Robust and secure beamforming method and system against jitter for movable antenna enabled drones

Abstract

The application discloses a movable antenna energized unmanned aerial vehicle anti-shaking robust safety beam forming method and system, the method comprises the following steps: constructing a downlink wireless communication system model of an unmanned aerial vehicle equipped with a movable antenna array under a shaking scene, and establishing a beam forming optimization problem under a safety capacity maximization criterion of a communication system; converting a movable antenna array angle of departure uncertainty problem caused by unmanned aerial vehicle shaking into a certainty optimization problem about sampling sample weight coefficients; splitting the beam forming optimization problem into a beam forming vector optimization sub-problem and a movable antenna position vector optimization sub-problem; solving the beam forming vector optimization sub-problem and the movable antenna position vector optimization sub-problem alternately with the sampling sample weight coefficients as known parameters to obtain an optimal beam forming vector and an optimal movable antenna position vector. The application solves the angle estimation uncertainty problem caused by unmanned aerial vehicle shaking, and realizes the balance between the safety capacity of a communication system and the anti-shaking robustness.

Description

Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) wireless communication technology, specifically relating to a method and system for robust and secure beamforming of unmanned aerial vehicles (UAVs) with a movable antenna. Background Technology

[0002] In recent years, unmanned aerial vehicle (UAV) communication has become one of the key technologies in wireless communication networks. Compared with traditional fixed ground base stations, UAVs, with their high mobility and flexible operating altitude, can provide high-quality line-of-sight (LOS) links for ground users (GUs) and have the ability to flexibly adjust beam coverage. These unique advantages significantly improve the service quality of communication systems, enabling UAVs to be widely used in many fields such as geological exploration, emergency rescue, smart city construction, and military applications. However, due to the limitations of wireless channel broadcast characteristics, signal transmission between UAVs and GUs is susceptible to interception and theft by eavesdroppers (EVEs), posing serious security risks. Especially in LOS link scenarios, while communication quality is improved, it also provides favorable signal reception conditions for EVEs, further exacerbating communication security risks.

[0003] In UAV communication networks, physical layer security is a core means of enhancing communication security, with beamforming technology playing a crucial role. Traditional beamforming technology relies on fixed antenna arrays, whose geometry remains static. The antenna array's steering vector remains fixed in a specific direction and exhibits fixed spatial correlation across different directional angles. When the physical locations of the UAV and the EVE are relatively close, traditional beamforming designs have significant limitations: it is difficult to effectively suppress signal leakage towards the EVE while ensuring maximum signal gain in the UAV direction. Especially when the two directions are further close, beam nulling design in the EVE direction often leads to a significant reduction in gain in the UAV direction, thereby weakening the overall performance of the communication system. Unlike fixed antenna arrays, movable antenna technology introduces additional spatial degrees of freedom in antenna position, allowing the antenna to move locally within a preset range, thus providing a new optimization dimension for improving communication system performance. Movable antenna technology improves communication system performance by flexibly adjusting antenna position to optimize channel conditions and can also effectively enhance physical layer security.

[0004] In practical applications, UAVs are susceptible to random jitter caused by adverse factors such as high-altitude turbulence and equipment vibration, which leads to increased estimation errors in the antenna array's Angle of Departure (AoD), causing beam shift and severely degrading communication link performance. This problem is particularly prominent in multi-antenna array systems. Previous research on UAV jitter mitigation has largely focused on fixed antenna arrays, failing to fully utilize the flexibility of movable antenna technology to further improve communication performance and security. In summary, existing research on UAV communication systems has not yet addressed the combined impact of movable antenna arrays and UAV jitter on both GU (Ground Unit) and EVE (Electronic Vehicle Emissions), leaving a significant technological gap and failing to meet the communication security requirements of complex real-world communication scenarios. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a robust and secure beamforming method and system for UAVs powered by a movable antenna, which effectively solves the problem of angle estimation uncertainty caused by UAV jitter and achieves a balance between the security capacity and jitter robustness of the communication system.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] Firstly, a robust and secure beamforming method for UAVs powered by movable antennas is provided, comprising: Step S1, constructing a downlink wireless communication system model for a UAV jitter scenario equipped with a movable antenna array, and establishing a beamforming optimization problem under the criterion of maximizing the security capacity of the communication system; Step S2, using a discretized sampling method to transform the uncertainty problem of the movable antenna array departure angle caused by UAV jitter into a deterministic optimization problem about the sampling sample weight coefficients, and solving for the sampling sample weight coefficients; Step S3, decomposing the beamforming optimization problem into a beamforming vector optimization subproblem and a movable antenna position vector optimization subproblem; using an alternating optimization method, with the sampling sample weight coefficients as known parameters, alternately solving the beamforming vector optimization subproblem and the movable antenna position vector optimization subproblem to obtain the optimal beamforming vector and the optimal movable antenna position vector.

