Interference-assisted multi-user covert communication beam forming design method

Abstract

The invention discloses an interference-assisted multi-user covert communication beam forming design method, and belongs to the technical field of wireless communication information security. The implementation method comprises the following steps: constructing a multi-user covert communication transmission system; the multi-user covert communication transmission system comprises a base station, K legal users and an eavesdropper Willie. The covert communication performance is realized in a multi-user scene, and the influence of multi-user interference is considered; an interference signal power randomization mechanism is introduced, and a quantile transmission rate concept is combined, so that the detection capability of an eavesdropper is effectively weakened, and the concealment and robustness of the system are improved; based on the optimization theory, the interference-assisted multi-user covert communication beam forming design is modeled as a maximum and minimum fairness problem, and the fairness among all legal users can be guaranteed while the concealment requirement is met; and the beam forming vectors of the confidential signals and the interference signals are jointly designed, so that the optimal distribution and balance between the interference power and the transmission power are realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication information security, and relates to a method for designing interference-assisted multi-user covert communication beamforming. Background Art

[0002] With the increasing progress of wireless communication technology, it has been widely applied to emerging fields such as smart healthcare and autonomous driving, posing higher requirements for the security of data transmission. Traditional secure communication methods, such as information encryption technology and physical layer security technology, although can improve the security of data transmission to a certain extent, still have the risk of being successfully cracked and intercepted when facing malicious eavesdroppers with powerful computing capabilities and advanced decoding technologies. In this context, covert communication technology emerges as an innovative secure communication paradigm. Its core idea is to hide communication signals in environmental noise or authorized signals through means such as intelligent signal design and resource optimization allocation, so as to fundamentally avoid the detection and interception of eavesdroppers. At the same time, beamforming technology, with its ability to form highly directive beams, provides another important technical path for enhancing communication security by precisely focusing the transmit power on the target receiver rather than the eavesdropper. Therefore, the beamforming design in covert communication has become a hot research issue.

[0003] Regarding the beamforming design in covert communication, many domestic and foreign scholars have carried out research. The existing research mainly focuses on the single-user scenario, and its core idea is to introduce interference signals to cover up legitimate communication. Scholars have deeply studied beamforming design based on the above core idea to achieve efficient and reliable covert communication performance. Although the covert communication beamforming scheme in the single-user scenario has shown good performance, in practical applications, the multi-user scenario is more common and complex, and the existing single-user schemes are difficult to be directly promoted and used. Therefore, the beamforming design for multi-user covert communication has become the focus and difficulty of current research. Specifically, how to effectively suppress the interference between multi-users while ensuring covertness, and how to achieve fair and efficient allocation of resources among multi-users are the key technical difficulties. Although existing research has considered the multi-user scenario, it uses the multicast mode to transmit confidential signals and fails to fully consider the impact of interference between users. Therefore, its beamforming design is difficult to be directly applied to more general multi-user covert communication scenarios. Summary of the Invention

[0004] To solve the problems that the existing technologies do not consider multi - user scenarios and multi - user interference, the object of the present invention is to provide an interference - assisted multi - user covert communication beamforming design method, which realizes covert communication performance in a multi - user scenario and considers the influence of multi - user interference; by introducing an interference signal power randomization mechanism and combining the concept of fractional transmission rate, the detection ability of eavesdroppers is effectively weakened, and the concealment and robustness of the system are improved; based on optimization theory, the interference - assisted multi - user covert communication beamforming design is modeled as a max - min fairness problem, which can ensure fairness among all legitimate users while meeting the concealment requirements; jointly design the beamforming vectors of the confidential signal and the interference signal, so as to achieve the optimal allocation and trade - off between interference power and transmission power.

[0005] The object of the present invention is achieved by the following technical solutions.

