MIMO space-air-ground integrated secure communication multi-objective optimization method

Abstract

The application discloses a MIMO space-air-ground integrated secure communication multi-objective optimization method, and belongs to the field of wireless communication.The application realizes the method as follows: a MIMO space-air-ground integrated secure communication network system is constructed, in the system, a LEO satellite integrates a high-gain antenna for a legal user in an ISUAVN (Integrated Satellite-Unmanned Aerial Vehicle Network), and there is a potential threat of eavesdropping on a GEO satellite network; the ISUAVN adopts a large-scale multiple-input multiple-output network without a cell to improve the spectrum efficiency of a ground user. By applying a weighted Chebyshev method to balance two mutually conflicting targets of total energy minimization and maximum secret transmission rate, a MIMO space-air-ground integrated secure communication multi-objective optimization problem is constructed. The weighted Chebyshev method is used to convert the multi-objective optimization problem into a single-objective problem, and the optimal solution of the joint beam forming problem is quickly obtained by using a successive convex approximation (SCA) method and a CVX optimization software package. The application can reduce the total transmission power on the basis of ensuring the communication quality, thereby optimizing the energy efficiency and reliability of the system.

Description

Technical Field

[0001] This invention relates to a multi-objective optimization method for MIMO integrated air-space-ground secure communication, belonging to the field of wireless communication. Background Technology

[0002] In recent years, with the increasing demand for sixth-generation (6G) communication technology, research focus has gradually shifted to the development of its key technologies. 6G communication systems are expected to achieve higher data transmission rates, lower latency, ubiquitous coverage, and enhanced security. Non-terrestrial networks (NTNs) are considered one of the key technologies supporting 6G communication systems because they can provide seamless global coverage and superior data throughput. Compared to traditional terrestrial networks, NTNs combine the extensive coverage of satellite communication with the high data transmission rates and low latency of terrestrial systems, becoming the core heterogeneous network supporting on-demand access across all global scenarios. With the increasing demand for higher data transmission rates, precoding and resource allocation technologies have become crucial in NTN systems. The core objective of these technologies is to improve the achievable data rates for both mobile and satellite users and effectively suppress interference between different network layers. However, the high dynamism of satellites poses a significant challenge to the deployment of high-quality service (QoS) for seamless global services, forcing researchers to explore new access technologies and optimization schemes. To meet the ever-increasing data rate demands, NTN systems must fully utilize all available spectrum, including millimeter waves, terahertz waves, and optical communication.

[0003] Despite the significant potential of NTN systems across various application areas, their wide coverage and broadcast nature make them vulnerable to serious cybersecurity threats, including eavesdropping, power interference, and denial-of-service (DoS) attacks. Therefore, ensuring the security and reliability of NTN system communication links has become a crucial research topic. Existing research primarily focuses on cross-layer interference management and secure communication design, such as using joint beamforming techniques to address the secure transmission problem of a single eavesdropper in NTN systems, or maximizing the secure communication rate for satellite users in multi-eavesdropper scenarios. However, due to the conflicting needs of NTN systems in ensuring data transmission efficiency and improving communication security, achieving an effective balance between these objectives, especially finding the optimal Pareto optimal solution between secure communication rate and other key objectives, remains a pressing challenge.

[0004] The following technical shortcomings exist in existing MIMO-based air-space-ground integrated systems: (I) In existing MIMO NTN systems, perfect Channel State Information (CSI) cannot be obtained between ground terminals and Unmanned Auxiliary Networks (UAPs). This problem prevents the system from accurately assessing channel quality, thus affecting efficient signal transmission and overall system performance. Furthermore, existing systems do not adequately consider potential security risks, especially in ISUAVN, where legitimate ground users (TUs) may use high-gain directional antennas for eavesdropping attacks, posing significant security risks. (II) Existing multi-objective optimized secure communication strategies typically employ a single optimization objective, neglecting the complex trade-off between communication quality and security. Due to the lack of a reasonable optimization framework, existing systems struggle to simultaneously address the conflicting objectives of minimizing transmission power and maximizing secret data rate, failing to achieve an ideal Pareto optimal solution in multi-objective optimization problems. This issue results in an unbalanced relationship between communication quality and system security, impacting the system's practical application effectiveness. Summary of the Invention

