Safety robustness improvement method for unmanned aerial vehicle cooperative interference based on assistance of reconfigurable intelligent reflecting surface

Abstract

The invention provides a security robustness improvement method for unmanned aerial vehicle cooperative interference based on assistance of a reconfigurable intelligent reflecting surface. The method comprises the following steps: setting parameters; initializing parameters; calculating the beamforming of the base station; interference source beamforming is calculated; calculating a reflection coefficient of the reconfigurable intelligent reflecting surface; and judging whether the maximum number of iterations is reached or not, or judging whether the target function is converged, if so, obtaining the optimal base station beam forming, interference source beam forming, intelligent reflecting surface reflection coefficient reconstruction and system secrecy rate output, and if not, continuing iteration. According to the invention, by optimizing the beamforming of the multi-antenna base station, the beamforming of the multi-antenna interference source and the reflection coefficient of the reconfigurable intelligent reflection surface, the influence of uncertain oscillation of the unmanned aerial vehicle in the air is overcome, the secrecy rate of the unmanned aerial vehicle cooperative interference source system is improved, and the safety of the system and the oscillation robustness of the unmanned aerial vehicle are improved.

Description

Technical Field

[0001] The present invention belongs to the field of communication technologies, and particularly relates to a method for improving the security and robustness of unmanned aerial vehicle (UAV) cooperative jamming assisted by a reconfigurable intelligent surface (RIS). Background Art

[0002] As one of the most important aerial communication platforms, different from traditional ground communication methods, the main characteristic of the UAV air-to-ground (A2G) channel is the line-of-sight (LOS) link, which is convenient for long-range coverage and reliable transmission. In addition, UAVs can fly close to target users to obtain better transmission conditions. Despite these advantages, A2G communication is vulnerable to various attacks, especially eavesdropping attacks from illegal eavesdroppers. Therefore, physical layer security (PLS) technology is considered a feasible method to ensure the security of UAV communication. Most related research has jointly optimized the flight trajectory and resource allocation of UAVs to improve the quality of secure communication. Zhong Canhui, Yao Jianping, Xu Jie et al. adopted a cooperative jamming method to prevent eavesdropping in their paper "Secure UAV communication with cooperative jamming and trajectory control" (IEEE Communications Letters, vol. 23, no. 2, pp. 286–289, 2019), which involves the jamming of other UAVs in the surrounding area. In this method, one UAV transmits confidential information to a ground node, while another UAV acts as a jammer by transmitting artificial noise to interfere with any eavesdropping attempt. This technology has been proven to be very successful in preventing unauthorized access to sensitive information.

[0003] As a technology with great potential, the reconfigurable intelligent surface (RIS) has received great attention from researchers and industry experts. By leveraging the power of passive reflecting elements, the RIS can control the phase shift of incident electromagnetic waves, thereby enhancing the security of wireless communication channels. In addition, the RIS can improve the reception quality of legitimate users by constructively adding reflected signals, while weakening the signal reception of eavesdroppers through destructive interference. This indicates that the RIS is an excellent solution to significantly improve the PLS performance. In addition, when combined with the RIS-assisted millimeter-wave network, UAVs can effectively improve the security capabilities and reliability of millimeter-wave UAV networks in the face of potential eavesdropping. Thus, the RIS plays a crucial role in improving the transmission performance of UAVs.

[0004] However, the secrecy performance of these UAV communications is still not satisfactory because the solutions mentioned above basically cannot avoid the negative impacts caused by UAV jitter. Wang Wei and Zhang Wei analyzed the impacts caused by UAV jitter in their paper "Jittering effects analysis and beam training design for UAV millimeter wave communications" (IEEE Transactions on Wireless Communications, vol. 21, no. 5, pp. 3131–3146, 2022). The unpredictable body vibration of the UAV will significantly affect the reliability and security of the communication link. Different from fixed and stable terrestrial cellular networks, UAVs are very vulnerable to accidental interference because they are subject to external interferences caused by environmental factors such as wind and turbulence, which may lead to unstable flight conditions. The jitter of the UAV results in an increase in the estimation errors of the angle of arrival and the angle of departure between the UAV and the ground users. Particularly importantly, in the UAV communication system, the impacts of the estimation errors of the angle of arrival and the angle of departure cannot be ignored, especially when the UAV is equipped with multiple antennas. Due to the estimation errors of the angle of arrival and the angle of departure, the gain introduced by multiple antennas cannot be fully utilized. These errors will cause deviations of the directional signal beams, thereby leading to serious performance losses. Therefore, how to enable the reconfigurable intelligent reflecting surface-assisted UAV cooperative jammer system to overcome the impacts of uncertain UAV oscillations has become an urgent problem to be solved. Summary of the Invention

[0005] Object of the Invention: Aiming at the deficiency of the existing reconfigurable intelligent reflecting surface-assisted UAV cooperative jammer system in overcoming the impacts of uncertain UAV oscillations, the present invention proposes a method for improving the security and robustness of UAV cooperative jamming assisted by a reconfigurable intelligent reflecting surface. It overcomes the impacts of UAV oscillations, improves the secrecy rate of the UAV cooperative jammer system under bounded and unbounded UAV oscillation models, and improves the security and UAV oscillation robustness of the system. The method of the present invention specifically includes the following steps:

[0006] Step 1, set parameters;

[0007] Step 2, establish a UAV cooperative jammer communication system and initialize parameters;

[0008] Step 3, calculate the base station beamforming \(b\) B and the jammer beamforming \(b\) J ;

[0009] Step 4, calculate the reflection coefficient \(\varTheta\) of the reconfigurable intelligent reflecting surface;

[0010] Step 5: Determine whether the maximum number of iterations T is reached or the objective function converges. If so, execute Step 7; otherwise, increment the iteration count by 1 and jump to Step 3.

[0011] Step 6: Obtain the optimal base station beamforming b B , interference source beamforming b J and the reflection coefficient Θ of the reconfigurable intelligent reflecting surface, and output the secrecy rate of the UAV cooperative interference source communication system.

[0012] Step 1 includes: Step 1-1: Set the base station signal frequency f and calculate the signal wavelength λ = c / f, where c is the speed of light.