[0008] Furthermore, the implementation process of step S1 includes: in a three-dimensional rectangular coordinate system, the x and y axes are parallel to the ground, and the z axis is along the vertical direction; the coordinates of the UAV are set as follows: The coordinates of the ground user are , No. The coordinates of the eavesdropper are , , The number of eavesdroppers, subscript Used to characterize attributes applicable to drones, subscript Subscript is used to characterize attributes applicable to ground users. Used to characterize attributes applicable to eavesdroppers;

[0009] The constraints on the movement range of the movable antenna array are:

[0010] (1)

[0011] (2)

[0012] in, This is the position of the first antenna. This is the location of the last antenna. This is the maximum length of the movable antenna array. The minimum antenna spacing required to avoid coupling effects between antenna elements, This represents the total number of antennas.

[0013] Channel vectors between drones and ground users or eavesdroppers Represented as:

[0014] (3)

[0015] in, For free space path loss, The channel power gain is given at a reference distance of 1m. The distance between the drone and ground users or eavesdroppers. The steering vector of the movable antenna, subscript Used to characterize attributes that apply to both ground users and eavesdroppers;

[0016] Steering vector of movable antenna Represented as:

[0017] (4)

[0018] in, For the signal wavelength, The position vector of the movable antenna. Let T be the natural constant and T be the vector transpose. The signal separation angle between the drone and the ground user or eavesdropper is expressed as:

[0019] (5)

[0020] in, This refers to the directional vector between the drone and the ground user or eavesdropper. This is the positive vector of the movable antenna array. This is the Hadamard product operation;

[0021] Received signals at ground users or eavesdroppers Represented as:

[0022] (6)

[0023] in, For beamforming vectors, The mean is 0 and the variance is Additive white Gaussian noise, For transmitting signals to the drone, H is the vector conjugate transpose symbol;

[0024] Security capacity of communication systems , is represented as:

[0025] (7)

[0026] in, This refers to the channel vector between the UAV and the ground user. This is the channel vector between the drone and the eavesdropper. For channel noise between the drone and ground users, For channel noise between the drone and the eavesdropper, ;

[0027] The deterministic error model for the departure angle of the movable antenna array is expressed as:

[0028] (8)

[0029] in, This is the estimated value of the departure angle. For departure angle jitter error, and These are the lower and upper limits of the departure angle jitter error, respectively;

[0030] Uncertainty set of the channel , is represented as:

[0031] (9)

[0032] in, , For the channel matrix, For guiding matrix;

[0033] The beamforming optimization problem (P1) under the criterion of maximizing the security capacity of a communication system is expressed as:

[0034] (P1) (10a)

[0035] st. (10b)

[0036] Equation (1), Equation (2) (10c)

[0037] in, This indicates the maximum transmission power.

[0038] Furthermore, the maximum length of the movable antenna array The minimum antenna spacing required to avoid coupling effects between antenna elements .

[0039] Furthermore, the variance of additive white Gaussian noise is Maximum transmit power .

[0040] Furthermore, the implementation process of step S2 includes: within the error interval Uniform sampling within the inner area yields the first... Angle of departure of each sample , is represented as:

[0041] (11)

[0042] in, , For the sample set, The number of samples collected. The sampling interval;

[0043] The set of channel sampling samples is represented as:

[0044] (12)

[0045] in, For the first The channel matrix of each sampled sample, For the first The steering matrix of each sampled sample. For the first The steering vector of the movable antenna corresponding to each sampled sample;

[0046] Alternative set , is represented as:

[0047] (13)

[0048] in, For the first One sample The weighting coefficients;

[0049] Safety capacity based on the sample set , is represented as:

[0050] (14)

[0051] in, , , For user number The weighting coefficients of each sampled sample. For user number The steering matrix of each sampled sample. For the eavesdropper The weighting coefficients of each sampled sample. For the eavesdropper The steering matrix of each sampled sample.

[0052] Furthermore, sampling samples weight coefficients .

