Anti-shielding covert communication beam forming design method based on cooperation of multiple base stations

Abstract

The invention discloses an anti-shielding covert communication beam forming design method based on multi-base-station cooperation, and belongs to the field of wireless communication information security. The implementation method comprises the following steps: weakening the detection capability of an eavesdropper by introducing an interference signal power randomization mechanism; joint probability distribution of aggregation interference signals of multiple base stations is deduced, the detection error probability of an eavesdropper is calculated according to the joint probability distribution, and quantifiable concealment constraint conditions are established; on the basis of an optimization theory, the beam forming scheme is modeled into a maximum and minimum fairness optimization problem, a target function of the beam forming scheme maximizes the transmission rate of the worst user under the condition that all potential shielding combinations are considered, and it is ensured that the minimum detection error probability of an eavesdropper is always higher than a set threshold value under all possible shielding combinations; for a non-convex optimization problem, a successive convex approximation SCA algorithm is designed to efficiently solve the anti-shielding covert communication beam forming design, the efficiency of the anti-shielding covert communication beam forming design is improved, and covert communication is realized according to a solving result.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wireless communication information security, and relates to a multi-base station cooperation-based anti-blocking covert communication beam forming design method. BACKGROUND

[0002] With the rapid development of wireless communication technology, it is widely used in emerging fields such as intelligent transportation and smart medical care, and poses unprecedented challenges to the security and reliability of information transmission. In order to realize secure communication, existing research mainly relies on information encryption technology and physical layer security mechanism, but these methods can only protect the data content and cannot hide the communication behavior itself. The eavesdropper can still initiate a targeted interference attack by detecting the transmission activity, resulting in communication interruption. In this context, the covert communication technology hides the signal in the environmental noise or authorized signal, so that the eavesdropper cannot effectively detect the communication behavior, and fundamentally avoids such threats. In addition, the millimeter wave frequency band has great potential in emerging applications due to its high speed, large bandwidth, low delay and other advantages. Millimeter wave communication combined with beam forming technology can accurately focus the transmission power on the target receiving end rather than the eavesdropper, providing another important technical path to enhance communication security. Therefore, the design of covert communication beam forming for millimeter wave communication has become a hot issue in current research.

[0003] For the beam forming design in millimeter wave covert communication, some existing research has achieved good results, and the core idea is to introduce interference signals to mask the legitimate communication. However, they generally assume ideal propagation environment, ignoring the challenges of severe attenuation and poor penetration faced by millimeter wave communication, which makes the signal vulnerable to dynamic blocking and seriously affects the reliability of communication. To solve this problem, a multi-base station cooperation system is proposed, which provides multiple transmission paths to improve the anti-blocking ability. However, the increased transmission paths will significantly increase the risk of signal detection by eavesdroppers, causing an inherent contradiction between reliability and concealment. This contradiction has become a key bottleneck restricting the practical application of millimeter wave covert communication, and needs to be solved through innovative system design. The ideal solution should be able to ensure sufficient anti-blocking ability while controlling the detection risk brought by multi-base station cooperation within an acceptable range. This requires collaborative optimization from multiple levels such as signal design, resource allocation and transmission strategy, and establishes a new communication paradigm that takes into account both reliability and concealment. SUMMARY

[0004] To solve the problem that the prior art fails to consider the reliability and concealment of millimeter wave communication, the application aims to provide a multi-base station cooperative anti-blocking concealment communication beam forming design method, which realizes anti-blocking and meets the concealment communication requirements in a millimeter wave communication system; a randomization mechanism of interference signal power is introduced to weaken the detection ability of the eavesdropper; the joint probability distribution of the multi-base station aggregated interference signal is derived, based on which the detection error probability of the eavesdropper is calculated, and a quantifiable concealment constraint condition is established; based on the optimization theory, the beam forming scheme is modeled as a max-min fairness optimization problem, the objective function of which maximizes the transmission rate of the worst user under the consideration of all potential blocking combinations, and ensures that the minimum detection error probability of the eavesdropper is always higher than the set threshold under all possible blocking combinations; for the non-convex optimization problem, a successive convex approximation (SCA) algorithm is designed to efficiently solve the anti-blocking concealment communication beam forming design and improve the efficiency of the anti-blocking concealment communication beam forming design.

