A method for communication coverage enhancement for low altitude aircraft path planning

Abstract

The application relates to a communication coverage enhanced low-altitude aircraft path planning method, belonging to the technical field of communication, and comprising the following steps: modeling a communication system composed of a low-altitude aircraft equipped with a movable antenna and at least one base station to obtain a joint state model; establishing a discretized optimization problem with a signal-to-interference-and-noise ratio, a maximum speed of the aircraft, a moving range and speed of the antenna, a minimum antenna spacing and base station association as constraints, and minimizing a task completion time of the aircraft from a starting point to an ending point as an optimization target; adopting a selective uniform cost search algorithm to iteratively expand nodes on a discrete grid, optimizing beamforming, antenna position and base station association each time of expansion, reserving nodes meeting the signal-to-interference-and-noise ratio and having a relatively small potential task time, and outputting an optimal path to the ending point; and flying the aircraft according to the optimal path and adjusting the antenna position and the beamforming in real time to maintain link quality. The application guarantees stable communication connection under a cellular network and significantly improves trajectory planning efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of communication technology and path planning technology, in particular to a communication coverage enhanced low-altitude aircraft path planning method. BACKGROUND

[0002] In recent years, with the rapid development of low-altitude economy, low-altitude aircraft have attracted widespread attention due to their maneuverability, flexibility, and ability to provide services on demand in various scenarios. In the context of wireless communication systems, low-altitude aircraft are considered an important technology for improving coverage, system capacity, and communication reliability. When low-altitude aircraft serve as aerial users, they usually rely on ground cellular networks to obtain reliable communication connections. Compared with traditional ground users, low-altitude aircraft usually fly at higher altitudes, forming a line-of-sight-dominant channel with ground base stations. On the one hand, this characteristic enables low-altitude aircraft to establish stable links even at long distances, thereby improving their connection opportunities; on the other hand, strong line-of-sight propagation also makes low-altitude aircraft more susceptible to interference from a large number of non-associated base stations, posing a serious challenge to communication performance assurance. Therefore, in the context of the rapid development of low-altitude economy, how to effectively suppress interference has become a key issue in low-altitude aircraft communication in cellular networks.

[0003] However, the current communication performance of low-altitude aircraft is often limited by the lack of spatial freedom due to fixed antenna structures, thereby limiting the ability to suppress interference, resulting in unsatisfactory trajectory planning results for low-altitude aircraft. Therefore, a communication coverage enhanced low-altitude aircraft path planning method is proposed. This method equips low-altitude aircraft with a movable antenna array, allowing the antenna to move flexibly within a limited area, providing additional spatial freedom and flexibility in beamforming, thereby achieving more effective interference suppression to minimize the task completion time of low-altitude aircraft while ensuring reliable communication performance throughout the journey. SUMMARY

[0004] In view of the above analysis, the present application aims to disclose a communication coverage enhanced low-altitude aircraft path planning method to solve the problem of trajectory planning for low-altitude aircraft being limited by fixed antenna structures.

[0005] The present application discloses a communication coverage enhanced low-altitude aircraft path planning method, which comprises:

[0006] Modeling a communication system composed of a low-altitude aircraft equipped with a movable antenna and at least one base station; obtaining a joint state model containing aircraft trajectory, antenna position, beamforming vector, and base station association;

[0007] Discretize the optimization problem of the model; the problem is constrained by signal-to-interference-and-noise ratio, maximum speed of the aircraft, antenna movement range and speed, minimum antenna spacing, base station association, and the optimization objective is to minimize the task completion time of the aircraft from the starting point to the ending point;

[0008] The selective uniform cost search algorithm is used to iteratively expand nodes on a discrete grid, and beamforming, antenna position and base station association are optimized jointly at each expansion. Nodes that meet the signal-to-interference-and-noise ratio and have a small potential task time are retained, and the optimal path is output at the end point.

[0009] The aircraft flies along the optimal path and adjusts the antenna position and beamforming in real time to maintain link quality.

[0010] Further, the low-altitude aircraft is equipped with a two-dimensional array of movable antennas at the bottom; when the low-altitude aircraft flies at a fixed height within an area where base stations are uniformly distributed, the aircraft and the base stations form a cellular networked communication system.

[0011] Further, The received signal-to-interference-and-noise ratio of the low-altitude aircraft at time is:

[0012] ;

[0013] where, is a set of base stations, represents the association of the low-altitude aircraft with base station at time , and the remaining base stations other than base station are considered as interference base stations; represents the beamforming vector for communication between the low-altitude aircraft and base station , and represents the conjugate transpose of the vector; is the transmit power of the base station; , are the channel vectors between the low-altitude aircraft and base station at time and base station , respectively; is the additive white Gaussian noise variance.

