CN119233246B

CN119233246B - MISO-oriented hidden communication optimization method and system

Info

Publication number: CN119233246B
Application number: CN202411756256.5A
Authority: CN
Inventors: 朱翔; 田文; 翟文雨; 徐一纯; 蔡伟晨; 石怀峰; 刘光杰
Original assignee: Nanjing University of Information Science and Technology
Current assignee: Nanjing University of Information Science and Technology
Priority date: 2024-12-03
Filing date: 2024-12-03
Publication date: 2025-06-27
Anticipated expiration: 2044-12-03
Also published as: CN119233246A

Abstract

The present invention discloses a MISO-oriented concealed communication optimization method and system, the method comprising the following steps: (1) constructing a MISO-oriented concealed communication system model, the concealed communication system model comprising a transmitter with multiple antennas, a receiver with both receiving and interference functions, and an eavesdropper; (2) constructing an optimization problem for MISO-oriented concealed communication; (3) converting the optimization problem into a convex optimization problem; (4) iteratively solving the convex optimization problem until the values of _Pa , _ua , and u _b are obtained when the average concealed rate R value is maximized, and the values are output as the concealed communication optimal strategy. The present invention simultaneously achieves high concealment and high communication rate.

Description

MISO-oriented hidden communication optimization method and system

Technical Field

The invention relates to a hidden communication technology, in particular to a hidden communication optimization method and a hidden communication optimization system for MISO (multiple input single output ).

Background

With the widespread use of wireless communication, communication security problems are increasingly emphasized because wireless channels have broadcast characteristics. Most of the existing secure transmission technologies focus on protecting contents from eavesdropping, such as encryption technology and physical layer security technology, but with the continuous development of eavesdropping technology, such protection measures are becoming increasingly inadequate. The security of the information content is ensured by only encryption, and advanced attack means such as flow analysis, side channel attack and the like may not be effectively prevented. Therefore, future security technologies should incorporate more comprehensive protection mechanisms, not only to ensure confidentiality of information content, but also to pay attention to integrity and authenticity of data and various security threats that may be encountered during transmission, so as to achieve information protection. An emerging technology is directed to concealing information content, i.e., making it impossible for a listener to determine whether information has been transmitted by a monitored target.

The covert communication technique aims to establish a communication link with low probability of being found, providing a strong security guarantee for communication, but its feasibility is limited by the high level of detectability of listeners. In addition, high power transmissions by legitimate users to achieve high data rate communications can easily result in signal transmission exposure. Thus, how to achieve both high concealment and high communication rates with listeners is the biggest challenge for covert communication.

Disclosure of Invention

Aiming at the problems existing in the prior art, the invention aims to provide a MISO-oriented hidden communication optimization method and system for simultaneously realizing high concealment and high communication rate.

In order to achieve the above object, the present invention provides the following technical solutions:

A MISO-oriented hidden communication optimization method comprises the following steps:

(1) Constructing a MISO-oriented covert communication system model, wherein the covert communication system model comprises a transmitter with multiple antennas, a receiver with both receiving and interference, and a listener;

(2) The optimization problem of constructing MISO-oriented covert communication is as follows:

,

in the formula, Indicating the average concealment rate, subscripts a, b, w indicate the transmitter, receiver and listener respectively,Representing the transmit power of the transmitter,Analog beamforming vectors for the transmitter and receiver respectively,For the power at which the receiver transmits the interfering signal,Representing the variance of the noise and,A channel coefficient vector representing the link between the transmitter and the receiver,A channel coefficient vector representing the self-interfering channel of the receiver,Representation pair relates toAndIs to be expected by a function of (a),Representing the probability of detection errors of the listener,Representation pair relates toAndIs to be expected by a function of (a),Representing the minimum required probability of a listener making an inaccurate decision,Representation ofIs selected from the group consisting of the (k) th element,Representation ofIs selected from the group consisting of the m-th element of (c),Indicating the number of transmit antennas of the transmitter,Indicating the number of transmit antennas of the receiver,Indicating the maximum transmit power of the transmitter, the superscript H indicates the conjugate transpose,A channel coefficient vector representing the link between the transmitter and listener,A channel coefficient vector representing a link between the receiver and the listener;

(3) Converting the optimization problem into a convex optimization problem;

(4) Iteratively solving the convex optimization problem until the average hiding speed value is maximized As a value of the covert communication optimal policy.

