A Robust Beamforming Optimization Method for Mitigating Jitter in Millimeter-Wave UAV Communication Systems

Abstract

The present invention discloses a method for optimizing anti-jitter robust beamforming in a millimeter-wave UAV communication system, which includes the millimeter-wave communication system of the UAV receiving real-time GPS positioning and feedback information of the user backhaul channel, obtaining the UAV transmission beamforming vector, obtaining the elevation angle and azimuth angle information between the UAV and the ground user, and thus obtaining the upper limit value of the UAV jitter error; introducing the jitter error model, and calculating the sum of the downlink transmission capacities of multiple ground users according to the UAV transmission beamforming vector and the noise power, and determining the transmission beamforming optimization problem; based on the convex hull theory, making a deterministic transformation of the jitter error model for the optimization problem, and using the sequential convex approximation method to solve it to obtain the beamforming vector parameters. The present invention is based on the UAV millimeter-wave transmission beamforming optimization problem model with known vector parameters, determines the UAV millimeter-wave communication system with the optimal anti-jitter robust wave performance, and improves the anti-jitter ability of the UAV millimeter-wave communication system.

Description

Technical Field

[0001] The present invention relates to the technical field of millimeter-wave communication for unmanned aerial vehicles, and particularly to a method for optimizing anti-jitter robust beamforming in a millimeter-wave unmanned aerial vehicle communication system. Background Art

[0002] In recent years, using millimeter-wave technology for unmanned aerial vehicle data communication has become a research hotspot in academia and industry. On the one hand, the characteristics of millimeter-wave signals with short wavelengths and high frequencies provide a feasible solution for solving the problems of limited payload of unmanned aerial vehicles and tight spectrum resources, which is beneficial to improving the information transmission rate. On the other hand, unmanned aerial vehicles can be flexibly arranged in the air, and their relatively high flight positions often result in line-of-sight paths during communication, which can greatly expand the coverage range of millimeter-wave communication and improve network connectivity, making it an excellent platform for millimeter-wave communication technology. However, different from ground cellular networks with stable infrastructure, due to the limitations of atmospheric turbulence and flight control capabilities, unmanned aerial vehicles are easily affected by airflows and their own vibrations, generating random jitters, such as yaw jitters in the horizontal direction or pitch jitters in the vertical direction, which cause angular deviations in the beam pointing, and further lead to low efficiency and instability in the information transmission of the air-ground transmission link.

[0003] Due to the characteristics of millimeter waves with narrow directional beams, they are more susceptible to angular errors caused by the jitter of unmanned aerial vehicles, and the performance of the communication system will be more adversely affected due to beam angle deviations. Therefore, the negative impact brought by the jitter characteristics of unmanned aerial vehicles in millimeter-wave unmanned aerial vehicle communication systems cannot be ignored. Summary of the Invention

[0004] Object of the Invention: In order to overcome the deficiencies in the prior art, the present invention provides a method for optimizing anti-jitter robust beamforming in a millimeter-wave unmanned aerial vehicle communication system; by optimizing the millimeter-wave transmission beamforming vector of the unmanned aerial vehicle, the sum of the multi-user downlink transmission capacities in the worst case is maximized, so that the millimeter-wave unmanned aerial vehicle communication system has strong robustness to the jitter of the unmanned aerial vehicle.

[0005] Technical Solution: In a first aspect, the present invention provides a method for optimizing anti-jitter robust beamforming in a millimeter-wave unmanned aerial vehicle communication system, including:

[0006] The millimeter-wave unmanned aerial vehicle communication system receives the feedback information of GPS positioning and the user backhaul channel in real time, analyzes the millimeter-wave transmission beams from the multi-antenna unmanned aerial vehicle base station to multiple ground users in the feedback information, obtains the unmanned aerial vehicle transmission beamforming vector according to the millimeter-wave transmission beams, and extracts the position data of the unmanned aerial vehicle and the ground users from the feedback information;

[0007] Based on the position data of the drone and the ground user, calculate to determine the elevation angle and azimuth angle information between the drone and the ground user, and calculate all the elevation angle and azimuth angle information between the drone and the ground user during the entire flight process of the drone to obtain the upper limit value of the jitter error during the flight process of the drone;

