Beam-forming-based covert communication method, system and equipment for multi-position monitors and medium

Abstract

The invention discloses a multi-position monitor-oriented covert communication method, system and device based on beam forming and a medium, and the method comprises the steps: building an active and passive beam forming overall optimization problem with the maximization of a covert communication rate as a target under a multi-constraint condition; the passive beamforming at the fixed IRS optimizes the active beamforming at the Alice; the active beam forming at the fixed Alice optimizes the passive beam forming at the IRS; beam forming in the three different covert communication scenes is optimized respectively; the system, the equipment and the medium realize the beamforming-based covert communication oriented to the multi-position monitor according to the method. The method can be used for realizing covert communication for covert communication tasks of multi-position monitors based on beam forming. The three covert communication schemes are high in effectiveness, and the covert communication performance of the three covert communication schemes is superior to that of respective reference schemes; the method provided by the invention has better effectiveness and wider universality.

Description

Technical Field

[0001] The present invention belongs to the field of communication technology, and in particular relates to a covert communication method, system, device and medium based on beamforming for multi-position monitors. Background Art

[0002] The rapid development and widespread application of wireless communications have brought many benefits to our lives, such as the Internet of Things (IoT) and Intelligent Transportation Systems (ITS). However, wireless communication channels are open, allowing all legitimate users and illicit eavesdroppers to receive information. This situation provides illicit eavesdroppers with opportunities to steal confidential information from legitimate users. Consequently, wireless communications face severe security challenges, and protecting confidential information in open channels has become a major challenge. Traditional wireless communication security research has primarily focused on protecting the content of communications from eavesdropping, such as physical layer security (PLS) and cryptography. However, these methods only protect the content of the information, not the transmission process. Therefore, if the content is not adequately encrypted, its security is still compromised. Furthermore, since anyone can access the information, its privacy cannot be guaranteed. To address the limitations of traditional wireless communication security methods, covert communication technology has been proposed as a method to protect the information transmission process. The goal of covert communication is to transmit communication information without being detected by a warden (monitor) while monitoring the channel, thereby concealing the communication process while ensuring that legitimate users can decrypt it. Therefore, covert communication has the advantage of not being alerted by the warden and has been applied in various scenarios such as multiple access channels, interleaved cognitive radio networks, and discrete memoryless channels.

[0003] In recent years, covert communication has been widely studied. For example, Yang et al. used two unmanned aerial vehicles (UAVs) to assist in covert communication, one as a communicator to send information, and the other as a jammer to interfere with the monitor (Yang G, Qian Y, Ren K, et al. Covert Wireless Communications for Augmented Reality Systems With DualCooperative UAVs[J]. IEEE J. Sel. Top. Signal Process., 2023, 17(5): 1119-1130.). Rao et al. studied the relay selection in covert communication and proposed a safety zone scheme that has the advantages of both covert transmission and D2D communication (Rao. H, Wu. M, Wang J, et al. D2D Covert Communications With Safety Area[J]. IEEE Syst. J., 2021, 15(2): 2331-2341.). In the millimeter wave (mmWave) covert communication system, Zhang et al. proposed a dual decomposition continuous convex approximation algorithm for the joint design of beam training and data transmission (Zhang J, Li M, Yan S, et al. Joint Beam Training and Data Transmission Design for Covert Millimeter-Wave Communication [J]. IEEE Trans. Inf. Forensics Secur., 2021, 16: 2232-2245.). He et al. proposed a method of using a jammer to generate intermittent artificial noise (AN) to enhance the covert communication of the warden (He W, Chen J, Li G, et al. Optimal Transmission Probabilities of Information and Artificial Noise in Covert Communications [J]. IEEE Commun. Lett., 2022, 26 (12): 2865-2869.).Li et al. proved that in Rayleigh block fading channels, faster-than-Nyquist (FTN) signaling has better maximum transmission power and covert communication rate than Nyquist signaling, illustrating the advantages of FTN signaling in covert communication (Li Y, Zhang Y, Wang J, et al. Performance Analysis for Covert Communications Under Faster-Than-Nyquist Signaling[J]. IEEE Commun. Lett., 2022, 26(6): 1240-1244.).

[0004] Through the above analysis, the problems and defects of the existing technology are as follows:

[0005] (1) In the existing covert communication research, most of them only consider the protection of the information transmission process, and ignore the protection of the communication content when protecting the information transmission process.

[0006] (2) Most existing covert communication studies do not take into account the diversity of the monitor's location. Summary of the Invention

[0007] In order to overcome the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a covert communication method, system, device and medium based on beamforming for multi-position monitors; under multiple constraints, an overall optimization problem of active and passive beamforming is established with the goal of maximizing the covert communication rate. The passive beamforming at the fixed intelligent reflecting surface (IRS) optimizes the active beamforming at the transmitting base station (Alice), and the active beamforming at the fixed Alice optimizes the passive beamforming at the intelligent reflecting surface (IRS). The beamforming in three different covert communication scenarios is optimized respectively, thereby improving the performance and effectiveness of covert communication.

[0008] In order to achieve the above object, the technical solution adopted by the present invention is:

[0009] A covert communication method based on beamforming for multi-position monitors comprises the following steps:

[0010] Step 1: Establish an overall optimization problem of active and passive beamforming with the goal of maximizing the covert communication rate under multiple constraints;

[0011] Step 2: Based on the overall optimization problem of active and passive beamforming obtained in step 1, the passive beamforming at IRS is fixed to optimize the active beamforming at Alice.

[0012] Step 3: Based on the overall optimization problem of active and passive beamforming obtained in step 1, the active beamforming at Alice is fixed and the passive beamforming at the IRS is optimized.

[0013] Step 4: Based on the contents of steps 2 and 3, the beamforming in three different covert communication scenarios is optimized respectively.

[0014] The specific process of step one is:

[0015] Step 1.1: Construct a covert communication system with multi-position monitors, including three scenarios. In Scenario 1, the covert communication system consists of a transmitting base station (Alice), a user (Bob), a warden (monitor) (Willie), and an intelligent reflecting surface (IRS). Alice transmits communication signals to Bob, while Willie monitors the transmission environment and detects whether Alice is transmitting communication signals to Bob. In addition, an IRS is deployed between Alice and Bob to increase Bob's covert communication rate. In Scenario 1, the distance between Alice and Willie is long (distance = F). In Scenarios 2 and 3, the covert communication system includes Alice, Bob, and Willie. In Scenario 2, the distance between Alice and Willie is short (distance = S). In Scenario 3, the distance between Alice and Willie is between F and S. Alice sends an integrated communication and interference (ICAJ) signal to Bob, while Willie monitors the transmission environment and detects whether Alice is transmitting ICAJ signals to Bob.