A MISO-oriented covert communication optimization system comprising:

The communication model building module is used for building a MISO-oriented covert communication system model, and the covert communication system model comprises a transmitter with multiple antennas, a receiver with both receiving and interference and a listener;

the optimization problem construction module is used for constructing the optimization problem of MISO-oriented hidden communication as follows:

,

the problem conversion module is used for converting the optimization problem into a convex optimization problem;

a problem solving module for iteratively solving the convex optimization problem until obtaining the maximum average hidden speed value As a value of the covert communication optimal policy.

Compared with the prior art, the invention has the beneficial effects that under the constraint of a certain concealment, the analog beam forming vector and the transmitting signal power are designed, meanwhile, the unit modulus constraint and the transmitting power constraint of the analog beam forming device are considered, and the communication rate between two legal users is improved as much as possible. The method comprehensively considers the channel condition, the interference environment and the user requirement, and under the condition of not obviously increasing the characteristic of the detectable signal, the communication rate between legal communication users is striven for improving, so that the efficient and difficultly detectable wireless communication is realized. In addition, compared with the existing work, the invention fills the research blank of interference-assisted full duplex hidden millimeter wave communication.

Drawings

Fig. 1 is a schematic flow chart of a MISO-oriented covert communication optimization method provided by an embodiment of the invention;

FIG. 2 is an architecture diagram of a covert communication system model in an embodiment of the invention;

FIG. 3 is a schematic diagram of a solution process for a convex optimization problem in an embodiment of the invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

The embodiment of the invention provides a MISO-oriented hidden communication optimization method, which comprises the following steps as shown in figure 1:

(1) And constructing a MISO-oriented hidden communication system model.

The covert communication system model includes a transmitter having multiple antennas, a receiver having both reception and interference, and a listener. In this embodiment, as shown in fig. 2, assuming that the transmitter is Alice, the receiver is Bob, the listener is Willie, bob receives the signal transmitted by Alice and sends an interference signal to affect the listening of Willie. Alice is equipped with multiple antennas for transmitting signals, bob is equipped with a single antenna for receiving signals and multiple antennas for transmitting interference signals, willie is equipped with an antenna for monitoring whether Alice transmits signals or not.

In this embodiment, a widely adopted cluster channel model is selected to construct a channel model between Alice, bob, willie pairs, and a self-interference channel model of Bob is specifically as follows:

Order the ,Channel coefficient vectors representing Alice-to-Bob link, alice-to-Willie link, bob-to-Willie link, bob self-interference channel, respectively, whereIndicating the number of Alice transmitting antennas,Indicating the number of Bob transmit antennas,Representation ofIs one ofIs used for the complex vector of (a),、、And the same is true. The channel model is built according to the 3GPP/ITU model as follows:

,

Subscript of ,A channel coefficient vector representing the link between x and y,Representing the number of sub-paths of the link between x and y,Representing the average path loss of the link between x and y,The number of antennas denoted by x is indicated,Representing the link between x and yThe small scale channel gain of the strip path,,Represents the normalized s-th response vector, an,Indicating the emission angle of the s-th sub-path signal emission end of the link between x and y,, ,Indicating the antenna spacing(s) and,Representing the carrier wavelength(s),Representation ofIs used as a reference to the number of the values,The number of transmit antennas at the transmit end of the link between x and y is indicated. To simplify the following discussion, let。

The above-mentioned clustered channel model is a far-field channel model, i.e. the receiving end regards the signal as a plane wave, and is generally not suitable for self-interference channels, because the distance between the transmitting antenna and the receiving antenna of the self-interference end is smaller than the wavelength of the carrier wave, and the condition of the far-field model is not satisfied(D is the distance between the transmit antenna array and the receive antenna array). The self-interference channel model adopted in the embodiment is thatWhereinIs the rice factor (rice factor) and,Respectively represent the line-of-sight component of the self-interference channel non-line-of-sight components. Since the transmission distance of the non-line-of-sight link is generally longer than that of the wavelength, the far field model is adopted) Modeling. The model of the line-of-sight component is shown as follows:

,

Wherein, the An nth element representing a line of sight component,Is to ensureWhile the called power normalization constant,Representing the averaging of the values,Is the distance between the Bob nth transmitting antenna and Bob receiving antenna, and is specifically as follows:

,

Is the wavelength and Θ is the angle between the arrays.

It will be appreciated that in other embodiments, other ways of constructing the channel model may be employed, such as a rayleigh channel model, a gaussian channel model, etc.

(2) And constructing an optimization problem of MISO-oriented hidden communication.