[0006] An interference - assisted multi - user covert communication beamforming design method disclosed by the present invention includes the following steps:

[0007] Step 1: Construct a multi - user covert communication transmission system;

[0008] The multi - user covert communication transmission system includes a base station, K legitimate users, and an eavesdropper Willie; the base station is equipped with a uniform linear array containing N t antennas, and all legitimate users and Willie use single - antenna reception; the base station transmits confidential signals to K legitimate users through beamforming technology, and the index set is At the same time, an interference signal is transmitted to confuse Willie, so as to effectively avoid the detection of the eavesdropper on the legitimate communication activity;

[0009] The signal received by the k - th legitimate user is:

[0010]

[0011] where x c,i is the confidential signal transmitted to the i - th user, x J is the interference signal, satisfying is the beamforming vector of the confidential signal of the i - th user, is the unit beamforming vector of the interference signal; the power P J of the interference signal follows a uniform distribution on [0, P J,max , where P J,max is the maximum interference signal power; is the additive white Gaussian noise with power at the k - th legitimate user; is the channel between the base station and the k - th legitimate user;

[0012] h k is expressed as follows:

[0013]

[0014] where L k is the number of transmission paths between the base station and the k-th legitimate user, and α k and are the path losses of the line-of-sight (LoS) direct path and the l-th non-line-of-sight (NLoS) path respectively; and are the angles of departure of the LoS path and the l-th NLoS path respectively; and are uniformly represented by , and the channel steering vector with the angle of departure of is expressed as follows: is expressed as follows:

[0015]

[0016] where λ is the wavelength and d = λ / 2 is the antenna array spacing;

[0017] The transmission rate between the base station and the k-th legitimate user is R k = log2(1 + γ k ), where the signal-to-interference-plus-noise ratio γ k at the k-th legitimate user is shown in Equation (4) as follows:

[0018]

[0019] where ω c,k is the beamforming vector of the k-th user's confidential signal;

[0020] The channel h w between the base station and Willie is expressed as:

[0021]

[0022] where L w is the number of transmission paths between the base station and Willie, and α w and are the path losses of the LoS path and the l-th NLoS path; and are the angles of departure of the LoS path and the l-th NLoS path respectively; and are uniformly represented by , as shown in Equation (3);

[0023] Step 2: Based on the optimization theory, construct an interference-aided multi-user covert communication beamforming optimization problem;

[0024] Step 2.1: Based on the signal detection theory, construct a covert constraint:

[0025]

[0026] where ∈(0,1) is the covertness threshold; the minimum detection error probability is expressed as:

[0027]

[0028] Step 2.2: Construct the Quantile Transmission Rate (QTR), which represents the transmission rate that can be achieved with a high probability;

[0029] The transmission rate R between the base station and the k-th legitimate user k should satisfy the probability that R is greater than or equal to QTR is not less than ξ, that is where is QTR, and ξ is the minimum tolerable probability; is expressed as:

[0030]

[0031] Since P J follows a uniform distribution on [0, P J,max , Equation (8) is expressed as:

[0032]

[0033] Since QTR represents the transmission rate that can be achieved with a high probability, it should be ensured that Therefore, given a ξ, is expressed as:

[0034]

[0035] Step 2.3: Construct a Max-Min Fairness (MMF) optimization problem; Combine e J and P J,max into a vector ω J,max , which represents the beamforming vector that transmits the interference signal with the maximum power; Therefore, Equation (7) is rewritten as:

[0036]

[0037] Equation (10) is rewritten as:

[0038]

[0039] Among them

[0040]

[0041] By jointly designing the beamforming vector of the confidential signal and the beamforming vector ω that transmits the interference signal at the maximum power J,max , to maximize the minimum QTR among all legitimate users; the MMF optimization problem is expressed as:

[0042]

[0043] where P max is the maximum transmission power, and Equation (14) is the power constraint; due to the non-convexity of the objective function and the secrecy constraint, problem P1 is difficult to solve directly;

[0044] Step 3. Solve the MMF optimization problem P1;

[0045] Step 3.1: Convert the MMF optimization problem into a maximization problem; since increases monotonically with , problem P1 is expressed as:

[0046]

[0047] s.t.:(6),(14)

[0048] By introducing an auxiliary variable ψ to represent the minimum among all legitimate users Problem P2 is reformulated as a maximization problem with an additional constraint on ψ

[0049]

[0050] s.t.:(6),(14)

[0051]

