Secure transmission optimization method, system and device of air-ground cooperative communication network and storage medium

Abstract

The invention discloses a secure transmission optimization method, system and device of an air-ground cooperative communication network and a storage medium, and belongs to the technical field of information communication. The method comprises the following steps: acquiring parameter information of a target air-ground cooperative communication network; constructing an air-to-ground transmission channel model and a ground end-to-end transmission channel model according to the parameter information of the air-to-ground cooperative communication network, and obtaining channel errors of the air-to-ground transmission channel model and the ground end-to-end transmission channel model; processing the channel error to obtain air-to-ground transmission robust channel information and ground end-to-end transmission robust channel information; and inputting the air-to-ground transmission robust channel information and the ground end-to-end transmission robust channel information into a pre-constructed transmission optimization model to obtain a secure transmission optimization scheme. According to the method, attacks of an anti-interference machine and an eavesdropping machine are effectively resisted, and the security of air-to-ground downlink data transmission is improved.

Description

Technical Field

[0001] The present invention belongs to the field of information and communication technologies, and particularly relates to a method, system, device, and storage medium for optimizing secure transmission in an air-ground cooperative communication network. Background Art

[0002] A High Altitude Platform (HAP) has the ability to provide seamless network services for space, air, sea, and ground users, can meet the network requirements of future all-domain communications, is considered to have great potential application prospects in future wireless networks, and has been identified by the Third Generation Partnership Project (3GPP) as a 5G radio access platform. The HAP has strong data processing capabilities and payload capabilities, and can deploy a large-scale antenna array to provide fast, reliable, and continuous communication services for the ground network, such as applications like computing, relaying, storage, and positioning, and has been widely studied in academia and industry.

[0003] Due to the inherent openness and broadcast nature of wireless channels, ground nodes in an adversarial communication environment are vulnerable to threats from enemy jammers and eavesdroppers. Jammers reduce the received signals of legitimate nodes by transmitting strong interference signals, causing interruptions in legitimate link communications. The purpose of an eavesdropper is to intercept legitimate data, and when the channel capacity of the eavesdropping link is higher than that of the legitimate link, the information of legitimate nodes will be leaked and eavesdropped. When both jammers and eavesdroppers exist, it is difficult to guarantee the secure transmission performance of air-to-ground downlink data transmission. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method, system, device, and storage medium for optimizing secure transmission in an air-ground cooperative communication network, effectively countering the attacks of jammers and eavesdroppers, and enhancing the security of air-to-ground downlink data transmission.

[0005] The present invention provides the following technical solutions:

[0006] In a first aspect, a method for optimizing secure transmission in an air-ground cooperative communication network is provided, including: obtaining parameter information of a target air-ground cooperative communication network including a high altitude platform, ground nodes, an eavesdropper, and a jammer, where the ground nodes include blocked nodes that cannot directly receive signals sent by the high altitude platform and cooperative nodes for forwarding the signals sent by the high altitude platform to the blocked nodes;

[0007] According to the parameter information of the air-ground cooperative communication network, an air-to-ground transmission channel model and a ground end-to-end transmission channel model are constructed, and channel errors of the air-to-ground transmission channel model and the ground end-to-end transmission channel model are obtained;

[0008] After processing the channel errors, robust channel information for air-to-ground transmission and robust channel information for ground end-to-end transmission are obtained;

[0009] Input the air-to-ground transmission robust channel information and the ground end-to-end transmission robust channel information into a pre-constructed transmission optimization model to obtain a secure transmission optimization scheme;

[0010] Among them, the original optimization problem of the transmission optimization model is to maximize the transmission rate sum of the jammed nodes under the satisfaction of the constraint conditions; the original optimization problem is transformed into an alternating optimization of the air beamforming vector and the anti-jamming coalition, so that the transmission rate sum of the jammed nodes reaches the maximum under the satisfaction of the constraint conditions;

[0011] Among them, the constraint conditions include the cooperative node rate constraint, the eavesdropping link rate constraint, and the lift-off platform transmit power constraint. The air beamforming vector represents the beamforming vector used by the lift-off platform to send signals; the anti-jamming coalition includes several cooperative nodes, and each jammed node corresponds to an anti-jamming coalition.

[0012] As an optional technical solution of the present invention, according to the parameter information of the air-ground cooperative communication network, an air-to-ground transmission channel model and a ground end-to-end transmission channel model are constructed, including:

[0013] The air-to-ground transmission channel model includes a transmission channel model of the lift-off platform to the eavesdropper, which is expressed as:

[0014] ;

[0015] Among them, represents the channel gain vector between the th lift-off platform and the eavesdropper , represents the channel gain when the distance is 1m, represents the distance between the th lift-off platform and the eavesdropper , represents the path loss exponent between the th lift-off platform and the eavesdropper , and respectively represent the number of NLoS paths and the Rice factor, and respectively represent the departure elevation angle of the LoS path and the departure elevation angle of the th NLoS path, and respectively represent the departure azimuth angle of the LoS path and the departure azimuth angle of the th NLoS path, and respectively represent the antenna array responses on one side and the other side of the airborne platform, and are respectively expressed as:

[0016] ;

[0017] ;

[0018] wherein, , represents the antenna spacing on one side of the airborne platform, represents the antenna spacing on the other side of the airborne platform, represents the wavelength, represents the Kronecker product, represents the number of antennas on one side of the airborne platform, represents the number of antennas on the other side of the airborne platform, represents the transpose;

[0019] The ground end-to-end transmission channel model includes the transmission channel model of the jammer to the ground node and the transmission channel model of the eavesdropper to the ground node, and are respectively expressed as:

[0020] ;

[0021] ;

[0022] wherein, represents the jammer and the th ground node represents the eavesdropper and the th ground node represents the jammer and the th ground node represents the eavesdropper and the th ground node represents the jammer and the th ground node represents the eavesdropper and the th ground node and respectively represent the total number of paths and the Rice factor in the ground network, represents the non-line-of-sight component, represents the th path in the ground network.

[0023] As an alternative technical solution of the present invention, the channel error in the transmission channel model of the lifting platform to the eavesdropping machine is expressed as:

[0024] ;

[0025] Wherein, represents the channel error in the transmission channel model of the lifting platform to the eavesdropping machine, and respectively represent the upper and lower bounds of the elevation angle between the th lifting platform and the eavesdropping machine departure, and respectively represent the upper and lower bounds of the azimuth angle between the th lifting platform and the eavesdropping machine departure, represents the set of lifting platforms;

[0026] The channel error in the transmission channel model of the jammer to the ground node is expressed as:

[0027] ;

[0028] Wherein, represents the channel error in the transmission channel model of the jammer to the ground node, and respectively represent the upper and lower bounds of the channel gain between the jammer and the th ground node, represents the set of ground nodes;

[0029] The channel error in the transmission channel model of the eavesdropping machine to the ground node is expressed as:

[0030] ;

[0031] Wherein, represents the channel error in the transmission channel model of the eavesdropping machine to the ground node, and respectively represent the upper and lower bounds of the channel gain between the eavesdropping machine and the th ground node.