[0005] To address the aforementioned technical deficiencies, the purpose of this invention is to provide a multi-objective optimization method for MIMO integrated air-space-ground secure communication. Employing a time-division duplex (TDD) communication system, this method enables the LEO satellite-integrated unmanned aerial vehicle (UAP) network (ISUAVN) to acquire the actual instantaneous CSI between the ground terminal and the UAP in real time, thereby avoiding the performance degradation caused by the perfect CSI assumption. This invention improves ISUAVN's ability to predict the channel quality of ground users through CSI estimation and ensures efficient signal transmission. This invention maintains the stability and efficiency of the secure communication system under dynamically changing channel conditions. This invention introduces a joint beamforming design based on multi-objective optimization (MOO), which can simultaneously optimize communication quality and security. Furthermore, by precisely balancing the conflicting objectives of minimizing transmission power and maximizing the secret data rate, it addresses the shortcomings of existing secure communication systems in multi-objective optimization. This invention can improve the system's anti-eavesdropping capability while ensuring communication quality, thus enhancing the security of the secure communication system.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] This invention discloses a multi-objective optimization method for MIMO integrated air-space-ground secure communication, constructing a MIMO integrated air-space-ground secure communication network system for secure communication in the CFmMIMONTN system. In this system, a legitimate user in an unmanned aerial vehicle (UAV)-based cellless network (ISUAVN) is equipped with a high-gain antenna, and there is a potential threat of eavesdropping on the GEO satellite network. In the considered NTN system, the ISUAVN employs a cellless massive MIMO network to improve the spectral efficiency of ground users. The multi-objective optimization method balances the conflicting objectives of minimizing total energy and maximizing secure transmission rate. The multi-objective optimization problem for MIMO integrated air-space-ground secure communication is obtained by applying the weighted Chebyshev method. The weighted Chebyshev method transforms the originally complex multi-objective optimization problem into a single-objective problem, significantly simplifying the optimization solution process. By employing the continuous convex approximation SCA method and the CVX optimization software package, the optimal solution to the joint beamforming problem can be quickly obtained. This invention can reduce the total transmission power while ensuring communication quality, thereby optimizing the system's energy efficiency and reliability.

[0008] This invention discloses a multi-objective optimization method for MIMO integrated air-space-ground secure communication, comprising the following steps:

[0009] Step 1: Construct a MIMO integrated air-space-ground secure communication network system. In this system, a legitimate user in an ISUAV is equipped with a high-gain antenna and faces a potential threat of eavesdropping on the GEO satellite network. In the considered NTN system, the ISUAVN employs a cell-free massive MIMO network to improve the spectral efficiency of ground users. The ISUAVN shares millimeter-wave spectrum with the GEO satellite multicast downlink communication link. There are a total of K cell-free UAV user TUs.

[0010] The signals received by the k-th ground user TU are respectively

[0011]

[0012] Where K represents the number of UAV users without cells, M is the number of UAV access points (UAPs) in the UAV without cells network, and x m Let s be the signal transmitted by the m-th UAP in downlink transmission. k This represents the data signal of the k-th ground user TU. This indicates that the noise energy of the k-th ground user during the downlink data transmission phase is... w mk Let represent the downlink precoding vector of the m-th UAP to the k-th ground user during the downlink data transmission phase in a UAV-less cell network. Let e ​​represent the set of all TUs. For the sake of brevity, we designate the Kth user as the eTU for eavesdropping on ground users. The channel expression for the k-th TU estimated by the m-th UAP is:

[0013]

[0014] Where τ p The pilot length for uplink training. For the pilot sequence assigned to the k-th TU in the NTN network, ρ TU This represents the signal-to-noise ratio of pilot transmission for ground users during the uplink pilot estimation phase. This represents the noise energy of the m-th ground base station during the uplink pilot estimation phase. This represents the user set that shares the pilot signal with the k-th TU. This represents the signal received by the m-th UAP during the uplink pilot training process. For the noise of the m-th UAP in the uplink pilot training, each element has Since the GEO satellite signal energy is relatively weak for UAV cellless networks, its downlink interference to the UAV cellless network is ignored in the modeling. Therefore, the TU signal-to-noise ratio is as follows:

[0015]

[0016] The data rate of this TU is written as

[0017] The signals received at the l ground stations ES are

[0018]

[0019] Where L represents the number of ground stations. h represents the set of ground stations. l This represents the channel between the GEO satellite and the l-th ground station. This indicates that the noise energy of the l-th ground station during the downlink data transmission phase is... v s This represents the precoding vector of the GEO satellite downlink. This indicates that the channel between the m-th UAP and the l-th ground station is...

[0020]

[0021] Where ρ sat This represents the pilot transmission signal-to-noise ratio of the ground station during the uplink pilot estimation phase. The pilot sequence allocated to the l-th ES by the NTN network. The received signal-to-noise ratio of the l-th ground station is obtained from the above formula.