According to the channel model, if Alice transmits signalsBob transmits an interference signalThen Bob receives the signal sequenceThe method comprises the following steps: wherein For signal indexing, N is the number of signals,For the channel noise between Alice and Bob,Representing the noise variance, subscripts a, b, w represent the transmitter, receiver and listener respectively,Representing the transmit power of Alice,Analog beamforming vectors for Alice and Bob respectively,The power of the interfering signal is transmitted for Bob.,,Obeying 0 toUniformly distributed on the surface. The randomness of Bob transmitting power is introduced in the embodiment, so that Willie cannot determine whether the fluctuation of the received signal is caused by Alice transmission or Bob interference, thereby improving the probability of detection error at the Willie end. After that toAndAveraging to obtain an average concealment rateThe calculation formula is as follows:

,

The minimum solution process for Willie to the probability of performing an erroneous decision is as follows: willie signal detection can be categorized as a binary hypothesis testing problem. Let the null hypothesis H0 represent Alice remains silent, i.e. no signal is transmitted, while the substitute hypothesis H1 represents Alice transmitting an information signal. In both cases, willie receives the following signals:

,

Wherein, the Representing the channel noise between Alice and Willie. Assume Willie that energy detection is performed using a radiometer as its detector to detect Alice's activity and Willie observes an unlimited number of channel uses, which represents the worst case for communication concealment. In this case Willie performs a likelihood ratio check to detect if Alice's signal transmission is present, which gives the formulaD0 represents detection performed when Willie considers that Alice is not transmitting a signal, D1 represents detection performed when Willie considers that Alice is transmitting a signal,The predetermined detection threshold employed by Willie is indicated,Representing statistical data, the expression of which is:

。

Because Willie is received by The energy introduced is random and Willie may be subject to errors in signal detection, including missed detection (Missed Detection, MD) and false positives (FALSE ALARM, FA). The missed detection event is defined as Willie executing detection D0 but H1 is true, the corresponding probability is. The misinformation event is defined Willie to perform detection D1 but H0 is true, the corresponding probability is. Suppose Willie has no information about when Alice is transmitting, so its best guess is that it will assumeAndIs considered equal, which results in. The detection error probability of Willie is defined as:

,

Wherein, the ,,AndRepresenting the energy of the signals transmitted by the receiver and the transmitter, respectively, arriving at the listener. Due to availability only of、Statistical channel information of (a) so that a pair is adopted、Average minimum detection error probability is taken to evaluate concealment of communication, i.e,

Wherein the method comprises the steps ofRepresentation pair、The average minimum probability of detection error is taken,, ,As an intermediate variable, the number of the variables,、Respectively representAndA covariance matrix of the complex gaussian distribution obeyed.

The optimization problem of constructing MISO-oriented covert communication is as follows:

,

in the formula, Representation pair relates toAndIs to be expected by a function of (a),Representation pair relates toAndIs to be expected by a function of (a),Representing the minimum required probability of a listener making an inaccurate decision,Representation ofIs selected from the group consisting of the (k) th element,Representation ofAnd H represents the conjugate transpose.

(3) And converting the optimization problem into a convex optimization problem.

When the problem is converted, the objective function and the constraint of the optimization problem of the hidden communication facing the MISO are converted into an easy-to-process formula. Due toAndCoupling between them is difficult to obtainIs easy to handle. Alternatively, a widely adopted lower bound optimization method is adopted toInstead of its lower limit and optimizing the lower limit to indirectly maximize the concealment rate. By means of the Jensen inequality,

,

Wherein, the Representation ofIs defined by the lower boundary of the (c),As an auxiliary variable, a control signal is provided,1 St, which represents self-interference channel normalization,The number of response vectors is chosen to be the number of response vectors,Indicating that the receiver is interfering with channel No. 1,The emission angle of the strip path signal emission end,Indicating the number of self-interference channel sub-paths for the receiver.

By introducing additional variablesAnd,Can be rewritten as:

,

in the formula, Representation ofIs used for the conjugation of (a),The function replaced by the lower bound optimization method is adopted for the average concealment rate R, and Re () represents the real part. Although a functionRatio ofWith more optimization variables, butIs helpful to implement the Imprecise Block Coordinate Descent (IBCD) algorithm becauseWhile keeping all other four variables fixed, it is the convex function for the remaining one.

Against covert constraintsBecause ofIs aboutIs used as a function of the increase of (2),Can be rewritten as,By binary search, i.e. whenIn the time-course of which the first and second contact surfaces,This is true. The concealment constraint can be expressed as:

,

And then the first-order Taylor expansion can be used for replacing the right non-convex part in the son, so that the method is obtained:

,

Wherein, the Respectively represent the%) At the time of iteration、Is a solution to the optimization of (3).