[0052] Step 3.2: Based on the Successive Convex Approximation (SCA) algorithm, find the optimal solution of problem P3;

[0053] Step 3.2.1. Based on the first-order Taylor approximation, approximate the non-convex constraint (6) as a convex constraint; (6) is rewritten as:

[0054]

[0055] Equation (16) is approximated as:

[0056]

[0057] where is the value taken in the n-th iteration for ω; J,max

[0058] Step 3.2.2: Based on the first-order Taylor approximation, approximate the non-convex constraint (15) as a convex constraint; (15) is rewritten as:

[0059]

[0060] Equation (18) is approximated as:

[0061]

[0062] where is the value taken in the n-th iteration for {ω J,max , ω c,k , ψ};

[0063] Step 3.2.3: Iteratively solve the convex optimization problem; the approximate convex sub-problem of Problem P3 in the n-th iteration is:

[0064]

[0065] P4 is solved by the CVX tool, and its solution will be used to solve the (n + 1)-th iteration of the optimization problem; through continuous iteration until convergence, the obtained optimal solution is the optimization result of interference-assisted multi-user covert communication beamforming.

[0066] Furthermore, the covert constraint in Step 2.1 is constructed by the following method:

[0067] There are the following two cases for the signal received by Willie:

[0068]

[0069] where y w [m], m ∈ {1, 2,..., M} is the m-th received signal sample collected by Willie, 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 confidential signals, represents that the base station transmits confidential signals;

[0070] Willie performs the following threshold detection on the average power of the received signal:

[0071] ​

[0072] where τ is the detection threshold, and respectively represent Willie's decisions under the hypotheses and ;

[0073] As M→∞, and the T under is expressed as:

[0074]

[0075] Willie's false alarm probability and miss - detection probability are respectively expressed as:

[0076]

[0077] The detection error probability is Generally speaking, Willie's goal is to achieve the minimum detection error probability while the base station has to ensure that is greater than or equal to 1 - ∈, where ∈∈(0,1) is the concealment threshold; It is expressed as:

[0078]

[0079] The concealment constraint is expressed as:

[0080]

[0081] Beneficial effects:

[0082] 1. Different from the traditional single - user scenario, an interference - assisted multi - user covert communication beamforming design method disclosed by the present invention realizes covert communication performance in a multi - user scenario, considers the influence of multi - user interference, and can ensure fairness among all legitimate users while meeting the concealment requirements by constructing and solving a max - min fairness optimization problem.

[0083] 2. An interference - assisted multi - user covert communication beamforming design method disclosed by the present invention effectively weakens the detection ability of eavesdroppers and significantly improves the concealment and robustness of the system by introducing an interference signal power randomization mechanism. Based on the reliability constraint of the transmission rate, the present invention constructs a quantile transmission rate to overcome the uncertainty introduced by the interference signal power randomization for the transmission rate.

[0084] 3. A method for designing interference-assisted multi-user covert communication beamforming disclosed by the present invention realizes the optimal allocation and trade-off between interference power and transmission power by jointly designing the beamforming vectors of confidential signals and interference signals. The present invention gives the covert communication performance under different system parameter settings, provides a reference value-taking method for how to achieve covert communication and maximize the effective transmission rate, and further improves the effect of interference-assisted multi-user covert communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 is a flowchart of a method for designing interference-assisted multi-user covert communication beamforming according to the present invention.

[0086] Figure 2 is a scenario diagram of a method for designing interference-assisted multi-user covert communication beamforming according to the present invention.

[0087] Figure 3 is the influence of different numbers of antennas and users on the minimum QTR.

[0088] Figure 4 is the influence of different maximum transmission powers and covertness thresholds on the minimum QTR.

[0089] Figure 5 is a schematic diagram of interference power and transmission power under different maximum transmission powers.

[0090] Figure 6 is a schematic diagram of the ratio of interference power to transmission power under different maximum transmission powers. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0091] To better understand the above technical solution, the following provides a specific analysis in combination with the accompanying drawings and specific embodiments.