[0016] Step 1.2: Based on the covert communication system constructed in step 1.1, establish an overall optimization problem of active and passive beamforming with the goal of maximizing the covert communication rate under multiple constraints:

[0017] Assume Alice is equipped with M antennas, the IRS is equipped with N reflective elements, and Bob and Willie are each equipped with one antenna; the phase shift matrix of the IRS is given by:

[0018]

[0019] in, φ j ∈(0,2π] is the phase shift of the IRS reflector element and j∈{1,2,...,N};

[0020] Assume that the channel state information of all links in the covert communication system is known; the channel matrix between Alice and IRS is expressed as The channel vectors between Alice and Willie, Alice and Bob, IRS and Bob, and IRS and Willie are expressed as Furthermore, all channels consist of large-scale path loss and small-scale Rayleigh fading:

[0021]

[0022] Where Q0 is the path loss at the reference distance d0, d i is the distance between nodes, α i d i The corresponding path loss index, is Rayleigh fading, and when i=AI, h i Change to H i ;

[0023] Let H0 represent that Alice does not send the ICAJ signal, and H1 represent that Alice sends the ICAJ signal to Bob; therefore, the ICAJ signal sent by Alice is:

[0024]

[0025] in, and They are respectively transmitted communication data symbols s i ~CN(0,1) and the beamforming vector of the transmitted interference signal q~CN(0,1);

[0026] The signal received by Bob is expressed as:

[0027]

[0028] in, represents the noise at Bob;

[0029] The signal-to-interference-plus-noise ratio (SINR) at Bob is expressed as:

[0030]

[0031] Using SINR B , the covert communication rate is as follows:

[0032]

[0033] In addition, the signal received by Willie is expressed as:

[0034]

[0035] in, represents the noise at Willie, and the effective interference power received by Willie is

[0036]

[0037] When Alice only sends the communication signal, the beamforming vector w of the transmitted interference signal is removed from the ICAJ signal. p Related items, ICAJ signals become communication signals;

[0038] Willie only monitors the received signal to determine whether Alice is transmitting a signal. The likelihood function of the received signal at Willie under H0 is:

[0039]

[0040] in, Similarly, under H1, the likelihood function of the signal received at Willie can be expressed as:

[0041]

[0042] in

[0043]

[0044] Assuming that the prior probabilities of H0 and H1 are equal, Willie uses the likelihood ratio test to minimize the detection error, which is expressed as follows:

[0045]

[0046] Among them, D0 and D1 are binary decisions corresponding to H0 and H1 respectively. In addition, Willie's total detection error probability is the sum of the false alarm probability and the missed detection probability, which is expressed as:

[0047] ξ=Pr(D1|H0)+Pr(D0|H1)

[0048] =Pr(p1(y W )≥1|H0)+Pr(p0(y W )≤1|H1)

[0049] Using the lower bound of ξ, it is expressed as:

[0050]

[0051] Among them, D(p0(y W )||p1(y W )) indicates that from p0(y W ) to p1(y W ) is as follows:

[0052]

[0053] In covert communication, the concealment constraint is expressed as:

[0054]

[0055] Here, ε is used to determine the required concealment level with a small value; the smaller the value of ε, the higher the required concealment level. The concealment constraint in the overall optimization problem of active and passive beamforming is obtained as follows:

[0056] D(p0(y W )||p1(y W ))≤2ε 2

[0057] In a covert communication system with a multi-position monitor named Willie, three fixed positions of Willie correspond to three scenarios: Scenario 1, the distance between Alice and Willie is far (distance = F); Scenario 2, the distance between Alice and Willie is close (distance = S); Scenario 3, the distance between Alice and Willie is between F and S;

[0058] First, an overall optimization problem of active and passive beamforming is proposed and optimized, which is expressed as (P1):

[0059]

[0060] Among them, (C1-1) is the transmission power constraint, P max is the maximum transmit power threshold at Alice; (C1-2) and (C1-3) are both effective interference power constraints, P wu 、P wl are the upper and lower limits of interference tolerance respectively; (C1-4) represents the covert communication rate constraint, R min represents the minimum concealment rate threshold; (C1-5) represents the concealment constraint;

[0061] We can get:

[0062]

[0063] make And f(a)=lna+1 / a-1, we can get:

[0064] f(a)≤2ε 2

[0065] f(a) is monotonically increasing on [1,+∞), let R be f(a)=2ε 2 The only solution on [1,+∞) is and (C1-5) becomes:

[0066]

[0067] Then, the overall optimization problem of active and passive beamforming is rewritten as (P2):

[0068]

[0069] Therefore, the overall optimization problem of active and passive beamforming is established.

[0070] The specific process of step 2 is:

[0071] For the overall optimization problem of active and passive beamforming established in step 1, fix Φ and solve the active beamforming.

[0072] make:

[0073]

[0074] in, Denote the combined channel vector between Alice and Bob; let in Satisfy W c ±0 and rank(W c )=1, we get:

[0075]

[0076] make

[0077]

[0078] in, Denote the combined channel vector between Alice and Willie; and let in Satisfy W p ±0 and rank(W p )=1, we get:

[0079]

[0080] In addition, the following expression is obtained:

[0081]

[0082] We get (P3):

[0083]

[0084] is the interference signal term. When it is minimum, the objective function is maximum. Therefore, let Right now Rewrite the active beamforming optimization problem (P3) as (P4)

[0085]

[0086] make

[0087]

[0088] get

[0089] w p =Qw pn

[0090] in, Co-located

[0091]

[0092] Among them, W pn Satisfy W pn ±0 and rank(W pn )=1; rewrite (P4) as (P5):

[0093]

[0094] In the active beamforming optimization problem (P5), only the rank-one constraint (C5-7) makes the active beamforming optimization problem (P5) non-convex. Removing the rank-one constraint (C5-7) results in a convex problem. To avoid the solution not satisfying the rank-one constraint, a penalty-based approach is adopted. First, the rank-one constraint (C5-7) is rewritten as follows:

[0095] ||W c || * -||W c ||2=0

[0096] ||W pn || * -||W pn ||2=0

[0097] Among them, ||·|| * and ||·||2 denote the nuclear norm and spectral norm respectively; meanwhile, ||·|| * is the sum of all singular values in the matrix, and ||·||2 is the largest singular value in the matrix;

[0098] W pn The following conditions are met:

[0099] The rank of a matrix is equal to the number of its nonzero singular values. pn )=1, we get

[0100] ||Wpn || * =||W pn ||2

[0101] And || W pn || * -||W pn ||2=0 holds; otherwise,

[0102] ||W pn || * >||W pn ||2

[0103] Right now

[0104] ||W pn || * -||W pn ||2>0

[0105] In the maximization problem, a penalty term is introduced into the objective function:

[0106]

[0107] Where η represents the penalty factor and η>0; when η→0, When W pn When it is not a rank one matrix and η→0, the penalty term is infinitesimal, and the value of the objective function introduced by the penalty term is infinitesimal, so we get a value that satisfies ||W pn || * -||W pn ||2=0 rank one solution; In addition, -||W pn ||2 is non-convex, use The first-order Taylor expansion of the point is -||W pn The upper bound of ||2 is as follows:

[0108]

[0109] in, express The eigenvector corresponding to the maximum eigenvalue of ;

[0110] Similarly, W c The above conditions are also met; the active beamforming optimization problem (P5) is rewritten as (P6):

[0111]

[0112] st{(C5-1),(C5-2),(C5-3),(C5-4),(C5-5),(C5-6)

[0113] in

[0114]

[0115] The active beamforming optimization problem (P6) is a standard convex problem that can be solved efficiently using the CVX toolbox. After solving the active beamforming optimization problem (P6), we get W c and W pn The optimal solution of ; then, through eigenvalue decomposition and w p =Qw pn , and finally get w c and w p The optimal solution of and express;

[0116] That is, the optimal solution of active beamforming is obtained.