[0053] Furthermore, the implementation process of step S3 includes: given the weight coefficients of the sampled samples and movable antenna position vector Beamforming vector The optimization subproblem (P2) is represented as:

[0054] (P2) (15a)

[0055] st (15b)

[0056] (15c)

[0057] (15d)

[0058] (15e)

[0059] (15f)

[0060] (15g)

[0061] in, and For the introduced auxiliary variables, , For matrix traces, , , For matrix rank;

[0062] The equivalent condition of equation (15f) is expressed as:

[0063] (16)

[0064] in, For matrix The largest eigenvalue;

[0065] Based on the idea of ​​a penalty function, As a penalty term, it is added to the objective function, and the new objective function is expressed as:

[0066] (17)

[0067] in, This represents the safety capacity in the i-th iteration. As a penalty factor, for Approximate lower bound in the i-th iteration;

[0068] Equation (15c) is a non-convex constraint, and its convex constraint form is expressed as:

[0069] (18)

[0070] in, For matrix traces, For the introduced auxiliary variables, for A feasible solution in the i-th iteration;

[0071] Beamforming vector optimal solution , is represented as:

[0072] (19)

[0073] in, for The largest eigenvalue, for The eigenvector corresponding to the largest eigenvalue.

[0074] Furthermore, the implementation process of step S3 also includes: given the weight coefficients of the sampled samples and beamforming vector Movable antenna position vector The optimization subproblem (P3) is represented as:

[0075] (P3) (20a)

[0076] st (20b)

[0077] (20c)

[0078] (20d)

[0079] Equation (1), Equation (2) (10c)

[0080] in, and Auxiliary variables introduced;

[0081] The convex constraint form of equation (20b) is expressed as:

[0082] (twenty one)

[0083] in, , , , , , Beamforming vector The absolute value of the nth element in the array, where n = 1, 2, 3, ..., N; , The element value is , , , Beamforming vector The absolute value of the m-th element in the array, where m = 1, 2, 3, ..., N. This represents the position of the nth antenna in the j-th iteration. This represents the position of the m-th antenna in the j-th iteration. , , In the j-th iteration The phase of the nth element, In the j-th iteration The phase of the m-th element; , , , , ;

[0084] The convex constraint form of equation (20c) is expressed as:

[0085] (twenty two)

[0086] in, , ; , The element value is , , , ; , , , , Alternately optimize the beamforming vector and the movable antenna position vector until convergence is achieved, thus obtaining the optimal beamforming vector and the optimal movable antenna position vector.

[0087] In a second aspect, a robust and secure beamforming system for unmanned aerial vehicles (UAVs) powered by a movable antenna is provided, comprising a storage medium and a processor; the storage medium is used to store instructions; the processor is used to operate according to the instructions to execute the robust and secure beamforming method for unmanned aerial vehicles powered by a movable antenna described in the first aspect.

[0088] Thirdly, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the mobile antenna-enabled UAV anti-shake robust and secure beamforming method as described in the first aspect. Compared with the prior art, the beneficial effects achieved by this invention are:

[0089] (1) This invention constructs a downlink wireless communication system model for a UAV jitter scenario equipped with a movable antenna array and establishes a beamforming optimization problem under the criterion of maximizing the security capacity of the communication system; it uses a discretized sampling method to transform the uncertainty problem of the movable antenna array departure angle caused by UAV jitter into a deterministic optimization problem about the sampling sample weight coefficients and solves the sampling sample weight coefficients; it decomposes the beamforming optimization problem into a beamforming vector optimization subproblem and a movable antenna position vector optimization subproblem; it uses an alternating optimization method, with the sampling sample weight coefficients as known parameters, to alternately solve the beamforming vector optimization subproblem and the movable antenna position vector optimization subproblem to obtain the optimal beamforming vector and the optimal movable antenna position vector; it effectively solves the angle estimation uncertainty problem caused by UAV jitter and achieves a balance between the security capacity of the communication system and the jitter resistance robustness.

[0090] (2) By combining the spatial degree of freedom of the movable antenna array, the present invention effectively solves the technical problem that traditional beamforming is difficult to balance GU direction gain and EVE signal suppression.

[0091] (3) The present invention adopts discretization sampling technology and simultaneously optimizes beamforming vector and movable antenna position vector alternately, which can effectively overcome the adverse effects of the coupling between the two on the optimization effect, and thus accurately deal with the AoD uncertainty caused by UAV jitter; under the premise of ensuring GU communication quality, it can significantly suppress signal leakage in the EVA direction and greatly improve the physical layer security performance of the communication system. Attached Figure Description

[0092] Figure 1 This is a schematic diagram of the main process of a movable antenna-enabled anti-shake robust and safe beamforming method for unmanned aerial vehicles provided in an embodiment of the present invention;

[0093] Figure 2 This is a schematic diagram of a downlink wireless communication system model for a drone jitter scenario equipped with a movable antenna array, as described in an embodiment of the present invention.

