Secure communication optimization method and device based on Lagrange multiplier method

Abstract

The invention discloses a secure communication optimization method and device based on a Lagrange multiplier method, and the system consists of an unmanned aerial vehicle (UAV) hovering in the air and facilities and equipment on the ground, and comprises a ground base station (BS), cellular user equipment (UC), transmission equipment (DT) and receiving equipment (DR) thereof, and an eavesdropper. The Eavesdropper tries to eavesdrop the content of a transmission link from the DT to the DR, and the UAV serves as a friendly interference node to transmit an interference signal to prevent the Eavesdropper from eavesdropping the content transmitted through the link; secondly, aiming at a safety rate key index for evaluating the safety communication performance, modeling a nonlinear optimization problem in which the safety rate is maximized to be constrained; thirdly, a Lagrange multiplier method is adopted to convert a constrained nonlinear optimization problem into an unconstrained problem, an optimal solution is obtained through solving, and the problem that a non-smooth and non-concave function is difficult to solve is solved; and finally, by jointly optimizing the transmission power of the UAV, the UC and the DT and the position of the UAV, the maximization of the safety rate is realized.

Description

Technical Field

[0001] This invention relates to the field of secure communication, and more specifically to a secure communication optimization method and apparatus based on the Lagrange multiplier method. Background Technology

[0002] In recent years, unmanned aerial vehicles (UAVs), with their advantages of flexibility, convenience, and mobility, have been applied to various emerging applications of wireless communication, playing a crucial role in auxiliary functions. However, with the increasing prevalence of UAVs, communication links are vulnerable to eavesdropping by unauthorized nodes; therefore, secure communication has received growing attention.

[0003] To address these issues, physical layer communication (PLC) is considered a promising defense method for ensuring the confidentiality of wireless communications, with the key metric being the secure rate. However, ensuring PLC security faces challenges due to factors such as the distance and location of drones, power control by eavesdroppers, high time complexity, and non-concave optimization problems, leading to difficulties or even unsolvable solutions. Therefore, it is necessary to introduce a secure communication optimization method based on the Lagrange multiplier method. Summary of the Invention

[0004] This invention aims to address the challenges of ensuring physical layer security, which can be difficult or even impossible to solve due to factors such as the distance and location of drones, power control of eavesdroppers, high time complexity, and non-concave optimization problems. The invention provides a secure communication optimization method and apparatus based on the Lagrange multiplier method.

[0005] The technical solution adopted in this invention is:

[0006] Firstly, a secure communication optimization method based on the Lagrange multiplier method is proposed. Firstly, a UAV-assisted secure communication system is established, comprising at least one hovering UAV, one ground base station (BS), one cellular user equipment (UC), one transmission device (DT), one receiving device (DR), and one eavesdropper. The secure communication rate is first evaluated, transforming the problem of solving this index into a constrained problem. Then, the Lagrange multiplier method is used to solve it, transforming the constrained problem into an unconstrained problem. Finally, the transmission power of the UAV, UC, and DT, as well as the position of the UAV, are jointly optimized to maximize the secure rate.

[0007] The entire system uses an uplink communication method. The communication between the transmission device DT and the receiving device DR adopts a D2D link. The cellular user equipment UC and the ground base station BS use a cellular link. The UAV and the ground base station BS form an interference link. The UAV, cellular user equipment UC and transmission device DT use power to transmit their information.

[0008] Preferably, the problem of finding the optimal safety rate index is transformed into a constrained problem, which is then solved using the Lagrange multiplier method, thus transforming the constrained problem into an unconstrained problem. The method is characterized by the following steps:

[0009] Step 1: Assign initial values ​​to the parameters. , , , , , k represents the number of iterations. ;

[0010] Step 2: By solving (20), we obtain ;

[0011] if , or k > M max Then the algorithm ends.

[0012] Otherwise, the algorithm proceeds to the next step;

[0013] Step 3: From ,get , Proceed to step 2;

[0014] illustrate: , Represents the anti-constraint function;

[0015] When the algorithm finishes solving, the optimal solution R for safe rate is obtained. * The four corresponding variables are

[0016] ( , , , The optimal flight strategy is: when the UAV's position is... The power corresponding to UAV, DT, and UC is , , At that time, the security rate of the entire secure communication system reaches its optimal level.