[0117] The specific process of step three is:

[0118] For the overall optimization problem of active and passive beamforming established in step 1, the passive beamforming solution is solved based on the optimal solution of active beamforming obtained in step 2:

[0119] Given and Optimize Φ; first, let and get

[0120]

[0121] make in, satisfy and And {ab}∈{c,p}; we get:

[0122]

[0123] in

[0124]

[0125] make

[0126]

[0127] in, and get:

[0128]

[0129] make

[0130]

[0131] And there are:

[0132]

[0133] in, and

[0134]

[0135] In addition, in satisfy and We get (P7):

[0136]

[0137] The passive beamforming optimization problem (P7) is a single-ratio fractional programming. The objective function of the passive beamforming optimization problem (P7) is rewritten using Dinkelbach transform as follows:

[0138]

[0139] Among them, β k′ Indicates the auxiliary variables introduced, as shown below

[0140]

[0141] Among them, m represents the index of iteration; when m reaches a certain number of iterations or β k′ When the modulus of the difference between the two iterations is less than the set convergence threshold, we get The optimal solution of ; using the penalty-based method to rewrite the passive beamforming optimization problem (P7) as (P8):

[0142]

[0143] in

[0144]

[0145] The passive beamforming optimization problem (P8) is a standard convex problem that can be solved using the CVX toolbox. Solving the passive beamforming optimization problem (P8) yields The optimal solution of Then through Get b, and finally pass Φ=diag(b H ) obtains the optimal solution of Φ, that is, the optimal solution of passive beamforming.

[0146] The specific process of step 4 is as follows:

[0147] According to steps 2 and 3, the beamforming optimization problems for scenarios 1, 2, and 3 are standard convex problems, which are solved using the CVX toolbox as follows:

[0148] Option 1:

[0149] When the distance between Alice and Willie is far (distance = F), the active beamforming optimization problem (P9) and the passive beamforming optimization problem (P10) of the scheme are as follows:

[0150]

[0151] Using the alternating iteration (AO) algorithm, by alternately solving (P9) and (P10), we can finally get w of the optimization problem in Scheme 1. c and the optimal solution of Φ; the process is as follows:

[0152] Input: Φ (0) : initial IRS phase shift matrix; δ: iteration threshold;

[0153] Output: The optimal solution of the beamforming vector for transmitting communication data symbols and the optimal solution of the IRS phase shift matrix;

[0154] S11, set l = 0;

[0155] S12. If l reaches the maximum value or the modulus of the difference between the objective function values of two adjacent iterations is less than δ, then proceed to S16; otherwise, proceed to S13;

[0156] S13, use Φ (l) Solve the active beamforming optimization problem (P9) of solution 1 and get The optimal solution of

[0157] For S14 Solve the passive beamforming optimization problem (P10) of solution 1 and obtain Φ (l+1) The optimal solution of

[0158] S15, set l=l+1, and proceed to S12;

[0159] S16: Based on the results of S13 and S14, the transmission communication data symbol is obtained. The optimal solution of the beamforming vector and the phase shift matrix Φ of the IRS (l) The optimal solution of .

[0160] Option 2:

[0161] When the distance between Alice and Willie is close (distance = S), Alice transmits an ICAJ signal. The active beamforming optimization problem of this scheme is the problem obtained by removing the IRS-related terms in h1 and h2 in the active beamforming optimization problem (P6).

[0162] Option 3:

[0163] When the distance between Alice and Willie is between F and S, the following active beamforming optimization problem (P11) is first given:

[0164]

[0165] st{(C5-1),(C5-2),(C5-4),(C5-5),(C5-6)

[0166] Among them, k is the scaling factor, which is used to keep the communication performance and interference energy dimensions consistent. The active beamforming optimization problem of this scheme is the problem obtained by removing the IRS-related terms from h1 and h2 in the active beamforming optimization problem (P11). The active beamforming optimization problems of schemes 2 and 3 are solved by the AO algorithm, and finally the w of the active beamforming optimization problems of schemes 2 and 3 are obtained. c and w p The optimal solution is as follows:

[0167] Input: δ: iteration threshold; Pb: active beamforming optimization problem;

[0168] Output: The optimal solution of the beamforming vector for transmitting communication data symbols and the optimal solution of the beamforming vector for transmitting deceptive interference signals;

[0169] S21, set l = 0;

[0170] S22. If l reaches the maximum value or the modulus of the difference between the objective function values of two adjacent iterations is less than δ, then proceed to S25; otherwise, proceed to S23;

[0171] S23, use the CVX toolbox to solve Pb and get and The optimal solution of

[0172] S24, set l=l+1, and proceed to S22;

[0173] S25, obtain the transmission communication data symbol according to the result of S23 The optimal solution of the beamforming vector and the transmission of deceptive jamming signals The optimal solution of the beamforming vector is obtained; that is, the optimization of beamforming in three different covert communication scenarios is achieved.

[0174] A covert communication system for multi-position monitors based on beamforming, comprising:

[0175] An active and passive beamforming overall optimization problem establishment module is used to establish an active and passive beamforming overall optimization problem in step 1 with the goal of maximizing the covert communication rate under multiple constraints;

[0176] an active beamforming optimization module, configured to optimize the active beamforming at Alice by fixing the passive beamforming at the IRS in step 2;

[0177] A passive beamforming optimization module, configured to optimize the passive beamforming at the IRS by fixing the active beamforming at Alice in step 3;

[0178] The beamforming optimization module for different covert communication scenarios is used to optimize the beamforming in three different covert communication scenarios in step four.

[0179] A device for covert communication based on beamforming for multi-position monitors, comprising: a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the device can implement the covert communication method based on beamforming for multi-position monitors described in any one of steps 1 to 4.

[0180] A computer storage medium for receiving a user input program, wherein when the computer program stored in the storage medium is executed by a processor, the computer program can perform covert communication based on beamforming for multi-position monitors based on the covert communication method based on beamforming for multi-position monitors described in any one of steps 1 to 4.

[0181] Compared with the prior art, the advantages and positive effects of the present invention are:

[0182] The present invention establishes an overall optimization problem of active and passive beamforming under multiple constraints with the goal of maximizing the covert communication rate; the passive beamforming at a fixed IRS optimizes the active beamforming at Alice; the active beamforming at a fixed Alice optimizes the passive beamforming at the IRS; and the beamforming in three different covert communication scenarios is optimized respectively. This invention fills a gap in this field.

[0183] We innovatively consider a covert communication system with multiple observers in different locations. The three scenarios are: Willie is far away from Alice (Scheme 1), close to the transmitter (Scheme 2), and the distance between Willie and Alice is somewhere between close and far (Scheme 3).

[0184] An overall optimization problem for active and passive beamforming was formulated and optimized. Three corresponding covert communication schemes were then proposed for three scenarios corresponding to three fixed-position observers. In each scheme, beamforming was optimized to achieve optimal covert communication performance. Specifically, in Scheme 1, Alice transmits only communication signals with the assistance of an IRS, and jointly optimizes the communication and IRS beamforming to achieve better performance for the covert communication system. In Scheme 2, Alice sends an ICAJ signal, optimizing both communication and interference beamforming. Scheme 3 builds on Scheme 2 by changing the objective function to the sum of communication and interference performance (overall performance), removing the lower bound of the interference tolerance in the constraints, and achieving better feasibility.