[0013] Step 1-2: Set the base station coordinates and the UAV coordinates as v = [v x , v y , v z , where v x , v y , v z represent the coordinates of the UAV on the x, y, and z axes in the three-dimensional coordinate system respectively, the user coordinates are u = [u x , u y , 0], where u x , u y represent the coordinates of the user on the x and y axes in the three-dimensional coordinate system respectively, the interference source coordinates are j = [j x , j y , j z , where j x , j y , j z represent the coordinates of the interference source on the x, y, and z axes in the three-dimensional coordinate system respectively, and the eavesdropper coordinates are e = [e x , e y , 0], where e x , e y represent the coordinates of the eavesdropper on the x and y axes in the three-dimensional coordinate system respectively; the antenna spacing of the multi-antenna base station and the interference source and the reflection unit spacing of the reconfigurable intelligent reflecting surface are both half of the signal wavelength, i.e., λ / 2.

[0014] Step 1-3: Set the maximum number of iterations as T, the number of base station antennas and the number of interference source antennas are both M, and the number of reflection units of the reconfigurable intelligent reflecting surface is N.

[0015] Step 1-4: Set the base station power P B and the interference source power P J .

[0016] Step 2 includes:

[0017] Step 2-1: Initialize the iteration count to 0.

[0018] Step 2-2, establish a UAV cooperative jammer communication system, where the UAV cooperative jammer communication system includes a base station, UAVs, jammers, and eavesdroppers; the channel from the base station to the UAVs is which represents an N×M complex matrix, and the channel from the jammer to the UAVs is The channel from the base station to the eavesdropper is which represents an M×1 complex matrix, and the channel from the jammer to the eavesdropper is The channel from the UAVs to the users is The channel from the UAVs to the eavesdropper is which represents an M×1 complex matrix. The cascaded channels all follow the Line-of-Sight (LoS) model, where h BE and h BE Since they contain direct paths, they follow the Ricean fading model;

[0019] Therefore, the signal-to-interference-plus-noise ratio Υ U and the signal-to-interference-plus-noise ratio γ E of the eavesdropper are respectively:

[0020]

[0021]

[0022] where represents the conjugate transpose of h RU , is the variance of the additive complex Gaussian white noise; is the reflection coefficient matrix of the reconfigurable intelligent reflecting surface, where j is the imaginary unit and exp is the natural exponential function, represents the phase shift of the Nth reflecting element of the reconfigurable intelligent reflecting surface; is the transmission beamforming of the base station, is the interference beamforming of the jammer. Therefore, the secrecy rate R is: R = log(1 + γ U ) - log(1 + γ E ); Considering that the UAVs may oscillate, set the perturbation vector γ = (γ x , γ y , γ z ), where γ x , γ y , γ z are the perturbations around the x, y, and z coordinate axes of the three-dimensional coordinate system respectively; For the bounded UAV oscillation model, γ = (γ x , γy , γ z ) in ξ 1 , ξ 2 , ξ 3 are respectively the perturbation ranges of γ x , γ y , γ z ;

[0023] The optimization problem is:

[0024]

[0025] s.t. ||b B || 2 ≤ P B

[0026] ||b J || 2 ≤ P J

[0027]

[0028]

[0029]

[0030]

[0031] where s.t. means subject to, means to maximize the security rate R by optimizing Θ, b B , b J ;

[0032] The above problem is non - convex and difficult to solve, so an auxiliary variable η 1 , η 2 is introduced, and η = [η 1 , η 2 is used to represent the whole of η 1 , η 2 ; the optimization problem becomes:

[0033]

[0034] s.t.

[0035] log(1 + Υ U ) ≥ η 1 (Constraint 1.1)

[0036] log(1 + Υ E ) ≤ η 2 (Constraint 1.1)

[0037] ||bB || 2 ≤P B

[0038] ||b J || 2 ≤P J

[0039]

[0040]

[0041]

[0042]

[0043] Constraint 1.1 becomes:

[0044]

[0045] Introduce auxiliary variables ι 1 、ι 2 、κ 1 , and obtain:

[0046]

[0047]

[0048]

[0049]

[0050] Constraint 2.1 becomes:

[0051]

[0052] Since the right side of the above equation is non-convex, but (κ 1 +ι 2 ) 2 is a convex function, and -(κ 1 -ι 2 ) 2 is a concave function, so the upper bound of -(κ 1 -ι 2 ) 2 is obtained by first-order Taylor expansion:

[0053]

[0054] Constraint 2.1 becomes:

[0055]

[0056] Constraint 2.1 becomes:

[0057]

[0058] Introduce an auxiliary variable ι 3 , ι 4 , κ 2 , and use ι = [ι 1 , ι 2 , ι 3 , ι 4 to represent the whole of ι 1 , ι 2 , ι 3 , ι 4 , and use κ = [κ 1 , κ 2 to represent the whole of κ 1 , κ 2 to obtain:

[0059]

[0060]

[0061]

[0062]

[0063] Among them, Constraint 2.2 is non-convex. Perform a first-order Taylor expansion on :

[0064]

[0065] Constraint 2.2 becomes:

[0066]

[0067] Constraint 2.3 becomes:

[0068]

[0069] Since the right side of the above formula is non-convex, but (κ 2 + ι 4 ) 2 is a convex function, and -(κ 2 - ι 4 ) 2 is a concave function. Therefore, use the first-order Taylor expansion to obtain the lower bound of (κ 2 + ι 4 ) 2 :

[0070]

[0071] Constraint 2.1 becomes:

[0072]

[0073] The new optimization problem becomes:

[0074]

[0075] s.t.