[0032] As an alternative technical solution of the present invention, after processing the channel error, the air-to-ground transmission robust channel information and the ground end-to-end transmission robust channel information are obtained, including:

[0033] Through the generalized discretization method, the channel error in the transmission channel model of the lifting platform to the eavesdropping machine in the elevation angle of departure and the azimuth angle of departure are uniformly sampled within the error range, and are respectively expressed as:

[0034] ;

[0035] ;

[0036] wherein, represents the elevation angle of departure of the th sample, represents the th sample of the azimuth angle of departure, and respectively represent the number of sampling points of the elevation angle of departure and the azimuth angle of departure, , ;

[0037] Based on the uniform sampling, the transmission robust channel of the lifting platform to the eavesdropping machine is expressed as:

[0038] ;

[0039] wherein, represents the transmission robust channel vector of the lifting platform to the eavesdropping machine, , represents the channel response vector at , represents the conjugate transpose of ;

[0040] For the channel error in the transmission channel model of the jammer to the ground node and the channel error in the transmission channel model of the eavesdropping machine to the ground node , let , and then obtain the corresponding transmission robust channel.

[0041] As an alternative technical solution of the present invention, the optimization of the air beamforming vector is expressed as:

[0042] ;

[0043] wherein, represents the expression for optimizing the air beamforming vector, represents the objective function for optimizing the air beamforming vector, represents the set of blocking nodes, represents finding the maximum value, denotes the aerial beamforming vector, denotes the transmission rate of the b-th jammer node, expressed as: , denotes the -th elevated platform, and L denotes the total number of elevated platforms, denotes the conjugate transpose of the channel gain vector between the -th elevated platform and the b-th jammer node, denotes the set of cooperative nodes, denotes the binary variable , indicating that this ground node is a cooperative node, indicating that this ground node is a jammer node, denotes the binary variable , denotes the -th cooperative node participating in the cooperative transmission of the -th jammer node, indicating not participating in the cooperative transmission, denotes the power amplification factor of the cooperative node for forwarding, denotes the channel gain between the -th cooperative node and the -th jammer node, denotes the channel gain between the jammer and the -th jammer node, denotes the transmit power of the jammer, denotes the Gaussian white noise received by the jammer node variance of, ; denotes the rate constraint of the cooperative node, denotes the rate of the cooperative node, denotes the minimum rate of the cooperative node, denotes the rate constraint of the eavesdropping link, denotes the rate of the eavesdropping link, denotes the maximum rate of the eavesdropping link, denotes the transmit power constraint of the elevated platform, denotes the transmit power of the elevated platform, denotes the maximum transmit power of the elevated platform, denotes the set of elevated platforms;

[0044] Introduce a number of auxiliary variables to transform the above objective function and the constraint conditions , , into a convex optimization problem; introduce auxiliary variables to transform the objective function as follows:

[0045] ;

[0046] Among them, respectively represent the first auxiliary variable, the second auxiliary variable, and the third auxiliary variable;

[0047] Reference the auxiliary slack variable For the newly added constraint perform conversion to obtain and two constraints, respectively expressed as:

[0048] ;

[0049] ;

[0050] Define as the result of the th iteration of the air beamforming vector By performing a first-order Taylor series expansion in , the newly added constraint in ;

[0051] Convert the newly added constraint to the constraint , expressed as:

[0052] ;

[0053] Among them ;

[0054] Introduce auxiliary variables to convert the constraint to obtain the constraint , respectively expressed as:

[0055] ;

[0056] ;

[0057] ;

[0058] Among them, respectively represent the fourth auxiliary variable and the fifth auxiliary variable, represents the variance of the Gaussian white noise received by the cooperative node of represents the channel gain between the jammer and the th cooperative node, represents the th airborne platform and the th cooperative node's channel gain vector Conjugate transpose;

[0059] Introduce auxiliary variables for the constraint conditions Perform transformation to obtain the constraint conditions , which are respectively expressed as:

[0060] ;

[0061] ;

[0062] Among them, represents the sixth auxiliary variable, represents the conjugate transpose of the channel gain vector between the th lift-off platform and the eavesdropping machine, represents the eavesdropping machine receiving Gaussian white noise variance;

[0063] Perform a first-order Taylor series expansion on the constraint condition to obtain :

[0064] ;

[0065] Among them, represents the sixth auxiliary variable the th iteration result;

[0066] Finally, the objective function and constraint conditions for optimizing the aerial beamforming vector are transformed into:

[0067] .

[0068] As an alternative technical solution of the present invention, the optimization of the anti-jamming coalition is expressed as:

[0069] ;

[0070] Among them, represents the expression for optimizing the anti-jamming coalition, represents the objective function for optimizing the anti-jamming coalition, represents the anti-jamming coalition corresponding to the bth blocking node, represents the th anti-jamming coalition corresponding to the blocking node, represents the set of cooperative nodes and the set of blocking nodes have no intersection, represents that each cooperative node can only join one anti-jamming coalition;

[0071] In the initial anti-interference alliance, all cooperative nodes randomly select blocked nodes to relay information, forming several initial anti-interference alliances;

[0072] Any collaboration node The current initial anti-interference alliance is , calculate the initial anti-interference coalition The utility function , expressed as:

[0073] ;

[0074] in, Represents the initial anti-interference alliance Except for the collaboration node Other collaborative nodes give The transmission rate brought by the blocked nodes is Indicates The transmission rate of the blocked nodes;

[0075] The collaboration node Randomly select another blocking node b and calculate the anti-interference coalition of the blocking node b The utility function , expressed as:

[0076] ;

[0077] in, Anti-interference alliance Except for the collaboration node The transmission rate brought by other cooperative nodes to the b-th blocked node is represents the transmission rate of the bth blocked node, ;

[0078] Comparison of initial anti-interference alliances The utility function and Anti-Interference Alliance The utility function ,like , then the collaboration node Leaving the old alliance Join a new alliance ;

[0079] Until all the cooperative nodes no longer undergo alliance transformation, the current iteration optimization of the anti-interference alliance is completed, and the nth iteration result of the anti-interference alliance is expressed as .

