An Optimization Method and System for Covert Communication Oriented to MISO

Abstract

The present invention discloses an optimization method and system for covert communication oriented to MISO. The method includes the following steps: (1) constructing a covert communication system model oriented to MISO, where the covert communication system model includes a transmitter with multiple antennas, a receiver with both receiving and interfering functions, and a monitor; (2) constructing an optimization problem for covert communication oriented to MISO; (3) transforming the optimization problem into a convex optimization problem; (4) iteratively solving the convex optimization problem until the values of P a , u a , u b are obtained and output as the optimal strategy for covert communication. The present invention simultaneously achieves high concealment and high communication rate.

Description

Technical Field

[0001] The present invention relates to covert communication technologies, and in particular, to an optimization method and system for covert communication oriented to MISO (multiple input single output). Background Art

[0002] With the wide application of wireless communication, communication security issues have attracted increasing attention due to the broadcast nature of wireless channels. Most existing secure transmission technologies focus on protecting the content from eavesdropping, such as encryption technologies and physical layer security technologies. However, with the continuous development of eavesdropping technologies, such protection measures are becoming increasingly insufficient. Relying solely on encryption to ensure the security of information content may not be able to effectively prevent advanced attack means, such as traffic analysis, side-channel attacks, etc. Therefore, future security technologies should incorporate more comprehensive protection mechanisms, not only ensuring the confidentiality of information content, but also paying attention to the integrity, authenticity of data, and various security threats that may be encountered during the transmission process, so as to achieve information protection. An emerging technology is dedicated to concealing information content, that is, making it impossible for eavesdroppers to determine whether there is information transmitted by the monitored target. This technology is covert communication.

[0003] Covert communication technologies aim to establish communication links with a low probability of being detected, providing strong security guarantees for communication. However, their feasibility is limited by the high detectability of eavesdroppers. In addition, high-power transmissions by legitimate users to achieve high data rate communication are likely to lead to signal transmission exposure. Therefore, how to achieve both high concealment and high communication rate in the presence of eavesdroppers has become the greatest challenge in covert communication. Summary of the Invention

[0004] Aiming at the problems existing in the prior art, the purpose of the present invention is to provide an optimization method and system for covert communication oriented to MISO that can achieve both high concealment and high communication rate.

[0005] To achieve the above invention purpose, the present invention provides the following technical solutions:

[0006] An optimization method for covert communication oriented to MISO includes the following steps:

[0007] (1) Construct a covert communication system model oriented to MISO, where the covert communication system model includes a transmitter with multiple antennas, a receiver with both receiving and jamming capabilities, and an eavesdropper;

[0008] (2) Construct the optimization problem for covert communication oriented to MISO as:

[0009] ,

[0010] Wherein, denotes the average covert rate, and the subscripts a, b, w represent the transmitter, receiver, and eavesdropper respectively. denotes the transmit power of the transmitter. are the analog beamforming vectors of the transmitter and receiver respectively. is the power of the interference signal transmitted by the receiver. denotes the noise variance. denotes the channel coefficient vector of the link between the transmitter and the receiver. denotes the channel coefficient vector of the self-interference channel of the receiver. denotes the expectation of a function with respect to and denotes the detection error probability of the eavesdropper. denotes the expectation of a function with respect to and denotes the minimum required probability for the eavesdropper to make an inaccurate decision. denotes the k-th element of denotes the m-th element of denotes the number of transmit antennas of the transmitter. denotes the number of transmit antennas of the receiver. denotes the maximum transmit power of the transmitter, and the superscript H denotes the conjugate transpose. denotes the channel coefficient vector of the link between the transmitter and the eavesdropper. denotes the channel coefficient vector of the link between the receiver and the eavesdropper;

[0011] (3) Transform the optimization problem into a convex optimization problem;

[0012] (4) Iteratively solve the convex optimization problem until the value of that maximizes the average covert rate value is obtained and output as the optimal strategy for covert communication.