For unit mode constraint, it is converted into by linear matrix inequality and the schulk-complement theorem:

,

Wherein, the 、Respectively the auxiliary variables are used for the control of the control system,Representation ofAn element of the ith row and the ith column,Representation ofThe elements of the j-th row and j-th column,Representing the tracing.

For the purpose of、Two non-convex terms, also using the same first order taylor expansion, then:

,

Thus, the optimization problem is translated into the following convex optimization problem:

,

。

It will be appreciated that in other embodiments, the optimization problem may be converted to other forms of convex optimization problem by means of a lower bound method and an introduced auxiliary variable method, as long as the convex optimization problem can be solved.

(4) Iteratively solving the convex optimization problem until an average concealment rate is obtainedAt maximum valueAs a value of the covert communication optimal policy.

As shown in fig. 3, the solving process specifically includes:

(4.1) setting Initial value of (1)Setting the iteration number l=1;

(4.2) fixing Solving the problemObtainingIs the optimal solution of (a):

,

(4.3) Optimal solution basedFixingSolving the problemObtainingIs the optimal solution of (a):

,

(4.4) WillUpdated toWill beUpdated toAnd solving the problem by adopting a successive convex approximation methodObtaining the current iteration、As the optimal solution,,;

(4.5) Judging whether the average hiding rate difference value reaches a preset threshold value, if so, executing (4.6), otherwise, returning l=l+1 to executing (4.2);

(4.6) at this time 、The value of (2) is output as a covert communication optimal policy.

It will be appreciated that the solution process can also be other ways, such as first fixing the solutionRe-solvingRe-solving、Or other ways of iterative loops, can be solved to obtain the optimal strategy.

The embodiment of the invention also provides a MISO-oriented hidden communication optimization system, which comprises:

,

Wherein, the detection error probability of the listener is specifically:

,

in the formula, Indicating the maximum transmit power at which the receiver transmits the interfering signal,,,AndRepresenting the energy of the signals transmitted by the receiver and the transmitter, respectively, arriving at the listener.

Wherein the convex optimization problem is specifically:

,

in the formula, The function after the substitution of the lower bound optimization method is adopted for the average concealment rate R,AndIn order to introduce auxiliary variables during the conversion,Representation ofRe () represents the real part,Representing the maximum transmit power at which the receiver transmits the interfering signal; The rice factor is represented by the formula, Representing the line-of-sight component of a self-interfering channel of a receiver, an,Representing the non-line-of-sight component of the self-interfering channel of the receiver,Represents the auxiliary variable(s),1 St, which represents self-interference channel normalization,The number of response vectors is chosen to be the number of response vectors,Indicating that the receiver is interfering with channel No. 1,The emission angle of the strip path signal emission end,Representing the number of self-interference channel sub-paths of the receiver;、 Respectively represent AndA covariance matrix of the complex gaussian distribution obeyed,The representation satisfiesA kind of electronic deviceIs used to determine the conversion value of (c),、As an intermediate variable, the number of the variables,Respectively represent the%) At the time of iteration、Is used for the optimal solution of (a),、Respectively the auxiliary variables are used for the control of the control system,Representation ofAn element of the ith row and the ith column,Representation ofThe elements of the j-th row and j-th column,Representing the tracing.

The problem solving module specifically comprises:

An initial value setting unit for setting Initial value of (1)Setting the iteration number l=1;

A first problem solving unit for fixing Solving the problemObtainingIs the optimal solution of (a):

,

A second problem solving unit for solving the problem based on the optimal solutionFixingSolving the problemObtainingIs the optimal solution of (a):

,

A third problem solving unit for solvingUpdated toWill beUpdated toAnd solving the problem by adopting a successive convex approximation methodObtaining the current iteration、As the optimal solution,,;

The cut-off judging unit is used for judging whether the average hiding rate difference value reaches a preset threshold value, if yes, executing the strategy output unit, otherwise, returning l=l+1 to execute the first problem solving unit;

A policy output unit for outputting the current time 、The value of (2) is output as a covert communication optimal policy.

The channel model of the MISO-oriented hidden communication system model is as follows:

,

Subscript of ,A channel coefficient vector representing the link between x and y,Representing the number of sub-paths of the link between x and y,Representing the average path loss of the link between x and y,The number of antennas denoted by x is indicated,Representing the link between x and yThe small scale channel gain of the strip path,,Represents the normalized s-th response vector, an,Indicating the emission angle of the s-th sub-path signal emission end of the link between x and y,, ,Indicating the antenna spacing(s) and,Representing the carrier wavelength(s),Representation ofIs used as a reference to the number of the values,The number of transmit antennas at the transmit end of the link between x and y is indicated.