[0080] As an alternative technical solution of the present invention, in each round of iterative optimization, the optimization of the aerial beamforming vector and the optimization of the anti-jamming coalition are alternately performed, including:

[0081] Obtain the th iteration result of the anti-jamming coalition generated by the transmission optimization model , and perform the nth iteration optimization on the aerial beamforming vector based on the transformed objective function and constraint conditions. The nth iteration result of the aerial beamforming vector is expressed as ;

[0082] Calculate the received signal-to-noise ratio of the ground node, expressed as:

[0083] ;

[0084] Wherein, represents the received signal-to-noise ratio of the rd ground node, represents the conjugate transpose of the channel gain vector between the th airborne platform and the th ground node, represents the channel gain between the jammer and the rd ground node, represents the variance of the Gaussian white noise received by the ground node;

[0085] If the received signal-to-noise ratio of the th ground node is greater than or equal to the received signal-to-noise ratio threshold , then the th ground node is used as a cooperative node, otherwise the th ground node is used as a blocking node, and the cooperative node set and the blocking node set are updated;

[0086] After the nth iteration optimization of the aerial beamforming vector is completed, based on the updated cooperative node set , the blocking node set and the nth iteration result of the aerial beamforming vector, perform the nth iteration optimization on the anti-jamming coalition to obtain the nth iteration result of the anti-jamming coalition;

[0087] Recalculate the received signal-to-noise ratio of all ground nodes and compare it with the received signal-to-noise ratio threshold , and update the cooperative node set and the blocking node set again;

[0088] The n-th iterative optimization of the anti-interference coalition is completed, and the air beamforming vector and the n-th iterative optimization of the anti-interference coalition are carried out until the number of iterations reaches the set maximum number of iterations . The result of the last iterative optimization of the air beamforming vector is used as the optimal air beamforming vector . The result of the last iterative optimization of the anti-interference coalition is used as the optimal anti-interference coalition .

[0089] In a second aspect, a secure transmission optimization system for an air-ground cooperative communication network is provided, including: a parameter acquisition module for acquiring parameter information of a target air-ground cooperative communication network including a lifting platform, a ground node, an eavesdropper, and a jammer, where the ground node includes a blocking node that cannot directly receive the signal sent by the lifting platform and a cooperative node for forwarding the signal sent by the lifting platform to the blocking node;

[0090] A channel model construction module for constructing an air-to-ground transmission channel model and a ground end-to-end transmission channel model according to the parameter information of the air-ground cooperative communication network, and obtaining channel errors of the air-to-ground transmission channel model and the ground end-to-end transmission channel model;

[0091] An error processing module for processing the channel errors to obtain air-to-ground transmission robust channel information and ground end-to-end transmission robust channel information;

[0092] A scheme generation module for inputting the air-to-ground transmission robust channel information and the ground end-to-end transmission robust channel information into a pre-constructed transmission optimization model to obtain a secure transmission optimization scheme;

[0093] Among them, the original optimization problem of the transmission optimization model is to maximize the transmission rate sum of the blocking nodes under the satisfaction of constraint conditions; the original optimization problem is converted into an alternating optimization of the air beamforming vector and the anti-interference coalition, so that the transmission rate sum of the blocking nodes reaches the maximum under the satisfaction of constraint conditions;

[0094] Among them, the constraint conditions include a cooperative node rate constraint, an eavesdropping link rate constraint, and a lifting platform transmit power constraint, and the air beamforming vector represents the beamforming vector used by the lifting platform to send signals; the anti-interference coalition includes a number of cooperative nodes, and each blocking node corresponds to an anti-interference coalition.

[0095] In a third aspect, a secure transmission optimization device for an air-ground cooperative communication network is provided, including a processor and a storage medium;

[0096] The storage medium is used for storing instructions;

[0097] The processor is used to operate according to the instructions to execute the steps of the secure transmission optimization method for the air-ground cooperative communication network described in the first aspect.

[0098] In a fourth aspect, a computer-readable storage medium is provided, on which a computer program is stored. The program, when executed by a processor, implements the steps of the secure transmission optimization method for the air-ground cooperative communication network described in the first aspect.

[0099] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0100] A secure transmission optimization method for an air-ground cooperative communication network provided by the present invention reduces the information leakage in the direction of the eavesdropper by optimizing the air beamforming vector, and at the same time optimizes the anti-jamming coalition, effectively resisting the attack of the jammer, and significantly improving the transmission security in the air-ground cooperative network; under the condition of meeting the constraints, the sum of the transmission rates of the blocking nodes is maximized, and the resources of the air-ground cooperative network can be utilized more effectively, significantly improving the transmission performance of the blocking nodes. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] Figure 1 is a schematic diagram of the system structure of the air-ground cooperative communication network in an embodiment of the present invention;

[0102] Figure 2 is a flowchart of the secure transmission optimization method for the air-ground cooperative communication network in an embodiment of the present invention;

[0103] Figure 3 is a performance comparison diagram of the coalition formation algorithm under different coalition preference criteria in an embodiment of the present invention;

[0104] Figure 4 is a relationship diagram between the sum of the blocking node rates and the number of HAP antennas in an embodiment of the present invention;

[0105] Figure 5 is a relationship diagram between the sum of the blocking node rates and the transmission power of the jammer in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0106] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention, and should not be used to limit the protection scope of the present invention.

[0107] Embodiment 1

[0108] As Figure 1 shown, a transmission system model of an air-ground cooperative communication network in a complex electromagnetic environment is given, in which a high-altitude platform (HAP) transmitter carrying a uniform planar array (UPA) sends signals to A single-antenna node broadcasts data information, where the set of aerial HAPs and the set of ground nodes are denoted as and . The th HAP and the th ground node's coordinates are denoted as and , where is the fixed flight altitude of the HAP. The number of antennas on each side of the HAP antenna is and , so the total number of antennas of the UPA is . While the HAP is broadcasting data downlink, there are two single-antenna malicious attack devices simultaneously, namely the passive eavesdropper and the active jammer . When the eavesdropper can obtain sufficient legal information, it can eavesdrop on the broadcast signal from the HAP; the jammer reduces the received signal-to-noise ratio by sending interference signals. The full-band strong interference suppression of the jammer will cause a sharp decline in the data transmission quality of some nodes, resulting in some ground nodes being unable to receive the broadcast signal normally. These ground nodes are denoted as blocked nodes. Due to the path loss and fading in the interference link, the power-limited jammer cannot block the signal reception of all ground nodes. Therefore, the ground nodes that can normally demodulate and receive the broadcast signal from the aerial HAP are denoted as cooperative nodes. The cooperative nodes act as ground relays to form an anti-jamming alliance to transmit information for the severely disturbed blocked nodes, thereby improving the reception performance of the blocked nodes. The cooperative nodes can distribute the information from the HAP to the severely disturbed blocked nodes through D2D links to form an anti-jamming subnetwork. When forming the anti-jamming subnetwork, it is necessary to consider the impact of the eavesdropper on the transmission security performance and prevent the leakage of relayed forwarding information. It is assumed that both the jammer and the eavesdropper are equipped with omnidirectional antennas to interfere with and eavesdrop on nodes in all directions.

[0109] Based on the above air-ground cooperative communication network, this embodiment provides a security transmission optimization method for an air-ground cooperative communication network. As Figure 2 shown, it specifically includes the following steps:

[0110] Step 1: Obtain the parameter information of the target air-ground cooperative communication network including the lifting platform, ground nodes, eavesdroppers, and jammers. The ground nodes include blocked nodes that cannot directly receive the signals sent by the lifting platform and cooperative nodes that are used to forward the signals sent by the lifting platform to the blocked nodes.

[0111] The parameter information of the target air-ground cooperative communication network includes the flight altitude of the HAP, antenna array parameters (such as the number of antennas, antenna spacing, wavelength, etc.), the location information of ground nodes, jammers and eavesdroppers, path loss index, Rice factor, and upper and lower bounds of channel gain.