[0094] Figure 3 In this embodiment of the invention, the system's safety capacity varies with the maximum jitter error. Change diagram;

[0095] Figure 4 In this embodiment of the invention, the safety capacity varies with the number of antennas. A graph showing the changes;

[0096] Figure 5 This is a graph showing the change in system safety capacity with EVE location in an embodiment of the present invention. Detailed Implementation

[0097] 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 solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0098] Example 1

[0099] like Figures 1-5 As shown, a robust and secure beamforming method for UAVs with movable antennas is proposed, comprising: constructing a downlink wireless communication system model for a UAV equipped with a movable antenna array in a jitter scenario, and establishing a beamforming optimization problem under the criterion of maximizing the security capacity of the communication system; using a discretized sampling method to transform the uncertainty problem of the movable antenna array departure angle caused by UAV jitter into a deterministic optimization problem about the sampling sample weight coefficients, and solving for the sampling sample weight coefficients; decomposing the beamforming optimization problem into a beamforming vector optimization subproblem and a movable antenna position vector optimization subproblem; and using an alternating optimization method, with the sampling sample weight coefficients as known parameters, alternately solving the beamforming vector optimization subproblem and the movable antenna position vector optimization subproblem to obtain the optimal beamforming vector and the optimal movable antenna position vector.

[0100] Step S1: Construct a downlink wireless communication system model for a drone jitter scenario equipped with a movable antenna array, and establish a beamforming optimization problem under the criterion of maximizing the security capacity of the communication system.

[0101] First, a downlink communication system model is established under UAV jitter scenarios. This model clarifies the positional relationships and signal transmission link characteristics of the UAV, GU, and EVE within the system, and defines the constraints on the movement range of the movable antenna. Figure 2 As shown, the communication system in this embodiment consists of a drone, a valid GU, and It consists of several illegal EVEs; among them, the legitimate GU and all illegal EVEs are equipped with a single antenna, while the drone is equipped with an antenna consisting of... A linear antenna array consisting of movable antennas. Based on the above system model, an optimization problem model is established with the goal of maximizing the system's safety capacity.

[0102] Step S1-1: Set the location information of the UAV, GU, and EVE in the communication system. Set the UAV's coordinates as follows: The coordinates of the ground user are The eavesdropper's coordinates are , , The number of eavesdroppers, subscript Used to characterize attributes applicable to drones, subscript Subscript is used to characterize attributes applicable to ground users. Used to characterize attributes applicable to eavesdroppers.

[0103] In this embodiment, the coordinates of the UAV are specifically set to (0, 0, 80), the coordinates of the GU are (0, 100, 0), and the coordinates of the EVE are (35, 65, 0) and (-35, 135, 0) respectively. Number of antennas Maximum length of antenna array minimum antenna spacing .

[0104] In step S1-2, each antenna in the movable linear antenna array can be moved left or right to adjust its position. The movement range of each movable antenna satisfies the following constraints: (1)

[0105] (2)

[0106] in, This is the position of the first antenna. This is the location of the last antenna. This is the maximum length of the movable antenna array. The minimum antenna spacing required to avoid coupling effects between antenna elements, This represents the total number of antennas. Steps S1-3: Since the UAV's air-to-ground wireless channel is primarily dominated by line-of-sight links, the UAV communicates with the GU or EVE... k Channel vectors between It can be represented as:

[0107] (3)

[0108] in, For free space path loss, The channel power gain is given at a reference distance of 1m. The distance between the drone and ground users or eavesdroppers. The steering vector of the movable antenna, subscript Used to characterize attributes that apply to both ground users and eavesdroppers.

[0109] Specifically, in this invention, the reference channel power gain Steps S1-4: Guiding vector of the movable antenna. It can be represented as:

[0110] (4)

[0111] in, For the signal wavelength, The position vector of the movable antenna. Let T be the natural constant and T be the vector transpose. The signal separation angle between the drone and the ground user or eavesdropper is expressed as:

[0112] (5)

[0113] in, This refers to the directional vector between the drone and the ground user or eavesdropper. This is the positive vector of the movable antenna array. This is the Hadamard product operation.

[0114] Steps S1-5: During the downlink transmission of the UAV, the signal... By transmitting beamforming vectors After processing, it is sent to the GU. Due to the broadcast nature of wireless communication, the GU or EVE... k Received signal at the location It can be represented as:

[0115] (6)

[0116] in, For beamforming vectors, The mean is 0 and the variance is Additive white Gaussian noise, For transmitting signals to the UAV, H is the vector conjugate transpose symbol.

[0117] Specifically, in this invention, the noise variance .

[0118] Steps S1-6: Assuming that the eavesdropping activities between multiple EVEs are independent of each other, the security capacity of the communication system... It can be represented as:

[0119] (7)

[0120] in, This refers to the channel vector between the UAV and the ground user. This is the channel vector between the drone and the eavesdropper. For channel noise between the drone and ground users, For channel noise between the drone and the eavesdropper, .