[0185] To address the passive beamforming optimization problem in Scheme 1, an AO algorithm based on the Dinkelbach transform is used to optimize both active and passive beamforming, subject to the constraints of transmit power, interference tolerance, minimum concealment rate, and concealment. Furthermore, an AO algorithm is proposed to address the active beamforming optimization problems in Schemes 2 and 3.

[0186] The present invention focuses on developing an algorithm for covert communication against multi-position monitors based on beamforming with faster convergence speed and better covert communication performance; the present invention explores the use of Dinkelback transformation method and alternating optimization algorithm, which can realize covert communication against multi-position monitors based on beamforming.

[0187] In summary, compared with the existing technology, the research of the present invention explores the problem of how to perform covert communication based on beamforming in the scenario of multi-position monitors, and emphasizes the importance of solving the problem of how to perform covert communication based on beamforming in the scenario of multi-position monitors based on beamforming; any covert communication task involving multi-position monitors based on beamforming can use the present invention for covert communication; the three proposed covert communication schemes are highly effective, and their covert communication performance is better than their respective benchmark schemes; the present invention has better effectiveness and wider versatility. BRIEF DESCRIPTION OF THE DRAWINGS

[0188] Figure 1 This is a flow chart of a covert communication method, system, medium, and device based on beamforming for multi-position monitors provided by an embodiment of the present invention.

[0189] Figure 2 1 is a schematic diagram of the structure of a covert communication system for multi-position monitors based on beamforming provided by an embodiment of the present invention;

[0190] Figure 2In: 1. Module for establishing the overall optimization problem of active and passive beamforming; 2. Active beamforming optimization module; 3. Passive beamforming optimization module; 4. Beamforming optimization module for different covert communication scenarios.

[0191] Figure 3 1 is a schematic diagram of convergence process simulation experimental results of Scheme 1 and Scheme 1 benchmark under different M for a covert communication system based on beamforming for multi-position monitors provided by an embodiment of the present invention.

[0192] Figure 4 The different M and P of the covert communication system for multi-position monitors based on beamforming provided by the embodiment of the present invention are max Schematic diagram of the convergence process simulation experimental results of Scheme 2 and Scheme 2 benchmark.

[0193] Figure 5 3 is a schematic diagram of simulation experimental results of the covert communication rate and scaled effective interference power of Scheme 3 and the benchmark of Scheme 3 under different M for a covert communication system based on beamforming for multi-position monitors provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0194] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0195] In response to the problems existing in the prior art, the present invention provides a covert communication method, system, medium and device based on beamforming for multi-position monitors. The present invention is described in detail below with reference to the accompanying drawings.

[0196] The covert communication method, system, medium and device based on beamforming for multi-position monitors provided by the present invention can also be implemented by ordinary technicians in the industry using other steps. Figure 1 The beamforming-based covert communication method, system, medium, and device for multi-position monitors provided by the present invention are only a specific embodiment.

[0197] like Figure 1 As shown, the embodiment of the present invention provides a covert communication method based on beamforming for multi-position monitors, and the specific steps are as follows:

[0198] Step 1: Establish an overall optimization problem for active and passive beamforming with the goal of maximizing the covert communication rate under multiple constraints. The specific process is as follows:

[0199] Step 1.1 Construct a covert communication system with multi-position monitors, including three scenarios. In scenario 1, the covert communication system consists of Alice, Bob, Willie, and an IRS. Alice transmits the communication signal to Bob, while Willie monitors the transmission environment and detects whether Alice is transmitting the communication signal to Bob. In addition, an IRS is deployed between Alice and Bob to increase Bob's covert communication rate. In scenario 1, the distance between Alice and Willie is far (distance = F). In scenarios 2 and 3, the covert communication system includes Alice, Bob, and Willie. In scenario 2, the distance between Alice and Willie is close (distance = S). In scenario 3, the distance between Alice and Willie is between F and S. Alice sends an ICAJ signal to Bob, while Willie monitors the transmission environment and detects whether Alice is transmitting the ICAJ signal to Bob.

[0200] Step 1.2: Based on the covert communication system constructed in step 1.1, establish an overall optimization problem of active and passive beamforming with the goal of maximizing the covert communication rate under multiple constraints:

[0201] Assume Alice is equipped with M antennas, the IRS is equipped with N reflective elements, and Bob and Willie are each equipped with one antenna; the phase shift matrix of the IRS is given by:

[0202]

[0203] in, φ j ∈(0,2π] is the phase shift of the IRS reflector element and j∈{1,2,...,N};

[0204] Assume that the channel state information of all links in the covert communication system is known; the channel matrix between Alice and IRS is expressed as The channel vectors between Alice and Willie, Alice and Bob, IRS and Bob, and IRS and Willie are expressed as Furthermore, all channels consist of large-scale path loss and small-scale Rayleigh fading:

[0205]

[0206] Where Q0 is the path loss at the reference distance d0, d i is the distance between nodes, α i d i The corresponding path loss index, is Rayleigh fading, and when i=AI, hi Change to H i ;

[0207] Let H0 represent that Alice does not send the ICAJ signal, and H1 represent that Alice sends the ICAJ signal to Bob; therefore, the ICAJ signal sent by Alice is:

[0208]

[0209] in, and They are respectively transmitted communication data symbols s i ~CN(0,1) and the beamforming vector of the transmitted interference signal q~CN(0,1);

[0210] The signal received by Bob is expressed as:

[0211]

[0212] in, represents the noise at Bob;

[0213] The signal-to-interference-plus-noise ratio (SINR) at Bob is expressed as:

[0214]

[0215] Using SINR B , the covert communication rate is as follows:

[0216]

[0217] In addition, the signal received by Willie is expressed as:

[0218]

[0219] in, represents the noise at Willie, and the effective interference power received by Willie is

[0220]

[0221] When Alice only sends the communication signal, the beamforming vector w of the transmitted interference signal is removed from the ICAJ signal. p Related items, ICAJ signals become communication signals;

[0222] Willie only monitors the received signal to determine whether Alice is transmitting a signal. The likelihood function of the received signal at Willie under H0 is:

[0223]

[0224] in, Similarly, under H1, the likelihood function of the signal received at Willie can be expressed as:

[0225]

[0226] in

[0227]

[0228] Assuming that the prior probabilities of H0 and H1 are equal, Willie uses the likelihood ratio test to minimize the detection error, which is expressed as follows:

[0229]

[0230] Among them, D0 and D1 are binary decisions corresponding to H0 and H1 respectively. In addition, Willie's total detection error probability is the sum of the false alarm probability and the missed detection probability, which is expressed as:

[0231] ξ=Pr(D1|H0)+Pr(D0|H1)

[0232] =Pr(p1(y W )≥1|H0)+Pr(p0(y W )≤1|H1)

[0233] Using the lower bound of ξ, it is expressed as:

[0234]

[0235] Among them, D(p0(y W )||p1(y W )) indicates that from p0(y W ) to p1(y W ) is as follows:

[0236]

[0237] In covert communication, the concealment constraint is expressed as:

[0238]

[0239] Here, ε is used to determine the required concealment level with a small value; the smaller the value of ε, the higher the required concealment level, resulting in a stricter concealment constraint as follows:

[0240] D(p0(y W )||p1(y W ))≤2ε 2

[0241] The obtained stealth constraint is a constraint in the overall optimization problem of active and passive beamforming.