[0008] Input the upper limit value of the jitter error into the drone millimeter-wave air-ground channel jitter error model, and calculate the sum of the downlink transmission capacities of multiple ground users according to the drone transmit beamforming vector and the noise power from the drone to the ground user to determine the drone millimeter-wave transmit beamforming optimization problem; wherein, the drone millimeter-wave air-ground channel jitter error model is constructed according to the communication characteristics of the drone millimeter-wave air-ground channel;

[0009] Based on the convex hull theory, perform a deterministic transformation of the jitter error model for the drone millimeter-wave transmit beamforming optimization problem to obtain a deterministic problem;

[0010] Solve the deterministic problem using the successive convex approximation method to obtain the vector parameters of the drone millimeter-wave transmit beamforming optimization problem;

[0011] Based on the drone millimeter-wave transmit beamforming optimization problem model with known vector parameters, determine the drone millimeter-wave communication system with the optimal anti-jitter robust wave performance.

[0012] In a further embodiment, the calculation formulas for the elevation angle and azimuth angle information between the drone and the ground user are respectively:

[0013]

[0014] where q u =(x u , y u ) T and q k (x k , y k ) T respectively represent the horizontal coordinates of the drone and the ground user, x τ and y τ , τ∈{u, k} respectively represent the horizontal x-direction and y-direction coordinates of the drone (ground user), h is the flight altitude of the drone, and T is the transpose symbol of the vector.

[0015] In a further embodiment, the calculation formula for the drone millimeter-wave air-ground channel jitter error model is:

[0016]

[0017] where h k is the channel vector, is a constant, c is the speed of light, and f c is the carrier center frequency, is the distance between the UAV and the ground user, is the antenna array vector, and θ k and are the elevation angle and azimuth angle between the UAV and the ground user respectively, and are the estimated elevation angle and estimated azimuth angle between the UAV and the ground user respectively, and Δθ k and are the elevation angle jitter error and azimuth angle jitter error caused by the UAV jitter respectively, and are the upper limit value of the elevation angle jitter error and the upper limit value of the azimuth angle jitter error respectively;

[0018] Among them, the antenna array vector has the following expression:

[0019]

[0020] In the formula, d is the distance between adjacent antenna elements of the uniform planar array, λ is the carrier wavelength, 1 ≤ m x ≤ M x , 1 ≤ m y ≤ M y , M x and M y are the number of row antennas and the number of column antennas of the uniform planar array respectively.

[0021] In a further embodiment, the expression for determining the UAV millimeter-wave transmission beamforming optimization problem is:

[0022]

[0023]

[0024] In the formula, is the upper limit value of the UAV transmission power, is the sum of the multi-user downlink transmission capacities, and w k is the UAV transmission beamforming vector;

[0025] Among them, the sum of the multi-user downlink transmission capacities has the following calculation formula:

[0026]

[0027] In the formula, H k is the channel matrix, Λ k is for H kThe uncertainty set, represents the noise power of the communication link from the UAV to the ground user, is the conjugate transpose vector of the k-th beamforming vector w k ; is the conjugate transpose vector of the beamforming vector w for i≠k i ;

[0028] where, H k is the uncertainty set Λ k The calculation expression is:

[0029]

[0030] In the formula, h k is the channel vector, is the conjugate transpose vector of h k ;

[0031] In a further embodiment, the method for obtaining the deterministic problem is:

[0032] According to the convex hull theory, the uncertain channel matrix with jitter error can be expressed as a deterministic form of the weighted sum of a finite or infinite number of discrete samples within the uncertainty set. The expression of the uncertain channel matrix is:

[0033]

[0034] In the formula, L k is the total number of samples, is the weighting coefficient of the j-th sample, is the j-th sample, determined by the discretized angle information; using to replace H k , the problem (P1) is approximately expressed as a deterministic problem (P2), and the calculation formula is:

[0035]

[0036] s.t. (4b) (8b)

[0037] In a further embodiment, the method for solving the deterministic problem using the successive convex approximation method is:

[0038] Using the successive convex approximation method, the non-convex problem is transformed into a convex optimization problem,

[0039] The transformation calculation formula is:

[0040] max wk，a，fk，pk a (9a)

[0041]

[0042]

[0043]

[0044] (4b) (9e)

[0045] In the formula, represents taking the real part of A, a, f k , p k represents the auxiliary variables introduced in the optimization problem, is w k , f k , p k is the feasible solution of.