[0112] Step 2: According to the parameter information of the air-ground cooperative communication network, an air-to-ground transmission channel model and a ground end-to-end transmission channel model are constructed, and channel errors of the air-to-ground transmission channel model and the ground end-to-end transmission channel model are obtained.

[0113] In the air-ground cooperative communication network, there are two types of channel models, namely the air-to-ground transmission channel model and the ground end-to-end transmission channel model.

[0114] (1) The air-to-ground transmission channel model includes the transmission channel model from the launch platform to the eavesdropping machine and the transmission channel model from the launch platform to the ground node.

[0115] The transmission channel model from the launch platform to the eavesdropping machine is expressed as:

[0116] ;

[0117] in, Indicates A launch platform and a bug The channel gain vector between , N represents the total number of antennas, Indicates the channel gain when the distance is 1m, Indicates A launch platform and a bug The distance between , eavesdropping machine The coordinates of , Indicates A launch platform and a bug The path loss exponent between and denote the number of NLoS paths and the Rice factor, respectively. and denote the departure elevation angle and the first The departure elevation angle of the NLoS path, and denote the departure azimuth and the first The departure azimuth of the NLoS path, and They represent the antenna array response on one side of the launch platform and the antenna array response on the other side, respectively:

[0118] ;

[0119] ;

[0120] Among them, , represents the antenna spacing on one side of the airborne platform, represents the antenna spacing on the other side of the airborne platform, represents the wavelength, represents the Kronecker product, represents the number of antennas on one side of the airborne platform, represents the number of antennas on the other side of the airborne platform, represents the transpose.

[0121] The transmission channel model of the airborne platform to the ground node is expressed as:

[0122] ;

[0123] Among them, represents the th airborne platform and the , represents the th airborne platform and the , represents the th airborne platform and the

[0124] (2) The ground end-to-end transmission channel model includes the transmission channel model of the jammer to the ground node, the transmission channel model of the eavesdropper to the ground node, and the transmission channel model of the cooperative node to the blocking node.

[0125] The transmission channel model of the jammer to the ground node is expressed as:

[0126] ;

[0127] The transmission channel model of the eavesdropper to the ground node is expressed as:

[0128] ;

[0129] The transmission channel model of the cooperative node to the blocking node is expressed as:

[0130] ;

[0131] Among them, Denote the jammer The channel gain vector between the jammer and the th ground node, Denote the eavesdropper The channel gain vector between the eavesdropper and the th ground node, Denote the cooperative node The channel gain vector between the cooperative node and the blocking node ; Denote the jammer The communication distance between the jammer and the th ground node, Denote the eavesdropper The communication distance between the eavesdropper and the th ground node, Denote the cooperative node The communication distance between the cooperative node and the blocking node ; Denote the jammer The path loss exponent between the jammer and the th ground node, Denote the eavesdropper The path loss exponent between the eavesdropper and the th ground node, Denote the cooperative node The path loss exponent between the cooperative node and the blocking node ; And respectively represent the total number of paths and the Rice factor in the ground network, Denote the non-line-of-sight component, which follows , Denote the th path in the ground network.

[0132] For the legitimate communication link (the solid line link in Figure 1 ), , It can be accurately obtained throughout the transmission process. However, since there is no cooperation between the eavesdropper and the jammer and the ground nodes, it is difficult to obtain the channel state information of the interference channel and the eavesdropping channel through estimation or prediction. By measuring the interference signal and the power leakage signal of the local oscillator of the eavesdropper, the relative positions of the jammer and the ground eavesdropper and the legitimate transmitter can be roughly obtained, but there is a certain estimation error.

[0133] (1) The channel error in the transmission channel model of the elevated platform to the eavesdropper is expressed as:

[0134] ;

[0135] Where Denote the channel error in the transmission channel model of the elevated platform to the eavesdropper, and respectively denote the upper and lower bounds of the elevation angle of departure between the th elevated platform and the eavesdropper, and and respectively denote the upper and lower bounds of the azimuth angle of departure between the th elevated platform and the eavesdropper, and denotes the set of elevated platforms.

[0136] (2) The channel error in the transmission channel model of the jammer to the ground node is expressed as:

[0137] ;

[0138] wherein, denotes the channel error in the transmission channel model of the jammer to the ground node, and respectively denote the upper and lower bounds of the channel gain between the jammer and the th ground node, and

[0139] denotes the set of ground nodes.

[0140] ;

[0141] wherein, denotes the channel error in the transmission channel model of the eavesdropper to the ground node, and respectively denote the upper and lower bounds of the channel gain between the eavesdropper and the th ground node.

[0142] Step 3: After processing the channel error, obtain the robust channel information for air-to-ground transmission and the robust channel information for ground end-to-end transmission.

[0143] From the perspective of countering jamming and eavesdropping, under the condition of channel error, jointly optimize the aerial beamforming vector and the anti-jamming coalition , and maximize the sum of the blocked node rates under the conditions of satisfying the rate constraints of the cooperative nodes, the rate constraints of the eavesdropping links, and the transmit power constraints of the elevated platforms. Therefore, the original optimization problem is expressed as:

[0144] ;

[0145] Among them, represents the original optimization problem, represents minimizing, and respectively represent the rate constraints of the legitimate link and the eavesdropping link, represents the transmit power constraint of the aerial platform, represents that the set of cooperative nodes and the set of jammer nodes cannot overlap, represents that each cooperative node can only relay data to one jammer node via unicast at most.

[0146] Due to the influence of the channel error the original optimization problem has infinite non-convexity and is processed by the generalized discretization method.

[0147] (1) For the channel error in the transmission channel model of the aerial platform to the eavesdropper, the elevation angle of departure and the azimuth angle of departure

[0148] are uniformly sampled within the error range and are respectively expressed as:

[0149] ;

[0150] Among them, represents the th sampled elevation angle of departure, represents the th sampled azimuth angle of departure, and respectively represent the number of sampling points of the elevation angle of departure and the azimuth angle of departure, , .

[0151] Based on the uniform sampling, the transmission robust channel of the aerial platform to the eavesdropper is expressed as:

[0152] ;

[0153] Among them, represents the transmission robust channel vector of the aerial platform to the eavesdropper, , represents at the channel response vector, represents the conjugate transpose of .

[0154] After discretization, in the original optimization problem can be removed.

[0155] (2) For the channel error in the transmission channel model of the jammer to the ground node and the channel error in the transmission channel model of the eavesdropper to the ground node , let , After that, the corresponding transmission robust channel is obtained. At this time, the transmission rates of the interference link and the eavesdropping link are the largest, which can ensure that the objective function is maximized under any possible channel error conditions.

[0156] After processing the channel error, and in the original optimization problem can be removed, which can effectively improve the robustness of the air beamforming and cooperative transmission.

[0157] Step 4: Input the air-to-ground transmission robust channel information and the ground end-to-end transmission robust channel information into the pre-constructed transmission optimization model to obtain a secure transmission optimization scheme.