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084] ||b B || 2 ≤P B

[0085] ||b J || 2 ≤P J

[0086]

[0087]

[0088]

[0089]

[0090] To decouple the beamforming and reflection coefficient of the reconfigurable intelligent surface in the problem constraints, define:

[0091]

[0092]

[0093]

[0094]

[0095] Where, θ represents the reflection coefficient vector of the reconfigurable intelligent reflecting surface,

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104] where represents the separated array response, h 1 、h 2 、h 3 、h 4 represent the separated channel parameters, β 0 is the path loss at the reference distance, is the antenna array response from the base station to the reconfigurable intelligent reflecting surface, is the antenna response from the interference source to the reconfigurable intelligent reflecting surface, is the receiving array response from the base station to the reconfigurable intelligent reflecting surface, is the receiving array response from the interference source to the reconfigurable intelligent reflecting surface, is the transmitting array response from the reconfigurable intelligent reflecting surface to the user, is the transmitting array response from the reconfigurable intelligent reflecting surface to the eavesdropper, d BE ,d JE ,d BR ,d JR ,d RU ,d RE are respectively the distances from the base station to the eavesdropper, from the interference source to the eavesdropper, from the base station to the UAV, from the interference source to the UAV, from the UAV to the user, and from the UAV to the eavesdropper;

[0105] To facilitate dealing with the impact of UAV oscillation on each channel, the impact of UAV oscillation on each channel is obtained by using the first-order Taylor expansion where Δh i represents the channel error, γ i represents the error range, specifically including:

[0106]

[0107] Then h 1 The n-th element of

[0108]

[0109]

[0110]

[0111]

[0112]

[0113] where n x and n y respectively represent the number of elements of the n-th reflection unit in the x-direction and the number of elements in the y-direction from the reference reflection unit. Then, use Taylor expansion:

[0114]

[0115]

[0116] Then define:

[0117]

[0118]

[0119]

[0120] At this time where represents the estimator of the channel h 1 The n-th element of is Δh 1 The n-th element of

[0121]

[0122] The optimization problem under the bounded oscillation model of the UAV is transformed into:

[0123]

[0124] s.t.

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133] ||b B || 2 ≤P B

[0134] ||b J || 2 ≤P J

[0135]

[0136]

[0137] For the UAV probability oscillation model, γ in γ=(γ x ,γ y ,γ z ) x , γ y , γ z respectively follows the Gaussian distribution with zero mean and is the variance of the Gaussian distribution; The optimization problem is:

[0138]

[0139] s.t.

[0140]

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147]

[0148] ||b B || 2 ≤P B

[0149] ||b J || 2 ≤P J

[0150]

[0151] where \(p\in(0,1]\) represents the maximum outage probability of the information security rate related to the UAV oscillation;

[0152] Step 2-3, initialize the base station beamforming \(\mathbf{b}\) B , the interferer beamforming \(\mathbf{b}\) J , and the reflection coefficient \(\boldsymbol{\Theta}\) of the reconfigurable intelligent reflecting surface;

[0153] Step 2-4, initialize the auxiliary variables \(\boldsymbol{\eta}=[\eta 1 ,\eta 2 , \boldsymbol{\iota}=[\iota 1 ,\iota 2 ,\iota 3 ,\iota 4 , \boldsymbol{\kappa}=[\kappa 1 ,\kappa 2 .

[0154] Step 3 includes:

[0155] Step 3-1, for the bounded oscillation model of the UAV, calculate the base station beamforming \(\mathbf{b}\) B , the interferer beamforming \(\mathbf{b}\) J ;

[0156] Step 3-2, for the probabilistic oscillation model of the UAV, calculate the base station beamforming \(\mathbf{b}\) B and the interferer beamforming \(\mathbf{b}\) J ;

[0157] Step 4 includes:

[0158] Step 4-1, for the bounded oscillation model of the UAV, calculate the reflection coefficient \(\boldsymbol{\Theta}\) of the reconfigurable intelligent reflecting surface;

[0159] Step 4-2, for the probabilistic oscillation model of the UAV, calculate the reflection coefficient \(\boldsymbol{\Theta}\) of the reconfigurable intelligent reflecting surface.

[0160] The present invention also provides an electronic device, including a processor and a memory, where the memory stores program code, and when the program code is executed by the processor, the processor is caused to execute the steps of the method.

[0161] The present invention also provides a storage medium storing a computer program or instruction, which, when running on a computer, executes the steps of the method described above.

[0162] By optimizing the beamforming of the multi-antenna base station, the beamforming of the multi-antenna interference source, and the reflection coefficient of the reconfigurable intelligent surface, the present invention overcomes the influence of the uncertain oscillation of the unmanned aerial vehicle (UAV) in the air, improves the secrecy rate of the UAV cooperative interference source system under the bounded oscillation model and the unbounded oscillation model of the UAV, and also improves the security of the system and the oscillation robustness of the UAV.

[0163] The present invention has the following beneficial effects: First, considering the influence of the UAV oscillation, by optimizing the beamforming of the multi-antenna base station, the beamforming of the multi-antenna interference source, and the reflection coefficient of the reconfigurable intelligent surface, the present invention overcomes the influence of the uncertain oscillation of the UAV in the air, and improves the security of the system and the oscillation robustness of the UAV.

[0164] Second, the present invention establishes a bounded oscillation model and an unbounded oscillation model of the UAV, and according to the channel characteristics, uses Taylor expansion to transform the UAV oscillation into a specific influence on the channel error.

[0165] Third, for the bounded oscillation model and the unbounded oscillation model of the UAV, the present invention respectively designs optimization methods to overcome the influence of the uncertain oscillation of the UAV in the air, and improves the secrecy rate of the UAV cooperative interference source system. BRIEF DESCRIPTION OF THE DRAWINGS

[0166] The following further specifically describes the present invention in conjunction with the drawings and specific embodiments, and the above and / or other advantages of the present invention will become clearer.

[0167] Figure 1 It is a flowchart of the method of the present invention.

[0168] Figure 2 It is a schematic diagram of a reconfigurable intelligent surface-assisted UAV cooperative interference system under the UAV uncertain oscillation scenario designed by the present invention.

[0169] Figure 3 It is a convergence comparison diagram of the system secrecy rate of the bounded oscillation scheme and the probabilistic oscillation scheme under different UAV uncertain oscillation levels of the present invention.

[0170] Figure 4 It is a comparison diagram of the system secrecy rate of the bounded oscillation scheme and the probabilistic oscillation scheme under different UAV uncertain oscillation levels on the Y-axis and different numbers of antennas of the present invention.

[0171] Figure 5It is a comparison chart of the system secrecy rate between the bounded oscillation scheme and the probabilistic oscillation scheme under different Z-axis UAV uncertain oscillation levels and the number of antennas in the present invention. Detailed implementation manner

[0172] As Figure 1 shown, an embodiment of the present invention provides a method for improving the security robustness of UAV cooperative interference assisted by a reconfigurable intelligent reflecting surface, including the following steps:

[0173] Step 1, set parameters.