[0022]

[0023] Therefore, its received data rate is written as

[0024] Analyze the data rate and eavesdropping rate of ground user eTUs, and let h k This represents the channel between the GEO satellite and the k-th ground user. Since the NTN network lacks precise channel information between the GEO satellite and the TU, modeling the channel between the GEO satellite and the k-th ground user is necessary. in Δ represents the channel estimate of the TU by the GEO satellite. k This represents the channel estimation error, which has an upper limit ||Δ k ||≤ε k The Kth TU is then called the eTU, which is equipped with a satellite antenna to receive GEO satellite signals. The signal received during the downlink transmission phase is represented as...

[0025]

[0026] in: Let Δ be the estimated channel value of the GEO satellite for the k-th ground user. k Let represent the estimation error of the channel for the k-th ground user by the GEO satellite. Then, the signal-to-noise ratio (SNR) of the downlink data for that user and the SNR of the GEO satellite signal are written as:

[0027]

[0028] The corresponding data rate is then written as R. K =log2(1+γ) K The eavesdropping rate is written as R. e =log2(1+γ) e Then the secure rate of the NTN network is calculated as follows:

[0029] Step 2: By applying the weighted Chebyshev method to balance the two conflicting objectives of minimizing total energy and maximizing secure transmission rate, a multi-objective optimization problem for MIMO integrated air-space-ground secure communication is constructed. Constraints C1 and C2 represent the user's Quality of Service (QoS) requirements, while C3 and C4 are the actual power constraints of the UAP and GEO satellites. This completes the multi-objective optimization problem for MIMO integrated air-space-ground secure communication.

[0030] The optimization problem is shown in the following equation.

[0031]

[0032] in To minimize the overall transmission power objective function, G2(w mk ,v s )=-R s Let Γ represent the objective function that maximizes the safe rate. l This indicates the minimum signal-to-noise ratio requirement for the ground station, Γ k P represents the minimum signal-to-noise ratio requirement for ground users. m P represents the maximum power constraint for base stations in a terrestrial un-cell network. sat This indicates the maximum power constraint for GEO satellites.

[0033] Step 3: For the multi-objective optimization problem of MIMO integrated air-space-ground secure communication, the continuous convex approximation SCA method is applied to transform the complex optimization problem into a convex problem. The worst-case transmission condition for the CFmMIMO NTN system, i.e., the transmission condition that maximizes the eavesdropping rate and minimizes the eTU receiving data rate within the error range of the eavesdropping channel, is written as:

[0034]

[0035] Feasibility points identified from the initialization algorithm based on semidefinite programming (SDP) and We begin by solving the equivalent convex problem using a standard optimization software package, and output the optimal precoding vector. Total power consumption With maximum confidentiality That is, to find the optimal Pareto balance between the two conflicting objective functions of maximizing the secure rate and minimizing the total transmission power in the integrated air-space-ground network, and to realize MIMO integrated air-space-ground secure communication based on the Pareto optimal solution.

[0036] Step 3.1: Input the channel h from the GEO satellite to the ESS l ;CSl estimation from UAPs to TUs CSI estimation from UAPs to ESs The maximum power P of UAPs and GEO satellites m and P sat Minimum Quality of Service (QoS) requirements for ground stations and ground users. l ,Γ k eTU eavesdropping channel estimation and upper limit of error ε K Predefined weight variables η1, η2; maximum number of iterations T max ; Tolerance e and t←1.

[0037] Step 3.2: Solve the optimization problem using convex optimization tools to obtain the solution that satisfies the constraints. and

[0038] Find{w k ,w0}

[0039]

[0040] Where N t The number of antennas in the UAP is represented by the channel set. The set of precoding vectors is represented as and This represents the covariance of the channel. Similarly... This represents the covariance matrix of GEO with respect to the ES channel. Let w0 represent the covariance matrix of the estimated eavesdropping channel. To simplify the problem, define w0 = v s To express the BS power constraint as a quadratic constraint problem, new variables are introduced. in By solving this optimization problem using SDP and convex optimization tools, the constraints can be satisfied. and

[0041] Step 3.3: Solve for the optimal value of minimizing the total transmission power. Since this problem is non-convex, the SCA algorithm is used to solve it. The optimization problem is rewritten using the SCA algorithm as follows:

[0042]

[0043] in To obtain the optimal value in j iterations of SCA, the problem is a convex problem in each iteration. Convex optimization tools are used to obtain the optimal solution in that iteration. The algorithm will eventually converge to... The optimal solution to this problem is... Thus, the optimal solution to the problem of minimizing transmission power under these initial conditions is obtained.

[0044] Step 3.4: Solve for the optimal value of maximizing the secure transmission rate. Since this problem is non-convex, the SCA algorithm is used to transform the complex optimization problem into a convex problem.