[0158] Among them, the original optimization problem of the transmission optimization model is to maximize the sum of the transmission rates of the blocked nodes under the satisfaction of the constraint conditions; the original optimization problem is converted into the alternating optimization of the air beamforming vector and the anti-jamming coalition, so that the sum of the transmission rates of the blocked nodes reaches the maximum under the satisfaction of the constraint conditions. The constraint conditions include the cooperative node rate constraint, the eavesdropping link rate constraint, and the launch power constraint of the airborne platform.

[0159] Decouple the original optimization problem into two optimization sub-problems respectively for the air beamforming vector and the anti-jamming coalition . They are respectively: Sub-problem 1: Optimize the air beamforming vector under the given anti-jamming coalition. Sub-problem 2: Optimize the anti-jamming coalition given the air beamforming vector. Among them, the air beamforming vector represents the beamforming vector used by the airborne platform to send signals; the anti-jamming coalition includes several cooperative nodes, which are used to forward the signals sent by the airborne platform to the blocked nodes, and each blocked node corresponds to an anti-jamming coalition.

[0160] (1) Given the anti-jamming coalition, the optimization of the air beamforming vector is expressed as:

[0161] ;

[0162] Among them, represents the expression for optimizing the air beamforming vector, represents the objective function for optimizing the air beamforming vector, represents the set of blocked nodes, represents finding the maximum value, denotes the aerial beamforming vector, denotes the transmission rate of the b-th jammer node, expressed as: , denotes the -th elevated platform, and L denotes the total number of elevated platforms, denotes the -th elevated platform and the conjugate transpose of the channel gain vector between the elevated platform and the b-th jammer node, denotes the set of cooperative nodes, denotes the binary variable , indicating that this ground node is a cooperative node, indicating that this ground node is a jammer node, denotes the binary variable , denotes the -th cooperative node participating in the cooperative transmission of the -th jammer node, indicating non-participation in cooperative transmission, denotes the power amplification factor of the cooperative node's forwarding, denotes the -th cooperative node and the -th jammer node's channel gain, denotes the channel gain between the jammer and the -th jammer node, denotes the jammer's transmission power, denotes the jammer node receiving Gaussian white noise variance, ; denotes the rate constraint of the cooperative node, denotes the rate of the cooperative node, denotes the minimum rate of the cooperative node, denotes the rate constraint of the eavesdropping link, denotes the rate of the eavesdropping link, , denotes the maximum rate of the eavesdropping link, denotes the transmission power constraint of the elevated platform, denotes the transmission power of the elevated platform, denotes the maximum transmission power of the elevated platform, denotes the set of elevated platforms.

[0163] Introduce a number of auxiliary variables to transform the above objective function and the constraint conditions 、 、 into a convex optimization problem; introduce auxiliary variables for the objective function Perform the conversion and represent it as:

[0164] ;

[0165] Among them, respectively represent the first auxiliary variable, the second auxiliary variable, and the third auxiliary variable.

[0166] Reference the auxiliary slack variable For the newly added constraint perform the conversion to obtain and two constraints, which are respectively represented as:

[0167] ;

[0168] ;

[0169] Define as the result of the th iteration of the airborne beamforming vector By performing a first-order Taylor series expansion in , the newly added constraint in .

[0170] Convert the newly added constraint to the constraint , which is represented as:

[0171] ;

[0172] Among them .

[0173] Introduce auxiliary variables to convert the constraint to obtain the constraint , which are respectively represented as:

[0174] ;

[0175] ;

[0176] ;

[0177] Among them, respectively represent the fourth auxiliary variable and the fifth auxiliary variable, represents the variance of the Gaussian white noise received by the cooperative node , represents the channel gain between the jammer and the th cooperative node, represents the th airborne platform and the Channel gain vector of conjugate transpose of

[0178] Introduce auxiliary variables for the constraint Perform transformation to obtain the constraint which are respectively expressed as:

[0179] ;

[0180] ;

[0181] where represents the sixth auxiliary variable, represents the conjugate transpose of the channel gain vector between the th airborne platform and the eavesdropper, represents the variance of the Gaussian white noise

[0182] Perform first-order Taylor series expansion on the constraint to obtain :

[0183] ;

[0184] where represents the sixth auxiliary variable the th iteration result.

[0185] Finally, the objective function and constraints for optimizing the airborne beamforming vector are transformed into:

[0186] .

[0187] Therefore, the original non-convex problem of the airborne beamforming vector is transformed into a convex problem, which can be solved by the CVX toolbox in MATLAB to obtain the optimization result of each iteration.

[0188] (2) Given the airborne beamforming vector, optimize the anti-jamming coalition, including:

[0189] Optimizing the anti-jamming coalition is expressed as:

[0190] ;

[0191] where represents the expression for optimizing the anti-jamming coalition, represents the objective function for optimizing the anti-jamming coalition, represents the anti-jamming coalition corresponding to the bth blocking node Indicates the anti-interference coalition corresponding to the th blocking node, Indicates that the set of cooperative nodes and the set of blocking nodes have no intersection, Indicates that each cooperative node can only join one anti-interference coalition;

[0192] In the initial anti-interference coalition, all cooperative nodes randomly select blocking nodes to forward relay information, forming several initial anti-interference coalitions;

[0193] Any cooperative node The current initial anti-interference coalition it belongs to is , calculate the utility function of the initial anti-interference coalition , expressed as: ;

[0194] ;

[0195] Among them, Indicates the transmission rate brought by other cooperative nodes in the initial anti-interference coalition except the cooperative node to the th blocking node, Indicates the transmission rate of the th blocking node;

[0196] The said cooperative node Randomly selects another blocking node b, and calculates the utility function of the anti-interference coalition of the blocking node b, , expressed as:

[0197] ;

[0198] Among them, Indicates the transmission rate brought by other cooperative nodes in the anti-interference coalition except the cooperative node to the bth blocking node, Indicates the transmission rate of the bth blocking node, ;

[0199] Based on the bilateral best criterion, compare the utility function of the initial anti-interference coalition and the utility function of the anti-interference coalition , if , then the cooperative node leaves the old coalition and joins the new coalition ;

[0200] Until no more coalition transformations occur in all the collaborative nodes, the current iterative optimization of the anti-interference coalition is completed, and the nth iteration result of the anti-interference coalition is denoted as .

[0201] Further prove that the increment of the utility function is the same as the increment of the sum of the transmission rates of the blocking nodes:

[0202] Define the potential function as the sum of the transmission rates of all blocking nodes, denoted as:

[0203] ;

[0204] When the collaborative node leaves the coalition , and joins the coalition , the change in the potential function is:

[0205] ;

[0206] Among them, represents all coalitions other than the coalition in all anti-interference coalitions.

[0207] Since the collaborative node changing its coalition selection only affects the transmission rates of the blocking nodes in the new coalition and the old coalition , and does not affect the coalitions other than the coalition and , that is

[0208] ;

[0209] Therefore, the increment of the potential function is denoted as:

[0210] ;

[0211] At the same time, the change in the potential function is denoted as:

[0212] ;

[0213] Therefore, the increase in the potential function is equal to the increase in the coalition formation utility function. If any collaborative node changes its coalition selection to increase its coalition formation utility function, the potential function can increase accordingly.