[0013] A covert communication optimization system for MISO includes:

[0014] A communication model establishment module for constructing a covert communication system model for MISO, where the covert communication system model includes a transmitter with multiple antennas, a receiver with both receiving and interfering capabilities, and an eavesdropper;

[0015] An optimization problem construction module for constructing the optimization problem for covert communication for MISO as:

[0016] ,

[0017] In the formula, represents the average covert rate, and the subscripts a, b, and w represent the transmitter, receiver, and eavesdropper respectively. represents the transmission power of the transmitter. are the analog beamforming vectors of the transmitter and receiver respectively. is the power of the interference signal transmitted by the receiver. represents the noise variance. represents the channel coefficient vector of the link between the transmitter and the receiver. represents the channel coefficient vector of the self-interference channel of the receiver. represents the expectation of the function with respect to and is the function of. represents the detection error probability of the eavesdropper. represents the expectation of the function with respect to and is the function of. represents the minimum required probability for the eavesdropper to make an inaccurate decision. represents the k-th element of. represents the m-th element of. represents the number of transmit antennas of the transmitter. represents the number of transmit antennas of the receiver. represents the maximum transmission power of the transmitter, and the superscript H represents the conjugate transpose. represents the channel coefficient vector of the link between the transmitter and the eavesdropper. represents the channel coefficient vector of the link between the receiver and the eavesdropper;

[0018] The problem transformation module is used to transform the optimization problem into a convex optimization problem;

[0019] The problem solving module is used to iteratively solve the convex optimization problem until the value of when the average covert rate value is maximized is obtained and output as the optimal strategy for covert communication.

[0020] Compared with the prior art, the beneficial effects of the present invention are as follows: Under the constraint of a certain degree of concealment, the present invention designs the analog beamforming vector and the transmit signal power, taking into account both the unit modulus constraint of the analog beamformer and the transmit power constraint, and improving the communication rate between two legitimate users as much as possible. This method comprehensively considers the channel conditions, interference environment and user requirements, and endeavors to improve the communication rate between legitimate communication users without significantly increasing the detectable signal characteristics, so as to achieve efficient and undetectable wireless communication. In addition, compared with the existing work, the present invention fills the research gap in interference-assisted full-duplex covert millimeter-wave communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 FIG. is a schematic flowchart of an optimization method for covert communication for MISO provided by an embodiment of the present invention;

[0022] Figure 2 FIG. is an architecture diagram of a covert communication system model in an embodiment of the present invention;

[0023] Figure 3 FIG. is a schematic diagram of the solution process of a convex optimization problem in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0024] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention.

[0025] An embodiment of the present invention provides an optimization method for covert communication for MISO, as Figure 1 shown, including the following steps:

[0026] (1) Construct a covert communication system model for MISO.

[0027] The covert communication system model includes a transmitter with multiple antennas, a receiver with both receiving and interfering functions, and a listener. In this embodiment, as Figure 2 shown, assume that the transmitter is Alice, the receiver is Bob, and the listener is Willie. Bob receives the signal transmitted by Alice while sending interference signals to affect Willie's listening. 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, and Willie is equipped with one antenna to monitor whether Alice transmits signals.

[0028] In this embodiment, a widely used cluster channel model is selected to construct the channel models between Alice, Bob, and Willie pairwise, and the self-interference channel model of Bob is as follows:

[0029] Let , respectively represent the channel coefficient vectors of the Alice-to-Bob link, the Alice-to-Willie link, the Bob-to-Willie link, and the Bob self-interference channel, where represents the number of Alice's transmit antennas, represents the number of Bob's transmit antennas, represents is a complex vector, , , Similarly. The channel model is established according to the 3GPP / ITU model as follows:

[0030] ,

[0031] The subscript , represents the channel coefficient vector of the link between x and y, represents the number of sub-paths of the link between x and y, represents the average path loss of the link between x and y, represents the number of antennas of x, represents the th sub-path small-scale channel gain of the link between x and y, , represents the normalized s-th response vector, and , represents the transmission angle of the signal transmitter of the s-th sub-path of the link between x and y, , , represents the antenna spacing, represents the carrier wavelength, represents any value in represents the number of transmit antennas of the transmitter of the link between x and y. To simplify the following discussion, let .