[0174] (1a) Set the base station signal frequency f, and calculate the signal wavelength λ = c / f, where c is the speed of light;

[0175] (1b) Set the base station coordinates, UAV coordinates as v = [v x , v y , v z , user coordinates as u = [u x , u y , 0], jammer coordinates as j = [j x , j y , j z , eavesdropper coordinates as e = [e x , e y , 0], the antenna spacing of the multi-antenna base station and the jammer, and the reflection unit spacing of the reconfigurable intelligent reflecting surface are both half of the signal wavelength, i.e., λ / 2;

[0176] (1d) Set the maximum number of iterations T, the number of base station antennas and the number of jammer antennas are both M, and the number of reflection units of the reconfigurable intelligent reflecting surface is N;

[0177] (1e) Set the base station power P B and the jammer power P J ;

[0178] Step 2, initialize parameters.

[0179] (2a) Initialize the number of iterations to 0;

[0180] (2b) As Figure 2 shown, there is an occlusion between the user and the base station and the jammer, so there is no direct connection channel. The dotted lines in the figure represent the reflected channels reflected by the reconfigurable intelligent reflecting surface, the black lines represent the paths of the signals sent from the base station, the green lines represent the paths of the signals sent from the jammer to the user, and the red lines represent the paths of the signals sent from the jammer to the eavesdropper. The channel from the base station to the UAV is The channel from the jammer to the UAV is The channel from the base station to the eavesdropper is The channel from the jammer to the eavesdropper is The channel from the UAV to the user is The channel from the UAV to the eavesdropper is The cascaded channels both follow the LoS model, where h BE and h BE Due to the existence of a direct link path, it follows the Rice fading model.

[0181] Therefore, the signal-to-interference-plus-noise ratios of the user and the eavesdropper are respectively:

[0182]

[0183]

[0184] where, is the variance of the additive complex Gaussian white noise. is the reflection coefficient matrix of the reconfigurable intelligent reflecting surface, where is the transmission beamforming of the base station, is the interference beamforming of the interference source. Therefore, the secrecy rate is R = log(1 + γ U ) - log(1 + γ E ). Considering that the UAV may oscillate, assume γ = (γ x , γ y , γ z ) represents the oscillation, where γ x , γ y , γ z are the perturbations around the x, y, and z axes respectively. For the bounded UAV oscillation model γ = (γ x , γ y , γ z ), γ x , γ y , γ z are all within a finite range, that is, The optimization problem is:

[0185]

[0186] s.t. ||b B || 2 ≤ P B

[0187] ||b J || 2 ≤ P J

[0188]

[0189]

[0190]

[0191]

[0192] The above problems are non-convex and difficult to solve. Therefore, auxiliary variables η = [η 1 , η 2 , ι = [ι 1 , ι 2 , ι 3 , ι 4 , κ = [κ 1 , κ 2 are introduced, and the new optimization problem becomes:

[0193]

[0194] s.t.

[0195]

[0196]

[0197]

[0198]

[0199]

[0200]

[0201]

[0202]

[0203] ||b B || 2 ≤ P B

[0204] ||b J || 2 ≤ P J

[0205]

[0206]

[0207]

[0208]

[0209] To decouple the beamforming and reflection coefficient of the reconfigurable intelligent surface in the above problem constraints, define:

[0210]

[0211]

[0212]

[0213]

[0214] Among them,

[0215]

[0216]

[0217]

[0218]

[0219]

[0220]

[0221]

[0222]

[0223] where β 0 is the path loss at the reference distance, is the antenna array response from the base station to the reconfigurable intelligent reflecting surface, is the antenna response from the interference source to the reconfigurable intelligent reflecting surface, is the receiving array response from the base station to the reconfigurable intelligent reflecting surface, is the receiving array response from the interference source to the reconfigurable intelligent reflecting surface, is the transmitting array response from the reconfigurable intelligent reflecting surface to the user, is the transmitting array response from the reconfigurable intelligent reflecting surface to the eavesdropper, d BE d JE d BR d JR d RU d RE d are the distances from the base station to the eavesdropper, from the interference source to the eavesdropper, from the base station to the UAV, from the interference source to the UAV, from the UAV to the user, and from the UAV to the eavesdropper, respectively.

[0224] In addition, to facilitate dealing with the impact of UAV oscillation on each channel, the impact of UAV oscillation on each channel is obtained by using the first-order Taylor expansion. The optimization problem under the bounded oscillation model of the unmanned aerial vehicle can be transformed into:

[0225]

[0226] s.t.

[0227]

[0228]

[0229]

[0230]

[0231]

[0232]

[0233]

[0234]

[0235] ||b B || 2 ≤ P B

[0236] ||b J || 2 ≤ P J

[0237]

[0238]

[0239] Similarly, for the probability oscillation model of the unmanned aerial vehicle, γ = (γ x , γ y , γ z ) where γ x , γ y , γ z respectively follow Gaussian distributions with zero mean is the variance of the Gaussian distribution.

[0240] The optimization problem is:

[0241]

[0242] s.t.

[0243]

[0244]

[0245]

[0246]

[0247]

[0248]

[0249]

[0250]

[0251] ||b B || 2 ≤P B

[0252] ||b J || 2 ≤P J

[0253]

[0254] where \(p\in(0,1]\) represents the maximum outage probability of the information security rate related to the UAV oscillation.

[0255] (2c) Initialize the base station beamforming \(b\) B , the interferer beamforming \(b\) J , and the reflection coefficient \(\Theta\) of the reconfigurable intelligent surface.

[0256] (2d) Initialize the auxiliary variables \(\eta = [\eta\) 1 , \(\eta\) 2 , \(\iota = [\iota\) 1 , \(\iota\) 2 , \(\iota\) 3 , \(\iota\) 4 , \(\kappa = [\kappa\) 1 , \(\kappa\) 2 ;

[0257] Step 3, calculate the base station beamforming \(b\) B , the interferer beamforming \(b\) J .