[0046] In a further embodiment, the method for obtaining the vector parameters of the UAV millimeter-wave transmission beamforming optimization problem includes:

[0047] In the UAV air-ground channel jitter error model, initialize the beamforming vector, and preset the auxiliary variables and the iteration accuracy;

[0048] Substitute the beamforming vector and the auxiliary variables into the formula of the successive convex approximation method for comparison, and select the beamforming vector and the auxiliary variables whose output satisfies the value range of the successive convex approximation method formula;

[0049] According to the multi-user downlink transmission capacity sum, judge whether the difference between the iterative values of the multi-user downlink transmission capacity sum in the previous and subsequent times is less than the iteration accuracy. If it is less, output the beamforming vector. If it is greater, loop to compare whether the beamforming vector and the auxiliary variables satisfy the value range of the convex approximation method.

[0050] Advantageous effects: Compared with the prior art, the present invention has the following advantages:

[0051] By combining the UAV communication system with millimeter-wave technology, the advantages of both are complementary. At the same time, a deterministic conversion method for the jitter error model based on the convex hull theory is proposed for the jitter characteristics of the UAV, effectively solving the problem of uncertain angular error caused by UAV jitter and improving the anti-jitter ability of the UAV millimeter-wave communication system.

[0052] For the problem of maximizing the sum of multi-user downlink transmission capacities in the worst-case UAV millimeter-wave system, an iterative solution algorithm based on successive convex approximation is proposed, which transforms the non-convex problem into a convex form. By optimizing the beamforming vector, the optimal sub-optimal solution of the original problem is obtained by convergence under a finite number of iterations, ensuring the quality-of-service requirements for the downlink data transmission of the UAV millimeter-wave in the mission window. Description of the Drawings

[0053] Figure 1This is the system model diagram of a millimeter-wave UAV communication system anti-jitter robust beamforming optimization method, which is the present invention.

[0054] Figure 2 This is the UAV jitter schematic diagram of a millimeter-wave UAV communication system anti-jitter robust beamforming optimization method, which is the present invention.

[0055] Figure 3 This is the algorithm flowchart of a millimeter-wave UAV communication system anti-jitter robust beamforming optimization method, which is the present invention.

[0056] Figure 4 This is the beam pattern of the beamforming vector w_1 under the anti-jitter robust beamforming scheme proposed by the present invention.

[0057] Figure 5 This is the graph of the variation trend of the multi-user downlink transmission capacity sum with the maximum jitter error under the anti-jitter robust beamforming scheme and the non-robust beamforming scheme. Specific embodiments

[0058] To more fully understand the technical content of the present invention, the technical solutions of the present invention will be further introduced and described below in conjunction with specific embodiments, but not limited thereto.

[0059] In the first aspect, the present invention provides a millimeter-wave UAV communication system anti-jitter robust beamforming optimization method, including:

[0060] Real-time receive the feedback information of GPS positioning and the user backhaul channel through the UAV millimeter-wave communication system, analyze the millimeter-wave transmission beams from the multi-antenna UAV base station to multiple ground users in the feedback information, obtain the UAV transmission beamforming vector according to the millimeter-wave transmission beams, and extract the position data of the UAV and the ground users from the feedback information;

[0061] Based on the position data of the UAV and the ground users, calculate to determine the elevation angle and azimuth angle information between the UAV and the ground users, and calculate all the elevation angle and azimuth angle information between the UAV and the ground users during the entire flight of the UAV, so as to obtain the upper limit value of the jitter error during the UAV flight process;

[0062] Input the upper limit value of the jitter error into the UAV millimeter-wave air-ground channel jitter error model, and calculate the multi-user downlink transmission capacity sum according to the UAV transmission beamforming vector and the noise power from the UAV to the ground users, and determine the UAV millimeter-wave transmission beamforming optimization problem; wherein, the UAV millimeter-wave air-ground channel jitter error model is constructed according to the communication characteristics of the UAV millimeter-wave air-ground channel.