[0032] The above clustering channel model is a far-field channel model, that is, the receiving end regards the signal as a plane wave, which is usually not applicable to the self-interference channel because the distance between the transmit antenna and the receive antenna of the self-interference end is small compared with the wavelength of the carrier, not meeting the conditions of the far-field model (D is the distance between the transmit antenna array and the receive antenna array). The self-interference channel model adopted in this embodiment is , where is the Rice factor, respectively represent the line-of-sight component and the non-line-of-sight component of the self-interference channel. Since the transmission distance of the non-line-of-sight link is usually longer than the wavelength transmission distance, the above far-field model ( ) is used for modeling . The model of the line-of-sight component is shown as the following formula:

[0033] ,

[0034] where, represents the nth element of the line-of-sight component, is the power normalization constant called to ensure , represents taking the average value, is the distance between the nth transmitting antenna of Bob and the receiving antenna of Bob, specifically as follows:

[0035] ,

[0036] is the wavelength, and Θ is the angle between the arrays.

[0037] It can be understood that in other embodiments, other methods can also be used to construct the channel model, such as the Rayleigh channel model, the Gaussian channel model, etc.

[0038] (2) Construct the optimization problem for the covert communication oriented to MISO.

[0039] According to the channel model, if Alice transmits the signal , and Bob transmits the interference signal , then the signal sequence received by Bob is: , where is the signal index, N is the number of signals, is the channel noise between Alice and Bob, represents the noise variance, and the subscripts a, b, w respectively represent the transmitter, the receiver, and the eavesdropper, represents the transmission power of Alice, are the analog beamforming vectors of Alice and Bob respectively, is the power of the interference signal transmitted by Bob. , , obeys the uniform distribution from 0 to . The randomness of the transmission power of Bob introduced in this embodiment aims to make Willie unable to determine whether the fluctuation of the received signal is caused by Alice's transmission or Bob's interference, thereby increasing the detection error probability at Willie's end. Then for and Take the average to obtain the average covert rate The calculation formula is as follows:

[0040] ,

[0041] The process of solving the minimum value of the probability that Willie makes an incorrect decision is as follows: Willie's signal detection can be classified as a binary hypothesis testing problem. Let the null hypothesis H0 represent that Alice remains silent, i.e., does not transmit a signal, while the alternative hypothesis H1 represents that Alice transmits an information signal. In both cases, the signals received by Willie are respectively:

[0042] ,

[0043] ,

[0044] where, represents the channel noise between Alice and Willie. Assume that Willie uses a radiometer as its detector for energy detection to detect Alice's activity, and Willie observes an infinite number of channel uses, which represents the worst-case scenario for communication concealment. In this case, Willie performs a likelihood ratio test to detect whether there is Alice's signal transmission, and the formula it gives is , D0 represents the detection performed when Willie believes that Alice does not transmit a signal, D1 represents the detection performed when Willie believes that Alice transmits a signal, represents the predetermined detection threshold adopted by Willie, represents the statistical data, and its expression is:

[0045] .

[0046] Because the energy introduced by received by Willie is random, Willie will make errors in signal detection, including missed detection (MD) and false alarm (FA). The missed detection event is defined as Willie performing detection D0 but H1 holds, and the corresponding probability is . The false alarm event is defined as Willie performing detection D1 but H0 holds, and the corresponding probability is . Assume that Willie has no information about when Alice transmits, so its best guess is to consider the prior probabilities of the hypotheses and to be equal, which results in . Define Willie's detection error probability as:

[0047] ,

[0048] Among them, , , and respectively represent the energies of the signals sent by the receiver and the transmitter arriving at the eavesdropper. Since only the statistical channel information of 、 can be obtained, the average minimum detection error probability of 、 is used to evaluate the concealment of communication, that is ,

[0049] where represents the average minimum detection error probability of 、 , , , is an intermediate variable, 、 respectively represent and the covariance matrices of the complex Gaussian distributions that

[0050] The optimization problem for MISO-oriented covert communication is constructed as:

[0051] ,

[0052] In the formula, represents the expectation of a function with respect to and , represents the expectation of a function with respect to and , represents the minimum required probability for the eavesdropper to make an inaccurate decision, represents the k-th element of represents the m-th element of H represents the conjugate transpose.

[0053] (3) Convert the optimization problem into a convex optimization problem.