[0005] The application aims to achieve the above technical solutions.

[0006] The application discloses a multi-base station cooperative anti-blocking concealment communication beam forming design method, which comprises the following steps:

[0007] Step one, a channel between the base station and the legitimate user is constructed, a channel between the base station and the eavesdropper is constructed, a blocking channel transmission model is constructed, and thus a multi-base station cooperative concealment communication transmission system is constructed.

[0008] The multi-base station cooperative millimeter wave concealment communication transmission system comprises B base stations, K legitimate users and an eavesdropper Willie; each base station is equipped with a uniform linear array comprising N t antennas, and all legitimate users and Willie are equipped with a single antenna; the base station index set is the user index set is The B base stations transmit secret signals to the K legitimate users through beam forming technology, and simultaneously transmit interference signals to confuse Willie, so as to effectively avoid the detection of the eavesdropper on the legitimate communication activities;

[0009] The channel between the bth base station and the kth legitimate user is:

[0010]

[0011] wherein L b,k is the transmission path number between the bth base station and the kth legitimate user; and are the line of sight (LoS) direct diameter and the non-line of sight (NLoS) diameter part respectively; α b,k and These are the path losses for the LoS direct path and the l-th NLoS path, respectively. and These are the departure angles of the LoS path and the l-th NLoS path, respectively; and Unified This indicates that the departure angle is... Channel steering vector It is expressed as follows:

[0012]

[0013] Where λ is the wavelength, and d = λ / 2 is the antenna array spacing; since the NLoS path component is almost negligible compared to the LoS path component in the millimeter-wave band, whether the link is blocked mainly depends on the LoS path component; random blocking between the b-th base station and the k-th legitimate user can be characterized by a Bernoulli distribution on the LoS path:

[0014]

[0015] Where q is a parameter determined by the density and average size of the obstructing object, s b,k It is the distance between the b-th base station and the k-th user;

[0016] The channel between the b-th base station and Willie is:

[0017]

[0018] Where L b,w This represents the number of transmission paths between the b-th base station and Willie. and These are the LosS path and NLoS path components, respectively; α b,w and These are the path losses for the LoS path and the l-th NLoS path, respectively. and These are the departure angles of the LoS path and the l-th NLoS path, respectively; and Unified express, As shown in equation (2);

[0019] The random occlusion between the b-th base station and Willie can be characterized by a Bernoulli distribution on the LoS path:

[0020]

[0021] Where s b,w It is the distance between the b-th base station and Willie;

[0022] The kth legitimate user has at least D k unblocked paths, Willie has at least D w unblocked paths; the set of unblocked base stations serving the kth legitimate user is The set of possible combinations of the C(D unblocked base stations serving the kth legitimate user is where c = 1, 2,..., C(D k ), and

[0023]

[0024] Under the cth possible combination, the channel between the bth base station and the kth legitimate user is where the indicator function is:

[0025]

[0026] The set of possible combinations of the jth interfering unblocked base station to Willie is where j = 1, 2,..., C(D w ); considering the system resource limitation and the location of Willie is known, only T = 2 unblocked base stations closest to Willie transmit interference signals, the set of unblocked base stations is denoted as Under the possible combinations and , the signal received by the kth legitimate user is:

[0027]

[0028] where x k is the confidential signal transmitted to the kth legitimate user, x J is the interference signal, satisfying is the beamforming vector of the bth base station to the kth user, is the unit beamforming vector of the bth base station to Willie; the interference signal power P b,J transmitted by the bth base station is subject to uniform distribution in [0, P Jmax ], where P Jmax is the maximum interference signal power; is the additive white Gaussian noise with power at the kth legitimate user;

[0029] Under the possible combinations and , the transmission rate of the kth legitimate user is where the signal-to-interference-plus-noise ratio at the kth legitimate user is For:

[0030]

[0031] Step two, based on optimization theory, construct the anti-shielding hidden communication beamforming optimization problem based on multi-base station cooperation.