[0045]

[0046] ||v s || 2 ≤P sat

[0047] Where β,μ, These are auxiliary variables introduced to solve this non-convex problem, and μ (j), To obtain the optimal value in j iterations of SCA, the problem is a convex problem in each iteration. Using convex optimization tools, the optimal solution in that iteration is obtained, and the optimization method eventually converges to... μ opt , At that location, obtained through calculation That is, to obtain the optimal solution to the problem. That is, we obtain the optimal solution to the problem of maximizing the system's security rate under the given initial conditions.

[0048] Step 3.5: Initialize the multi-objective optimization problem based on the optimal solutions to the above two problems and the initial precoding.

[0049]

[0050] Step 3.6: When |α (t) -α (t-1) | 2 ≥e, t≤T max Solve the multi-objective optimization problem in time; otherwise, proceed to step 3.9.

[0051] Since this problem is non-convex, it needs to be solved using the SCA algorithm. The problem can be rewritten using the SCA algorithm as follows:

[0052]

[0053] ||v s || 2 ≤P sat

[0054] Where α,β,μ, This is an auxiliary variable introduced to solve the non-convex problem. A convex optimization tool is used to solve the optimization problem, and α is updated. (t) ,β (t) ,μ (t) , And α (t) ,β (t) ,μ (t) , This represents the optimal result after the t-th SCA iteration.

[0055] Step 3.8 t = t + 1, return to step 3.6.

[0056] Step 3.9: When the multi-objective optimization problem converges, the Pareto optimal solution to the multi-objective optimization problem has been found, and the optimal precoding vector is output. Total power consumption With maximum confidentiality That is, to find the optimal Pareto balance between the two conflicting objective functions of maximizing the secure rate and minimizing the total transmission power in the integrated air-space-ground network, and to realize MIMO integrated air-space-ground secure communication based on the Pareto optimal solution, thereby improving spectrum efficiency and communication security.

[0057] Beneficial effects:

[0058] 1. This invention discloses a multi-objective optimization method for MIMO integrated air-space-ground secure communication. It aims to balance the two conflicting objective functions of maximizing secure rate and minimizing total transmission power. Constraints include service quality requirements for ground stations and ground users, as well as power limitations for GEO satellites and UAV access points. The method constructs a robust precoding optimization problem under conditions of significant errors in the eavesdropping channel. This invention ensures that an integrated air-space-ground NTN system based on a cellless network achieves the optimal Pareto balance between maximizing secure rate and minimizing total transmission power in downlink transmission.

[0059] 2. The multi-objective optimization method for MIMO integrated air-space-ground secure communication disclosed in this invention can not only solve the downlink secure communication problem in CFm-MIMO NTN systems, but also achieve the optimal Pareto balance between minimizing total transmission power and maximizing secret data rate in complex scenarios where legitimate ground users (TUs) may attempt to eavesdrop on GEO satellite network signals, especially in the case of complex scenarios where legitimate ground users (TUs) may attempt to eavesdrop on GEO satellite network signals. By using a joint beamforming design method, it can meet the basic quality of service (QoS) requirements of ground users and satellite users while meeting the basic QoS requirements of both ground users and satellite users.

[0060] 3. This invention discloses a multi-objective optimization method for MIMO integrated air-space-ground secure communication. It employs a weighted Tchebycheff method to transform the originally complex multi-objective optimization problem into a single-objective problem, thus significantly simplifying the optimization solution process. By using the continuous convex approximation SCA method and the CVX optimization software package, the optimal solution to the joint beamforming problem can be quickly obtained. This invention can reduce the total transmission power while ensuring communication quality, thereby optimizing the system's energy efficiency and reliability. Attached Figure Description

[0061] Figure 1 This is a block diagram of a secure communication system structure for a space-air-ground integrated network (NTN) based on MIMO, as described in this invention.

[0062] Figure 2 This is a system topology diagram of a MIMO-based integrated air-space secure communication system described in this invention.

[0063] Figure 3 This is a comparison chart of the performance curves of the method described in this invention for minimizing total transmission power as a function of ground station QoS constraints and that of traditional methods;

[0064] Figure 4 This is a comparison chart of the performance curves of the method described in this invention for maximizing the security rate of eTU and ordinary passive eavesdropping.

[0065] Figure 5 This is a comparison of the performance curves of the method described in this invention in maximizing the security rate as a function of satellite transmission power constraints in an eTU scenario with that of traditional methods;

[0066] Figure 6 This is a comparison of the performance curves of the method described in this invention in the eTU scenario, which maximizes the security rate and minimizes the total transmission power at the Pareto boundary, with the traditional method.