[0054] When transforming the problem, first convert the objective function and constraints of the optimization problem for MISO-oriented covert communication into formulas that are easy to handle. Due to the coupling between and , it is difficult to obtain an easy-to-handle analytical result for . As an alternative, the widely used lower bound optimization method is adopted to Replace it with its lower bound and optimize the lower bound to indirectly maximize the secrecy rate. By Jensen's inequality,

[0055] ,

[0056] where denotes the lower bound of is an auxiliary variable, denotes the first,..., th response vectors of the self-interference channel normalization, denotes the angles of departure of the transmitter of the signals of the first,..., sub-path signals of the receiver's self-interference channel, denotes the number of sub-paths of the receiver's self-interference channel.

[0057] By introducing auxiliary variables and , can be rewritten as:

[0058] ,

[0059] wherein, denotes the conjugate of is the function after replacing the lower bound optimization method for the average secrecy rate R, and Re() represents taking the real part. Although the function has more optimization variables than , the formula of helps to implement the inexact block coordinate descent (IBCD) algorithm because is a convex function with respect to the remaining variable when keeping all other four variables fixed.

[0060] For the secrecy constraint , since is an increasing function of , can be rewritten as , determined by bisection search, i.e., when , holds. The secrecy constraint can be expressed as:

[0061] ,

[0062] By first-order Taylor expansion, the non-convex part on the right side of the equation can be replaced by its first-order Taylor expansion, thus obtaining:

[0063] ,

[0064] Among them, respectively represent the -th iteration and optimal solutions.

[0065] For the unimodular constraint, it is transformed into:

[0066] ,

[0067] where and are auxiliary variables respectively, represents the element in the i-th row and i-th column of represents the element in the j-th row and j-th column of represents taking the trace.

[0068] For and the two non-convex terms, the same first-order Taylor expansion is also adopted, then:

[0069] ,

[0070] ,

[0071] Thus, the optimization problem is transformed into the following convex optimization problem:

[0072] ,

[0073] ,

[0074] ,

[0075] ,

[0076] .

[0077] It can be understood that in other embodiments, the optimization problem can also be transformed into other forms of convex optimization problems by means of the variable lower bound method and the method of introducing auxiliary variables, as long as it is a solvable convex optimization problem.

[0078] (4) Iteratively solve the convex optimization problem until the value of when the average covert rate reaches the maximum is obtained, and it is output as the optimal strategy for covert communication.

[0079] As Figure 3 shown, the solution process specifically includes:

[0080] (4.1) Set the initial value of , set the number of iterations l = 1;

[0081] (4.2) Fix , solve the problem , and obtain the optimal solution of :

[0082] ,

[0083] (4.3) Based on the optimal solution , fix , solve the problem , and obtain the optimal solution of :

[0084] ,

[0085] (4.4) Update to , update to , and use the successive convex approximation method to solve the problem , and obtain the values of , at the current iteration as the optimal solution , , ;

[0086] (4.5) Determine whether the average covert rate difference reaches the preset threshold. If so, execute (4.6); otherwise, set l = l + 1, and return to execute (4.2);

[0087] (4.6) Output the values of , at this time as the optimal strategy for covert communication.

[0088] It can be understood that the solution process can also be other methods. For example, first fix and solve , then solve , then solve , in an iterative loop, or an iterative loop in other ways, and the optimal strategy can be obtained by solving.

[0089] The embodiment of the present invention also provides a covert communication optimization system for MISO, including:

[0090] A communication model establishment module, which is used to construct a covert communication system model for MISO. The covert communication system model includes a transmitter with multiple antennas, a receiver with both receiving and interfering functions, and a listener;

[0091] An optimization problem construction module, which is used to construct the optimization problem for covert communication for MISO as:

[0092] ,

[0093] where, represents the average covert rate. The subscripts a, b, and w represent the transmitter, the receiver, and the listener respectively, represents the transmit power of the transmitter, are the analog beamforming vectors of the transmitter and the receiver respectively, is the power of the interference signal transmitted by the receiver, represents the noise variance, represents the channel coefficient vector of the link between the transmitter and the receiver, represents the channel coefficient vector of the self-interference channel of the receiver, represents the expectation of the function with respect to and of the function, represents the detection error probability of the listener, represents the expectation of the function with respect to and of the function, represents the minimum required probability for the listener to make an inaccurate decision, represents the k-th element of, represents the m-th element of, represents the number of transmit antennas of the transmitter, represents the number of transmit antennas of the receiver, represents the maximum transmit power of the transmitter. The superscript H represents the conjugate transpose, represents the channel coefficient vector of the link between the transmitter and the listener, represents the channel coefficient vector of the link between the receiver and the listener;