[0214] (3) In each round of iterative optimization, the optimization of the air beamforming vector and the optimization of the anti-interference coalition are carried out alternately. Specifically as follows:

[0215] Obtain the The result of the n-th iteration , and based on the transformed objective function and constraint conditions, perform the n-th iteration optimization on the aerial beamforming vector. The result of the n-th iteration of the aerial beamforming vector is expressed as .

[0216] Calculate the received signal-to-noise ratio (SNR) of the ground node, which is expressed as:

[0217] ;

[0218] where represents the received SNR of the -th ground node, represents the conjugate transpose of the channel gain vector between the -th airborne platform and the -th ground node, represents the channel gain between the jammer and the -th ground node, represents the variance of the Gaussian white noise received by the ground node.

[0219] If the received SNR of the -th ground node is greater than or equal to the received SNR threshold , then regard the -th ground node as a cooperative node; otherwise, regard the -th ground node as a blocking node, and update the cooperative node set and the blocking node set .

[0220] After the n-th iteration optimization of the aerial beamforming vector is completed, based on the updated cooperative node set , the blocking node set , and the result of the n-th iteration of the aerial beamforming vector , perform the n-th iteration optimization on the anti-jamming coalition to obtain the result of the n-th iteration of the anti-jamming coalition .

[0221] Recalculate the received SNR of all ground nodes and compare it with the received SNR threshold , and update the cooperative node set and the blocking node set again.

[0222] After the n-th iteration optimization of the anti-jamming coalition is completed, perform the (n + 1)-th iteration optimization on the aerial beamforming vector and the anti-jamming coalition until the number of iterations reaches the set maximum number of iterations ​, use the optimization result of the last iteration of the aerial beamforming vector as the optimal aerial beamforming vector , use the optimization result of the last iteration of the anti-jamming coalition as the optimal anti-jamming coalition . The secure transmission optimization scheme includes the optimal aerial beamforming vector and the optimal anti-jamming coalition .

[0223] In this embodiment, the number of iterations and the maximum number of iterations need to be set before the iteration starts and generate an initial feasible solution . .

[0224] Embodiment 2

[0225] Based on Embodiment 1, this embodiment combines three comparison schemes to prove the effectiveness of the method. The three comparison schemes are the beamforming optimization scheme based on SCA, the anti-jamming coalition formation optimization scheme based on CFG, and the random beamforming and relay forwarding scheme.

[0226] As Figure 3 shown, the Pareto criterion has limited ability to improve the sum rate of blocked nodes. Once a cooperative node enters a certain anti-jamming coalition, due to the strict coalition switching conditions under the Pareto criterion, it is difficult for this node to leave the current coalition. When the selfish criterion selects a coalition, it only focuses on the transmission rate of the blocked nodes in the new coalition and ignores the transmission rate of the blocked nodes in other coalitions, which may lead to the improvement of the rate of the blocked nodes in the new coalition while damaging the rate of other blocked nodes. Compared with the other two coalition preference criteria, the bilateral best criterion proposed by this method can obtain the highest sum rate of blocked nodes. This is because the bilateral best criterion considers the sum of the rates of the old and new coalitions, not only relaxes the strict requirements for coalition switching in the Pareto criterion, but also ensures the improvement of the sum rate of blocked nodes.

[0227] As Figure 4 shown, the sum of the rates of blocked nodes in the four schemes increases with the increase of the number of HAP antennas. This is because the increase in the number of antennas can significantly improve the resolution and gain of the spatial beam and can form a stronger beam direction. When a large-scale antenna is deployed at the HAP, as when, the performance of the beamforming optimization scheme based on SCA has been significantly improved and is similar to the performance of the air-ground cooperative joint optimization scheme proposed by this method. This shows that the spatial gain brought by a large number of antennas can effectively improve the secure transmission performance of blocked nodes.

[0228] As Figure 5As shown in the figure, with the increase of the jammer power, the performance of all four schemes decreases. The proposed air-ground cooperative joint optimization scheme in this method effectively improves the transmission rate of the blocked nodes and achieves the purpose of anti-jamming transmission by scheduling the air-ground communication resources, considering the beamforming effect and the formation of anti-jamming coalitions simultaneously, and satisfying the rate constraint of the eavesdropping link. The anti-jamming coalition formation optimization scheme based on CFG and the beamforming optimization scheme based on SCA are limited by the limited number of antennas and transmission power of the HAP and cooperative nodes and cannot counter malicious jamming in the anti-jamming environment, resulting in some blocked nodes unable to meet the rate constraint requirements. In the random beamforming and relay forwarding schemes, the air-ground communication resources are not fully utilized and optimized, so the obtained performance is the worst.

[0229] Embodiment 3

[0230] This embodiment provides a security transmission optimization system for an air-ground cooperative communication network, including:

[0231] A parameter acquisition module, configured to acquire parameter information of a target air-ground cooperative communication network including a lift-off platform, ground nodes, an eavesdropper, and a jammer, where the ground nodes include blocked nodes that cannot directly receive signals sent by the lift-off platform and cooperative nodes for forwarding the signals sent by the lift-off platform to the blocked nodes;

[0232] A channel model construction module, configured to construct an air-to-ground transmission channel model and a ground end-to-end transmission channel model according to the parameter information of the air-ground cooperative communication network, and acquire channel errors of the air-to-ground transmission channel model and the ground end-to-end transmission channel model;

[0233] An error processing module, configured to process the channel errors to obtain air-to-ground transmission robust channel information and ground end-to-end transmission robust channel information;

[0234] A scheme generation module, configured to input the air-to-ground transmission robust channel information and the ground end-to-end transmission robust channel information into a pre-constructed transmission optimization model to obtain a security transmission optimization scheme;

[0235] Among them, the original optimization problem of the transmission optimization model is to maximize the transmission rate sum of the blocked nodes under the satisfaction of constraint conditions; the original optimization problem is converted into an alternative optimization of the air beamforming vector and the anti-jamming coalition, so that the transmission rate sum of the blocked nodes reaches the maximum under the satisfaction of constraint conditions;

[0236] Among them, the constraint conditions include the rate constraint of the cooperative nodes, the rate constraint of the eavesdropping link, and the transmit power constraint of the lift-off platform, and the air beamforming vector represents the beamforming vector used by the lift-off platform to send signals; the anti-jamming coalition includes several cooperative nodes, and each blocked node corresponds to an anti-jamming coalition.

[0237] Example 4

[0238] This embodiment provides a security transmission optimization device for an air-ground collaborative communication network, including a processor and a storage medium; the storage medium is used to store instructions; the processor is used to operate according to the instructions to execute the steps of the security transmission optimization method for the air-ground collaborative communication network described in Embodiment 1.

[0239] Example 5

[0240] This embodiment provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, it implements the steps of the security transmission optimization method for the air-ground collaborative communication network described in Embodiment 1.

[0241] Those skilled in the art should understand that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0242] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram can be implemented by computer program instructions, and the combination of the flows and / or blocks in the flowchart and / or block diagram can also be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for implementing the specified functions in Figure 1 one or more flows and / or blocks Figure 1 one or more blocks.