[0121] Steps S1-7: Considering the impact of random jitter during actual flight, the UAV may have difficulty obtaining accurate AoD information with the GU or EVE. To characterize the UAV jitter effect, this invention employs a deterministic error model to represent the uncertainty of AoD. The deterministic error model for the departure angle of the movable antenna array can be expressed as:

[0122] (8)

[0123] in, This is the estimated value of the departure angle. For departure angle jitter error, and These are the lower and upper limits of the departure angle jitter error, respectively.

[0124] Steps S1-8, the set of uncertainties in the channel It can be represented as:

[0125] (9)

[0126] in, , For the channel matrix, This is the guiding matrix.

[0127] Steps S1-9: For drone jitter scenarios, jointly optimize the beamforming vector of the movable antenna array. and position vector Maximizing the downlink security capacity of drones under AoD uncertainty conditions The optimization problem of maximizing system security capacity, i.e., the beamforming optimization problem under the criterion of maximizing the security capacity of a communication system (P1), is expressed as:

[0128] (P1) (10a)

[0129] st. (10b)

[0130] Equation (1), Equation (2) (10c)

[0131] in, This indicates the maximum transmission power.

[0132] Specifically, the maximum transmission power in this invention .

[0133] Step S2: The uncertainty problem of the departure angle of the movable antenna array caused by UAV jitter is transformed into a deterministic optimization problem about the sampling weight coefficients by using a discretized sampling method, and the sampling weight coefficients are obtained by solving the problem.

[0134] To address the uncertainty of AoD information caused by drone jitter, the possible value range of AoD is uniformly discretized and sampled to generate several AoD sample samples. The weight coefficients of each sample are defined, transforming the robust optimization problem under AoD uncertainty into a deterministic optimization problem about the weight coefficients of the sample samples, thus simplifying the solution difficulty of the uncertainty problem.

[0135] Step S2-1, within the error range Uniform sampling within the inner area yields the first... Angle of departure of each sample , is represented as:

[0136] (11)

[0137] in, , For the sample set, The number of samples collected. The sampling interval is denoted as .

[0138] Step S2-2, the discrete sample set of the channel can be represented as:

[0139] (12)

[0140] in, For the first The channel matrix of each sampled sample, For the first The steering matrix of each sampled sample. For the first The steering vector of the movable antenna corresponding to each sampled sample.

[0141] Step S2-3, due to the channel uncertainty set any channel All of these can be approximately represented as a weighted combination of all samples in the sample set. Alternative set It can be represented as:

[0142] (13)

[0143] in, For the first One sample The weighting coefficients.

[0144] Step S2-4, based on the safe capacity of the sample set It can be represented as:

[0145] (14)

[0146] in, , , For user number The weighting coefficients of each sampled sample. For user number The steering matrix of each sampled sample. For the eavesdropper The weighting coefficients of each sampled sample. For the eavesdropper The steering matrix of each sampled sample.

[0147] Specifically, the sampling sample in this invention The weighting coefficients are .

[0148] Step S3: Decompose the beamforming optimization problem into a beamforming vector optimization subproblem and a movable antenna position vector optimization subproblem; use the alternating optimization method, with the sample weight coefficients as known parameters, alternately solve the beamforming vector optimization subproblem and the movable antenna position vector optimization subproblem to obtain the optimal beamforming vector and the optimal movable antenna position vector.

[0149] Optimization variables in optimization problems and There is mutual coupling between them, and an alternating optimization method can be used to solve the problem, that is, fix some variables, optimize the remaining variables, and approach the global optimal solution of the optimization problem through multiple alternating iterations. Specifically, taking the sample weight coefficients obtained in step 2 as known parameters, the optimization problem in this embodiment can be divided into the following two optimization sub-problems for separate solution: (1) Given and ,optimization (2) Given and ,optimization .

[0150] Step S3-1, given the weight coefficients of the sampled samples and movable antenna position vector Beamforming vector The optimization subproblem (P2) is represented as:

[0151] (P2) (15a)

[0152] st (15b)

[0153] (15c)

[0154] (15d)

[0155] (15e)

[0156] (15f)

[0157] (15g)

[0158] in, and For the introduced auxiliary variables, , For matrix traces, , , For matrix The rank. In the optimization subproblem (P2), constraints (15f) and (15g) are introduced. The required rank-1 constraints are used to ensure the equivalent transformation of the optimization problem. Since the non-convexity of constraints (15c) and (15f) makes it difficult to solve (P2) directly, the penalty function and the continuous convex approximation method will be used to approximate the non-convex constraints (15c) and (15f) respectively.

[0159] Step S3-2, for the non-convex rank 1 constraint (15f), can be transformed into the following equivalent condition:

[0160] (16)

[0161] in, For matrix The largest eigenvalue.