[0242] In a covert communication system with a multi-position monitor named Willie, three fixed positions of Willie correspond to three scenarios: Scenario 1, the distance between Alice and Willie is far (distance = F); Scenario 2, the distance between Alice and Willie is close (distance = S); Scenario 3, the distance between Alice and Willie is between F and S;

[0243] First, an overall optimization problem of active and passive beamforming is proposed and optimized, which is expressed as (P1):

[0244]

[0245] Among them, (C1-1) is the transmission power constraint, P max is the maximum transmit power threshold at Alice; (C1-2) and (C1-3) are both effective interference power constraints, P wu 、P wl are the upper and lower limits of interference tolerance respectively; (C1-4) represents the covert communication rate constraint, R min represents the minimum concealment rate threshold; (C1-5) represents the concealment constraint;

[0246] We can get:

[0247]

[0248] make And f(a)=lna+1 / a-1, we can get:

[0249] f(a)≤2ε 2

[0250] f(a) is monotonically increasing on [1,+∞), let R be f(a)=2ε 2 The only solution on [1,+∞), and (C1-5) becomes:

[0251]

[0252] Then, the overall optimization problem of active and passive beamforming is rewritten as (P2):

[0253]

[0254] Therefore, the overall optimization problem of active and passive beamforming is established.

[0255] In step 2, the passive beamforming at the fixed IRS optimizes the active beamforming at Alice. The specific process is as follows:

[0256] For the overall optimization problem of active and passive beamforming established in step 1, fix Φ and solve the active beamforming.

[0257] make:

[0258]

[0259] in, Denote the combined channel vector between Alice and Bob; let in Satisfy W c ±0 and rank(W c )=1, we get:

[0260]

[0261] make

[0262]

[0263] in, Denote the combined channel vector between Alice and Willie; and let in Satisfy W p ±0 and rank(W p )=1, we get:

[0264]

[0265] In addition, the following expression is obtained:

[0266]

[0267] We get (P3):

[0268]

[0269] is the interference signal term. When it is minimum, the objective function is maximum. Therefore, let Right now Rewrite the active beamforming optimization problem (P3) as (P4)

[0270]

[0271] make

[0272]

[0273] get

[0274] w p =Qw pn

[0275] in, Co-located

[0276]

[0277] Among them, W pn Satisfy W pn ±0 and rank(W pn )=1; rewrite (P4) as (P5):

[0278]

[0279] In the active beamforming optimization problem (P5), only the rank-one constraint (C5-7) makes the active beamforming optimization problem (P5) non-convex. Removing the rank-one constraint (C5-7) results in a convex problem. To avoid the solution not satisfying the rank-one constraint, a penalty-based approach is adopted. First, the rank-one constraint (C5-7) is rewritten as follows:

[0280] ||W c || * -||W c ||2=0

[0281] ||W pn || * -||W pn ||2=0

[0282] Among them, ||·|| * and ||·||2 denote the nuclear norm and spectral norm respectively; meanwhile, ||·|| * is the sum of all singular values in the matrix, and ||·||2 is the largest singular value in the matrix;

[0283] W pn For example, analyze:

[0284] Analysis 1:

[0285] The rank of a matrix is equal to the number of its non-zero singular values. pn )=1, we get

[0286] ||W pn || * =||W pn ||2

[0287] And || W pn || * -||W pn ||2=0 holds; otherwise,

[0288] ||W pn || * >||W pn ||2

[0289] Right now

[0290] ||W pn || * -||W pn ||2>0

[0291] In the maximization problem, a penalty term is introduced into the objective function:

[0292]

[0293] Where η represents the penalty factor and η>0; when η→0, When W pn When it is not a rank one matrix and η→0, the penalty term is infinitesimal, and the value of the objective function introduced by the penalty term is infinitesimal, so we get a value that satisfies ||W pn || * -||W pn ||2=0 rank one solution; In addition, -||W pn ||2 is non-convex, use The first-order Taylor expansion of the point is -||W pn The upper bound of ||2 is as follows:

[0294]

[0295] in, express The eigenvector corresponding to the largest eigenvalue of .

[0296] This concludes the introduction to Analysis 1.

[0297] Similarly, W c The above analysis 1 is also satisfied; the active beamforming optimization problem (P5) is rewritten as (P6):

[0298]

[0299] st{(C5-1),(C5-2),(C5-3),(C5-4),(C5-5),(C5-6)

[0300] in

[0301]

[0302] The active beamforming optimization problem (P6) is a standard convex problem that can be solved efficiently using the CVX toolbox. After solving the active beamforming optimization problem (P6), we get Wc and W pn The optimal solution of ; then, through eigenvalue decomposition and w p =Qw pn , and finally get w c and w p The optimal solution of and express.

[0303] Therefore, the optimal solution of active beamforming is obtained.

[0304] In step 3, the active beamforming at Alice is fixed to optimize the passive beamforming at the IRS. The specific process is as follows:

[0305] For the overall optimization problem of active and passive beamforming established in step 1, the passive beamforming is solved based on the optimal solution of active beamforming obtained in step 2.

[0306] Given and Optimize Φ; first, let and get

[0307]

[0308] make in, satisfy and And {ab}∈{c,p}; we get:

[0309]

[0310] in

[0311]

[0312] make

[0313]

[0314] in, and get:

[0315]

[0316] make

[0317]

[0318] And there are:

[0319]

[0320] in, and

[0321]

[0322] In addition, in satisfy and We get (P7):

[0323]

[0324] The passive beamforming optimization problem (P7) is a single-ratio fractional programming. The objective function of the passive beamforming optimization problem (P7) is rewritten using Dinkelbach transform as follows:

[0325]

[0326] Among them, β k′ Indicates the auxiliary variables introduced, as shown below

[0327]

[0328] Among them, m represents the index of iteration; when m reaches a certain number of iterations or β k′ When the modulus of the difference between the two iterations is less than the set convergence threshold, we get The optimal solution of ; using the penalty-based method to rewrite the passive beamforming optimization problem (P7) as (P8):

[0329]

[0330] in

[0331]

[0332] The passive beamforming optimization problem (P8) is a standard convex problem that can be solved using the CVX toolbox. Solving the passive beamforming optimization problem (P8) yields The optimal solution of Then through Get b, and finally pass Φ=diag(b H ) to obtain the optimal solution of Φ.

[0333] Therefore, the optimal solution of passive beamforming is obtained.