[0243] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured product including an instruction device, and the instruction device implements the specified functions in Figure 1 one or more flows and / or blocks Figure 1 one or more blocks.

[0244] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus, so that a series of operation steps are performed on the computer or other programmable apparatus to generate a computer-implemented process, thereby providing instructions for implementing the process Figure 1 in one process or a plurality of processes and / or boxes Figure 1 steps for the functions specified in one box or a plurality of boxes.

[0245] The above are only the preferred embodiments of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. A method for optimizing secure transmission of an air-ground collaborative communication network, characterized in that: include: Acquiring parameter information of a target air-to-ground collaborative communication network including an aerial platform, ground nodes, eavesdropping machines, and jammers, wherein the ground nodes include blocking nodes that cannot directly receive signals sent by the aerial platform and collaborative nodes for forwarding signals sent by the aerial platform to the blocking nodes; According to the parameter information of the air-to-ground cooperative communication network, an air-to-ground transmission channel model and a ground end-to-end transmission channel model are constructed, and channel errors of the air-to-ground transmission channel model and the ground end-to-end transmission channel model are obtained; After processing the channel error, the robust channel information of air-to-ground transmission and the robust channel information of ground end-to-end transmission are obtained; Inputting the air-to-ground transmission robust channel information and the ground end-to-end transmission robust channel information into a pre-built transmission optimization model to obtain a secure transmission optimization solution; The original optimization problem of the transmission optimization model is to maximize the sum of the transmission rates of the blocked nodes while satisfying the constraints. The original optimization problem is converted into an alternating optimization of the air beamforming vector and the anti-interference alliance, so that the sum of the transmission rates of the blocked nodes is maximized while satisfying the constraints. The constraints include cooperative node rate constraints, eavesdropping link rate constraints and launch platform transmission power constraints. The air beamforming vector represents the beamforming vector used by the launch platform to send signals. The anti-interference alliance includes several cooperative nodes, and each blocking node corresponds to an anti-interference alliance.

2. The method for optimizing the secure transmission of an air-ground collaborative communication network according to claim 1, characterized in that: According to the parameter information of the air-ground cooperative communication network, an air-to-ground transmission channel model and a ground end-to-end transmission channel model are constructed, including: The air-to-ground transmission channel model includes the transmission channel model from the launch platform to the eavesdropping machine, which is expressed as: ； in, Indicates A launch platform and a bug The channel gain vector between Indicates the channel gain when the distance is 1m, Indicates A launch platform and a bug The distance between Indicates A launch platform and a bug The path loss exponent between and denote the number of NLoS paths and the Rice factor, respectively. and denote the departure elevation angle and the first The departure elevation angle of the NLoS path, and denote the departure azimuth and the first The departure azimuth of the NLoS path, and They represent the antenna array response on one side of the launch platform and the antenna array response on the other side, respectively: ； ； in, , represents the antenna spacing on one side of the launch platform, Indicates the antenna room on the other side of the launch platform. represents the wavelength, represents the Kronecker product, Indicates the number of antennas on one side of the launch platform, Indicates the number of antennas on the other side of the launch platform, represents transpose; The ground end-to-end transmission channel model includes a transmission channel model of a jammer to a ground node and a transmission channel model of an eavesdropper to a ground node, which are respectively expressed as: ； ； in, Indicates jammer With The channel gain vector between ground nodes is Indicates eavesdropping machine With The channel gain vector between ground nodes is Indicates jammer With The communication distance of the ground nodes is Indicates eavesdropping machine With The communication distance of the ground nodes is Indicates jammer With The path loss index of the ground nodes, Indicates eavesdropping machine With The path loss index of the ground nodes, and denote the total number of paths and the Rice factor in the ground network, respectively. represents the non-line-of-sight component, Indicates the first path.

3. The method for optimizing the secure transmission of an air-ground collaborative communication network according to claim 2, characterized in that: The channel error in the transmission channel model of the launch platform to the eavesdropping machine is expressed as: ； in, represents the channel error in the transmission channel model from the launch platform to the eavesdropping machine, and Respectively represent A launch platform and a bug Departure angle The upper and lower bounds of and Respectively represent A launch platform and a bug Departure angle The upper and lower bounds of Indicates the collection of lift-off platforms; The channel error in the transmission channel model of the jammer to the ground node is expressed as: ； in, represents the channel error in the transmission channel model from the jammer to the ground node, and Represent the jammer and Channel gain between ground nodes The upper and lower bounds of represents the set of ground nodes; The channel error in the transmission channel model of the eavesdropping machine to the ground node is expressed as: ； in, represents the channel error in the transmission channel model from the eavesdropping machine to the ground node, and Respectively represent the eavesdropping machine and Channel gain between ground nodes The upper and lower bounds of .

4. The method for optimizing the secure transmission of an air-ground collaborative communication network according to claim 3 is characterized in that: After processing the channel error, the robust channel information of air-to-ground transmission and the robust channel information of ground end-to-end transmission are obtained, including: The channel error in the transmission channel model of the aerial platform to the eavesdropping machine is calculated by the generalized discretization method. Departure elevation angle and departure azimuth Uniform sampling within the error range is expressed as: ； ； in, Indicates The departure elevation angle of the samples, Indicates The departure azimuth of the samples, and Respectively represent the number of sampling points leaving the elevation angle and leaving the azimuth angle, , ; Based on uniform sampling, the robust transmission channel of the launch platform to the eavesdropping machine is expressed as: ； in, represents the robust channel vector of the transmission from the launch platform to the eavesdropping machine, , Indicated in The channel response vector at Express The conjugate transpose of ; For the channel error in the transmission channel model of the jammer to the ground node Channel error in the transmission channel model from the eavesdropper to the ground node ,make , Then the corresponding transmission robust channel is obtained.