[0162] Step S3-3, based on the idea of ​​a penalty function, can be... As a penalty term added to the objective function, during the optimization process, when hour, It has only one non-zero eigenvalue, thus satisfying the rank-1 constraint. Also, because... Since the function is convex, its first-order Taylor expansion can be iteratively approximated using a continuous convex approximation method. The new objective function can be expressed as:

[0163] (17)

[0164] in, This represents the safety capacity in the i-th iteration. As a penalty factor, for The approximate lower bound in the i-th iteration.

[0165] Step S3-4, because It is a convex function, and can be obtained using the continuous convex approximation method. The lower bound of the non-convex constraint (15c) can be expressed in convex form as follows:

[0166] (18)

[0167] in, For matrix traces, For the introduced auxiliary variables, for A feasible solution in the i-th iteration.

[0168] Steps S3-5 can be directly performed by... Eigenvalue decomposition yields beamforming vectors The optimal solution, beamforming vector optimal solution It can be represented as:

[0169] (19)

[0170] in, for The largest eigenvalue, for The eigenvector corresponding to the largest eigenvalue.

[0171] Step S3-6, given the weight coefficients of the sampled samples and beamforming vector Movable antenna position vector The optimization subproblem (P3) is represented as:

[0172] (P3) (20a)

[0173] st (20b)

[0174] (20c)

[0175] (20d)

[0176] Equation (1), Equation (2) (10c)

[0177] in, and These are the auxiliary variables introduced.

[0178] Step S3-7, use a second-order Taylor expansion to apply the constraint condition (20b) to... The terms are approximated using a convex method, and then the convex approximation expression is... exist Perform a second-order Taylor expansion at that point, combined with and Its lower bound can be obtained, and the convex approximate lower bound expression of equation (20b) can be expressed as:

[0179] (twenty one)

[0180] in, , , , , , Beamforming vector The absolute value of the nth element in the array, where n = 1, 2, 3, ..., N; , The element value is , , , Beamforming vector The absolute value of the m-th element in the array, where m = 1, 2, 3, ..., N. This represents the position of the nth antenna in the j-th iteration. This represents the position of the m-th antenna in the j-th iteration. , , In the j-th iteration The phase of the nth element, In the j-th iteration The phase of the m-th element; , , , , .

[0181] Steps S3-8 follow the same processing method as step S3-7, combined with... and against In feasible solutions Performing a first-order Taylor expansion at point (20c), the convex approximate upper bound expression of equation (20c) can be expressed as:

[0182] (twenty two)

[0183] in, , ; , The element value is , , , ; , , , , .

[0184] Step S3-9: Alternately optimize the beamforming vector and the movable antenna position vector until convergence is achieved, thus obtaining the optimal beamforming vector and the optimal movable antenna position vector.

[0185] This invention first establishes a downlink communication system model under UAV jitter scenarios. Second, addressing the uncertainty of AoD information caused by UAV jitter, a discretization sampling method is used to transform this uncertainty into an optimization problem of sampling sample weight coefficients, thereby reducing the solution complexity. Based on this, considering the coupling characteristics and non-convex properties of the beamforming vector and the movable antenna position vector in the original optimization problem, a continuous convex approximation method and an alternating optimization method are used to decompose the original non-convex optimization problem into two independent convex optimization subproblems: beamforming vector optimization and movable antenna position vector optimization. Finally, through iterative optimization, the optimal solution of the original problem is gradually approximated, achieving the solution for the maximum system safety capacity and ensuring communication security and transmission performance in complex scenarios.

[0186] See Figures 3 to 5The performance of the method of the present invention was compared with that of a robust method for fixed antennas and a non-robust method for movable antennas. The results show that the performance of the method of the present invention is better than the other two comparison methods, demonstrating better anti-jitter performance and physical layer security performance.

[0187] like Figure 3 As shown, this embodiment analyzes the change in security capacity with the maximum jitter error range under different methods. The results show that as the maximum jitter error range increases, the security capacity of each method exhibits a significant decreasing trend. This is because, under a larger jitter error range, the antenna array has difficulty effectively aligning the signal beam with the GU, resulting in a decrease in security rate performance. Under the same maximum jitter error range, the movable antenna robust method proposed in this embodiment consistently outperforms the other two methods in terms of security performance. Furthermore, as the jitter error range increases, the performance advantage of the proposed method becomes more significant. This advantage is mainly attributed to the robust security beamforming design employed in the proposed method, which maintains high security performance even under conditions of significant angular information uncertainty.