[0067] Figure 7 This is a flowchart of a multi-objective optimization method for MIMO integrated air-space-ground secure communication disclosed in this invention. Detailed Implementation

[0068] Example 1:

[0069] like Figure 7 As shown in the figure, this embodiment discloses a multi-objective optimization method for MIMO integrated air-space-ground secure communication. The specific implementation method is as follows:

[0070] Step 1: Construct a MIMO integrated air-space-ground secure communication network, such as... Figure 2 As shown. In this system, a legitimate user in an unmanned aerial vehicle-based cellless network (ISUAVN) is equipped with a high-gain antenna, posing a potential threat of eavesdropping on the GEO satellite network. In the NTN system under consideration, the ISUAVN employs a cellless massive MIMO network to improve the spectral efficiency of ground users. Simultaneously, the ISUAVN shares millimeter-wave spectrum with the GEO satellite multicast downlink communication link.

[0071] Parameters: Carrier frequency 28GHz, bandwidth 20MHz, number of beams Ns=7, maximum link gain from GEO satellite to ES 52dB, maximum link gain from GEO satellite to eTU 42dB, 3dB angle of GEO satellite beam 0.4°, rain attenuation parameters -3.125 and 1.591, UAP antenna gain 25dB, LOS channel parameters 1.9 and 1.1, NLOS channel parameters 3.4 and 9.7, noise figure 9.79dB. Figure 2The topology of the considered CFmMIMO NTN system is shown, where UAPS, TUS, and ESS are randomly distributed within a 1 km² area. In the demonstrated test simulation environment, six UAPS cooperate to serve five TUs located within this area, one of which is assumed to be an eTU attempting to eavesdrop on the GEO satellite network. Three ESSs are located within this area, served by GEO satellites, requiring the elimination of strong cross-layer interference caused by ISUAVN. Furthermore, the altitude of the Earth observation satellites is considered to be 35,786 km, while the altitudes of UAP, TU, and ESS are set to 200 m, 1.5 m, and 6 m, respectively.

[0072] During downlink transmission, the signals received by the k-th ground user TU are respectively

[0073]

[0074] Where K represents the number of UAV users without cells, M is the number of UAV access points (UAPs) in the UAV without cells network, and x m Let s be the signal transmitted by the m-th UAP in downlink transmission. k This represents the data signal of the k-th ground user (TU). This indicates that the noise energy of the k-th ground user during the downlink data transmission phase is... w mk Let represent the downlink precoding vector of the m-th UAP to the k-th ground user during the downlink data transmission phase in a UAV-less cell network. Denotes the set of all TUs. The specific expression for the channel of the k-th TU estimated by the m-th UAP is as follows:

[0075]

[0076] Where τ p The pilot length for uplink training. For the pilot sequence assigned to the k-th TU in the NTN network, ρ TU This represents the signal-to-noise ratio of pilot transmission for ground users during the uplink pilot estimation phase. This represents the noise energy of the m-th ground base station during the uplink pilot estimation phase. This represents the user set that shares the pilot signal with the k-th TU. This represents the signal received by the m-th UAP during the uplink pilot training process. For the noise of the m-th UAP in the uplink pilot training, each element has Since the GEO satellite signal energy is relatively weak for UAV cellless networks, we can reasonably ignore its downlink interference to the UAV cellless network in the modeling. Therefore, the TU signal-to-noise ratio can be written as:

[0077]

[0078] The data rate of this TU is written as

[0079] The signal received at the l-th ground station (ES) is

[0080]

[0081] Where L represents the number of ground stations. h represents the set of ground stations. l This represents the channel between the GEO satellite and the l-th ground station. This indicates that the noise energy of the l-th ground station during the downlink data transmission phase is... v s This represents the precoding vector of the GEO satellite downlink. The channel from the m-th UAP to the l-th ground station can be written as:

[0082]

[0083] Where ρ sat This represents the pilot transmission signal-to-noise ratio of the ground station during the uplink pilot estimation phase. The pilot sequence assigned to the l-th ES by the NTN network. From the above equation, we can obtain the received signal-to-noise ratio of the l-th ground station.

[0084]

[0085] Therefore, its received data rate is written as

[0086] This leads to the analysis of the data rate and eavesdropping rate of the eTU (eTU), allowing h k This represents the channel between the GEO satellite and the k-th ground user. Since the NTN network lacks precise channel information between the GEO satellite and the TU, modeling the channel between the GEO satellite and the k-th ground user is necessary. in Δ represents the channel estimate of the TU by the GEO satellite. k This represents the channel estimation error, which has an upper limit ||Δ k ||≤ε k Therefore, the assumed Kth TU is the eavesdropping TU, equipped with a special satellite antenna to receive GEO satellite signals. The signal received during the downlink transmission phase is represented as...