[0094] A problem transformation module, which is used to transform the optimization problem into a convex optimization problem;

[0095] A problem solving module, which is used to iteratively solve the convex optimization problem until the value of when the average covert rate value is maximized is obtained and output as the optimal strategy for covert communication.

[0096] Among them, the detection error probability of the listener is specifically:

[0097] ,

[0098] In the formula, represents the maximum transmission power of the receiver transmitting the interference signal, , , and respectively represent the energies of the signals sent by the receiver and the transmitter arriving at the eavesdropper.

[0099] Among them, the convex optimization problem is specifically:

[0100] ,

[0101] ,

[0102] ,

[0103] ,

[0104] ,

[0105] In the formula, is the function after replacing the lower bound optimization method for the average secrecy rate R, and are auxiliary variables introduced during the transformation, represents conjugate, Re() represents taking the real part, represents the maximum transmission power of the receiver transmitting the interference signal; represents the Rice factor, represents the line-of-sight component of the receiver's self-interference channel, and , represents the non-line-of-sight component of the receiver's self-interference channel, represents an auxiliary variable, represents the normalized first,..., th response vectors of the self-interference channel, represents the first,..., th departure angles of the transmitter ends of the sub-path signals of the receiver's self-interference channel, represents the number of sub-paths of the receiver's self-interference channel; , respectively represent and the covariance matrices of the complex Gaussian distributions that represents satisfying of conversion value, , are intermediate variables, respectively represent the optimal solutions at the ([ )-th iteration and . and are auxiliary variables respectively, represents the element in the i-th row and i-th column of represents the element in the j-th row and j-th column of represents taking the trace.

[0106] Among them, the problem-solving module specifically includes:

[0107] The initial value setting unit is used to set the initial value of , set the number of iterations l = 1;

[0108] The first problem-solving unit is used to fix , solve the problem , and obtain the optimal solution of :

[0109] ,

[0110] The second problem-solving unit is used to, based on the optimal solution , fix , solve the problem , and obtain the optimal solution of :

[0111] ,

[0112] The third problem-solving unit is used to update to , update to , and use the successive convex approximation method to solve the problem , and obtain the values of and at the current iteration as the optimal solution , , ;

[0113] The cut-off determination unit is used to determine whether the average covert rate difference reaches a preset threshold. If so, execute the policy output unit; otherwise, set l = l + 1, and return to execute the first problem-solving unit;

[0114] The policy output unit is used to, at this time , Output the value as the optimal strategy for covert communication.

[0115] Among them, the channel model of the MISO-oriented covert communication system model is:

[0116] ,

[0117] The subscript , represents the channel coefficient vector of the link between x and y, represents the number of sub-paths of the link between x and y, represents the average path loss of the link between x and y, represents the number of antennas of x, represents the th sub-path of the link between x and y, , represents the normalized s-th response vector, and , represents the angle of departure of the transmitting end of the signal on the s-th sub-path of the link between x and y, , , represents the antenna spacing, represents the carrier wavelength, represents any value in represents the number of transmitting antennas of the transmitting end of the link between x and y.

[0118] The system provided by the embodiments of the present invention can be used to execute the method provided by Embodiment 1 of the present invention, and has the corresponding functions and beneficial effects for executing the method. The same parts are referred to the description of the method and will not be repeated.

[0119] It should be noted that in the embodiments of the above system, the various units and modules included are only divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be achieved; in addition, the specific names of the functional units are only for the convenience of mutual distinction and do not limit the protection scope of the present invention.

[0120] The embodiments described above are merely illustrative. The modules described as separate components may or may not be physically separated, and the components shown as modules may or may not be physical modules, that is, they may be located in one place or distributed to multiple network modules. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those skilled in the art can clearly understand that each implementation manner can be realized by means of software plus a necessary general hardware platform, and of course, it can also be realized only by hardware, as long as the functions or effects can be achieved.