[0092] As Figure 1 shown, a method for designing interference-assisted multi-user covert communication beamforming disclosed in this embodiment is specifically implemented as follows:

[0093] Step 1: Construct a multi-user covert communication transmission system;

[0094] In an intelligent medical system, a medical data center is equipped with a uniform linear array including N t antennas. The data center transmits confidential medical data to K single-antenna medical workstations through beamforming technology, and the index set is Due to the sensitivity of medical data, the data center also transmits interference signals to confuse potential single-antenna malicious eavesdroppers Willie, thereby effectively avoiding the eavesdropping of patients' privacy information by eavesdroppers;

[0095] The signal received by the k-th legitimate user is:

[0096]

[0097] where x c,i is the confidential signal transmitted to the i-th user, and x J is the interference signal, satisfying is the beamforming vector of the confidential signal of the i-th user, is the unit beamforming vector of the interference signal; the power P J of the interference signal follows a uniform distribution over [0, P J,max , where P J,max is the maximum interference signal power; is the additive white Gaussian noise with power at the k-th legitimate user; is the channel between the base station and the k-th legitimate user;

[0098] h k is expressed as follows:

[0099]

[0100] where L k is the number of transmission paths between the base station and the k-th legitimate user, and α k and are the path losses of the LoS path and the l-th NLoS path, respectively; and are the angles of departure of the LoS path and the l-th NLoS path, respectively; and are uniformly represented by , and the channel steering vector with the angle of departure of is expressed as follows:

[0101]

[0102] where λ is the wavelength and d = λ / 2 is the antenna array spacing;

[0103] The transmission rate between the base station and the k-th legitimate user is R k = log2(1 + γ k ), where the signal-to-interference-plus-noise ratio γ k at the k-th legitimate user is shown in Equation (4):

[0104]

[0105] where ω c,k is the beamforming vector of the confidential signal of the k-th user;

[0106] Channel \(h\) between the base station and Willie w It is expressed as:

[0107]

[0108] where \(L\) w is the number of transmission paths between the base station and Willie, and \(\alpha\) w and are the path losses of the LoS path and the \(l\)-th NLoS path; and are the angles of departure of the LoS path and the \(l\)-th NLoS path, respectively; and are uniformly represented by as shown in Equation (3); Specifically in this embodiment, \(L\) k

[0109] k = 3, For the \(k\)-th legitimate user, where the distance \(s\) between the base station and the \(k\)-th legitimate user k = 100 m, the antenna-related constant \(\upsilon\) k = 0.1, is the random complex gain, and the path loss exponents of the LoS path and the NLoS paths are \(\zeta = 4\). The corresponding parameter settings of \(h\) w are the same as the parameter settings of the above \(h\) k

[0110] Step 2: Based on the optimization theory, construct an interference-assisted multi-user covert communication beamforming optimization problem;

[0111] Step 2.1: Based on the signal detection theory, construct a covert constraint:

[0112]

[0113] where \(\epsilon\in(0,1)\) is the covertness threshold; the minimum detection error probability is expressed as:

[0114]

[0115] Step 2.2: Construct the quantile transmission rate QTR, which represents the transmission rate that can be achieved with high probability;

[0116] The transmission rate \(R\) between the base station and the \(k\)-th legitimate user k should be no less than \(\xi\) with a probability greater than or equal to QTR, that is where is QTR, and \(\xi\) is the minimum tolerable probability; It is expressed as:​

[0117]

[0118] Since P J obeys the uniform distribution on [0, P J,max , Equation (8) is expressed as:

[0119]

[0120] Since QTR represents the transmission rate that can be achieved with a high probability, it should be ensured that Therefore, given a ξ, It is expressed as:

[0121]

[0122] Specifically in this embodiment, ξ = 0.9.