[0258] (3a) For the UAV bounded oscillation model, calculate the base station beamforming \(b\) B , the interferer beamforming \(b\) J ;

[0259] When optimizing \(b\) B and \(b\) J , keep \(\Theta\) fixed, and the optimization problem for the UAV bounded oscillation model becomes:

[0260]

[0261] such that

[0262]

[0263]

[0264]

[0265]

[0266]

[0267]

[0268]

[0269]

[0270] ||b B || 2 ≤P B

[0271] ||b J || 2 ≤P J

[0272]

[0273] Define A 1 =α 1 θ, A 2 =α 2 θ, and satisfy rank(B B ) = 1, Tr(B B ) ≤ P B , B B ≥ 0, rank(B J ) = 1, Tr(B J ) ≤ P J , B J ≥ 0; Using the S - procedure, introduce non - negative auxiliary variables λ 1 , λ 2 , λ 3 , λ 4 , and use λ = [λ 1 , λ 2 , λ 3 , λ 4 to represent λ 1 , λ 2 , λ 3 , λ 4As a whole, the first four constraints for dealing with the above problems are processed, and the new optimization problem is obtained as follows:

[0274]

[0275] s.t.

[0276]

[0277]

[0278]

[0279]

[0280]

[0281]

[0282]

[0283]

[0284] Tr(B B ) ≤ P B

[0285] Tr(B J ) ≤ P J

[0286] B B ≥ 0

[0287] B J ≥ 0

[0288] λ i ≥ 0, i = 1, 2, 3, 4

[0289] Among them, is the channel estimation. At this time, this is a convex problem, and the convex optimization toolbox (CVX) can be used to solve for B B and B J , and b B and b J can be obtained through Gaussian randomization.

[0290] (3b) For the UAV probability oscillation model, calculate the base station beamforming b B and the interference source beamforming b J ;

[0291] When optimizing b B and b JWhen \(\Theta\) is fixed, the problem of optimizing the UAV probability oscillation model becomes:

[0292]

[0293] s.t.

[0294]

[0295]

[0296]

[0297]

[0298]

[0299]

[0300]

[0301]

[0302] \(\|b\) B \|\ 2 \(\leq P\) B

[0303] \(\|b\) J \|\ 2 \(\leq P\) J

[0304] The first four constraints of the above problem are probability constraints and are difficult to handle. To convert the probability constraints into a deterministic form, the Bernstein-type inequality is applied, and auxiliary variables \(k\) 1 , \(k\) 2 , \(k\) 3 , \(k\) 4 are introduced, and \(k = [k\) 1 , \(k\) 2 , \(k\) 3 , \(k\) 4 is used to represent the whole of \(k\) 1 , \(k\) 2 , \(k\) 3 , \(k\) 4 , and \(z\) 1 , \(z\) 2 , \(z\) 3 , \(z\) 4 are introduced, and \(z = [z\) 1 , \(z\) 2 , \(z\) 3 , \(z\) 4 is used to represent the whole of \(z\) 1 , \(z\) 2 , \(z\) 3 , \(z\)4 as a whole, provides a safe approximation:

[0305]

[0306]

[0307]

[0308]

[0309]

[0310]

[0311]

[0312]

[0313]

[0314]

[0315]

[0316]

[0317] where R m is the variance probability matrix of the UAV oscillation. At this time, the optimization problem becomes:

[0318]

[0319] s.t.

[0320] Formulas (15) to (26);

[0321]

[0322]

[0323]

[0324]

[0325] Tr(B B ) ≤ P B

[0326] Tr(B J ) ≤ P J

[0327] B B ≥ 0

[0328] B J ≥ 0

[0329] At this time, this is a convex problem and can be solved by CVX for B B and B J , and b is obtained through Gaussian randomization B and b J . The following method is used to calculate the drone oscillation variance probability matrix R m :

[0330]

[0331] To compare the performance of the unbounded model and the bounded model:

[0332]

[0333]

[0334]

[0335] where represents the cumulative distribution function of a chi-square random variable with 1 degree of freedom, thus ensuring that:

[0336]

[0337] Therefore:

[0338] After that, the Taylor expansion in the bounded problem is used to obtain the channel error caused by the drone oscillation:

[0339] Δh 1,i represents the i-th element of Δh 1 :

[0340] Therefore, Δh 1,i follows a complex Gaussian distribution with zero mean

[0341] Define the vector The vector The i-th elements of are respectively

[0342] Δh 1 follows Similarly, Δh 2 follows Δh 3 follows Δh 4 follows

[0343] Define

[0344] Step 4, calculate the reflection coefficient ΘW of the reconfigurable intelligent reflecting surface.

[0345] (4a) For the bounded oscillation model of the UAV, calculate the reflection coefficient Θ of the reconfigurable intelligent reflecting surface;

[0346] When optimizing Θ, fix b B and b J unchanged. For the bounded oscillation model optimization problem of the UAV, it becomes:

[0347]

[0348] s.t.

[0349]

[0350]

[0351]

[0352]

[0353]

[0354]

[0355]

[0356]

[0357]

[0358]

[0359] Let Therefore

[0360]

[0361]

[0362]

[0363]

[0364] Let V = vv H , and V nn = 1, n = 1, 2,..., N, rank(V) = 1, V ≥ 0. Using the S method, introduce a non - negative auxiliary variable μ 1 , μ 2, μ 3 , μ 4 and use μ = [μ 1 , μ 2 , μ 3 , μ 4 to represent μ 1 , μ 2 , μ 3 , μ 4 as a whole, deal with the first four constraints of the above problems, and thus obtain the new optimization problem as:

[0365]

[0366] s.t.

[0367]

[0368]

[0369]

[0370]

[0371]

[0372]

[0373]

[0374]

[0375] V nn = 1, n = 1, 2,..., N, V ≥ 0, μ i ≥ 0, i = 1, 2, 3, 4;

[0376] At this time, this is a convex problem, and CVX can be used to solve for V, and v can be obtained through Gaussian randomization, thereby obtaining θ, and Θ = diag(θ) can be obtained.

[0377] (4b) For the UAV probability oscillation model, calculate the reflection coefficient Θ of the reconfigurable intelligent reflecting surface;

[0378] When optimizing Θ, fix b B and b J unchanged, and for the UAV probability oscillation model, the optimization problem becomes:

[0379]

[0380] s.t.