[0032] Step 2.1: Based on the signal detection theory, simulate Willie's binary hypothesis testing process:

[0033] Willie received signal has the following two cases:

[0034]

[0035] Where j = 1, 2,..., C(D w ), m = 1, 2,..., M is the mth received signal sample collected by Willie in the possible combination M is the total number of samples; is the additive white Gaussian noise with power at Willie; represents that the base station does not transmit the secret signal, represents that the base station transmits the secret signal;

[0036] Willie performs threshold detection on the average power of the received signal as follows:

[0037]

[0038] Where τ is the detection threshold, and respectively represent Willie's decisions under and

[0039] M→∞, T in and respectively represent:

[0040]

[0041] Where is the power of the secret signal received by Willie;

[0042] Step 2.2: Derive the joint probability distribution of the aggregated interference signal of multiple base stations, based on which calculate the detection error probability of Willie, and establish the concealment constraint:

[0043] In equations (13) and (14) ​The probability density function and probability distribution function of the sum of multiple random variables can be derived; based on this, the probability distribution function of the false alarm probability of Willie is:

[0044]

[0045] The probability distribution function of the missed detection probability of Willie is:

[0046]

[0047] where and

[0048] The detection error probability is Willie's goal is to achieve the minimum detection error probability The base station, however, needs to ensure that is greater than or equal to 1-∈, where ∈∈(0,1) is the concealment threshold; is expressed as:

[0049]

[0050] The concealment constraint is expressed as:

[0051]

[0052] Step 2.3: Construct the maximum-minimum fairness optimization problem; in the possible combination and , the transmission rate of the kth user under the worst case P b,J = P Jmax is where is the signal-to-interference-and-noise ratio:

[0053]

[0054] Combine e J and P Jmax into a vector ω b,Jmax , where ω b,Jmax represents the beamforming vector of the bth base station to Willie's maximum power transmission interference signal; therefore, equation (19) is rewritten as:

[0055]

[0056] Equation (17) is rewritten as:

[0057]

[0058] The beamforming scheme is modeled as a min-max fairness optimization problem, whose objective function maximizes the transmission rate of the worst user considering all potential occlusion combinations, and ensures that the concealment constraint can be satisfied under all possible occlusion combinations; the optimization problem is expressed as:

[0059]

[0060] where is the beamforming vector of the confidential signal, is the beamforming vector of the interference signal transmitted with maximum power, P max is the maximum transmission power; equation (22) is the concealment constraint, and equation (23) is the power constraint; since the objective function and the concealment constraint are non-convex, the problem P1 is difficult to solve directly;

[0061] Step three, solving the min-max fairness optimization problem P1 in step two, thereby obtaining the anti-occlusion covert communication beamforming result based on multi-base station cooperation, and realizing anti-occlusion covert communication according to the anti-occlusion covert communication beamforming result.

[0062] Step 3.1: based on the monotonicity of the function, converting the problem P1 into P2, and then into the maximization problem P3;

[0063] Since increases monotonically with P1 is expressed as:

[0064]

[0065] s.t.:(22), (23)

[0066] By introducing an auxiliary variable ψ to represent the minimum P2 is expressed as a maximization problem with an additional constraint on ψ:

[0067]

[0068] s.t.:(22), (23)

[0069]

[0070] Since the concealment constraint (22) and the constraint (24) are non-convex, the problem P3 is still difficult to solve;

[0071] Step 3.2: based on the SCA algorithm, finding the optimal solution of the problem P3, obtaining the anti-occlusion covert communication beamforming result based on multi-base station cooperation, and realizing anti-occlusion covert communication according to the anti-occlusion covert communication beamforming result;

[0072] Step 3.2.1, based on the first-order Taylor approximation, the non-convex concealment constraint (22) is approximated as a convex constraint; (22) is written as:

[0073]

[0074] Formula (25) is approximated as:

[0075]

[0076] Wherein is the value taken by {ω Jmax ,ω c} in the nth iteration;

[0077] Step 3.2.2, based on the first-order Taylor approximation, the non-convex constraint (24) is approximated as a convex constraint; (24) is written as:

[0078]

[0079] Formula (27) is approximated as:

[0080]

[0081] Wherein is the value taken by in the nth iteration; If then Otherwise

[0082] Step 3.2.3, iteratively solve the approximate convex optimization sub-problems to solve the optimal beamforming scheme; the approximate convex optimization sub-problem of P3 in the (n+1)th iteration is:

[0083]

[0084] P4 is solved by the CVX tool, and the obtained solution will be used for the solution of the (n+1)th iteration; after continuous iteration until convergence, the optimal solution is the optimal solution of the anti-blocking covert communication beamforming based on multi-base station cooperation, and the anti-blocking covert communication is realized according to the anti-blocking covert communication beamforming result.