[0334] In step 4, the beamforming in three different covert communication scenarios is optimized. The specific process is as follows:

[0335] From steps 2 and 3, we can see that the beamforming optimization problems for scenarios 1, 2, and 3 are standard convex problems and can be solved using the CVX toolbox as follows:

[0336] Option 1:

[0337] When the distance between Alice and Willie is far (distance = F), the active beamforming optimization problem (P9) and the passive beamforming optimization problem (P10) of the scheme are as follows:

[0338]

[0339] Using the alternating iteration (AO) algorithm, by alternately solving (P9) and (P10), we can finally get w of the optimization problem in Scheme 1. c and the optimal solution of Φ; the process is as follows:

[0340] Input: Φ (0) : initial IRS phase shift matrix; δ: iteration threshold;

[0341] Output: The optimal solution of the beamforming vector for transmitting communication data symbols and the optimal solution of the IRS phase shift matrix;

[0342] S11, set l = 0;

[0343] S12. If l reaches the maximum value or the modulus of the difference between the objective function values of two adjacent iterations is less than δ, then proceed to S16; otherwise, proceed to S13;

[0344] S13, use Φ (l) Solve the active beamforming optimization problem (P9) of solution 1 and get The optimal solution of

[0345] For S14 Solve the passive beamforming optimization problem (P10) of solution 1 and obtain Φ (l+1) The optimal solution of

[0346] S15, set l=l+1, and proceed to S12;

[0347] S16: Based on the results of S13 and S14, the transmission communication data symbol is obtained. The optimal solution of the beamforming vector and the phase shift matrix Φ of the IRS (l) The optimal solution of .

[0348] Option 2:

[0349] When the distance between Alice and Willie is close (distance = S), Alice transmits an ICAJ signal. The active beamforming optimization problem of this scheme is the problem obtained by removing the IRS-related terms in h1 and h2 in the active beamforming optimization problem (P6).

[0350] Option 3:

[0351] When the distance between Alice and Willie is between F and S, the following active beamforming optimization problem (P11) is first given:

[0352]

[0353] st{(C5-1),(C5-2),(C5-4),(C5-5),(C5-6)

[0354] Among them, k is the scaling factor, which is used to keep the communication performance and interference energy dimensions consistent. The active beamforming optimization problem of this scheme is the problem obtained by removing the IRS-related terms from h1 and h2 in the active beamforming optimization problem (P11). The active beamforming optimization problems of schemes 2 and 3 are solved by the AO algorithm, and finally the w of the active beamforming optimization problems of schemes 2 and 3 are obtained. c and w p The optimal solution is as follows:

[0355] Input: δ: iteration threshold; Pb: active beamforming optimization problem;

[0356] Output: The optimal solution of the beamforming vector for transmitting communication data symbols and the optimal solution of the beamforming vector for transmitting deceptive interference signals;

[0357] S21, set l = 0;

[0358] S22. If l reaches the maximum value or the modulus of the difference between the objective function values of two adjacent iterations is less than δ, then proceed to S25; otherwise, proceed to S23;

[0359] S23, use the CVX toolbox to solve Pb and get and The optimal solution of

[0360] S24, set l=l+1, and proceed to S22;

[0361] S25, obtain the transmission communication data symbol according to the result of S23 The optimal solution of the beamforming vector and the transmission of deceptive jamming signals The optimal solution for the beamforming vector .

[0362] Therefore, the optimization of beamforming in three different covert communication scenarios is achieved.

[0363] like Figure 2 As shown, the covert communication system for multi-position monitors based on beamforming provided by an embodiment of the present invention includes:

[0364] The active and passive beamforming overall optimization problem establishment module 1 is used to establish an active and passive beamforming overall optimization problem under multiple constraints with the goal of maximizing the covert communication rate.

[0365] The active beamforming optimization module 2 is configured to optimize the active beamforming at Alice by fixing the passive beamforming at the IRS.

[0366] The passive beamforming optimization module 3 is configured to optimize the passive beamforming at the IRS by fixing the active beamforming at Alice.

[0367] The beamforming optimization module 4 for different covert communication scenarios is used to optimize the beamforming in three different covert communication scenarios respectively.

[0368] The covert communication method provided by the present invention can be used for covert communication targeting monitors at multiple locations based on beamforming.

[0369] The technical effects of the present invention are described in detail below in conjunction with simulation experiments.

[0370] In order to evaluate the performance of the present invention, simulation verification is carried out. In the simulation experiment, a covert communication system based on beamforming for multi-position monitors is considered, and the specific parameters of the simulation experiment are as follows: For Scheme 1, IRS and Willie are located at (50, 30) m and (80, -10) m, respectively. For Scheme 2, Willie is located at (10, -10) m. For Scheme 3, Willie has 6 positions, which are located at (20, -10) m, (30, -10) m, (40, -10) m, (50, -10) m, (60, -10) m and (70, -10) m, respectively. In addition, the general parameter configurations of Scheme 1, Scheme 2 and Scheme 3 are as follows: Alice's position is (0, 0) m, Bob's position is (100, 0) m, the reference distance d0 = 1 m, the path loss at the reference distance Q0 = -30 dB, d AI The corresponding path loss index α AI =2.4,d AW The corresponding path loss index α AW , d AB The corresponding path loss index α AB =4.2,d IB The corresponding path loss index α IB =3,dIW The corresponding path loss index α IW =3, penalty factor η = 0.1, noise variance at Bob Noise variance at Willie Minimum concealment rate threshold R min =0.5 bps / Hz, required concealment level ε = 0.001, scaling factor k = 10 12 , iterative threshold δ = 10 -4 , the baseline scenario is as follows:

[0371] 1. Option 1 baseline: Similar to Option 1, but without the IRS assistance;

[0372] 2. Scheme 2 benchmark: Similar to Scheme 2, a split design is used, that is, the number of antennas used for communication and interference at Alice is M / 2 respectively. The transmit power constraint becomes two constraints: the transmit power of communication and interference at Alice should be less than or equal to P respectively. max / 2;

[0373] 3. Alternative 3 baseline: Similar to Alternative 3, using a separation design;

[0374] Figure 3 The convergence process of Scheme 1 and Scheme 1 benchmark under different M is shown. Figure 3 As can be seen, the covert communication rates of both Scheme 1 and the Scheme 1 baseline increase as Alice's number of antennas increases, indicating that increasing M improves covert communication performance when Willie is far away from Alice. This is because a larger number of M improves spatial utilization and increases the gain of transmit beamforming, thereby improving covert communication performance. Furthermore, under the same M condition, Scheme 1 consistently outperforms the Scheme 1 baseline in covert communication rate. Figure 4 Shows different M and P max The convergence process of Scheme 2 and Scheme 2 benchmark is shown below. Figure 4 It can be seen that when P max =30dBm, when the number of iterations is about 25, Scheme 2 can fully converge, which shows the effectiveness of Scheme 2. max =32dBm, Scheme 2 basically converges after about 30 iterations. This is because P max The increase in leads to a larger optimization space, so the convergence speed of Scheme 2 is slightly slower. In addition, the covert communication rate of Scheme 2 is always significantly higher than that of the Scheme 2 baseline. Therefore, when Willie is close to Alice, the covert communication performance of the ICAJ signal is better than that of the separated design signal, which proves the superiority of the ICAJ design. Figure 5 The figure shows the covert communication rate and scaled effective interference power of Scheme 3 and Scheme 3 benchmark under different M. Figure 5As can be seen, the communication and interference performance of Scheme 3 consistently outperforms the Scheme 3 baseline. Furthermore, as M increases, the covert communication rate and scaled effective interference power of both Scheme 3 and the Scheme 3 baseline increase. This indicates that when the distance between Willie and Alice is between close and far, increasing M not only effectively improves the covert communication performance but also the interference performance, making covert communication more secure. Therefore, Scheme 3 demonstrates good effectiveness, and simulation experiments validate the inventiveness of the covert communication method proposed in this invention.