[0188] like Figure 4 As shown, this embodiment analyzes the change in security capacity with the number of antennas under different methods. The results show that the security capacity of each method increases with the number of antennas. Furthermore, the security capacity gap between the movable antenna robust method and the fixed antenna robust method proposed in this embodiment gradually narrows with the increase in the number of antennas. This phenomenon can be explained by the fact that, within a given maximum movable antenna array movement range... When the number of antennas is small, each antenna has a high degree of spatial freedom, providing more room for movement and improving the overall system safety. However, as the number of antennas increases, the movable space between antennas is compressed, and the degree of spatial freedom decreases. Furthermore, from... Figure 4 As can be seen, increasing the maximum transmission power can effectively improve the system's safety performance.

[0189] like Figure 5 As shown, this embodiment analyzes the change in the location of the safety capacity EVE under different methods. The results show that as the EVE moves towards the GU direction, the safety rate of both the proposed movable antenna robust method and the fixed antenna robust method decreases. This phenomenon is mainly attributed to the increased threat to the physical layer security of the system as the EVE gradually approaches the GU direction, leading to a decrease in the system's safety rate. Further analysis reveals that the safety performance difference between the two schemes is small when the EVE is far from the GU direction, but the safety performance difference significantly widens as the EVE gradually approaches the GU direction. This indicates that the movable antenna robust method proposed in this embodiment can provide superior safety performance when the EVE poses a greater security threat to the GU.

[0190] This invention can be widely applied to various wireless communication security scenarios where there is a risk of drone jitter, and has good practicality and application prospects.

[0191] Example 2

[0192] Based on the movable antenna-enabled robust and secure beamforming method for UAVs described in Embodiment 1, this embodiment provides a movable antenna-enabled robust and secure beamforming system for UAVs, including a storage medium and a processor; the storage medium is used to store instructions; the processor is used to operate according to the instructions to execute the movable antenna-enabled robust and secure beamforming method for UAVs described in Embodiment 1.

[0193] Example 3

[0194] Based on the movable antenna-enabled UAV anti-shake robust and safe beamforming method described in Embodiment 1, this embodiment provides a computer-readable storage medium storing a computer program thereon. When the computer program is executed by a processor, it implements the movable antenna-enabled UAV anti-shake robust and safe beamforming method as described in Embodiment 1.

[0195] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied 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.

[0196] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0197] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0198] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

Claims

1. A robust and secure beamforming method for unmanned aerial vehicles (UAVs) powered by a movable antenna, characterized in that, include: Step S1: Construct a downlink wireless communication system model for a drone jitter scenario equipped with a movable antenna array, and establish a beamforming optimization problem under the criterion of maximizing the security capacity of the communication system. Step S2: The uncertainty problem of the departure angle of the movable antenna array caused by UAV jitter is transformed into a deterministic optimization problem about the sampling sample weight coefficients by using a discretized sampling method, and the sampling sample weight coefficients are obtained by solving the problem. Step S3: Decompose the beamforming optimization problem into a beamforming vector optimization subproblem and a movable antenna position vector optimization subproblem; use the alternating optimization method, with the sample weight coefficients as known parameters, alternately solve the beamforming vector optimization subproblem and the movable antenna position vector optimization subproblem to obtain the optimal beamforming vector and the optimal movable antenna position vector. The implementation process of step S1 includes: In a three-dimensional Cartesian coordinate system, the x and y axes are parallel to the ground, and the z axis is along the vertical direction; the coordinates of the UAV are set as follows: The coordinates of the ground user are , No. The coordinates of the eavesdropper are , , The number of eavesdroppers, subscript Used to characterize attributes applicable to drones, subscript Subscript is used to characterize attributes applicable to ground users. Used to characterize attributes applicable to eavesdroppers; The movement range constraint for the movable antenna array is: （1） （2） in, This is the position of the first antenna. This is the location of the last antenna. This is the maximum length of the movable antenna array. The minimum antenna spacing required to avoid coupling effects between antenna elements, This represents the total number of antennas. Channel vectors between drones and ground users or eavesdroppers Represented as: （3） in, For free space path loss, The channel power gain is given at a reference distance of 1m. The distance between the drone and ground users or eavesdroppers. The steering vector of the movable antenna, subscript Used to characterize attributes that apply to both ground users and eavesdroppers; Steering vector of movable antenna Represented as: （4） in, For the signal wavelength, This is the position vector of the movable antenna. Let T be the natural constant and T be the vector transpose. The signal separation angle between the drone and the ground user or eavesdropper is expressed as: （5） in, This refers to the directional vector between the drone and the ground user or eavesdropper. This is the positive vector of the movable antenna array. This is the Hadamard product operation; Received signals at ground users or eavesdroppers Represented as: （6） in, For beamforming vectors, The mean is 0 and the variance is Additive white Gaussian noise, For transmitting signals to the drone, H is the vector conjugate transpose symbol; Security capacity of communication systems , represented as: （7） in, This refers to the channel vector between the UAV and the ground user. This is the channel vector between the drone and the eavesdropper. For channel noise between the drone and ground users, For channel noise between the drone and the eavesdropper, ; The deterministic error model for the departure angle of the movable antenna array is expressed as: （8） in, This is the estimated value of the departure angle. For departure angle jitter error, and These are the lower and upper limits of the departure angle jitter error, respectively; Uncertainty set of the channel , represented as: （9） in, , For the channel matrix, For guiding matrix; The beamforming optimization problem (P1) under the criterion of maximizing the security capacity of a communication system is expressed as: (P1) (10a) s.t. (10b) Equation (1), Equation (2) (10c) in, This indicates the maximum transmission power.