[0017] Furthermore, by introducing the Lagrange multiplier method, the Lagrange function can be obtained. The system's safe rate can be expressed as ,

[0018] in, Let be the Lagrange coefficient, and M be the penalty factor.

[0019] Furthermore, the most crucial point is to take the partial derivative with respect to P, when... When the minimum value is obtained at point P, we can get: ∇ P F ( P UAV , P DT , P UC , λ , M ) = [ ∂ F () ∂ P UAV , ∂ F () ∂ P DT , ∂ F () ∂ P UC ] T = 0 .

[0020] Furthermore, the Lagrange coefficient The iteration method is as follows:

[0021]

[0022] Among them, M max The maximum value representing the number of iterations;

[0023] The update rule for power P is:

[0024] ;

[0025] Time complexity: Given 4 variables ( , , , The time complexities are respectively , , and , ( , , The smallest change scale is p1, p2, p3, from which we can know: , , Let n represent the number of UAV positions. Using the Lagrange multiplier method, the time complexity is O(n). Where k represents the number of iterations. , , ; can be obtained .

[0026] Secondly, the present invention also provides a communication device, the device comprising: at least one processing unit and at least one storage unit, wherein the storage unit stores program code, and when the program code is executed by the processing unit, the processing unit performs the steps of any of the methods described above.

[0027] Thirdly, the present invention also provides a computer storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0028] Compared with the prior art, the present invention has the following beneficial technical effects:

[0029] In the process of secure communication modeling, the problem of finding the optimal security rate is transformed into a constrained optimization problem;

[0030] The Lagrange multiplier method is used to find the optimal solution, which greatly reduces the computational complexity compared to the traditional exhaustive search method. Compared with other methods, the Lagrange multiplier method effectively solves the dilemma of non-smooth and non-concave optimization. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the secure communication system of the present invention. Detailed Implementation

[0032] The present invention will be further described in detail below with reference to specific embodiments. These descriptions are for explanation purposes only and are not intended to limit the scope of the invention.

[0033] Example 1

[0034] This embodiment provides a secure communication optimization method based on the Lagrange multiplier method. First, a UAV-assisted secure communication system is established; then, the problem of maximizing the secure rate is transformed into a constrained problem; next, the Lagrange multiplier method is used to solve for the optimal solution, transforming the constrained problem into an unconstrained problem; finally, the secure rate is maximized.

[0035] Secure Communication System Model: This secure communication system consists of one hovering unmanned aerial vehicle (UAV) and ground facilities and equipment, including one ground base station (BS), one cellular user equipment (UC), one transmission equipment (DT), one receiving equipment (DR), and one eavesdropper.

[0036] Eavesdropper attempts to eavesdrop on the DT to DR transmission link. UAV, acting as a friendly jamming node, emits jamming signals to prevent Eavesdropper from eavesdropping on the content transmitted through the link.

[0037] The entire system uses an uplink communication method. The communication between DT and DR uses a D2D link, UC and BS use a cellular link, and UAV and BS use an interference link.

[0038] UAV, UC, and DT use electrical power to transmit their information.

[0039] The entire secure communication system can find the optimal secure rate by controlling UAV power, UC power, DT power, and UAV position.

[0040] like Figure 1 As shown.

[0041] Assume that the power of UAV, UC, and DT are expressed as follows: , , .

[0042] Except for the UAV, the positions of all other devices are fixed, and the position coordinates of the UAV are denoted as follows: , i ∈ [ i , ⋯ , n ] .

[0043] The channel gains between UAV→DR, UC→DR, UAV→Eavesdropper, UC→Eavesdropper, UAV→BS, and DT→BS follow an exponential distribution, and the path loss exponents between them are all greater than a fixed value. .

[0044] The optimal reachability of the entire system is the dependent variable. The corresponding independent variable is , , and ,in Represents the signal-to-interference-to-noise ratio. Represents bandwidth.

[0045] In a D2D link,

[0046] Let the corresponding reachability, signal-to-interference-plus-noise ratio, and link interference be denoted as follows: , , ,but It can be represented as:

[0047] (1)

[0048] in, The channel gain between UAV and DR.

[0049] The distance between the UAV and the DR.