[0381]

[0382]

[0383]

[0384]

[0385]

[0386]

[0387]

[0388]

[0389]

[0390] Definition To convert the probabilistic constraints into a deterministic form, the Bernstein-type inequality is applied and auxiliary variables are introduced Provide a safe approximation:

[0391]

[0392]

[0393]

[0394]

[0395]

[0396]

[0397]

[0398]

[0399]

[0400]

[0401]

[0402]

[0403] At this time, the optimization problem becomes:

[0404]

[0405] s.t.

[0406] Formulas (31) to (42);

[0407]

[0408]

[0409]

[0410]

[0411] V nn = 1, n = 1, 2, ..., N, V ≥ 0;

[0412] At this time, this is a convex problem, and CVX can be used to solve for V, and v can be obtained through Gaussian randomization, so as to obtain θ, and Θ = diag(θ) can be obtained.

[0413] Step 5: Determine whether the maximum number of iterations T is reached, or the objective function converges. If so, execute Step 7; otherwise, increment the number of iterations by 1 and jump to Step 3;

[0414] Step 6: Obtain the optimal base station beamforming b B and the interfering source beamforming b J and the reflection coefficient Θ of the reconfigurable intelligent reflecting surface, and output the secrecy rate of the system.

[0415] The effects of the present invention will be further described below in conjunction with simulation experiments.

[0416] 1. Simulation conditions and parameter settings:

[0417] The simulation experiment of the present invention is carried out under the MATLAB R2020a software. Our base station is placed at the coordinate (0, 0, 20) m, the UAV is located at the coordinate (5, 50, 50) m, the cooperative interfering source is located at the coordinate (0, 0, 10) m, the single-antenna user is located at the coordinate (2, 100, 0) m, and the eavesdropper is located at the coordinate (10, 90, 0) m. Unless otherwise specified, the number of antennas of the base station and the cooperative interfering source is M = 3, and the number of reflection elements of the reconfigurable intelligent reflecting surface along the X-axis and Y-axis is N x = N y = 4, the maximum power settings of the base station and the cooperative interfering source are P B = 23 dBm, P J = 23 dBm, the spacing between the antennas and the reflection elements is both λ / 2, and the noise power is set to In addition, the base station frequency is set to f = 2.4 GHz. Finally, the channel power gain at the reference distance is β 0=-30 dB. All simulation results are based on Monte Carlo experiments. The simulations are carried out on 50 groups of randomly generated Rician channels and the average values are taken. The Rician factor of the Rician channel is equal to 10 and the path loss exponent is 2.2. The way for the present invention to measure the uncertain oscillation level of the UAV is the ratio of the oscillation angle of the UAV to the pitch angle between the UAV and the target.

[0418] 2. Simulation content:

[0419] Figure 3 It is a comparison chart of the convergence of the system secrecy rate of the bounded oscillation scheme and the probabilistic oscillation scheme under different uncertain oscillation levels of the UAV in the present invention. The perfect channel case means that the UAV oscillation level is 0, that is, no oscillation occurs; the bounded oscillation scheme 1 and the probabilistic oscillation scheme 1 refer to the two schemes in the present invention under the UAV bounded oscillation model and the probabilistic oscillation model when the uncertain oscillation levels of the UAV on the X, Y, and Z axes are all 0.01; the bounded oscillation scheme 2 and the probabilistic oscillation scheme 2 refer to the two schemes in the present invention under the UAV bounded oscillation model and the probabilistic oscillation model when the uncertain oscillation levels of the UAV on the X, Y, and Z axes are all 0.03. The random phase shift scheme means that the reflection coefficient of the reconfigurable intelligent reflecting surface is a random value without optimization. It can be seen from the figure that the system secrecy rate of the present invention can converge to the optimal value, which is only slightly lower than the perfect channel case, but is significantly higher than the random phase shift scheme. By comparing the bounded oscillation schemes 1 and 2, it can be found that as the uncertain oscillation level of the UAV increases, the system secrecy rate will slightly decrease. For the probabilistic oscillation schemes 1 and 2, as the uncertain oscillation level of the UAV increases, the system secrecy rate will also slightly decrease, but the decreasing trend is significantly lower than that of the bounded oscillation scheme. This can prove that the present invention can effectively overcome the influence of the uncertain oscillation of the UAV in the air and improve the security of the system and the robustness of the UAV oscillation.

[0420] Figure 4 It is a comparison chart of the system secrecy rate of the bounded oscillation scheme and the probabilistic oscillation scheme in the present invention under different uncertain oscillation levels of the UAV on the Y axis and different numbers of antennas. By comparing the UAV bounded oscillation scheme and the probabilistic oscillation scheme with the same number of antennas, as the uncertain oscillation level of the UAV increases, the decreasing speed of the system secrecy rate will gradually accelerate, but the decreasing speed of the probabilistic oscillation scheme is significantly lower than that of the bounded oscillation scheme. When the number of antennas increases, the system secrecy rate will increase, and the decreasing speed of the system secrecy rate as the uncertain oscillation level of the UAV increases will also decrease and gradually tend to be stable. This shows that in the case of a sufficient number of antennas, the present invention can almost completely overcome the influence of the uncertain oscillation of the UAV in the air and improve the security of the system and the robustness of the UAV oscillation.

[0421] Figure 5Comparison chart of the system secrecy rate between the bounded oscillation scheme and the probabilistic oscillation scheme under different Z-axis UAV uncertain oscillation levels and the number of antennas. It can be seen from the figure that the changing trend of the system secrecy rate is almost the same as that of Figure 4 and is almost the same, but due to the setting of the simulation coordinates, the degree of the UAV pitch angle is slightly lower than the horizontal azimuth angle, so the impact caused by the uncertain oscillation of the UAV in the Z-axis will be slightly lower than that in the Y-axis. Since the coordinate gap between the UAV, the base station, and the user in the X-axis is very small, the impact caused by the uncertain oscillation of the UAV in the X-axis is not significant. Therefore, the present invention does not show the impact caused by the uncertain oscillation of the UAV in the X-axis. This shows that the impact caused by the uncertain oscillation of the UAV is closely related to the position and angle between the UAV and the target, and also shows that the present invention can overcome the impact of the uncertain oscillation of the UAV at various angles, thereby improving the security of the system and the robustness of the UAV oscillation.