[0123] Step 2.3: Construct the MMF optimization problem; First, combine e J and P J,max into a vector ω J,max , which represents the beamforming vector that transmits the interference signal with the maximum power; Therefore, Equation (7) is rewritten as:

[0124]

[0125] Similarly, Equation (10) is rewritten as:

[0126]

[0127] where

[0128]

[0129] By jointly designing the beamforming vector of the confidential signal and the beamforming vector ω J,max that transmits the interference signal with the maximum power, to maximize the minimum QTR among all legitimate users; The MMF optimization problem is expressed as:

[0130]

[0131] where P max is the maximum transmission power, and Equation (14) is the power constraint; Due to the non-convexity of the objective function and the secrecy constraint, Problem P1 is difficult to solve directly;

[0132] Step Three: Solve the MMF optimization problem P1;

[0133] Step 3.1: Convert the MMF optimization problem into a maximization problem; Since varies with Monotonically increasing, problem P1 is expressed as:

[0134]

[0135] s.t.: (6), (14)

[0136] By introducing an auxiliary variable ψ to represent the minimum among all legitimate users Problem P2 is reformulated as a maximization problem with an additional constraint on ψ

[0137]

[0138] s.t.: (6), (14)

[0139]

[0140] Step 3.2: Based on the SCA algorithm, find the optimal solution of problem P3;

[0141] 3.2.1. Based on the first-order Taylor approximation, approximate the non-convex constraint (6) as a convex constraint; (6) is rewritten as:

[0142]

[0143] Equation (16) is approximated as:

[0144]

[0145] where is the value taken by ω J,max in the nth iteration;

[0146] 3.2.2. Based on the first-order Taylor approximation, approximate the non-convex constraint (15) as a convex constraint; (15) is rewritten as:

[0147]

[0148] Equation (18) is approximated as:

[0149]

[0150] where is the value taken by {ω J,max , ω c,k , ψ} in the nth iteration;

[0151] 3.2.3. Iteratively solve the convex optimization problem; the approximate convex sub-problem of problem P3 in the nth iteration is:

[0152]

[0153] P4 is solved by the CVX tool, and its solution will be used to solve the (n + 1)-th iteration of the optimization problem; through continuous iteration until convergence, the obtained optimal solution is the optimization result of interference-aided multi-user covert communication beamforming.

[0154] 2. The method according to claim 1, wherein: the covert constraint in step 2.1 is constructed by the following method:

[0155] There are the following two cases for the signals received by Willie:

[0156]

[0157] where y w [m], m ∈ {1, 2,..., M} is the m-th received signal sample collected by Willie, 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 confidential signals, represents that the base station transmits confidential signals;

[0158] Willie performs the following threshold detection on the average power of the received signals:

[0159]

[0160] where τ is the detection threshold, and respectively represent Willie's decisions under the assumptions and ;

[0161] When M → ∞, and The T under are expressed as:

[0162]

[0163] Willie's false alarm probability and miss detection probability are respectively expressed as:

[0164]

[0165] The detection error probability is Generally speaking, Willie's goal is to achieve the minimum detection error probability while the base station has to ensure that is greater than or equal to 1 - ∈, where ∈ ∈ (0, 1) is the covertness threshold; It is expressed as:

[0166]

[0167] Thus, the covert constraint is expressed as:

[0168]

[0169] Specifically for this embodiment,

[0170] According to the above parameters, the influence of different numbers of antennas and users on the minimum QTR is as Figure 3 shown, where P max = -4 dBW, ∈ = 0.01. It can be seen from Figure 3 that the minimum QTR increases with the increase of the number of antennas N t , which is attributed to the enhanced spatial multiplexing ability brought about by the increase in the number of antennas. In addition, the increase in the number of legitimate users K will lead to a decrease in the minimum QTR because the resources are allocated to more users, resulting in less resources allocated to each user.

[0171] Figure 4 shows the influence of different maximum transmission powers and covertness thresholds on the minimum QTR, where N t = 2, K = 3. The analysis from Figure 4 shows that the minimum QTR first increases with the increase of the maximum transmission power P max , because more resources can be allocated to the transmission of confidential signals. However, further increasing the transmission power of the confidential signal will inevitably increase the risk of being detected by Willie, so more power is allocated to the interference signal. Considering the influence of the interference signal and multi-user interference on the transmission rate, further increasing the maximum transmission power cannot obtain a higher QTR. On the other hand, a higher covertness requirement (smaller ∈) leads to more power being allocated to the interference signal to hide the confidential signal from being detected by Willie, thus less power is allocated to data transmission. Therefore, a smaller ∈ results in a lower minimum QTR.