[0050] This represents the path loss index for UAVs.

[0051] The channel gain between UC and DR.

[0052] The distance between UC and DR.

[0053] This is the path loss index for D2D links.

[0054] At the same time, there exists This ensures that the entire system can communicate normally.

[0055] It can be represented as:

[0056] (2)

[0057] in, For the channel gain of the D2D link, The distance between DT and DR. This represents the noise power of the D2D link.

[0058] It can be represented as:

[0059] (3)

[0060] In the eavesdropping link,

[0061] Let the corresponding reachability, signal-to-interference-plus-noise ratio, and link interference be denoted as follows: , , ,but It can be represented as:

[0062] (4)

[0063] in, The channel gain between UAV and Eavesdropper.

[0064] The distance between the UAV and the Eavesdropper.

[0065] The channel gain between UC and Eavesdropper.

[0066] The distance between UC and Eavesdropper.

[0067] This represents the path loss index of the eavesdropping link.

[0068] Similarly, there exists This ensures that the entire system can communicate normally.

[0069] It can be represented as:

[0070] (5)

[0071] in, For the channel gain of the eavesdropping link, The distance between DT and Eavesdropper. This represents the noise power of the eavesdropping link.

[0072] It can be represented as:

[0073] (6)

[0074] In cellular links,

[0075] Let the corresponding reachability, signal-to-interference-plus-noise ratio, and link interference be denoted as follows: , , ,but It can be represented as:

[0076] (7)

[0077] in, For the channel gain between UAV and BS, The distance between the UAV and the BS. The channel gain between DT and BS. The distance between DT and BS. This represents the path loss exponent for cellular links. Similarly, there exists... This ensures that the entire system can communicate normally.

[0078] It can be represented as:

[0079] (8)

[0080] in, For the channel gain of the cellular link, The distance between UC and BS. This represents the noise power of the eavesdropping link.

[0081] It can be represented as:

[0082] (9)

[0083] Next, consider the relevant constraints of UAV, DT, UC and other devices.

[0084] (10)

[0085] in, This represents the maximum power of the UAV.

[0086] (11)

[0087] in, This represents the maximum power of DT.

[0088] (12)

[0089] in, This represents the maximum power of UC.

[0090] The reachability between UC and BS should be greater than or equal to a threshold. To ensure that cellular links can maintain normal communication, that is

[0091] (13)

[0092] The candidate location set for UAVs is:

[0093] (14)

[0094] Finally, the system's safe rate can be expressed as:

[0095] <m> max < / m> [ R m − R e ] + s . t .( 10 ),( 11 ),( 12 ),( 13 ),( 14 ). (15)

[0096] in, [ x ] + = max( x , 0 ) .

[0097] When solving formula (15), the following problems will be encountered:

[0098] A) If we use an exhaustive search method to solve this problem, the time complexity will be very high;

[0099] B) [ ⋅ ] + It is a non-smooth function;

[0100] C) The objective function is a non-concave function.

[0101] Non-smooth functions: Equation (15) can be transformed into Equation (16), avoiding... [ ⋅ ] + The operation solves the problem of finding solutions for non-smooth functions.

[0102] The preceding section is the explanatory section of this application, which describes the specific problems encountered in the actual model calculations.

[0103] (16)

[0104] Equation (16) and Equation (15) have the same optimal solution.

[0105] Therefore, the difficulty in solving non-smooth functions can be resolved.

[0106] Non-concave functions: When using the Lagrange multiplier method to solve equation (16), first transform the expression into equation (17).

[0107] (17)

[0108] That is, for each position of the UAV The objective function is transformed into solving for the minimum value min, and the constraints are unified into the form of "≥".

[0109] Then, remember ,

[0110] ,

[0111] ,

[0112] ,

[0113] ,

[0114] ,

[0115] ,

[0116] P = [ P UAV , P DT , P UC ] T .

[0117] Introducing the Lagrange multiplier method, for equation (17), we can obtain the Lagrange function. :

[0118] (18)

[0119] in, Let be the Lagrange coefficient, and M be the penalty factor.

[0120] Assumption P * = [ P UAV * , P DT * , P UC * ] T If the solution to problem (17) is denoted as , then let .