[0375] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware portion can be implemented using dedicated logic; the software portion can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. Those skilled in the art will appreciate that the above-mentioned devices and methods can be implemented using computer-executable instructions and / or contained in processor control code, for example, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, or can be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0376] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A covert communication method based on beamforming for multi-position monitors, characterized in that: The specific steps include: Step 1: Establish an overall optimization problem of active and passive beamforming with the goal of maximizing the covert communication rate under multiple constraints; Step 2: Based on the overall optimization problem of active and passive beamforming obtained in step 1, the passive beamforming at IRS is fixed to optimize the active beamforming at Alice. Step 3: Based on the overall optimization problem of active and passive beamforming obtained in step 1, the active beamforming at Alice is fixed and the passive beamforming at the IRS is optimized. Step 4: Based on the optimization results of steps 2 and 3, the beamforming in three different covert communication scenarios is optimized respectively.

2. The covert communication method based on beamforming for multi-position monitors according to claim 1, characterized in that: The specific process of step one is: Step 1.1 constructs a covert communication system with multi-position monitors, including three scenarios. In scenario 1, the covert communication system consists of Alice, Bob, Willie, and an IRS. Alice transmits communication signals to Bob, while Willie monitors the transmission environment and detects whether Alice is transmitting communication signals to Bob. In addition, an IRS is deployed between Alice and Bob to increase Bob's covert communication rate. In scenario 1, the distance between Alice and Willie is far (distance = F). In scenarios 2 and 3, the covert communication system also consists of Alice, Bob, and Willie. In scenario 2, the distance between Alice and Willie is close (distance = S). In scenario 3, the distance between Alice and Willie is between F and S. Alice sends an ICAJ signal to Bob, while Willie monitors the transmission environment and detects whether Alice is transmitting an ICAJ signal to Bob. Step 1.2: Based on the covert communication system constructed in step 1.1, establish an overall optimization problem of active and passive beamforming with the goal of maximizing the covert communication rate under multiple constraints: Assume Alice is equipped with M antennas, the IRS is equipped with N reflective elements, and Bob and Willie are each equipped with one antenna; the phase shift matrix of the IRS is given by: in, is the phase shift of the IRS reflector element and j∈{1,2,...,N}; Assume that the channel state information of all links in the covert communication system is known; the channel matrix between Alice and IRS is expressed as The channel vectors between Alice and Willie, Alice and Bob, IRS and Bob, and IRS and Willie are expressed as Furthermore, all channels consist of large-scale path loss and small-scale Rayleigh fading: Where Q0 is the path loss at the reference distance d0, d i is the distance between nodes, α i d i The corresponding path loss index, is Rayleigh fading, and when i=AI, h i Change to H i ; Let H0 represent that Alice does not send the ICAJ signal, and H1 represent that Alice sends the ICAJ signal to Bob; therefore, the ICAJ signal sent by Alice is: in, and They are respectively transmitted communication data symbols s i ~CN(0,1) and the beamforming vector of the transmitted interference signal q~CN(0,1); The signal received by Bob is expressed as: in, represents the noise at Bob; The signal-to-interference-plus-noise ratio (SINR) at Bob is expressed as: Using SINR B , the covert communication rate is as follows: In addition, the signal received by Willie is expressed as: in, represents the noise at Willie, and the effective interference power received by Willie is When Alice only sends the communication signal, the beamforming vector w of the transmitted interference signal is removed from the ICAJ signal. p Related items, ICAJ signals become communication signals; Willie only monitors the received signal to determine whether Alice is transmitting a signal. The likelihood function of the received signal at Willie under H0 is: in, Similarly, under H1, the likelihood function of the signal received at Willie can be expressed as: in Assuming that the prior probabilities of H0 and H1 are equal, Willie uses the likelihood ratio test to minimize the detection error, which is expressed as follows: Among them, D0 and D1 are binary decisions corresponding to H0 and H1 respectively. In addition, Willie's total detection error probability is the sum of the false alarm probability and the missed detection probability, which is expressed as: ξ=Pr(D1|H0)+Pr(D0|H1) =Pr(p1(y W )≥1|H0)+Pr(p0(y W )≤1|H1) Using the lower bound of ξ, it is expressed as: Among them, D(p0(y W )||p1(y W )) indicates that from p0(y W ) to p1(y W ) is as follows: In covert communication, the concealment constraint is expressed as: Here, ε is used to determine the required concealment level with a small value; the smaller the value of ε, the higher the required concealment level. The concealment constraint in the overall optimization problem of active and passive beamforming is obtained as follows: D(p0(y W )||p1(y W ))≤2ε 2 In a covert communication system with a multi-position monitor named Willie, three fixed positions of Willie correspond to three scenarios: Scenario 1, the distance between Alice and Willie is far (distance = F); Scenario 2, the distance between Alice and Willie is close (distance = S); Scenario 3, the distance between Alice and Willie is between F and S; First, an overall optimization problem of active and passive beamforming is proposed and optimized, which is expressed as (P1): Among them, (C1-1) is the transmission power constraint, P max is the maximum transmit power threshold at Alice; (C1-2) and (C1-3) are both effective interference power constraints, P wu 、P wl are the upper and lower limits of interference tolerance respectively; (C1-4) represents the covert communication rate constraint, R min represents the minimum concealment rate threshold; (C1-5) represents the concealment constraint; We can get: make And f(a)=lna+1 / a-1, we can get: f(a)≤2ε 2 f(a) is monotonically increasing on [1,+∞), let R be f(a)=2ε 2 The only solution on [1,+∞), and (C1-5) becomes: Then, the overall optimization problem of active and passive beamforming is rewritten as (P2): Therefore, the overall optimization problem of active and passive beamforming is established.