[0172] To verify the above analysis, Figure 5 and Figure 6 further analyze the power allocation, and the simulation results with ∈ = 0.05 in Figure 4 are adopted for its parameters. Figure 5 shows the schematic diagram of the interference power and transmission power under different maximum transmission powers. It can be seen from Figure 5 that with the increase of the maximum transmission power P max , the maximum power ||ω J,max || 2 allocated to the interference signal and the power ||ω c || 2 allocated to the confidential signal both increase. Figure 6It is a schematic diagram of the ratio of interference power to transmission power under different maximum transmission powers. From Figure 6 it can be seen that at first, with the increase of P max , a relatively small proportion of ||ω J,max || 2 is sufficient to meet the concealment requirements, so the ratio increases first. As P max further increases, ||ω c || 2 also further increases. The proportion of ||ω J,max || 2 needs to be increased compared with before to hide the confidential signal from being detected by Willie. Therefore, the ratio tends to be stable.

[0173] The above specific description further details the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above is only a specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. An interference-assisted multi-user covert communication beamforming design method, characterized in that: including the following steps, Step 1: Construct a multi-user covert communication transmission system; Step 2: Based on the optimization theory, construct an interference-aided multi-user covert communication beamforming optimization problem; Step 2.1: Based on the signal detection theory, construct a covert constraint; Step 2.2: Construct the Quantile Transmission Rate (QTR), which represents the transmission rate that can be achieved with high probability; Step 2.3: Construct the Max-Min Fairness (MMF) optimization problem; combine e J and P J,max into a vector ω J,max , which represents the beamforming vector that emits interference signals at the maximum power; Step 3: Solve the MMF optimization problem P1; Step 3.1: Convert the MMF optimization problem into a maximization problem; Since increases monotonically with the problem P1 is expressed as problem P2; By introducing an auxiliary variable ψ to represent the minimum among all legitimate users problem P2 is reformulated as a maximization problem P3 with an additional constraint on ψ; Step 3.2: Based on the Successive Convex Approximation (SCA) algorithm, find the optimal solution of problem P3, and the optimal solution is the interference-aided multi-user covert communication beamforming optimization result, realizing the multi-user covert communication beamforming design.

2. The interference-aided multi-user covert communication beamforming design method according to claim 1, characterized in that: The implementation method of Step 1 is as follows. The multi - user covert communication transmission system includes a base station, K legitimate users, and an eavesdropper Willie. The base station is equipped with a uniform linear array containing N t antennas, and all legitimate users and Willie use single - antenna reception. The base station transmits confidential signals to K legitimate users through beamforming technology, and the index set is while simultaneously transmitting interference signals to confuse Willie, thus effectively avoiding the detection of legitimate communication activities by the eavesdropper. The signal received by the k-th legitimate user is: where x c,i is the confidential signal transmitted to the i-th user, and x J is the interference signal, satisfying is the beamforming vector of the confidential signal of the i-th user, is the unit beamforming vector of the interference signal; the power P J of the interference signal follows a uniform distribution over [0, P J,max , where P J,max is the maximum interference signal power; is the additive white Gaussian noise with power at the k-th legitimate user; is the channel between the base station and the k-th legitimate user; h k is expressed as follows: where L k is the number of transmission paths between the base station and the k-th legitimate user, and α k and are the path losses of the line-of-sight (LoS) direct path and the l-th non-line-of-sight (NLoS) path, respectively; and are the angles of departure of the LoS path and the l-th NLoS path, respectively; and are uniformly represented by , and the channel steering vector with the angle of departure of is expressed as follows: is shown below: where λ is the wavelength and d = λ / 2 is the antenna array spacing; The transmission rate between the base station and the k-th legitimate user is R k = log2(1 + γ k ), where the signal-to-interference-plus-noise ratio γ at the k-th legitimate user k is as shown in Equation (4): where ω c,k is the beamforming vector of the k-th user confidential signal; Channel h between the base station and Willie w Denoted as: where L w is the number of transmission paths between the base station and Willie, and α w and are the path losses of the LoS path and the l-th NLoS path; and are the departure angles of the LoS path and the l-th NLoS path, respectively; and are uniformly denoted by , as shown in Equation (3). ​ 3. The method for designing an interference-aided multi-user covert communication beamforming according to claim 2, wherein: The implementation method of Step 2.1 is as follows. Based on the signal detection theory, construct a covert constraint: where ∈∈(0,1) is the concealment threshold; the minimum detection error probability is expressed as:

4. The interference-aided multi-user covert communication beamforming design method according to claim 3, characterized in that: The implementation method of Step 2.2 is as follows. Construct the Quantile Transmission Rate (QTR), which represents the transmission rate that can be achieved with high probability; The transmission rate R between the base station and the k-th legitimate user k The probability that it is greater than or equal to QTR should be no less than ξ, that is where is QTR, and ξ is the minimum tolerable probability; It is expressed as: Since P J obeys a uniform distribution over [0, P J,max , Equation (8) can be expressed as: Since the QTR represents the transmission rate that can be achieved with high probability, it should be ensured that Therefore, given a ξ, It is expressed as:

5. The method for designing interference-assisted multi-user covert communication beamforming according to claim 4, wherein: The implementation method of Step 2.3 is as follows. Construct the Max-Min Fairness (MMF) optimization problem; first, combine e J and P J,max into a vector ω J,max , which represents the beamforming vector that emits interference signals at the maximum power; thus, Equation (7) is rewritten as: Similarly, Equation (10) is rewritten as: where By jointly designing the beamforming vector of the confidential signal and the beamforming vector ω that transmits the interfering signal at the maximum power J,max , to maximize the minimum QTR among all legitimate users; the MMF optimization problem is expressed as: where P max is the maximum transmission power, and Equation (14) is the power constraint.

6. The interference-assisted multi-user covert communication beamforming design method according to claim 5, characterized in that: The implementation method of Step 3.1 is as follows. Convert the MMF optimization problem into a maximization problem; since increases monotonically with , problem P1 is expressed as: By introducing an auxiliary variable ψ to represent the minimum among all legitimate users Problem P2 is reformulated as a maximization problem with additional constraints on ψ 7. The interference-aided multi-user covert communication beamforming design method according to claim 6, characterized in that: The implementation method of Step 3.2 is as follows. Based on the Successive Convex Approximation (SCA) algorithm, find the optimal solution of problem P3; Step 3.2.1: Based on the first-order Taylor approximation, approximate the non-convex constraint (6) as a convex constraint; (6) is rewritten as: Equation (16) is approximated as: wherein is the value taken at the nth iteration for ω J,max ; Step 3.2.2: Based on the first-order Taylor approximation, approximate the non-convex constraint (15) as a convex constraint; (15) is rewritten as: Equation (18) is approximated as: wherein is the value taken by {ω J,max , ω c,k , ψ} in the n-th iteration; Step 3.2.3: Iteratively solve the convex optimization problem; the approximate convex sub-problem of problem P3 in the n-th iteration is: P4 is solved by the CVX tool, and its solution will be used to solve the (n + 1)-th iteration of the optimization problem; after continuous iteration until convergence, the obtained optimal solution is the optimization result of interference-aided multi-user covert communication beamforming.

8. The interference-aided multi-user covert communication beamforming design method according to claim 7, characterized in that: The covert constraint in Step 2.1 is constructed by the following method: There are the following two cases for the signal received by Willie: where y w [m], m ∈ {1, 2, ..., M} is the m-th received signal sample collected by Willie, 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 confidential signal, and 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 the detection threshold, and represent Willie's decisions under the hypotheses and respectively; M → ∞, and T under is expressed as: The false alarm probability and miss detection probability of Willie are respectively expressed as: The detection error probability is Generally speaking, Willie's goal is to achieve the minimum detection error probability The base station should ensure that is greater than or equal to 1 - ∈, where ∈(0,1) is the concealment threshold; It is expressed as: The covert constraint is expressed as:

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