[0422] Based on the above simulation results and analysis, the present invention can overcome the impact of the uncertain oscillation of the UAV in the air by optimizing the beamforming of the multi-antenna base station, the beamforming of the multi-antenna interference source, and the reflection coefficient of the reconfigurable intelligent surface, improve the secrecy rate of the UAV cooperative interference source system, and improve the security of the system and the robustness of the UAV oscillation. And the performance can be further improved by increasing the number of antennas of the base station and the cooperative interference source.

[0423] The present invention provides a method for improving the security and robustness of UAV cooperative interference assisted by a reconfigurable intelligent surface. There are many methods and ways to specifically implement this technical solution. The above is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. Each component not clearly defined in this embodiment can be implemented by existing technologies.

Claims

1. A method for improving the safety robustness of UAV cooperative jamming based on reconfigurable intelligent reflective surface assistance, characterized in that: The following steps are involved: Step 1, set parameters; Step 2: Establish the UAV cooperative interference source communication system and initialize the parameters; Step 3: Calculate the base station beamforming b B , Interference source beamforming b J ; Step 4, calculating the reflection coefficient Θ of the reconfigurable intelligent reflection surface; Step 5: Determine whether the maximum number of iterations T has been reached or the objective function has converged. If so, execute step 7; otherwise, increase the number of iterations by 1 and jump to step 3. Step 6: Get the optimal base station beamforming b B , Interference source beamforming b J And reconstruct the reflection coefficient Θ of the intelligent reflection surface, and output the confidentiality rate of the UAV cooperative interference source communication system.

2. The method according to claim 1, characterized in that Step 1 includes: Step 1-1, set the base station signal frequency f, and calculate the signal wavelength λ=c / f, where c is the speed of light; Step 1-2, set the base station coordinates and the UAV coordinates to v = [v x ,v y ,v z ],v x ,v y ,v z They represent the coordinates of the UAV on the x, y, and z axes in the three-dimensional coordinate system, and the user coordinate is u=[u x ,u y ,0],u x ,u y They represent the coordinates of the user on the x and y axes in the three-dimensional coordinate system, and the interference source coordinate is j=[j x ,j y ,j z ],j x ,j y ,j z represents the coordinates of the interference source on the x, y, and z axes in the three-dimensional coordinate system, and the eavesdropper’s coordinates are e=[e x ,e y ,0],e x ,e y They represent the coordinates of the eavesdropper on the x and y axes in the three-dimensional coordinate system respectively; the antenna spacing of the multi-antenna base station and the interference source and the reflection unit spacing of the reconfigurable intelligent reflection surface are all half of the signal wavelength, that is, λ / 2; Step 1-3, set the maximum number of iterations to T, the number of base station antennas and the number of interference source antennas to M, and the number of reflection units of the reconfigurable smart reflection surface to N; Step 1-4, set the base station power P B and interference source power P J .

3. The method according to claim 2, characterized in that Step 2 includes: Step 2-1, initialize the number of iterations to 0; Step 2-2, establish a UAV cooperative interference source communication system, the UAV cooperative interference source communication system includes a base station, a UAV, an interference source and an eavesdropper; wherein the channel from the base station to the UAV is Represents a complex matrix with N rows and M columns. The channel from the interference source to the drone is The channel from the base station to the eavesdropper is Represents a complex matrix with M rows and 1 column. The channel from the interference source to the eavesdropper is The channel from the drone to the user is The channel from the drone to the eavesdropper is represents a complex matrix with M rows and 1 column. The cascaded channels all obey the line-of-sight model, where h BE and h BE Since it contains direct paths, it obeys the Rice fading model; Therefore, the user's signal-to-interference-noise ratio γ U and the eavesdropper’s signal-to-interference-noise ratio γ E They are: in Indicates h RU The conjugate transpose of is the variance of the additive complex Gaussian white noise; is the reflection coefficient matrix of the reconfigurable smart reflective surface, where j is an imaginary number, exp is the natural exponential function, represents the phase shift of the Nth reflective element of the reconfigurable smart reflective surface; is the transmission beamforming of the base station, is the interference beamforming of the interference source, so the safety rate R is: R = log (1 + γ U )-log(1+γ E ); Considering the possibility of oscillation of the UAV, the disturbance vector γ is set to (γ x ,γ y ,γ z ), where γ x , γ y , γ z are the disturbances around the x, y, and z axes of the three-dimensional coordinate system respectively; for the bounded UAV oscillation model, γ=(γ x ,γ y ,γ z )middle, ξ1, ξ2, ξ3 are γ x ,γ y ,γ z The disturbance range; The optimization problem is: s.t.||b B || 2 ≤P B ||b J || 2 ≤P J Where st means restricted by, By optimizing Θ, b B , b J , maximize the safety rate R; Introducing auxiliary variables η1, η2, and using η = [η1, η2] to represent the whole of η1, η2, the optimization problem becomes: st log(1+Υ U )≥η1(constraint 1.1) log(1+γ E )≤η2(constraint 1.1) ||b B || 2 ≤P B ||b J || 2 ≤P J Constraint 1.1 becomes: Introducing auxiliary variables ι1, ι2, κ1, we get: Constraint 2.1 becomes: Using the first-order Taylor expansion, we can obtain -(κ1-ι2) 2 The upper bound of : Constraint 2.1 becomes: Constraint 2.1 becomes: Introduce auxiliary variables ι3, ι4, κ2, and use ι=[ι1,ι2,ι3,ι4] to represent the whole of ι1,ι2,ι3,ι4, and use κ=[κ1,κ2] to represent the whole of κ1,κ2 to obtain: The constraint 2.2 is non-convex, Do a first-order Taylor expansion: Constraint 2.2 becomes: Constraint 2.3 becomes: Using the first-order Taylor expansion, we can obtain (κ2+ι4) 2 The lower bound of is: Constraint 2.1 becomes: The new optimization problem becomes: st ||b B || 2 ≤P B ||b J || 2 ≤P J In order to separate the problem of coupling between beamforming and the reflection coefficient of the reconfigurable smart reflector in the problem constraints, we define: in, θ represents the reflection vector of the reconfigurable smart reflective surface, in represents the array response after separation, h1, h2, h3, h4 represent the channel parameters after separation, β0 is the path loss at the reference distance, is the antenna array response from the base station to the reconfigurable smart reflector, is the antenna response from the interference source to the reconfigurable smart reflector, is the receiving array response from the base station to the reconfigurable smart reflector, is the receiving array response from the interference source to the reconfigurable smart reflector, Reconfigurable smart reflective surface to generate array response to the user, The array response of the reconfigurable smart reflective surface to the eavesdropper, d BE , d JE , d BR , d JR , d RU , d RE They are the distance from the base station to the eavesdropper, the distance from the interference source to the eavesdropper, the distance from the base station to the drone, the distance from the interference source to the drone, the distance from the drone to the user, and the distance from the drone to the eavesdropper; Using the first-order Taylor expansion, the impact of drone oscillation on each channel is obtained Where Δh i represents the channel error, γ i Indicates the error range, including: Then the nth element of h1 is: Where n x and n y They represent the number of elements in the x-direction and the number of elements in the y-direction of the nth reflection unit from the reference reflection unit, respectively, and then Taylor expansion is used: Then define: at this time in represents the estimate of channel h1, The nth element of The nth element of Δh1 is The optimization problem under the UAV bounded oscillation model is transformed into: st ||b B || 2 ≤P B ||b J || 2 ≤P J For the drone probability oscillation model, γ=(γ x ,γ y ,γ z ) in γ x , γ y , γ z They follow a Gaussian distribution with a mean of 0 and is the variance of the Gaussian distribution; the optimization problem is: st ||b B || 2 ≤P B ||b J || 2 ≤P J Where p∈(0,1] represents the maximum interruption probability of the information security rate related to the UAV shock; Step 2-3: Initialize the base station beamforming b in the feasible domain B , Interference source beamforming b J , reconstruct the reflection coefficient Θ of the smart reflection surface; Step 2-4, initialize the auxiliary variables η = [η1, η2], ι = [ι1, ι2, ι3, ι4], κ = [κ1, κ2].