[0063] Based on the convex hull theory, the deterministic transformation of the problem of optimizing the UAV millimeter-wave transmission beamforming for the jitter error model is carried out to obtain a deterministic problem;

[0064] The deterministic problem is solved by using the successive convex approximation method to obtain the vector parameters of the UAV millimeter-wave transmission beamforming optimization problem;

[0065] Based on the UAV millimeter-wave transmission beamforming optimization problem model with known vector parameters, a UAV millimeter-wave communication system with the optimal anti-jitter robust wave performance is determined.

[0066] In a further embodiment, the calculation formulas for the elevation angle and azimuth angle information between the UAV and the ground user are respectively:

[0067]

[0068] where q u =(x u , y u ) T and q k (x k , y k ) T respectively represent the horizontal coordinates of the UAV and the ground user, x τ and y τ , τ∈{u, k} respectively represent the horizontal x-direction and y-direction coordinates of the UAV (ground user), h is the flight altitude of the UAV, and T is the transpose symbol of the vector.

[0069] In a further embodiment, the calculation formula for the UAV millimeter-wave air-ground channel jitter error model is:

[0070]

[0071] where h k is the channel vector, is a constant, c is the speed of light, f c is the carrier center frequency, is the distance between the UAV and the ground user, is the antenna array vector, θ k and are respectively the elevation angle and azimuth angle between the UAV and the ground user, and are respectively the elevation angle estimated value and azimuth angle estimated value between the UAV and the ground user, Δθ k and are respectively the elevation angle jitter error and azimuth angle jitter error caused by the UAV jitter, and They are the upper limit values of the pitch angle jitter error and the azimuth angle jitter error, respectively;

[0072] Among them, the antenna array vector has the following expression:

[0073]

[0074] In the formula, d is the distance between adjacent antenna elements of the uniform planar array, λ is the carrier wavelength, 1 ≤ m x ≤ M x , 1 ≤ m y ≤ M y , M x and M y are the number of row antennas and the number of column antennas of the uniform planar array, respectively.

[0075] In a further embodiment, the optimization algorithm expression for establishing the optimization problem of the UAV millimeter-wave transmission beamforming is:

[0076]

[0077]

[0078] In the formula, is the upper limit value of the UAV transmission power, is the sum of the multi-user downlink transmission capacities, and w k is the UAV transmission beamforming vector;

[0079] Among them, the sum of the multi-user downlink transmission capacities has the following calculation formula:

[0080]

[0081] In the formula, H k is the channel matrix, Λ k is the uncertainty set of H k , represents the noise power of the communication link from the UAV to the ground user, is the conjugate transpose vector of the k-th beamforming vector w k , is the conjugate transpose vector of the i≠k-th beamforming vector w i ;

[0082] Among them, the uncertainty set Λ k of H k has the following calculation expression:

[0083]

[0084] In the formula, h k is the channel vector, is h k the conjugate transpose vector of

[0085] In a further embodiment, the optimization algorithm combines the use of convex hull theory to deterministically transform the jitter error model. The method for obtaining the deterministic problem is as follows:

[0086] According to convex hull theory, the uncertain channel matrix containing jitter error can be expressed as a deterministic form of the weighted sum of a finite or infinite number of discrete samples within the uncertain set. The expression of the uncertain channel matrix is:

[0087]

[0088] where L k is the total number of samples, is the weighting coefficient of the j-th sample, is the j-th sample, which is determined by the discretized angle information; using to replace H k , the problem (P1) is approximately represented as the deterministic problem (P2), and the calculation formula is:

[0089]

[0090] s.t. (4b) (8b)

[0091] In a further embodiment, the method for solving the deterministic problem using the continuous convex approximation method is as follows:

[0092] Using the continuous convex approximation method, the non-convex problem is transformed into a convex optimization problem,

[0093] The transformation calculation formula is:

[0094]

[0095]

[0096]

[0097]

[0098] (4b) (9e)

[0099] where denotes taking the real part of A, a, f k , p k denote the auxiliary variables introduced in the optimization problem, is w k , f k , p k is a feasible solution of

[0100] In a further embodiment, the method for outputting the anti-jitter robust beamforming vector parameters of a millimeter-wave UAV includes:

[0101] In the UAV air-ground channel jitter error model, initialize the beamforming vector, and preset the auxiliary variables and the iteration accuracy;

[0102] Substitute the beamforming vector and the auxiliary variables into the formula of the successive convex approximation method for comparison, and select the beamforming vector and the auxiliary variables that satisfy the value range of the successive convex approximation method formula for output;

[0103] According to the multi-user downlink transmission capacity sum, determine whether the difference between the iterative values of the multi-user downlink transmission capacity sum in the previous and subsequent iterations is less than the iteration accuracy. If it is less, output the beamforming vector; if it is greater, loop to compare whether the beamforming vector and the auxiliary variables satisfy the value range of the convex approximation method.

[0104] The output vector parameters adaptively adjust the signal weighting values of each element in the antenna array according to the beamforming technology in the multi-antenna millimeter-wave UAV system; furthermore, adjust the transmission beam direction of the millimeter-wave UAV, so that the main lobe direction of the beam is aligned with the target user, and at the same time make other users in the null space of the target user, reduce the interference between users, and effectively improve the anti-jitter ability of the UAV millimeter-wave communication system.

[0105] And further illustrate the present invention in combination with Embodiment 1:

[0106] As Figure 1 shown, the system model of the present invention considers a UAV millimeter-wave downlink communication system, including a UAV base station and K ground users. The UAV adopts a uniform planar antenna array and is equipped with M = M x M y transmitting antennas, and the ground users are equipped with single antennas.

[0107] Assume that the air-ground node transmission channel is a line-of-sight transmission channel. Considering the communication characteristics of the UAV millimeter-wave air-ground channel, the UAV air-ground channel model based on the angular jitter error is established as follows: +

[0108]

[0109] Where c is the speed of light, f c is the carrier center frequency, q u =(x u , y u ) T and q k =(x k , y k ) Trespectively represent the horizontal coordinates of the UAV and the ground user, h is the flight altitude of the UAV, a k is the antenna array vector and can be expressed as:

[0110]

[0111] where d is the distance between adjacent antenna elements of the uniform planar array, λ is the carrier wavelength, 1 ≤ m x ≤ M x ,1 ≤ m y ≤ M y ,M = M x × M y is the total number of antennas of the uniform planar array. θ k and respectively represent the elevation angle and azimuth angle between the UAV and the ground user. The angle information between the UAV and the ground user can be expressed as:

[0112]

[0113] Different from the ground cellular network, due to the lack of fixed ground support facilities, the stability of the UAV cannot be guaranteed, resulting in angular jitter errors in its vertical and horizontal directions. The UAV jitter model is as Figure 2 shown. The left figure is the schematic diagram of the UAV millimeter-wave emission beam in the vertical section, and the right figure is the schematic diagram of the UAV millimeter-wave emission beam in the horizontal section. Considering the jitter characteristics of the UAV, the angular jitter error model based on the UAV jitter can be established as:

[0114]

[0115]

[0116] where and are respectively the estimated values of the elevation angle and azimuth angle between the UAV and the ground user, Δθ k and are respectively the elevation angle jitter error and azimuth angle jitter error caused by the UAV jitter, and are respectively the maximum values of the elevation angle jitter error and azimuth angle jitter error. Using the uncertainty angular jitter error model to characterize the uncertain channel matrix, it can be expressed as:

[0117]

[0118]

[0119] where

[0120] Assume that the signal transmitted by the UAV can be expressed as:

[0121]

[0122] where s k is the information sent by the UAV, represents the millimeter-wave transmission beamforming vector of the UAV. Thus, the signal received by the k-th ground user can be specifically expressed as:

[0123]

[0124] where is the additive white Gaussian noise of the communication link from the UAV to the ground user. From the above formula, the signal-to-interference-plus-noise ratio from the UAV to the k-th ground user can be expressed in the following form:

[0125]

[0126] According to formula (1-8), considering the worst-case scenario, the sum of the multi-user downlink transmission capacities can be expressed as:

[0127]

[0128] Furthermore, an optimization problem of the UAV millimeter-wave transmission beamforming with angular jitter error is constructed to maximize the sum of the multi-user downlink transmission capacities, which is specifically modeled as:

[0129]

[0130]

[0131] where represents the maximum value of the UAV transmission power.