3. The covert communication method based on beamforming for multi-position monitors according to claim 1, characterized in that: The specific process of step 2 is as follows: For the overall optimization problem of active and passive beamforming established in step 1, fix Φ and solve the active beamforming: make: in, Denote the combined channel vector between Alice and Bob; let in Meet W c ±0 and rank(W c )=1, we get: make in, Denote the combined channel vector between Alice and Willie; and let in Meet W p ±0 and rank(W p )=1, we get: In addition, the following expression is obtained: We get (P3): is the interference signal term. When it is minimum, the objective function is maximum. Therefore, let Right now Rewrite the active beamforming optimization problem (P3) as (P4) make get w p =Qw pn in, Co-located Among them, W pn Satisfy W pn ±0 and rank(W pn )=1; rewrite (P4) as (P5): In the active beamforming optimization problem (P5), only the rank-one constraint (C5-7) makes the active beamforming optimization problem (P5) non-convex. Removing the rank-one constraint (C5-7) results in a convex problem. To avoid the solution not satisfying the rank-one constraint, a penalty-based approach is adopted. First, the rank-one constraint (C5-7) is rewritten as follows: ||In c || * -||In c ||2=0 ||In pn ||*-||In pn ||2=0 Among them, ||·|| * and ||·||2 denote the nuclear norm and spectral norm respectively; meanwhile, ||·|| * is the sum of all singular values in the matrix, and ||·||2 is the largest singular value in the matrix; W pn The following conditions are met: The rank of a matrix is equal to the number of its nonzero singular values. pn )=1, we get ||In pn ||*=||In pn ||2 And || W pn || * -||W pn ||2=0 holds; otherwise, ||In pn ||*>||In pn ||2 Right now ||In pn ||*-||In pn ||2>0 In the maximization problem, a penalty term is introduced into the objective function: Where η represents the penalty factor and η>0; when When W pn When it is not a rank one matrix and η→0, the penalty term is infinitesimal, and the value of the objective function introduced by the penalty term is infinitesimal, so we get a value that satisfies ||W pn || * -||W pn ||2=0 rank one solution; In addition, -||W pn ||2 is non-convex, use The first-order Taylor expansion of the point is -||W pn The upper bound of ||2 is as follows: in, express The eigenvector corresponding to the maximum eigenvalue of ; Similarly, W c The above conditions are also met; the active beamforming optimization problem (P5) is rewritten as (P6): st{(C5-1),(C5-2),(C5-3),(C5-4),(C5-5),(C5-6) in The active beamforming optimization problem (P6) is a standard convex problem that can be solved efficiently using the CVX toolbox. After solving the active beamforming optimization problem (P6), we get W c and W pn The optimal solution of ; then, through eigenvalue decomposition and w p =Qw pn , and finally get w c and w p The optimal solution of and express; That is, the optimal solution of active beamforming is obtained.

4. The covert communication method based on beamforming for multi-position monitors according to claim 1, characterized in that: The specific process of step three is: For the overall optimization problem of active and passive beamforming established in step 1, the passive beamforming solution is solved based on the optimal solution of active beamforming obtained in step 2: Given and Optimize Φ; first, let and get make in, satisfy and And {ab}∈{c,p}; we get: in make in, and get: make And there are: in, and In addition, in satisfy and We get (P7): The passive beamforming optimization problem (P7) is a single-ratio fractional programming. The objective function of the passive beamforming optimization problem (P7) is rewritten using Dinkelbach transform as follows: Among them, β k′ Indicates the auxiliary variables introduced, as shown below Among them, m represents the index of iteration; when m reaches a certain number of iterations or β k′ When the modulus of the difference between the two iterations is less than the set convergence threshold, we get The optimal solution of ; using the penalty-based method to rewrite the passive beamforming optimization problem (P7) as (P8): in The passive beamforming optimization problem (P8) is a standard convex problem that can be solved using the CVX toolbox. Solving the passive beamforming optimization problem (P8) yields The optimal solution of Then through Get b, and finally pass Φ=diag(b H ) obtains the optimal solution of Φ, that is, the optimal solution of passive beamforming.

5. The covert communication method based on beamforming for multi-position monitors according to claim 1, characterized in that: The specific process of step 4 is as follows: According to steps 2 and 3, the beamforming optimization problems for scenarios 1, 2, and 3 are standard convex problems, which are solved using the CVX toolbox as follows: Option 1: When the distance between Alice and Willie is far (distance = F), the active beamforming optimization problem (P9) and the passive beamforming optimization problem (P10) of the scheme are as follows: Using the alternating iteration (AO) algorithm, by alternately solving (P9) and (P10), we can finally get w of the optimization problem in Scheme 1. c and the optimal solution of Φ; the process is as follows: Input: Φ (0) : initial IRS phase shift matrix; δ: iteration threshold; Output: The optimal solution of the beamforming vector for transmitting communication data symbols and the optimal solution of the IRS phase shift matrix; S11, set l = 0; S12. If l reaches the maximum value or the modulus of the difference between the objective function values of two adjacent iterations is less than δ, then proceed to S16; otherwise, proceed to S13; S13, use Φ (l) Solve the active beamforming optimization problem (P9) of solution 1 and get The optimal solution of For S14 Solve the passive beamforming optimization problem (P10) of solution 1 and obtain Φ (l+1) The optimal solution of S15, set l=l+1, and proceed to S12; S16: Based on the results of S13 and S14, the transmission communication data symbol is obtained. The optimal solution of the beamforming vector and the phase shift matrix Φ of the IRS (l) The optimal solution of . Option 2: When the distance between Alice and Willie is close (distance = S), Alice transmits an ICAJ signal. The active beamforming optimization problem of this scheme is the problem obtained by removing the IRS-related terms in h1 and h2 in the active beamforming optimization problem (P6). Option 3: When the distance between Alice and Willie is between F and S, the following active beamforming optimization problem (P11) is first given: st{(C5-1),(C5-2),(C5-4),(C5-5),(C5-6) Among them, k is the scaling factor, which is used to keep the communication performance and interference energy dimensions consistent. The active beamforming optimization problem of this scheme is the problem obtained by removing the IRS-related terms from h1 and h2 in the active beamforming optimization problem (P11). The active beamforming optimization problems of schemes 2 and 3 are solved by the AO algorithm, and finally the w of the active beamforming optimization problems of schemes 2 and 3 are obtained. c and w p The optimal solution is as follows: Input: δ: iteration threshold; Pb: active beamforming optimization problem; Output: The optimal solution of the beamforming vector for transmitting communication data symbols and the optimal solution of the beamforming vector for transmitting deceptive interference signals; S21, set l = 0; S22. If l reaches the maximum value or the modulus of the difference between the objective function values of two adjacent iterations is less than δ, then proceed to S25; otherwise, proceed to S23; S23, use the CVX toolbox to solve Pb and get and The optimal solution of S24, set l=l+1, and proceed to S22; S25, obtain the transmission communication data symbol according to the result of S23 The optimal solution of the beamforming vector and the transmission of deceptive jamming signals The optimal solution of the beamforming vector is obtained; that is, the optimization of beamforming in three different covert communication scenarios is achieved.

6. The system for a covert communication method based on beamforming for multi-position monitors according to any one of claims 1 to 5, characterized in that: include: An active and passive beamforming overall optimization problem establishment module is used to establish an active and passive beamforming overall optimization problem in step 1 with the goal of maximizing the covert communication rate under multiple constraints; an active beamforming optimization module, configured to optimize the active beamforming at Alice by fixing the passive beamforming at the IRS in step 2; A passive beamforming optimization module, configured to optimize the passive beamforming at the IRS by fixing the active beamforming at Alice in step 3; The beamforming optimization module for different covert communication scenarios is used to optimize the beamforming in three different covert communication scenarios in step four.

7. The device for a covert communication method based on beamforming for multi-position monitors according to any one of claims 1 to 5, characterized in that: include: A memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, it can implement the covert communication method based on beamforming for multi-position monitors as described in any one of claims 1 to 5.

8. A computer storage medium for receiving a user input program, characterized in that: When the computer program stored in the storage medium is executed by the processor, the computer program can perform beamforming-based covert communication for multi-position monitors based on the beamforming-based covert communication method for multi-position monitors according to any one of claims 1 to 5.

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