[0085] Beneficial effects:

[0086] ​​1. The application discloses a kind of based on the beam forming design method of anti-shielding covert communication of multi-base station cooperation, through multi-base station cooperation transmission mechanism, when the link between any base station and user is shielded, other available base station can be used to maintain connection, ensure that communication reliability is maintained in dynamic shielding scenario;While designing the beam forming scheme satisfying the concealment constraint, ensure that concealment index is not degraded in the process of anti-shielding, can solve the contradictory demand of dynamic shielding and covert communication in millimeter wave communication system.

[0087] 2. The application discloses a kind of based on the beam forming design method of anti-shielding covert communication of multi-base station cooperation, introduce interference power randomization mechanism, weaken the detection ability of eavesdropper. The joint probability distribution of the interference signal of multi-base station aggregation is deduced, the detection error probability of eavesdropper is accurately described, and the quantifiable concealment constraint condition is established to ensure communication security.

[0088] 3. The application discloses a kind of based on the beam forming design method of anti-shielding covert communication of multi-base station cooperation, establishes the joint optimization model of confidential signal and interference signal beam forming vector, realizes the optimal distribution and trade-off between interference power and transmission power.The application gives the covert communication performance under different system parameter settings, and is compared with the beam forming scheme without considering dynamic shielding, to provide a solution for the contradiction between reliability and security in millimeter wave communication. BRIEF DESCRIPTION OF DRAWINGS

[0089] Figure 1 It is the flow chart of the beam forming design method of anti-shielding covert communication of multi-base station cooperation of the application.

[0090] Figure 2 It is the scene diagram of the beam forming design method of anti-shielding covert communication of multi-base station cooperation of the application.

[0091] Figure 3 It is the influence of different shielding density and different beam forming scheme on minimum transmission rate.

[0092] Figure 4 It is the influence of different shielding density and different beam forming scheme on minimum detection error probability.

[0093] Figure 5 It is the influence of different concealment threshold and shielding density on minimum transmission rate. DETAILED DESCRIPTION

[0094] In order to better understand the above technical solutions, the following specific embodiments are given in combination with the drawings.

[0095] As shown in Figure 1 The beam forming design method of anti-shielding covert communication of multi-base station cooperation disclosed in the embodiment, the specific implementation steps are as follows:

[0096] Step one, construct the channel between the base station and the legitimate user, construct the channel between the base station and the eavesdropper, construct the shielding channel transmission model, and thus construct the multi-base station cooperative covert communication transmission system.

[0097] Modern medical data centers store a large amount of sensitive information, such as patient electronic medical records, medical images, genetic data, etc., and need to ensure high security, low delay, and high reliability of communication, and the multi-base station cooperative millimeter wave covert communication system can perfectly adapt to this scenario; a medical data center deploys B base stations, and there are K medical workstations and malicious eavesdroppers Willie; each base station is equipped with a uniform linear array containing N t antennas, and all medical workstations and Willie are equipped with a single antenna; the base station index set is The medical workstation index set is B base stations transmit encrypted medical records or image data of patients to K medical workstations through beamforming technology, and at the same time, transmit interference signals to confuse Willie, thereby effectively avoiding detection of confidential medical information by eavesdroppers;

[0098] The channel between the bth base station and the kth medical workstation is:

[0099]

[0100] Where L b,k is the transmission path number between the bth base station and the kth medical workstation; and are the line-of-sight (LoS) direct path and the non-line-of-sight (NLoS) path part, respectively; b,k and are the path loss of the LoS direct path and the lth NLoS path, respectively; and are the departure angles of the LoS path and the lth NLoS path, respectively; and are uniformly denoted as , and the departure angle is The channel steering vector is represented as follows:

[0101]

[0102] where λ is the wavelength, d = λ / 2 is the antenna array spacing; since in the mmWave band, the NLoS path is almost negligible compared to the LoS path, whether the link is blocked mainly depends on the LoS path; the random blockage between the b-th base station and the k-th medical workstation can be characterized by a Bernoulli distribution on the LoS path:

[0103]

[0104] where q is a parameter determined by the density and average size of blockers, s b,k is the distance between the b-th base station and the k-th medical workstation;

[0105] The channel between the b-th base station and Willie is:

[0106]

[0107] where L b,w is the number of transmission paths between the b-th base station and Willie; and are the LoS path and NLoS path parts, respectively; b,w and are the path loss of the LoS path and the l-th NLoS path, respectively; and are the angle of departure of the LoS path and the l-th NLoS path, respectively; and are denoted by , as shown in equation (2);

[0108] The random blockage between the b-th base station and Willie can be characterized by a Bernoulli distribution on the LoS path:

[0109]

[0110] where s b,w is the distance between the b-th base station and Willie;

[0111] The k-th medical workstation has at least D k unblocked paths, and Willie has at least D w unblocked paths; the set of unblocked base stations serving the k-th medical workstation is The set of possible combinations of The possible combination of the c-th unblocked base station serving the medical workstation k is where c = 1, 2,..., C(D k ), and

[0112]

[0113] Under the cth possible combination, the channel between the bth base station and the kth medical workstation is where the indicator function is:

[0114]

[0115] The possible combinations of unblocked base stations that interfere with Willie are where j = 1, 2,..., C(D w ); considering the system resource limitation and the known location of Willie, only T = 2 unblocked base stations closest to Willie transmit interference signals, and the set of unblocked base stations is denoted as Under the possible combinations and , the signal received by the kth medical workstation is:

[0116]

[0117] where x k is the confidential signal transmitted to the kth medical workstation, x J is the interference signal, and satisfies is the beamforming vector of the bth base station to the kth medical workstation, is the unit beamforming vector of the bth base station to Willie; the interference signal power P b,J transmitted by the bth base station is uniformly distributed in [0, P Jmax ], where P Jmax is the maximum interference signal power; is the additive white Gaussian noise at the kth medical workstation with power ;

[0118] Under the possible combinations and , the transmission rate of the kth workstation is where the signal-to-interference-plus-noise ratio at the kth medical workstation is:

[0119]

[0120] Specifically, in this embodiment, the medical data center deploys B = 4 base stations and has K = 3 medical workstations and a malicious eavesdropper Willie; each base station is equipped with a uniform linear array containing N t = 4 antennas, and all medical workstations and Willie are equipped with a single antenna; the kth medical workstation has at least D k = 2 unblocked paths, and Willie has at least Dw = 2 unblocked paths; L b,k = 3, and where the antenna correlation coefficient υ b,k = 0.1, is a random complex gain, and the path loss exponents of LoS and NLoS paths are ζ = 4; h b,w has the same parameter settings as h b,k ;

[0121] Step 2: Based on optimization theory, construct the optimization problem of anti-occlusion covert communication beamforming based on multi-base station cooperation.

[0122] Step 2.1: Based on signal detection theory, simulate Willie's binary hypothesis testing process:

[0123] There are two cases for the signal received by Willie:

[0124]

[0125] where j = 1, 2,..., C(D w ), m = 1, 2,..., M is the mth received signal sample collected by Willie under possible combinations , and M is the total number of samples; is the additive white Gaussian noise with power at Willie; represents that the base station does not transmit the secret signal, represents that the base station transmits the secret signal;

[0126] Willie performs threshold detection on the average power of the received signal as follows:

[0127]

[0128] where τ is the detection threshold, and represent Willie's decisions under and , respectively;

[0129] M→∞, T under and are represented as:

[0130]

[0131]

[0132] where is the confidential signal power received by Willie;

[0133] Step 2.2: Derive the joint probability distribution of the aggregate multi- base station jamming signal, based on which the false alarm probability of Willie is calculated, and the concealment constraint is established:

[0134] is the sum of multiple random variables, whose probability density function and probability distribution function can be derived; based on which, the probability distribution function of the false alarm probability of Willie is:

[0135]

[0136] The probability distribution function of the missed detection probability of Willie is:

[0137]

[0138] where and

[0139] The false alarm probability is The target of Willie is to achieve the minimum false alarm probability The base station, on the other hand, wants to guarantee is greater than or equal to 1 - e, where e e (0, 1) is the concealment threshold; is expressed as:

[0140]

[0141] The concealment constraint is expressed as:

[0142]

[0143] Step 2.3: Construct the max-min fair optimization problem; under the possible combinations and , the transmission rate of the k-th base station under the worst case P b,J = P Jmax is where is the signal-to-interference-and-noise ratio:

[0144]

[0145] Combine e J and P Jmax into a vector w b,Jmax , w b,Jmax represents the beamforming vector of the b-th base station transmitting the jamming signal to Willie with the maximum power; therefore, equation (19) is rewritten as:​

[0146]

[0147] Rewrite formula (17) as:

[0148]

[0149] The beamforming scheme is modeled as a max-min fairness optimization problem, whose objective function maximizes the transmission rate of the worst medical workstation while considering all potential occlusion combinations, and ensures that the concealment constraint can be satisfied under all possible occlusion combinations; the optimization problem is represented as:

[0150]

[0151] where is the beamforming vector of the confidential signal, is the beamforming vector of the interference signal transmitted with maximum power, P max is the maximum transmission power; formula (22) is the concealment constraint, and formula (23) is the power constraint; due to the non-convexity of the objective function and the concealment constraint, problem P1 is difficult to solve directly;

[0152] Specifically, in this embodiment, P max = 10 dBW;

[0153] Step three, solve the max-min fairness optimization problem P1 of step two, thereby obtaining the anti-occlusion concealment communication beamforming result based on multi-base station cooperation; realize anti-occlusion concealment communication according to the anti-occlusion concealment communication beamforming result.

[0154] Step 3.1: Based on the monotonicity of the function, convert problem P1 to P2, and then to the maximization problem P3;

[0155] Since increases monotonically with P1 is represented as:

[0156]

[0157] s.t.:(22), (23)

[0158] By introducing an auxiliary variable ψ to represent the minimum P2 is expressed as a maximization problem with additional constraints on ψ:

[0159]

[0160] s.t.:(22), (23)

[0161]

[0162] Due to the non-convexity of the concealment constraint (22) and the constraint (24), the problem P3 is still difficult to solve;

[0163] Step 3.2: Based on the SCA algorithm, the optimal solution of the problem P3 is found, and the anti-occlusion concealment communication beamforming result based on multi-base station cooperation is obtained. According to the anti-occlusion concealment communication beamforming result, the anti-occlusion concealment communication is realized.

[0164] Step 3.2.1, based on the first-order Taylor approximation, the non-convex concealment constraint (22) is approximated as a convex constraint; (22) is written as:

[0165]

[0166] The formula (25) is approximated as:

[0167]

[0168] Wherein is the value taken by {ω Jmax ,ω c} in the nth iteration;

[0169] Step 3.2.2, based on the first-order Taylor approximation, the non-convex constraint (24) is approximated as a convex constraint; (24) is written as:

[0170]

[0171] The formula (27) is approximated as:

[0172]

[0173] Wherein is the value taken by in the nth iteration; If then Otherwise

[0174] Step 3.2.3, the approximate convex optimization sub-problem is solved iteratively, and the optimal beamforming scheme is solved; the approximate convex optimization sub-problem of P3 in the (n+1)th iteration is:

[0175]

[0176] P4 is solved by CVX tool, and the obtained solution will be used for the solution of the (n+1)th iteration; through continuous iteration until convergence, the optimal solution ​​That is, the beamforming optimization result of the anti-occlusion covert communication based on multi-base station cooperation.

[0177] According to the above parameters, the influence of different occlusion densities and different beamforming schemes on the minimum transmission rate is as shown in Figure 3 , wherein ∈=0.01. It can be seen from Figure 3 that the minimum transmission rate decreases with the increase of the occlusion density q, because the increase of the occlusion density leads to the increase of the occlusion probability, thereby weakening the transmission rate. In addition, compared with the beamforming scheme without considering the occlusion, the transmission rate of the scheme proposed in the application is relatively more stable and decreases more slowly, which embodies the improvement of the proposed scheme in communication stability.

[0178] Figure 4 is the influence of different occlusion densities and different beamforming schemes on the minimum detection error probability, wherein ∈=0.01. It can be seen from Figure 4 that the minimum detection error probability decreases with the increase of the occlusion density q, because the increase of the occlusion probability leads to the inability of the interference signal to stably weaken the eavesdropping ability of the eavesdropper. In addition, compared with the beamforming scheme without considering the occlusion, the application ensures that the concealment constraint under all occlusion conditions is met, thereby being more stable in the detection error probability and not easily affected by the occlusion density.