[0132] Next, the optimization problem (1-10) is processed to transform it into a solvable form. First, a deterministic transformation method for the jitter error model based on the convex hull theory is proposed. According to the convex hull theory, the uncertain channel matrix with jitter error can be expressed as a deterministic form of the weighted sum of a finite or infinite number of discrete samples within the uncertain set, that is

[0133]

[0134] where L k is the total number of samples, is the weighting coefficient of the j-th sample, is the j-th sample. Determined by and discretized through the following formula to obtain: through the following formula:

[0135]

[0136]

[0137] Therefore, by using to replace H k , problem (P1) can be equivalently expressed as a deterministic problem (P2):

[0138]

[0139] s.t. (10b) (1 - 13b)

[0140] The objective function in the optimization problem (1 - 13) is in a non - convex form. By introducing auxiliary variables a, f k , p k , it is equivalently transformed into the following form:

[0141]

[0142]

[0143]

[0144]

[0145] (10b) (1 - 14e)

[0146] Since the constraint condition (1 - 14c) is non - convex and difficult to solve, we apply the continuous convex approximation method and transform it into a convex form through the first - order Taylor expansion. Given there is

[0147]

[0148] Thus, (1 - 14c) can be transformed into:

[0149]

[0150] So far, the original non - convex optimization problem can be equivalently transformed into the following form:

[0151]

[0152] s.t. (10b), (14b), (14d), (16) (1 - 17b)

[0153] Finally, a robust beamforming algorithm against jitter for the UAV millimeter - wave communication system is designed. By iteratively solving through continuous convex approximation, the UAV transmit beamforming vector that maximizes the sum of multi - user downlink transmission capacities is obtained. The specific algorithm is as Figure 3As shown below, the process is as follows:

[0154] Step 1: Initialize the beamforming vector Auxiliary variable and Let n = 0 and ε = 10 -4 .

[0155] Step 2: Based on the beamforming vector and the auxiliary variable , calculate the beamforming vector and the auxiliary variable

[0156] Step 3: Determine whether the objective function value of formula (1-9) converges to ε, that is, whether the difference between the two consecutive iteration values is less than the iteration precision. If it holds, continue to Step 4; otherwise, let n = n + 1 and then go back to Step 2.

[0157] Step 4: Obtain the optimal solution of the beamforming vector

[0158] The output vector parameters adaptively adjust the signal weighting values of each element in the antenna array according to the beamforming technology in the multi-antenna millimeter-wave UAV system; thereby adjusting the transmission beam direction of the millimeter-wave UAV so that the main lobe direction of the beam is aligned with the target user, and at the same time making other users in the null space of the target user to reduce the interference between users. Refer to Figure 4 For further explanation; Figure 4 This is the beam pattern of the beamforming vector w1 under the anti-jitter robust beamforming scheme proposed by the present invention. The rectangular area in the figure is the angular jitter error range caused by the UAV jitter. It can be seen from the figure that the main lobe of w1 points to the direction where User 1 is located, and the normalized transmission power is higher than -0.1 dB. At the same time, the null space of w1 is aligned with the uncertain areas where User 2 and User 3 are located, and their normalized transmission powers are both lower than -50 dB, which means that the anti-jitter robust beamforming scheme proposed by the present invention can effectively improve the anti-jitter ability of the UAV millimeter-wave communication system and reduce the interference between users.