[0014] Further, the channel vectors between the low-altitude aircraft and base station at time are represented as:

[0015] ;

[0016] ​wherein, represents the path loss at a reference distance of 1 meter; is a base station to the low-altitude aircraft Euclidean distance; is the carrier wavelength; represents the time from the base station is the steering vector pointing to the movable antenna array;

[0017] ;

[0018] wherein, , is the antenna two-dimensional coordinates in the movable antenna panel local coordinate system; is a base station to the low-altitude aircraft wave vector at time.

[0019] Further, the discretization optimization problem of the model is:

[0020] ,

[0021] ,

[0022] ,

[0023] ,

[0024] ,

[0025] ,

[0026] ,

[0027] ,

[0028] ,

[0029] wherein , is the antenna position vector of antennas at time, is the beamforming matrix of the low-altitude aircraft communicating with base stations at time, is the position of the low-altitude aircraft at time, is the connection indication vector of the low-altitude aircraft and the base station at time; The mission completion time for a low-altitude aircraft from the starting point to the destination; It is the minimum signal-to-interference-plus-noise ratio threshold at which low-altitude aircraft can maintain reliable communication. It is the starting point for low-altitude aircraft flights. It is the destination for low-altitude aircraft. It is the maximum speed of a low-altitude aircraft. It refers to the range of motion of the movable antenna. This is the maximum moving speed of the movable antenna. To exclude the first Any antenna position outside the antenna; It is the minimum antenna spacing required to avoid antenna coupling effects.

[0030] Furthermore, during the iterative expansion of nodes on the discrete grid using the selective consistent cost search algorithm, the intermediate expansion nodes are set as follows:

[0031] ;

[0032] in, This indicates the index of a visited grid point in the trajectory of a low-altitude aircraft. For grid point locations, For the corresponding antenna position, This is the low-altitude aircraft-base station association indication vector. As of the date The history of low-altitude aircraft trajectories at each access grid point.

[0033] Furthermore, during the iterative expansion of nodes on the discrete grid using the selective consistent cost search algorithm, for each node... The defined cost functions include:

[0034] Flight time cost function , for starting from the initial position Along the trajectory Reaching the grid point The cumulative flight time;

[0035] Potential minimum task completion time cost function , for starting from the initial position To grid point Flight time and from To the finish line The sum of the lower bounds of achievable flight times;

[0036] ;

[0037] in, For the first The time taken for a segment of the flight path;

[0038] ;

[0039] wherein, and represent the x-axis, y-axis coordinates of the end point respectively, and and represent the x-axis, y-axis coordinates of the grid point respectively.

[0040] Further, the planning process comprises:

[0041] Step S301, initialization; check whether the starting point satisfies the signal-to-interference-and-noise ratio constraint, if yes, generate an initial node and add it to the node set;

[0042] Step S302, when the node set is not empty, perform hierarchical screening, from the first node subset of the node set, screen the low-altitude aircraft potential minimum task completion time minimum, then screen the second node subset of the low-altitude aircraft cumulative flight time maximum, randomly select a node in the second node subset for expansion, and delete the node in the node set;

[0043] Step S303, judge whether the grid point position of the selected node is the end point, if yes, find the minimum feasible low-altitude aircraft path; otherwise, go to the next step;

[0044] Step S304, for all neighbor grid points of the grid point position of the selected node, perform joint optimization of the neighbor grid point's beamforming vector, antenna position vector, and the association between the low-altitude aircraft and the base station, obtain the maximum signal-to-interference-and-noise ratio, and take the neighbor grid point satisfying the low-altitude aircraft signal-to-interference-and-noise ratio constraint as a feasible neighbor grid point;

[0045] Step S305, compare the next layer of nodes composed of each feasible neighbor grid point with the nodes already existing in the node set, which have the same grid point position, antenna position, and the association between the low-altitude aircraft and the base station, retain the node with smaller potential minimum task completion time as the candidate node, and add it to the node set;

[0046] Step S306, limit the number of candidate nodes stored in each trajectory level in the node set to a fixed value;

[0047] Step S307, when the node set is empty and no node reaching the end point is found, there is no low-altitude aircraft trajectory meeting the constraint in this scenario; when the node set is not empty, return to step S302.