2. The method for robust and secure beamforming of a UAV powered by a movable antenna according to claim 1, characterized in that, Maximum length of movable antenna array The minimum antenna spacing required to avoid coupling effects between antenna elements .

3. The method for robust and secure beamforming of a UAV powered by a movable antenna according to claim 1, characterized in that, The variance of additive white Gaussian noise is Maximum transmit power .

4. The method for robust and secure beamforming of a UAV powered by a movable antenna according to claim 1, characterized in that, The implementation process of step S2 includes: Within the error range Uniform sampling within the inner area yields the first... Angle of departure of each sample , represented as: （11） in, , For the sample set, The number of samples collected. The sampling interval; The set of channel sampling samples is represented as: （12） in, For the first The channel matrix of each sampled sample, For the first The steering matrix of each sampled sample. For the first The steering vector of the movable antenna corresponding to each sampled sample; Alternative set , represented as: （13） in, For the first One sample The weighting coefficients; Safety capacity based on the sample set , represented as: （14） in, , , For user number The weighting coefficients of each sampled sample. For user number The steering matrix of each sampled sample. For the eavesdropper The weighting coefficients of each sampled sample. For the eavesdropper The steering matrix of each sampled sample.

5. The method for robust and secure beamforming of a UAV powered by a movable antenna according to claim 4, characterized in that, Sample weight coefficients .

6. The method for robust and secure beamforming of a UAV powered by a movable antenna according to claim 4, characterized in that, The implementation process of step S3 includes: Given the weight coefficients of the sampled samples and movable antenna position vector Beamforming vector The optimization subproblem (P2) is represented as: (P2) (15a) s.t. (15b) （15c） （15d） （15e） （15f） （15g） in, and For the introduced auxiliary variables, , For matrix traces, , , For matrix rank; The equivalent condition of equation (15f) is expressed as: （16） in, For matrix The largest eigenvalue; Based on the idea of ​​a penalty function, As a penalty term, it is added to the objective function, and the new objective function is expressed as: （17） in, This represents the safety capacity in the i-th iteration. As a penalty factor, for Approximate lower bound in the i-th iteration; Equation (15c) is a non-convex constraint, and its convex constraint form is expressed as: （18） in, For matrix traces, For the introduced auxiliary variables, for A feasible solution in the i-th iteration; Beamforming vector optimal solution , represented as: （19） in, for The largest eigenvalue, for The eigenvector corresponding to the largest eigenvalue.

7. The method for robust and secure beamforming of a UAV powered by a movable antenna according to claim 6, characterized in that, The implementation process of step S3 also includes: Given the weight coefficients of the sampled samples and beamforming vector Movable antenna position vector The optimization subproblem (P3) is represented as: (P3) (20a) s.t. (20b) （20c） （20d） Equation (1), Equation (2) (10c) in, and Auxiliary variables introduced; The convex constraint form of equation (20b) is expressed as: （21） in, , , , , , Beamforming vector The absolute value of the nth element in the array, where n = 1, 2, 3, ..., N; , The element value is , , , Beamforming vector The absolute value of the m-th element in the array, where m = 1, 2, 3, ..., N. This represents the position of the nth antenna in the j-th iteration. This represents the position of the m-th antenna in the j-th iteration. , , In the j-th iteration The phase of the nth element, In the j-th iteration The phase of the m-th element; , , , , ; The convex constraint form of equation (20c) is expressed as: （22） in, , ; , The element value is , , , ; , , , , Alternately optimize the beamforming vector and the movable antenna position vector until convergence is achieved, thus obtaining the optimal beamforming vector and the optimal movable antenna position vector.

8. A robust and secure beamforming system for unmanned aerial vehicles (UAVs) powered by a movable antenna, characterized in that, Including storage media and processor; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to execute the anti-shake robust and secure beamforming method for unmanned aerial vehicles empowered by a movable antenna as described in any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the anti-shake robust and safe beamforming method for unmanned aerial vehicles empowered by a movable antenna as described in any one of claims 1 to 7.

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