[0087]

[0088] in: Let Δ be the estimated channel value of the GEO satellite for the k-th ground user. k Let represent the estimation error of the channel for the k-th ground user by the GEO satellite. Then, the signal-to-noise ratio (SNR) of the downlink data for that user and the SNR of the GEO satellite signal are written as:

[0089]

[0090] The corresponding data rate is then written as R. K =log2(1+γ) K The eavesdropping rate is written as R. e =log2(1+γ) e Then the secure rate of the NTN network can be calculated.

[0091] Step Two: The optimization objective is a non-trivial trade-off design. A multi-objective optimization method is used to balance the conflicting objectives of minimizing total energy and maximizing secure transmission rate. The multi-objective optimization problem is obtained by applying the weighted Chebyshev method. Constraints C1 and C2 represent the user's Quality of Service (QoS) requirements, while C3 and C4 are the actual power constraints of the UAP and GEO satellites. A multi-objective optimization problem for MIMO integrated air-space-ground secure communication is constructed. The optimization problem is shown in the following equation.

[0092]

[0093] in To minimize the overall transmission power objective function, G2(w mk ,v s )=-R s Let Γ represent the objective function that maximizes the safe rate. l This indicates the minimum signal-to-noise ratio requirement for the ground station, Γ k P represents the minimum signal-to-noise ratio requirement for ground users. m P represents the maximum power constraint for base stations in a terrestrial un-cell network. sat This indicates the maximum power constraint for GEO satellites.

[0094] Step 3: For the multi-objective optimization problem of MIMO integrated air-space-ground secure communication, the MOO joint beamforming design problem is a mathematically difficult optimization problem. We first apply the well-known weighted Chebyshev method to transform this MOO problem into a traditional optimization problem, and then apply the Continuous Convex Approximation (SCA) method to transform the complex optimization problem into a convex problem, focusing on the worst-case transmission conditions of the CFmMIMO NTN system under consideration. Subsequently, starting from the feasible points identified by the SDP-based initialization algorithm, we use standard optimization software packages to solve the equivalent convex problem.

[0095] Step 3.1: Input the channel h from the GEO satellite to the ESS l ;CSl estimation from UAPs to TUs CSI estimation from UAPs to ESs The maximum power P of UAPs and GEO satellites m and P sat Predefined weight variables η1, η2; maximum number of iterations T max Tolerance e and t←1

[0096] Step 3.2: Initialization: By solving the problem

[0097] Find{w k ,w0}

[0098]

[0099] Where N t The number of antennas in the UAP is represented by the channel set. The set of precoding vectors is represented as and This represents the covariance of the channel. Similarly... This represents the covariance matrix of GEO with respect to the ES channel. Let w0 represent the covariance matrix of the estimated eavesdropping channel. To simplify the problem, define w0 = v s To express the BS power constraint as a quadratic constraint problem, new variables are introduced. in The optimization problem is solved using convex optimization tools to obtain the solution that satisfies the constraints. and

[0100] Step 3.3: Solve for the optimal value of minimizing the total transmission power. Since this problem is non-convex, we need to use the SCA algorithm to solve it. Using the SCA algorithm, we can rewrite the problem as follows:

[0101]

[0102] ||v s || 2 ≤P sat

[0103] in To obtain the optimal value in j iterations of SCA, the problem is a convex problem in each iteration. Convex optimization tools can be used to obtain the optimal solution in that iteration. Ultimately, the algorithm will converge to... At this point, we obtain the optimal solution to the problem.

[0104] Step 3.4: Solve for the optimal value of maximizing the secure transmission rate. Since this problem is non-convex, we need to use the SCA algorithm to solve it. Using the SCA algorithm, we can rewrite the problem as follows:

[0105]

[0106] ||v s || 2 ≤P sat

[0107] Where β,μ, These are auxiliary variables introduced to solve this non-convex problem, and μ (j) , To obtain the optimal value in j iterations of SCA, the problem is a convex problem in each iteration. Convex optimization tools can be used to obtain the optimal solution in that iteration. Ultimately, the algorithm will converge to... μ opt , At this point, through the improvement of the mouthpiece quality, we calculated that... We have obtained the optimal solution to this problem.

[0108] Step 3.5: Initialize based on the optimal solutions to the above two problems.

[0109]

[0110] Step 3.6: When |α (t) -α (t-1) | 2 ≥e, t≤T max Solve the multi-objective optimization problem in time; otherwise, proceed to step 3.9.