[0121] It should be understood that the above embodiments and the descriptions in the specification only illustrate the principles, main features and advantages of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements fall within the protection scope of the present invention.

Claims

1. A covert communication optimization method for MISO, characterized in that: The steps include: (1) Constructing a covert communication system model for MISO, the covert communication system model includes a transmitter with multiple antennas, a receiver with both receiving and jamming functions, and an eavesdropper; (2) The optimization problem for constructing covert communication for MISO is: , In the formula, represents the average concealment rate, and the subscripts a, b, and w represent the transmitter, receiver, and listener, respectively. Indicates the transmission power of the transmitter. are the simulated beamforming vectors for the transmitter and receiver, respectively, is the power of the interference signal transmitted by the receiver, represents the noise variance, represents the channel coefficient vector of the link between the transmitter and the receiver, represents the channel coefficient vector of the receiver's self-interference channel, Express about and Find the expectation of the function, Express about and Find the expectation of the function, represents the minimum required probability that the listener makes an inaccurate decision, express The kth element of express The mth element of Indicates the number of transmitting antennas of the transmitter, Indicates the number of receiver transmit antennas, Indicates the maximum transmission power of the transmitter, the superscript H represents the conjugate transpose, represents the channel coefficient vector of the link between the transmitter and the listener, A vector of channel coefficients representing the link between the receiver and the listener; It represents the probability of detection error of the listener, which is: , In the formula, Indicates the maximum transmission power of the receiver transmitting the interference signal, , , and They represent the energy of the signal sent by the receiver and transmitter reaching the listener respectively; (3) transforming the optimization problem into a convex optimization problem; (4) Iterate the convex optimization problem until the maximum average concealment rate is obtained. The value of is output as the optimal strategy for covert communication.

2. The MISO-oriented covert communication optimization method according to claim 1, characterized in that: The convex optimization problem in step (3) is specifically: , , , , , In the formula, is the function after the average concealment rate R is replaced by the lower bound optimization method, and is the auxiliary variable introduced during conversion. express The conjugate of , Re() means taking the real part, Indicates the maximum transmission power of the interference signal transmitted by the receiver; represents the Rice factor, represents the line-of-sight component of the receiver's self-interference channel, and , represents the non-line-of-sight component of the receiver’s self-interference channel, represents auxiliary variables, represents the normalized 1st,…, response vector, represents the receiver self-interference channel No. 1,…, The emission angle of the signal transmitting end of the strip path, represents the number of receiver self-interference channel subpaths; , Respectively and The covariance matrix of the complex Gaussian distribution is, Express satisfaction of The conversion value of , , , is the intermediate variable, Respectively represent the ) iterations , The optimal solution of , are auxiliary variables, express The element in the i-th row and i-th column of express The element at row j and column j, Indicates seeking trace.

3. The MISO-oriented covert communication optimization method according to claim 2, characterized in that: Step (4) specifically includes: (4.1) Settings Initial value of , set the number of iterations l =1; (4.2) Fixed , solve the problem ,get The optimal solution : , (4.3) Based on the optimal solution ,fixed , solve the problem ,get The optimal solution : , (4.4) Updated to ,Will Updated to , and use the successive convex approximation method to solve the problem , get the current iteration time , The value of , , ; (4.5) Determine whether the average concealment rate difference reaches the preset threshold. If so, execute (4.6). Otherwise, l = l +1, return to execution (4.2); (4.6) At this time , The value of is output as the optimal strategy for covert communication.

4. The MISO-oriented covert communication optimization method according to claim 1, characterized in that: The channel model of the MISO-oriented covert communication system model is: , Subscript , represents the channel coefficient vector of the link between x and y, represents the number of sub-paths of the link between x and y, represents the average path loss of the link between x and y, represents the number of antennas of x, Indicates the link between x and y The small-scale channel gain of the sliver path, , represents the normalized sth response vector, and , represents the transmission angle of the signal transmitter of the sth subpath of the link between x and y, , , represents the antenna spacing, represents the carrier wavelength, express Any value in Represents the number of transmit antennas at the transmitting end of the link between x and y.