[0179] Figure 5 is the influence of different concealment thresholds and occlusion densities on the minimum transmission rate. It can be seen from Figure 5 that with the increase of the concealment threshold ∈, the minimum transmission rate also increases, because a larger ∈ represents a looser concealment requirement, and the looser concealment requirement makes more power allocated to the transmission of the confidential signal rather than the transmission of the interference signal.

[0180] The above specific description further details the purpose, technical scheme and beneficial effects of the application. It should be understood that the above description is only a specific embodiment of the application and is not used to limit the protection scope of the application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the application should be included in the protection scope of the application.

Claims

1. A method for designing a multi-base station cooperative anti-occlusion covert communication beamforming scheme, comprising the following steps: Step one, constructing a channel between a base station and a legitimate user, constructing a channel between a base station and a eavesdropper, constructing an occlusion channel transmission model, thereby constructing a multi-base station cooperative covert communication transmission system; Step two, constructing a multi-base station cooperative anti-occlusion covert communication beamforming optimization problem; Step 2.1: simulating Willie's binary hypothesis testing process; Step 2.2: establishing a covert constraint; Step 2.3: constructing a max-min fairness optimization problem P1; Step three, solving the problem P1 in step two, obtaining the multi-base station cooperative anti-occlusion covert communication beamforming result; Step 3.1: based on the monotonicity of the function, converting the problem P1 into P2, and then into the maximization problem P3; Step 3.2: based on the successive convex approximation algorithm, finding the optimal solution of the problem P3, obtaining the multi-base station cooperative anti-occlusion covert communication beamforming result.

2. The method of claim 1, wherein: The method for constructing the channel between the base station and the legitimate user in step one is, A multi-base-station cooperative mmWave covert communication transmission system contains B base stations, K legitimate users and a passive eavesdropper Willie; each base station is equipped with a uniform linear array containing N t antennas, and all legitimate users and Willie are equipped with a single antenna; the base station index set is the user index set is The B base stations transmit confidential signals to the K legitimate users through beamforming technology, while transmitting interference signals to confuse Willie, avoiding the detection of the legitimate communication activities by the eavesdropper. The channel between the bth base station and the kth legitimate user is: where L b,k is the number of transmission paths between the bth base station and the kth legitimate user; and are the LoS (Line of Sight) direct path and NLoS (Non Line of Sight) path components, respectively; a b,k and are the path losses of the LoS direct path and the lth NLoS path, respectively; and are the angles of departure of the LoS path and the lth NLoS path, respectively; and are the angles of arrival of the LoS path and the lth NLoS path, respectively; are denoted by is the channel steering vector is denoted as follows: Where λ is the wavelength, d = λ / 2 is the antenna array spacing; in the millimeter wave frequency band, whether the link is occluded mainly depends on the LoS path part; the random occlusion between the bth base station and the kth legitimate user is represented by the Bernoulli distribution on the LoS path: where q is a parameter determined by the density and average size of the occluders, s b,k is the distance between the bth base station and the kth user.

3. The method of claim 2, wherein: The method for constructing the channel between the base station and the eavesdropper in step one is, The channel between the bth base station and Willie is: where L b,w is the number of transmission paths between the bth base station and Willie; and are the LoS and NLoS path portions, respectively; a b,w and are the path losses for the LoS path and the lth NLoS path, respectively; and are the angles of departure for the LoS path and the lth NLoS path, respectively; and are the angles of departure for the LoS path and the lth NLoS path, respectively; are represented by as shown in equation (2); The random occlusion between the bth base station and Willie is represented by the Bernoulli distribution on the LoS path: where s b,w is the distance between the bth base station and Willie.