[0111] Since this problem is non-convex, we need to solve it using the SCA algorithm. The problem can be rewritten using the SCA algorithm as follows:

[0112]

[0113] ||v s || 2 ≤P sat

[0114] Where α,β,μ, This is an auxiliary variable introduced to solve the non-convex problem. A convex optimization tool is used to solve the optimization problem, and α is updated. (t) ,β (t) ,μ (t) ,

[0115] Step 3.8 t = t + 1, return to step 3.6.

[0116] Step 3.9: The multi-objective optimization problem has converged, therefore the Pareto optimal solution to the multi-objective optimization problem has been found. Output the optimal precoding vector. Total power consumption With maximum confidentiality

[0117] Figure 3 In equations 4, 5, and 6, δ represents the channel uncertainty level of the eavesdropping channel, defined by the following formula:

[0118]

[0119] The performance of this embodiment under different channel uncertainty levels has been shown in the figure. It can be confirmed that the proposed algorithm can effectively solve the multi-objective optimization problem of MIMO air-space-ground integrated secure communication and can achieve a balance between the optimal secure rate and total transmission power in the considered scenario.

[0120] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-objective optimization method for MIMO integrated air-space-ground secure communication, characterized in that: Comprising the following steps, Step one: build a MIMO space-air-ground integrated secure communication network system; in this system, a LEO satellite integrates a legitimate user of a cell-free unmanned aerial vehicle network ISUAVN equipped with a high-gain antenna, and there is a potential threat of eavesdropping on a GEO satellite network; in the considered NTN system, ISUAVN adopts a cell-free large-scale multiple-input multiple-output network to improve the spectral efficiency of ground users; ISUAVN shares the millimeter wave spectrum with the GEO satellite multicast downlink communication link; there are K UAV cell-free users TU in total; In step one, The signals received by the kth ground user TU are respectively where K denotes the number of UAV-cellular users, M is the number of unmanned aerial access points (UAPs) in the UAV-cellular network, denotes the signal transmitted by the mth UAP in the downlink transmission, denotes the data signal of the kth ground user TU, denotes the noise energy of the kth ground user in the downlink data transmission phase, denotes the downlink precoding vector of the mth UAP to the kth ground user in the downlink data transmission phase of the UAV-cellular network, denotes the set of all TUs, while we designate the kth user as the eavesdropping ground user eTU for brevity of the writing, denotes the channel expression of the kth TU estimated by the mth UAP​ where is the pilot length for uplink training, is the pilot sequence assigned to the k-th TU by the NTN network, denotes the pilot transmission signal-to-noise ratio of the ground users in the uplink pilot estimation phase, denotes the noise energy of the m-th ground base station in the uplink pilot estimation phase, denotes the set of users sharing the pilot with the k-th TU, is the signal received by the m-th UAP in the uplink pilot training process, is the noise of the m-th UAP in the uplink pilot training, each element of which has Since the GEO satellite signal energy is relatively weak for the UAV cell-free network, the downlink interference of the GEO satellite to the UAV cell-free network is ignored in the modeling, and the TU signal-to-noise ratio is as follows The data rate of the TU is written as ; The signal received at the ground station ES is where L is the number of ground stations, denotes a set of ground stations, denotes the channel of the GEO satellite to the mth ground station, denotes the noise energy of the mth ground station in the downlink data transmission phase, denotes the precoding vector of the GEO satellite downlink, denotes the channel of the mth UAP to the mth ground station,​​ wherein denotes the pilot transmission signal-to-noise ratio of the ground station in the uplink pilot estimation phase, is the pilot sequence assigned to the ES by the NTN network; the received signal-to-noise ratio of the ground station is obtained from the above equation The received data rate is written as ; Let denote the channel of the GEO satellite to the kth ground user, model the channel of the GEO satellite to the kth ground user where denote the estimate of the channel of the GEO satellite to the TU, denote the error in the channel estimate, which has an upper bound , is the error upper bound for the eTU eavesdropping channel; Then the Kth TU is the eavesdropping TU, which is equipped with a satellite antenna to receive GEO satellite signals, and the signal received in the downlink transmission phase is represented as where: is the estimate of the GEO satellite's channel to the kth ground user, denotes the estimation error of the GEO satellite's channel to the kth ground user, then the signal-to-noise ratio of the downlink data for this user and the GEO satellite signal-to-noise ratio are written as The corresponding data rate is written as The eavesdropping rate is written as The security rate of the NTN network is calculated as ; Step two: balance the two conflicting objective functions of minimizing the total transmission energy and maximizing the maximum secure transmission rate by applying the weighted Chebyshev method to build a MIMO space-air-ground integrated secure communication multi-objective optimization problem; the constraint conditions C1 and C2 represent the quality of service QoS requirements of users, and C3 and C4 are the realistic power constraints of UAP and GEO satellites, to