[0121] (19)

[0122] Finding the optimal solution to equation (17) is then transformed into finding the optimal solution to equation (19).

[0123] The most crucial point in solving (19) is to take the partial derivative with respect to P, when When the minimum value is obtained at point P, we can get:

[0124] ∇ P F ( P UAV , P DT , P UC , λ , M ) = [ ∂ F () ∂ P UAV , ∂ F () ∂ P DT , ∂ F () ∂ P UC ] T = 0 (20)

[0125] in,

[0126] (twenty one)

[0127] (twenty two)

[0128] (twenty three)

[0129] (twenty four)

[0130] (25)

[0131] (26)

[0132] (27)

[0133] (28)

[0134] (29)

[0135] (30)

[0136] (31)

[0137] (32)

[0138] Lagrange coefficient The iteration method is as follows:

[0139] (33)

[0140] Among them, M max This represents the maximum number of iterations.

[0141] The update rule for power P is:

[0142] (34)

[0143] (35)

[0144] The detailed steps of the entire Lagrange multiplier method solution are as follows:

[0145] Step 1: Assign initial values ​​to the parameters. , , , , , (Error precision), k represents the number of iterations. ;

[0146] Step 2: By solving (20), we obtain ;

[0147] if , or k > M max Then the algorithm ends.

[0148] Otherwise, the algorithm proceeds to the next step;

[0149] Step 3: From ,get , Proceed to step 2;

[0150] illustrate: , This represents the anti-constraint function.

[0151] When the algorithm finishes solving...

[0152] Obtain the optimal solution R for safe rate * The four corresponding variables are ( , , , The optimal flight strategy is: when the UAV's position is... The power corresponding to UAV, DT, and UC is , , At that time, the security rate of the entire secure communication system reaches its optimal level.

[0153] Therefore, the difficulty in solving non-concave functions can be resolved.

[0154] Time complexity: Given 4 variables ( , , , The time complexities are respectively , , and , ( , , The smallest increments on the scale are p1, p2, and p3. Therefore: , , Let n represent the number of UAV positions, from which we can draw the following conclusions:

[0155] If we use an exhaustive search method to solve this problem, the time complexity is O(n log n). ;

[0156] If the Lagrange multiplier method is used to solve this problem, the time complexity is O(n log n). Where k represents the number of iterations, , , ;

[0157] In summary, we can conclude that .

[0158] Therefore, compared with the exhaustive search method, this method reduces the time complexity.

[0159] Example 2

[0160] This embodiment uses one hovering unmanned aerial vehicle (UAV), one ground base station (BS), one cellular user equipment (UC), one transmission device (DT), one receiving device (DR), and one eavesdropper as an example.

[0161] First, initial values ​​are assigned to each parameter. The coordinates of DR, DT, BS, and UC are (300, 75, -50)m, (200, 200, -75)m, (100, 100, 0)m, and (50, 50, -25)m, respectively, with a bandwidth of 15.5MHz. Power ( , , The maximum values ​​are 800dBm, 500dBm and 1000dBm, respectively, and the corresponding minimum values ​​are all 0dBm. Take 1000dB, ( , , , , , , , All are set to the same value of 5dB. , , , The values ​​are 4, 3, 4, and 4. Take 0.01, Take -0.001, Take -0.01, The value is -0.01. There are 5 candidate positions for the UAV, i.e.

[0162] Serial Number Candidate coordinates <![CDATA[L1]]> (400,50,5) <![CDATA[L2]]> (250,150,4) <![CDATA[L3]]> (190,199,-70) <![CDATA[L4]]> (299,70,-51) <![CDATA[L5]]> (150,60,-21)

[0163] Solve using the Lagrange multiplier method, given the parameters. M, , M maxThe values ​​were assigned to 1, 100, 0.5, 0.0001, and 5000 respectively. The final solution is as follows:

[0164] The optimal flight strategy can be derived from the results in the table above: when the UAV is in... L 1 ,and( , , When the power value is (2.7020, 996.4401, 443.9467), the security rate of the entire secure communication system reaches its maximum, i.e. R * =111.3426.

[0165] Moreover, the time complexity of using the Lagrange multiplier method is O(2+3+2+3+5) = O(15), while the time complexity of using the exhaustive method is O(5*(8000+1)*(10000+1)*(5000+1)) = O(2000850115005), which significantly reduces the time complexity.