4. The method according to claim 3, characterized in that Step 3 includes: Step 3-1: Calculate the base station beamforming b for the UAV bounded oscillation model B , Interference source beamforming b J ; When optimizing b B and b J When Θ is fixed, the optimization problem of the bounded oscillation model of the UAV becomes: st ||b B || 2 ≤P B ||b J || 2 ≤P J Define A1=α1θ, A2=α2θ, And satisfy rank(B B )=1,Tr(B B )≤P B , rank(B J )=1,Tr(B J )≤P J , Using the S method, we introduce non-negative auxiliary variables λ1, λ2, λ3, λ4, and use λ = [λ1, λ2, λ3, λ4] to represent the whole of λ1, λ2, λ3, λ4, and obtain the new optimization problem: st B B )≤P B B J )≤P J l i ≥0,i=1,2,3,4 in, is the channel estimate, and B is solved using the convex optimization toolkit B and B J , and obtain b by Gaussian randomization B and b J ; Step 3-2: Calculate the base station beamforming b for the drone probability oscillation model B and interference source beamforming b J ; When optimizing b B and b J When Θ is fixed, the optimization problem of the drone probability oscillation model becomes: st ||b B || 2 ≤P B ||b J || 2 ≤P J Applying Bernstein-type inequalities, introducing auxiliary variables k1, k2, k3, k4, and using k = [k1, k2, k3, k4] to represent the whole of k1, k2, k3, k4, z1, z2, z3, z4, and using z = [z1, z2, z3, z4] to represent the whole of z1, z2, z3, z4, provides a safe approximation: Among them, Tr represents the trace of the matrix, vec represents rearranging the matrix into a vector, and R m is the probability matrix of the UAV oscillation variance, and the optimization problem becomes: st Formula (42) ~ Formula (53), B B )≤P B , B J )≤P J , Solve B using CVX B and B J , and obtain b by Gaussian randomization B and b J .

5. The method according to claim 4, characterized in that In step 3-2, the following method is used to calculate the drone oscillation variance probability matrix R m : To compare the performance of the unbounded model with the bounded model: in represents the cumulative distribution function of a chi-squared random variable with 1 degree of freedom, ensuring that: therefore: Then, the Taylor expansion in the bounded problem is used to obtain the channel error caused by the oscillation of the drone: Δh 1,i Represents the i-th element of Δh1: Therefore Δh 1,i Obeys a complex Gaussian distribution with zero mean Defining vectors vector The i-th elements of Δh1 obeys Δh2 obeys Δh3 obeys Δh4 obeys definition 6. The method according to claim 5, characterized in that Step 4 includes: Step 4-1, for the bounded oscillation model of the UAV, calculate the reflection coefficient Θ of the reconfigurable intelligent reflection surface; Step 4-2, calculate the reflection coefficient Θ of the reconfigurable intelligent reflection surface based on the UAV probabilistic oscillation model.

7. The method according to claim 6, characterized in that Step 4-1 includes: when optimizing Θ, fix b B and b J The optimization problem of the bounded oscillation model of the UAV becomes: st make therefore Let V = vv H , and V nn =1,n=1,2,...,N, rank(V)=1, Using the S method, we introduce non-negative auxiliary variables μ1, μ2, μ3, μ4, and use μ = [μ1, μ2, μ3, μ4] to represent the whole of μ1, μ2, μ3, μ4, and get the new optimization problem: st V nn =1,n=1,2,...,N m i ≥0,i=1,2,3,4 Use CVX to solve for V, and obtain v through Gaussian randomization to obtain θ, and then find θ=diag(θ).

8. The method according to claim 7, characterized in that Step 4-2 includes: when optimizing Θ, fix b B and b J The optimization problem of the drone probability oscillation model becomes: st definition In order to transform the probabilistic constraints into deterministic form, Bernstein-type inequalities are applied and auxiliary variables are introduced Provides a safe approximation: At this time, the optimization problem becomes: st Formula (58)~(69); V nn =1,n=1,2,...,N, At this time, this is a convex problem. We can use CVX to solve V and obtain v through Gaussian randomization to obtain θ, and then find θ=diag(θ).

9. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores program codes, and when the program codes are executed by the processor, the processor executes the steps of the method according to any one of claims 1 to 8.

10. A storage medium, characterized in that: A computer program or instruction is stored, and when the computer program or instruction is run on a computer, the steps of the method according to any one of claims 1 to 8 are executed.

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