[0159] Figure 5It is a graph showing the variation trend of the multi-user downlink transmission sum capacity with the maximum angle error for the anti-jitter robust beamforming scheme and the non-robust beamforming scheme. It can be seen from the graph that as the maximum pitch angle jitter error and the maximum azimuth angle jitter error increase, the downlink transmission sum capacity of both the robust and non-robust schemes decreases continuously. However, the decreasing rate of the robust scheme is significantly slower than that of the non-robust scheme because the robust scheme takes into account the angle jitter error caused by UAV jitter during optimization and is robust to the jitter error, while the non-robust scheme does not consider the influence of UAV jitter, resulting in a deviation of the beam direction and a rapid decline in the performance of the UAV millimeter-wave system.

[0160] Therefore, through the present invention, the advantages of the UAV communication system and the millimeter-wave technology are combined to achieve complementary advantages. At the same time, a deterministic conversion method for the jitter error model based on the convex hull theory is proposed for the jitter characteristics of UAV jitter, effectively solving the problem of uncertain angle error caused by UAV jitter and improving the anti-jitter ability of the UAV millimeter-wave communication system.

[0161] Aiming at the multi-user downlink transmission capacity maximization problem of the UAV millimeter-wave system in the worst case, an iterative solution algorithm based on successive convex approximation is proposed to transform the non-convex problem into a convex form. By optimizing the beamforming vector, the optimal sub-optimal solution of the original problem can be obtained by convergence within a finite number of iterations, ensuring the quality-of-service requirements of the UAV millimeter-wave downlink data transmission within the mission window.

[0162] Embodiments of the present application may be provided as a method, a system, or a computer program product. Therefore, the present application may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0163] Embodiments of the present application may be provided as a method, a system, or a computer program product. Therefore, the present application may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0164] This application is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate a means for implementing the functions specified in the Figure 1 one or more flows and / or blocks Figure 1 one or more blocks.

[0165] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including an instruction means that implements the functions specified in the Figure 1 one or more flows and / or blocks Figure 1 one or more blocks.

[0166] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, so that the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in the Figure 1 one or more flows and / or blocks Figure 1 one or more blocks.

[0167] The above is only the preferred embodiment of the present invention. Without departing from the technical principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. A method for optimizing anti-jitter robust beamforming in a millimeter-wave UAV communication system, characterized in that Including: Receiving in real time the GPS positioning and the feedback information of the user backhaul channel through the UAV millimeter-wave communication system, analyzing the millimeter-wave transmission beams emitted by the multi-antenna UAV base station to multiple ground users in the feedback information, obtaining the UAV transmission beamforming vector according to the millimeter-wave transmission beams, and extracting the position data of the UAV and the ground users from the feedback information; Calculating based on the position data of the UAV and the ground users to determine the elevation angle and azimuth angle information between the UAV and the ground users, and calculating all the elevation angle and azimuth angle information between the UAV and the ground users during the entire flight of the UAV to obtain the upper limit value of the jitter error during the flight of the UAV; Inputting the upper limit value of the jitter error into the UAV millimeter-wave air-ground channel jitter error model, and calculating the sum of the downlink transmission capacities of multiple ground users according to the UAV transmission beamforming vector and the noise power from the UAV to the ground users to determine the UAV millimeter-wave transmission beamforming optimization problem; wherein, the UAV millimeter-wave air-ground channel jitter error model is constructed according to the communication characteristics of the UAV millimeter-wave air-ground channel; Based on the convex hull theory, performing a deterministic transformation of the UAV millimeter-wave transmission beamforming optimization problem for the jitter error model to obtain a deterministic problem; Solving the deterministic problem by using the successive convex approximation method to obtain the vector parameters of the UAV millimeter-wave transmission beamforming optimization problem; Based on the UAV millimeter-wave transmission beamforming optimization problem model with known vector parameters, determining the UAV millimeter-wave communication system with the optimal anti-jitter robust wave performance; Determining the expression of the UAV millimeter-wave transmission beamforming optimization problem as: wherein, is the upper limit value of the UAV transmission power, is the sum of multi-user downlink transmission capacities, and w k is the UAV transmission beamforming vector; Among them, the multi-user downlink transmission capacity and The calculation formula is as follows: where \(H\) k is the channel matrix, \(\Lambda\) k is the uncertainty set of \(H\) k , \(\sigma^2\) denotes the noise power of the communication link from the UAV to the ground user, \(\mathbf{w}_k\) k is the conjugate transpose vector of the \(k\)-th beamforming vector \(\mathbf{w}_k\), \(\mathbf{w}_i^H\) (\(i\neq k\)) i is the conjugate transpose vector of the \(i\neq k\)-th beamforming vector \(\mathbf{w}_i\); The method for obtaining the deterministic problem is: According to the convex hull theory, the uncertain channel matrix containing the jitter error is expressed in the deterministic form of the weighted sum of a finite or infinite number of discrete samples within the uncertain set, and the expression of the uncertain channel matrix is: where L k is the total number of samples, is the weighting coefficient of the j-th sample, is the j-th sample, which is determined by the discretized angular information; using to replace H k , the problem (P1) is approximately expressed as a deterministic problem (P2), and the calculation formula is:

2. The anti-jitter robust beamforming optimization method for a millimeter-wave UAV communication system according to claim 1, characterized in that The calculation formulas for the elevation angle and azimuth angle information between the UAV and the ground users are respectively: where q u =(x u , y u ) T and q k (x k , y k ) T represent the horizontal coordinates of the UAV and the ground user respectively, x τ and y τ , τ ∈ {u, k} represent the horizontal x-direction and y-direction coordinates of the UAV and the ground user respectively, k ∈ h is the flight altitude of the UAV, and T is the transpose symbol of the vector.

3. The anti-jitter robust beamforming optimization method for a millimeter-wave UAV communication system according to claim 1, characterized in that, The calculation formula for the UAV millimeter-wave air-ground channel jitter error model is: where h k is the channel vector, is a constant, c is the speed of light, f c is the carrier center frequency, is the distance between the UAV and the ground user, is the antenna array vector, θ k and are respectively the elevation angle and the azimuth angle between the UAV and the ground user, and are respectively the estimated values of the elevation angle and the azimuth angle between the UAV and the ground user, Δθ k and are respectively the elevation angle jitter error and the azimuth angle jitter error caused by the UAV jitter, and are respectively the upper limit value of the elevation angle jitter error and the upper limit value of the azimuth angle jitter error; Among them, the antenna array vector has the following expression: where d is the distance between adjacent antenna elements of the uniform planar array, λ is the carrier wavelength, 1 ≤ m x ≤ M x , 1 ≤ m y ≤ M y , M x and M y are the number of row antennas and the number of column antennas of the uniform planar array, respectively.

4. The anti-jitter robust beamforming optimization method for a millimeter-wave UAV communication system according to claim 1, characterized in that Wherein, H k uncertain set Λ k The calculation expression is as follows: where h k is the channel vector, and h k is the conjugate transpose vector of h.

5. The anti-jitter robust beamforming optimization method for a millimeter-wave UAV communication system according to claim 1, characterized in that The method for solving the deterministic problem by using the successive convex approximation method is: Using the successive convex approximation method to transform the non-convex problem into a convex optimization problem, The transformation calculation formula is: wherein, denotes taking the real part of A, a, f k , p k denotes the auxiliary variables introduced in the optimization problem, is the feasible solution of w k , f k , p k .

6. The anti-jitter robust beamforming optimization method for a millimeter-wave UAV communication system according to claim 1, characterized in that The method for obtaining the vector parameters of the UAV millimeter-wave transmission beamforming optimization problem includes: In the UAV air-ground channel jitter error model, initializing the beamforming vector, and presetting the auxiliary variables and the iteration precision; Substituting the beamforming vector and the auxiliary variables into the formula of the successive convex approximation method for comparison, and selecting the beamforming vector and the auxiliary variables whose output satisfies the value range of the successive convex approximation method formula; According to the sum of the multi-user downlink transmission capacities, judging whether the difference between the iterative values of the sum of the multi-user downlink transmission capacities in the previous and subsequent times is less than the iteration precision. If it is less, the beamforming vector is output. If it is greater, the beamforming vector and the auxiliary variables are cyclically compared to see if they satisfy the value range of the convex approximation method.

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