[0166] This invention also provides a readable storage medium for performing synchronous communication operations, including program code. When the program code is run on a computing device, the program code is used to cause the computing device to perform the steps of a detection method.

[0167] The present application has been described above with reference to block diagrams and / or flowcharts illustrating methods, apparatus (systems), and / or computer program products according to embodiments of the present application. It should be understood that a block of a block diagram and / or flowchart, as well as combinations of blocks of block diagrams and / or flowcharts, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, and / or other programmable data processing means to produce a machine such that the instructions, executable via the computer processor and / or other programmable data processing means, create methods for implementing the functions / actions specified in the blocks of the block diagrams and / or flowcharts.

[0168] Accordingly, this application can also be implemented using hardware and / or software (including firmware, resident software, microcode, etc.). Furthermore, this application can take the form of a computer program product on a computer-usable or computer-readable storage medium, having computer-usable or computer-readable program code implemented in the medium for use by or in conjunction with an instruction execution system. In the context of this application, a computer-usable or computer-readable medium can be any medium that can contain, store, communicate, transmit, or deliver a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0169] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A secure communication optimization method based on the Lagrange multiplier method, firstly establishing a UAV-assisted secure communication system, the system comprising at least one hovering UAV, one ground base station (BS), one cellular user equipment (UC), one transmission device (DT), one receiving device (DR), and one eavesdropper; characterized in that, First, the secure communication rate is evaluated, transforming the problem of solving this index into a constrained problem. Then, the Lagrange multiplier method is used to solve the problem, transforming the constrained problem into an unconstrained problem. Finally, the transmission power of the UAV, cellular user equipment (UC), and transmission equipment (DT), as well as the location of the UAV, are jointly optimized to maximize the secure rate. The entire system uses an uplink communication method. The communication between the transmission device DT and the receiving device DR adopts a D2D link. The cellular user equipment UC and the ground base station BS use a cellular link. The UAV and the ground base station BS form an interference link. The UAV, cellular user equipment UC and transmission device DT use power to transmit their information.

2. The secure communication optimization method based on the Lagrange multiplier method according to claim 1 transforms the problem of solving the optimal security rate index into a constrained problem, and uses the Lagrange multiplier method to solve it, thus transforming the constrained problem into an unconstrained problem, characterized in that... Specifically, the steps include the following: Step 1: Assign initial values ​​to the parameters. , , , , , , k Represents the number of iterations. ; Step 2: Solve ,get ; if ,or k > M max Then the algorithm ends. Otherwise, the algorithm proceeds to the next step; Step 3: From ,get , Proceed to step 2; illustrate: , Represents the anti-constraint function; When the algorithm finishes solving, the optimal solution for safe speed is obtained. R * The four corresponding variables are ( , , , The optimal flight strategy is: when the UAV's position is... The power corresponding to UAV, DT, and UC is , , At that time, the security rate of the entire secure communication system reaches its optimal level.

3. The secure communication optimization method based on the Lagrange multiplier method according to claim 2, characterized in that: By introducing the method of Lagrange multipliers, the Lagrange function can be obtained. The system's safe rate can be expressed as , in, For Lagrange coefficients, M As a penalty factor.

4. The secure communication optimization method based on the Lagrange multiplier method according to claim 2, characterized in that: Take the partial derivative with respect to P, when When the minimum value is obtained at point P, we can get: .

5. The secure communication optimization method based on the Lagrange multiplier method according to claim 2, characterized in that: Lagrange coefficient The iteration method is as follows: in, M max The maximum value representing the number of iterations; The update rule for power P is: ; ， Time complexity: 4 variables ( , , , The time complexities are respectively , , and , ( , , The smallest scale increment is p 1 , p 2 , p 3 Therefore, we can conclude that: , , , n The number of UAV positions is represented by the Lagrange multiplier method, which is used to solve for the time complexity. Where k represents the number of iterations. , , ; can be obtained .

6. A communication device, characterized in that, The apparatus includes at least one processing unit and at least one storage unit, wherein the storage unit stores program code that, when executed by the processing unit, causes the processing unit to perform the steps of the method according to any one of claims 1 to 5.

7. A computer storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1 to 5.

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