build a MIMO space-air-ground integrated secure communication multi-objective optimization problem; In step two, The optimization problem is shown in the following formula wherein is an objective function to minimize the overall transmission power, is an objective function to maximize the safety rate, is a minimum signal-to-noise ratio requirement for the ground station, is a minimum signal-to-noise ratio requirement for the ground users, is a maximum power constraint for the base stations in the ground cell-free network, is a maximum power constraint for the GEO satellite; Step three: for the MIMO space-air-ground integrated secure communication multi-objective optimization problem, apply the continuous convex approximation SCA method to convert the complex optimization problem into a convex problem; for the eavesdropping channel uncertainty of the CFmMIMO NTN system, the worst transmission condition is adopted, that is, the transmission condition that maximizes the eavesdropping rate and minimizes the eTU received data rate within the error range of the eavesdropping channel; Feasible points identified from a semidefinite programming (SDP) based initialization algorithm and Initially, a standard optimization package is used to solve the equivalent convex problem, outputting the optimal precoding vector 、 total power consumption and maximum secrecy rate , that is, to find the best Pareto balance between the two conflicting objective functions of maximizing the secure rate and minimizing the total transmission power in the integrated space-air-ground network, and to achieve MIMO integrated space-air-ground secure communication according to the Pareto optimal solution. 2.The MIMO space-air-ground integrated secure communication multi-objective optimization method of claim 1, wherein: In step three, The transmission condition that maximizes the eavesdropping rate and minimizes the eTU received data rate within the error range of the eavesdropping channel is written as 。 3.The MIMO space-air-ground integrated secure communication multi-objective optimization method of claim 1, wherein: The implementation method of step three is Step 3.1: Input GEO satellite to ESs channel ; UAPs to TUs CSl estimates UAPs to ESs CSl estimates Maximum power of UAPs and GEO satellites and Minimum quality of service QoS requirements for ground stations and ground users Estimation of eTU eavesdropping channel and error upper bound Predefined weight variable Maximum number of iterations Tolerance , ​ Step 3.2: Solve the optimization problem by convex optimization tools to get and where denotes the number of antennas of the UAP, the channel set is denoted as , the set of precoding vectors is denoted as and , denotes the covariance of the channel, and similarly denotes the covariance matrix of the GEO-to-ES channel, denotes the covariance matrix of the estimated eavesdropping channel, for simplicity, define , to express the BS power constraint as a quadratic constraint problem, introduce a new variable where , by solving the optimization problem by SDP and convex optimization tools, we can get and that satisfy the constraint conditions. Step 3.3: solve the optimal value of the minimum total transmission power problem, since this problem is a non-convex problem, solve this problem by SCA algorithm, and rewrite the optimization problem by SCA algorithm as where , is the optimal value produced in the jth SCA iteration, which is a convex problem in each iteration of the SCA, the optimal solution in this iteration is obtained using convex optimization tools, and the final algorithm will converge to , , the optimal solution of the problem , which is the optimal solution of the minimum transmit power problem under the initial condition. Step 3.4: solve the optimal value of the maximum secure transmission rate problem, since this problem is a non-convex problem, convert the complex optimization problem into a convex problem by SCA algorithm as where are auxiliary variables introduced to solve the non-convex problem, and , , , is the optimal value generated at the jth SCA iteration, which is a convex problem at each iteration of the SCA, and the optimal solution at the jth iteration is obtained using convex optimization tools. The final optimization method converges to , , , , , i.e., the optimal solution of the problem is obtained to obtain , i.e., the optimal solution of the problem of maximizing the system secrecy rate under the initial condition is obtained. Step 3.5: Initialize the multi-objective optimization problem according to the optimal solution of the two problems above and the initial precoding Step 3.6: Solve the multi-objective optimization problem when , otherwise go to Step 3.9; Since this problem is a non-convex problem, it needs to be solved by SCA algorithm, and the problem is rewritten by SCA algorithm as where are auxiliary variables introduced to solve the non-convex problem, the optimization problem is solved using convex optimization tools, and while denotes the optimal result after the t-th SCA iteration; Step 3.8 , return to step 3.6; Step 3.9: When the multi-objective optimization problem converges, the Pareto optimal solution of the multi-objective optimization problem has been found, and the optimal precoding vector is output 、 , total power consumption and maximum secrecy rate , that is, to find the best Pareto balance between the two conflicting objective functions of maximizing the security rate and minimizing the total transmission power in the space-air-ground integrated network, to realize MIMO space-air-ground integrated secure communication according to the Pareto optimal solution, and to improve spectrum efficiency and communication security.

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