5. A covert communication optimization system for MISO, characterized in that: include: A communication model building module, used to build a covert communication system model for MISO, wherein the covert communication system model includes a transmitter with multiple antennas, a receiver with both receiving and interference functions, and an eavesdropper; The optimization problem building module used to construct the optimization problem for covert communication for MISO is: , In the formula, represents the average concealment rate, and the subscripts a, b, and w represent the transmitter, receiver, and listener, respectively. Indicates the transmission power of the transmitter. are the simulated beamforming vectors for the transmitter and receiver, respectively, is the power of the interference signal transmitted by the receiver, represents the noise variance, represents the channel coefficient vector of the link between the transmitter and the receiver, represents the channel coefficient vector of the receiver's self-interference channel, Express about and Find the expectation of the function, Express about and Find the expectation of the function, represents the minimum required probability that the listener makes an inaccurate decision, express The kth element of express The mth element of Indicates the number of transmitting antennas of the transmitter, Indicates the number of receiver transmit antennas, Indicates the maximum transmission power of the transmitter, the superscript H represents the conjugate transpose, represents the channel coefficient vector of the link between the transmitter and the listener, A vector of channel coefficients representing the link between the receiver and the listener; It represents the probability of detection error of the listener, which is: , In the formula, Indicates the maximum transmission power of the receiver transmitting the interference signal, , , and They represent the energy of the signal sent by the receiver and transmitter reaching the listener respectively; A problem conversion module, used for converting the optimization problem into a convex optimization problem; The problem solving module is used to iteratively solve the convex optimization problem until the maximum average concealment rate value is obtained. The value of is output as the optimal strategy for covert communication.

6. The MISO-oriented covert communication optimization system according to claim 5, characterized in that: The convex optimization problem is specifically: , , , , , In the formula, is the function after the average concealment rate R is replaced by the lower bound optimization method, and is the auxiliary variable introduced during conversion. express The conjugate of , Re() means taking the real part, Indicates the maximum transmission power of the interference signal transmitted by the receiver; represents the Rice factor, represents the line-of-sight component of the receiver's self-interference channel, and , represents the non-line-of-sight component of the receiver’s self-interference channel, represents auxiliary variables, represents the normalized 1st,…, response vector, represents the receiver self-interference channel No. 1,…, The emission angle of the signal transmitting end of the strip path, represents the number of receiver self-interference channel subpaths; , Respectively and The covariance matrix of the complex Gaussian distribution is, Express satisfaction of The conversion value of , , , is the intermediate variable, Respectively represent the ) iterations , The optimal solution of , are auxiliary variables, express The element in the i-th row and i-th column of express The element at row j and column j, Indicates seeking trace.

7. The MISO-oriented covert communication optimization system according to claim 6, characterized in that: The problem-solving module specifically includes: Initial value setting unit, used to set Initial value of , set the number of iterations l =1; The first problem solving unit is used to fix , solve the problem ,get The optimal solution : , The second problem solving unit is used to solve the problem based on the optimal solution. ,fixed , solve the problem ,get The optimal solution : , The third problem solving unit is used to Updated to ,Will Updated to , and use the successive convex approximation method to solve the problem , get the current iteration time , The value of , , ; The cut-off judgment unit is used to judge whether the average concealment rate difference reaches a preset threshold. If so, the strategy output unit is executed, otherwise l = l +1, return to execute the first problem solving unit; The strategy output unit is used to output the , The value of is output as the optimal strategy for covert communication.

8. The MISO-oriented covert communication optimization system according to claim 5, characterized in that: The channel model of the MISO-oriented covert communication system model is: , Subscript , represents the channel coefficient vector of the link between x and y, represents the number of sub-paths of the link between x and y, represents the average path loss of the link between x and y, represents the number of antennas of x, Indicates the link between x and y The small-scale channel gain of the sliver path, , represents the normalized sth response vector, and , represents the transmission angle of the signal transmitter of the sth subpath of the link between x and y, , , represents the antenna spacing, represents the carrier wavelength, express Any value in Represents the number of transmit antennas at the transmitting end of the link between x and y.

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