The system provided by the embodiment of the invention can be used for executing the method provided by the first embodiment of the invention, has the corresponding functions and beneficial effects of the executing method, and is the same as that described with reference to the method, and is not repeated.

It should be noted that, in the embodiment of the system, the included units and modules are only divided according to the functional logic, but not limited to the above-mentioned division, so long as the corresponding functions can be implemented, and the specific names of the functional units are only for convenience of distinguishing from each other, and are not used for limiting the protection scope of the present invention.

The embodiments described above are merely illustrative, wherein the modules illustrated as separate components may or may not be physically separate, and the components shown as modules may or may not be physical, i.e., may be located in one place, or may be distributed over a plurality of network modules. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. It will be apparent to those skilled in the art that the embodiments may be implemented by means of software plus necessary general hardware platforms, or of course, may be implemented solely by hardware, as long as the function or function is achieved.

It should be understood that the foregoing embodiments and description are merely illustrative of the principles, features, and advantages of this invention, and that various changes and modifications can be made in the invention without departing from the spirit and scope of the invention, which is defined in the claims.

Claims

1. The MISO-oriented covert communication optimization method is characterized by comprising the following steps of:

,

in the formula, Indicating the average concealment rate, subscripts a, b, w indicate the transmitter, receiver and listener respectively,Representing the transmit power of the transmitter,Analog beamforming vectors for the transmitter and receiver respectively,For the power at which the receiver transmits the interfering signal,Representing the variance of the noise and,A channel coefficient vector representing the link between the transmitter and the receiver,A channel coefficient vector representing the self-interfering channel of the receiver,Representation pair relates toAndIs to be expected by a function of (a),Representation pair relates toAndIs to be expected by a function of (a),Representing the minimum required probability of a listener making an inaccurate decision,Representation ofIs selected from the group consisting of the (k) th element,Representation ofIs selected from the group consisting of the m-th element of (c),Indicating the number of transmit antennas of the transmitter,Indicating the number of transmit antennas of the receiver,Indicating the maximum transmit power of the transmitter, the superscript H indicates the conjugate transpose,A channel coefficient vector representing the link between the transmitter and listener,A channel coefficient vector representing a link between the receiver and the listener; The detection error probability of the listener is expressed specifically as follows:

,

in the formula, Indicating the maximum transmit power at which the receiver transmits the interfering signal,,,AndRepresenting the energy of the signals transmitted by the receiver and the transmitter, respectively, arriving at the listener;

(3) Converting the optimization problem into a convex optimization problem;

2. The MISO-oriented covert communication optimization method of claim 1, wherein the convex optimization problem in step (3) is specifically:

,

in the formula, The function after the substitution of the lower bound optimization method is adopted for the average concealment rate R,AndIn order to introduce auxiliary variables during the conversion,Representation ofRe () represents the real part,Representing the maximum transmit power at which the receiver transmits the interfering signal; The rice factor is represented by the formula, Representing the line-of-sight component of a self-interfering channel of a receiver, an,Representing the non-line-of-sight component of the self-interfering channel of the receiver,Represents the auxiliary variable(s),1 St, which represents self-interference channel normalization,The number of response vectors is chosen to be the number of response vectors,Indicating that the receiver is interfering with channel No. 1,The emission angle of the strip path signal emission end,Representing the number of self-interference channel sub-paths of the receiver;、 Respectively represent AndA covariance matrix of the complex gaussian distribution obeyed,The representation satisfiesA kind of electronic deviceIs used to determine the conversion value of (c),, ,、As an intermediate variable, the number of the variables,Respectively represent the%) At the time of iteration、Is used for the optimal solution of (a),、Respectively the auxiliary variables are used for the control of the control system,Representation ofAn element of the ith row and the ith column,Representation ofThe elements of the j-th row and j-th column,Representing the tracing.

3. The MISO-oriented covert communication optimization method of claim 2, wherein step (4) specifically comprises:

(4.1) setting Initial value of (1)Setting the iteration number l=1;

(4.2) fixing Solving the problemObtainingIs the optimal solution of (a):

,

4. The MISO-oriented covert communication optimization method of claim 1, wherein the channel model of the MISO-oriented covert communication system model is:

,

5. A MISO-oriented covert communication optimization system, comprising:

,

6. The MISO-oriented covert communication optimization system of claim 5, wherein the convex optimization problem is specifically:

,

7. The MISO-oriented covert communication optimization system of claim 6, wherein the problem solving module specifically comprises:

,

8. The MISO-oriented covert communication optimization system of claim 5, wherein the channel model of the MISO-oriented covert communication system model is:

,