capacity expression and a hidden transmission rate expression are determined, and the specific process is as follows:
in a multi-eavesdropping node network, a sending node carries out hidden transmission; the received signal at the legal receiving destination node is:
Figure FDA0003895648250000047
wherein, P a Is the transmit power of the transmitting node; p b Transmitting power of noise of a target node for legal receiving;
Figure FDA0003895648250000048
representing the path loss coefficient from Alice to Bob; h is a,b Channel coefficients for Alice to Bob; h is a total of b,b Channel coefficients between Bob transmit antennas and Bob receive antennas; x is the number of a (k) A covert signal sent for Alice; x is the number of b (k) For the artificial noise at Bob, satisfy E [ | x b (k)| 2 ]＝1；n b (k) Is the noise at Bob, satisfies
Figure FDA0003895648250000049
Phi (phi is more than 0 and less than or equal to 1) is an interference cancellation coefficient; k =1,2, \8230;, n denotes the kth symbol in the slot;
P b compliance
Figure FDA00038956482500000410
The uniformity of the distribution of the water content in the water,
Figure FDA00038956482500000411
is P b Maximum transmit power, probability density function
Figure FDA00038956482500000412
Comprises the following steps:
Figure FDA00038956482500000413
receiving the signal-to-interference-and-noise ratio gamma at the destination node b Comprises the following steps:
Figure FDA00038956482500000414
wherein P is a Is the transmit power of the transmitting node; p b Receiving the noise emission power of the destination node for legal purpose;
Figure FDA00038956482500000415
representing the path loss coefficient from Alice to Bob; h is a total of a,b Channel coefficients for Alice to Bob; h is a total of b,b Channel coefficients between Bob transmit antennas and Bob receive antennas; l. capillary 2 Represents the square of the modulus; phi (phi is more than 0 and less than or equal to 1) is an interference cancellation coefficient;
transmission rate formula, capacity expression C a,b Comprises the following steps:
C a,b ＝log 2 (1+γ b )
given a system target transmission rate of R s Probability of system outage P out Comprises the following steps:
P out ＝Pr{C a,b ＜R s }＝Pr{log 2 (1+γ b )＜R s }
probability of connection O a,b ＝1-P out The system concealing transmission rate is
Figure FDA0003895648250000051
π 1 Probability of sending concealed messages for Alice, assuming Alice sends equal probability
Figure FDA0003895648250000052
6. The hidden transmission method under multi-eavesdropper joint detection environment according to claim 1, wherein, under the condition of satisfying given concealment constraints and minimizing detection error probability of eavesdropping nodes, the hidden transmission rate of the system is maximized by power allocation and selecting the most suitable transmission power of the interfering nodes, and the specific process of obtaining the optimal hidden transmission rate of the system is as follows:
(41) Setting a required detection error probability threshold epsilon;
(42) Establishing a constraint condition: in combination with a minimum detection error probability of the system, it is required that the error probability of the eavesdropping node cannot be lower than a set error threshold, i.e. it is required that
Figure FDA0003895648250000053
(43) And (3) forming optimized content: the capacity expression is combined with the constraint condition to obtain optimized content, and the hidden transmission rate R is required to meet the given constraint condition when the detection error probability of the eavesdropping node meets the requirement c Maximum:
Figure FDA0003895648250000054
Figure FDA0003895648250000055
7. the hidden transmission method under the environment of joint detection of multiple eavesdroppers according to claim 1, wherein the specific method for solving the maximum effective rate of the sending node is as follows:
the total transmitting power of the system is P, and the transmitting power of a transmitting node and the transmitting power of a target node are made
Figure FDA0003895648250000056
Solving the total transmitting power P of the system, wherein when the concealment condition constraint is met, the value range of P is as follows:
Figure FDA0003895648250000061
due to R c The optimal transmitting power of the system is obtained according to the value range of P as the increasing function of P:
Figure FDA0003895648250000062
wherein the content of the first and second substances,
Figure FDA0003895648250000063
Figure FDA0003895648250000064
wherein
Figure FDA0003895648250000065
Are the channel coefficients of Alice to Willie (i),
Figure FDA0003895648250000066
channel coefficients Bob to Willie (i); l. capillary 2 Represents the square of the modulus;
Figure FDA0003895648250000067
represents the path loss coefficient from Alice to Willie (i);
Figure FDA0003895648250000068
represents the path loss coefficient from Bob to Willie (i).
CN202211272563.7A 2022-10-18 2022-10-18 Hidden transmission method under multi-eavesdropper joint detection environment Pending CN115665729A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116456391A (en) * 2023-06-16 2023-07-18 中国人民解放军军事科学院国防科技创新研究院 Uplink non-orthogonal multiple access hidden wireless communication method and system
CN117614650A (en) * 2023-10-26 2024-02-27 国网湖北省电力有限公司宜昌供电公司 Concealed communication method and system of electric power Internet of things

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116456391A (en) * 2023-06-16 2023-07-18 中国人民解放军军事科学院国防科技创新研究院 Uplink non-orthogonal multiple access hidden wireless communication method and system
CN116456391B (en) * 2023-06-16 2023-09-05 中国人民解放军军事科学院国防科技创新研究院 Uplink non-orthogonal multiple access hidden wireless communication method and system
CN117614650A (en) * 2023-10-26 2024-02-27 国网湖北省电力有限公司宜昌供电公司 Concealed communication method and system of electric power Internet of things

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