5. The method for optimizing the secure transmission of an air-ground collaborative communication network according to claim 1, characterized in that: The optimization of the aerial beamforming vector is expressed as: ； in, represents the expression for optimizing the aerial beamforming vector, represents the objective function for optimizing the aerial beamforming vector, Represents a set of blocked nodes, It means to find the maximum value, represents the aerial beamforming vector, represents the transmission rate of the bth blocked node, expressed as: , Indicates launch platforms, L represents the total number of launch platforms, Indicates The conjugate transpose of the channel gain vector of the launch platform and the bth blocking node, represents a set of collaborative nodes, Represents a binary variable , Indicates that the ground node is a collaborative node. Indicates that the ground node is a blocking node. Represents a binary variable , Indicates The collaboration nodes participate in The cooperative transmission of blocked nodes, Indicates not to participate in collaborative transmission. represents the forwarding power amplification factor of the cooperative node, Indicates The collaboration node and The channel gain between blocked nodes, Indicates the jammer and The channel gain between blocked nodes, represents the jammer transmit power, Indicates that the blocked node receives Gaussian white noise The variance of ; represents the rate constraint of the cooperative node, represents the rate of cooperative nodes, Indicates the minimum rate of the collaborative node, represents the rate constraint of the eavesdropping link, Indicates the eavesdropping link rate, Indicates the maximum value of the eavesdropping link rate. represents the launch power constraint of the launch platform, Indicates the launch power of the launch platform, Indicates the maximum transmission power of the launch platform, Indicates the collection of lift-off platforms; Introduce several auxiliary variables and transform the above objective function and constraints , , Convert to a convex optimization problem; introduce auxiliary variables to the objective function The conversion is expressed as: ； in, represent the first auxiliary variable, the second auxiliary variable and the third auxiliary variable respectively; Referencing auxiliary slack variables Add new constraints Convert it to get and The two constraints are expressed as: ； ； Will Defined as the air beamforming vector No. The results of the iterations are Perform a first-order Taylor series expansion and add constraints middle ; New constraints will be added Convert to constraints , expressed as: ； in ; Introducing auxiliary variables to constrain conditions Convert and get the constraints , respectively expressed as: ； ； ； in, represent the fourth auxiliary variable and the fifth auxiliary variable respectively, Indicates that the cooperative node receives Gaussian white noise The variance of Indicates the jammer and The channel gain between the cooperating nodes is Indicates The first launch platform and the The channel gain vector of the cooperating nodes The conjugate transpose of ; Introducing auxiliary variables to constrain conditions Convert and get the constraints , respectively expressed as: ； ； in, represents the sixth auxiliary variable, Indicates The conjugate transpose of the channel gain vector between the launch platform and the eavesdropping machine, Indicates that the eavesdropping machine receives Gaussian white noise The variance of For constraints Perform a first-order Taylor series expansion and we get : ； in, Represents the sixth auxiliary variable No. Iteration results; Finally, the objective function and constraints of the air beamforming vector optimization are converted to: 。 6. The method for optimizing secure transmission of an air-ground collaborative communication network according to claim 5, characterized in that: The optimization of the anti-interference alliance is expressed as: ； in, represents the expression for optimizing the anti-interference coalition, represents the objective function to be optimized by the anti-jamming alliance, represents the anti-interference coalition corresponding to the b-th blocked node, Indicates The anti-interference alliance corresponding to the blocked nodes, Represents a collection of collaborative nodes and the set of blocked nodes There is no intersection between them. It means that each collaborative node can only join one anti-interference alliance; In the initial anti-interference alliance, all cooperative nodes randomly select blocked nodes to relay information, forming several initial anti-interference alliances; Any collaboration node The current initial anti-interference alliance is , calculate the initial anti-interference coalition The utility function , expressed as: ； in, Represents the initial anti-interference alliance Except for the collaboration node Other collaborative nodes give The transmission rate brought by the blocked nodes is Indicates The transmission rate of the blocked nodes; The collaboration node Randomly select another blocking node b and calculate the anti-interference coalition of the blocking node b The utility function , expressed as: ； in, Anti-interference alliance Except for the collaboration node The transmission rate brought by other cooperative nodes to the b-th blocked node is represents the transmission rate of the bth blocked node, ; Comparison of initial anti-interference alliances The utility function and Anti-Interference Alliance The utility function ,like , then the collaboration node Leaving the old alliance Join a new alliance ; Until all the cooperative nodes no longer undergo alliance transformation, the current iteration optimization of the anti-interference alliance is completed, and the nth iteration result of the anti-interference alliance is expressed as .

7. The method for optimizing secure transmission of an air-ground collaborative communication network according to claim 6, characterized in that: In each round of iterative optimization, the optimization of the aerial beamforming vector and the optimization of the anti-interference alliance are performed alternately, including: Obtain the first Iteration results , and the air beamforming vector is optimized for the nth iteration based on the converted objective function and constraints. The nth iteration result of the air beamforming vector is expressed as ; The received signal-to-noise ratio of the ground node is calculated and expressed as: ； in, Indicates The received signal-to-noise ratio of the ground node is Indicates The first launch platform and the The conjugate transpose of the channel gain vector of the ground nodes, Indicates the jammer and The channel gain between ground nodes, Represents the variance of Gaussian white noise received by the ground node; Jordi The received signal-to-noise ratio of the ground node Greater than or equal to the receive signal-to-noise ratio threshold , then the The first ground node is used as a collaborative node. ground nodes as blocking nodes and update the set of collaborative nodes and the set of blocked nodes ; After the nth iteration optimization of the aerial beamforming vector is completed, based on the updated cooperative node set , blocking node set And the nth iteration result of the aerial beamforming vector , perform the nth iteration optimization on the anti-interference alliance, and obtain the nth iteration result of the anti-interference alliance ; Recalculate the received signal-to-noise ratio of all ground nodes and compare it with the received signal-to-noise ratio threshold Compare and update the collaboration node set again and the set of blocked nodes ; The nth iteration optimization of the anti-interference alliance is completed, and the air beamforming vector and the anti-interference alliance are optimized. Iterate optimization until the number of iterations reaches the set maximum number of iterations , the last iterative optimization result of the air beamforming vector is taken as the optimal air beamforming vector , the last iterative optimization result of the anti-interference alliance is taken as the optimal anti-interference alliance .

8. A secure transmission optimization system for an air-ground collaborative communication network, characterized in that: include: A parameter acquisition module, used to acquire parameter information of a target air-to-ground collaborative communication network including an aerial platform, ground nodes, eavesdroppers and jammers, wherein the ground nodes include blocking nodes that cannot directly receive signals sent by the aerial platform and collaboration nodes that forward signals sent by the aerial platform to the blocking nodes; A channel model construction module, used to construct an air-to-ground transmission channel model and a ground end-to-end transmission channel model according to parameter information of the air-to-ground cooperative communication network, and obtain channel errors of the air-to-ground transmission channel model and the ground end-to-end transmission channel model; An error processing module, used to process the channel error to obtain robust channel information of air-to-ground transmission and robust channel information of ground end-to-end transmission; A scheme generating module, used for inputting the air-to-ground transmission robust channel information and the ground end-to-end transmission robust channel information into a pre-built transmission optimization model to obtain a secure transmission optimization scheme; The original optimization problem of the transmission optimization model is to maximize the sum of the transmission rates of the blocked nodes while satisfying the constraints. The original optimization problem is converted into an alternating optimization of the air beamforming vector and the anti-interference alliance, so that the sum of the transmission rates of the blocked nodes is maximized while satisfying the constraints. The constraints include cooperative node rate constraints, eavesdropping link rate constraints and launch platform transmission power constraints. The air beamforming vector represents the beamforming vector used by the launch platform to send signals. The anti-interference alliance includes several cooperative nodes, and each blocking node corresponds to an anti-interference alliance.

9. A secure transmission optimization device for an air-ground collaborative communication network, characterized in that: including processor and storage medium; The storage medium is used to store instructions; The processor is used to operate according to the instructions to execute the steps of the safe transmission optimization method of the air-ground collaborative communication network described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method for optimizing safe transmission of an air-to-ground collaborative communication network described in any one of claims 1 to 7 are implemented.

Images