4. The method of claim 3, wherein: The method for constructing the occlusion channel transmission model in step one is, The kth legitimate user has at least D k unblocked paths, Willie has at least D w unblocked paths; the set of unblocked base stations serving the kth legitimate user is The set of possible combinations of The possible combinations of unblocked base stations serving the kth legitimate user c is where c = 1, 2,..., C(D k ), and Under the cth possible combination, the channel between the bth base station and the kth legitimate user is where the indicator function is: The possible combinations of jth interfering unblocked base stations for Willie are where j = 1, 2,..., C(D w ); considering system resource limitation and Willie's location known, only T = 2 unblocked base stations closest to Willie transmit interfering signals, and the unblocked base station set is denoted as In the possible combinations and , the signal received by the kth legitimate user is: where x k is the confidential signal transmitted to the kth legitimate user, x J is the interference signal, satisfying is the beamforming vector of the bth base station to the kth user, is the unit beamforming vector of the bth base station to Willie; the interference signal power P b,J transmitted by the bth base station obeys the uniform distribution of [0, P Jmax ], where P Jmax is the maximum interference signal power; is the additive white Gaussian noise with power at the kth legitimate user; In possible combinations and The transmission rate of the kth legitimate user is where the signal-to-interference-plus-noise ratio at the kth legitimate user is is:

5. The method of claim 4, wherein: The implementation method of step 2.1 is, There are two cases for the signal received by Willie: wherein is the Willie in the possible combination is the mth received signal sample collected at the downlink, M is the total number of samples; is the power at the Willie is the additive white Gaussian noise; represents that the base station does not transmit the confidential signal, represents that the base station transmits the confidential signal; Willie performs the following threshold detection on the average power of the received signal: where τ is a detection threshold, and denote Willie's decisions at and respectively. M→∞, T at and are respectively given by: wherein is the confidential signal power received by Willie.

6. The method of claim 5, wherein: The implementation method of step 2.2 is, wherein the variables in formula (13) and formula (14) are is the sum of a plurality of random variables, the probability density function and the probability distribution function of which can be derived; based on this, the probability distribution function of the false alarm probability of Willie is: The probability distribution function of the false alarm probability of Willie is: wherein and The detection error probability is Willie's goal is to achieve a minimum detection error probability The base station, on the other hand, wants to ensure greater than or equal to 1 - ε, where ε ∈ (0, 1) is a concealability threshold; is expressed as: The covert constraint is expressed as:

7. The method of claim 6, wherein: The implementation method of step 2.3 is, In possible combinations and Under the worst case P b,J = P Jmax the transmission rate of the kth user is where is the signal to interference and noise ratio: e J and P Jmax are combined into a vector ω b,Jmax , ω b,Jmax represents the beamforming vector of the bth base station transmitting an interference signal to Willie with maximum power; thus, equation (19) is rewritten as: Equation (17) is rewritten as: Model the beamforming scheme as a max-min fairness optimization problem, whose objective function maximizes the transmission rate of the worst user under all potential occlusion combinations, and ensures that the covert constraint can be met under all possible occlusion combinations; the optimization problem is expressed as: where is the beamforming vector for the confidential signal, is the beamforming vector for transmitting the jamming signal with maximum power, P max is the maximum transmission power; equation (22) is the concealment constraint and equation (23) is the power constraint.

8. The method of claim 7, wherein: The implementation method of step 3.1 is, Due to With Monotonically increasing, P1 is expressed as: s.t.:(22), (23) By introducing an auxiliary variable ψ to represent the minimum of all legitimate users under all possible combinations P2 is expressed as a maximization problem with additional constraints on ψ: s.t.:(22), (23) 9. The method of claim 8, wherein: The implementation method of step 3.2 is, Step 3.2.1, based on the first-order Taylor approximation, the non-convex covert constraint (22) is approximated as a convex constraint; (22) is written as: Formula (25) is approximated as: Formula (25) is approximated as: wherein is {ω Jmax ,ω c} at the n-th iteration; Step 3.2.2, based on the first-order Taylor approximation, the non-convex constraint (24) is approximated as a convex constraint; (24) is written as: Formula (27) is approximated as: Formula (27) is approximated as: wherein is the value taken in the nth iteration; if then else Step 3.2.3, iteratively solve the approximate convex optimization subproblem, solve the optimal beamforming scheme; the approximate convex optimization subproblem of P3 in the (n+1)th iteration is: P4 is solved by CVX tool, and the obtained solution will be used for the solution of the (n+1) th iteration; through continuous iteration until convergence, the optimal solution is solved That is, the optimization result of the anti-blocking covert communication beamforming based on multi-base station cooperation.

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