[0048] Further, in the joint optimization in step 304, the beamforming vectors of the neighbor grid points are solved by the minimum mean square error method; the antenna position vectors are solved by the continuous optimization method; in the association of the low-altitude aircraft and the base station, the low-altitude aircraft is always connected with the base station that can bring the maximum signal-to-interference-and-noise ratio.

[0049] Further, in the calculation of the beamforming vectors of the neighbor grid points,

[0050] For the first low-altitude aircraft trajectory point, the closed-form solution of the beamforming vector is calculated as:

[0051]

[0052] wherein, is a unit matrix, the channel vector of the low-altitude aircraft and the base station when the low-altitude aircraft is located at the first trajectory point, .

[0053] The present application can realize one of the following beneficial effects:

[0054] The low-altitude aircraft path planning method for communication coverage enhancement disclosed in the present application significantly suppresses the strong line-of-sight interference of non-associated base stations by means of movable antenna arrays and joint optimization beamforming, maintains a high signal-to-interference-and-noise ratio throughout the journey, and guarantees stable connection of the low-altitude aircraft in the cellular network; minimizes the task completion time of the low-altitude aircraft under the condition of meeting the communication link quality, significantly improves the trajectory planning efficiency of the low-altitude aircraft; and provides a new and effective design mode beyond the traditional antenna architecture for future air communication networks. BRIEF DESCRIPTION OF DRAWINGS

[0055] The accompanying drawings are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the principles of the application, and, wherein like reference numerals refer to like parts throughout the several views of the drawings;

[0056] Figure 1 The flow chart of the low-altitude aircraft path planning method for communication coverage enhancement in the embodiment of the present application;

[0057] Figure 2 The model diagram of the low-altitude aircraft path planning method for communication coverage enhancement in the embodiment of the present application;

[0058] Figure 3 The flow chart of the trajectory planning process in the embodiment of the present application;

[0059] Figure 4 The comparison diagram of the low-altitude aircraft trajectory planning results in the embodiment of the present application.​​ DETAILED DESCRIPTION

[0060] The preferred embodiments of the present application will be described in detail below with reference to the drawings, which form a part of this application. The drawings illustrate embodiments of the application and, together with the description, serve to explain the principles of the application.

[0061] One embodiment of the present application discloses a communication coverage enhanced low-altitude aerial vehicle path planning method, as shown in the formula (1), comprising: Figure 1

[0062] Step S1, model the communication system composed of the low-altitude aerial vehicle equipped with a movable antenna and at least one base station; obtain a joint state model containing the aerial vehicle trajectory, antenna position, beamforming vector and base station association;

[0063] Step S2, establish a discretized optimization problem of the model; the problem is constrained by the signal-to-interference-and-noise ratio, maximum speed of the aerial vehicle, moving range and speed of the antenna, minimum antenna spacing, and base station association, and the optimization objective is to minimize the task completion time of the aerial vehicle from the starting point to the ending point;

[0064] Step S3, use the selective uniform cost search algorithm to iteratively expand nodes on the discrete grid, jointly optimize the beamforming, antenna position and base station association at each expansion, retain the nodes that meet the signal-to-interference-and-noise ratio and have smaller potential task time, and output the optimal path to the ending point;

[0065] Step S4, the aerial vehicle flies along the optimal path and adjusts the antenna position and beamforming in real time to maintain the link quality.

[0066] Specifically, in the present embodiment, a two-dimensional array composed of one movable antenna is installed at the bottom of the low-altitude aerial vehicle; when the low-altitude aerial vehicle flies at a fixed height in an area where base stations are uniformly distributed, the aerial vehicle and the base stations form a cellular network communication system.

[0067] In one specific example in the present embodiment, a communication system taking the downlink communication between the base station and the low-altitude aerial vehicle as an example is given, as shown in the formula (2), Figure 2

[0068] In a square area with a side length of m, the low-altitude aerial vehicle flies at a fixed height of m, the starting point and the ending point are m and m respectively. The maximum flight speed of the low-altitude aerial vehicle is m / s. In the square area, there are base stations uniformly distributed, and the antenna height of each base station is m. The low-altitude aerial vehicle is equipped with​​ A movable antenna with a maximum moving speed of m / s. The carrier wavelength is m, and the minimum antenna spacing is m. The side length of the antenna moving area is m. The transmit power of each base station is dBm, the noise power is dBm, and the average channel power gain at the reference distance is dB. The granularity of the low-altitude aircraft trajectory planning is m.

[0069] Specifically, in the communication system modeling in step S1, the following are included:

[0070] 1) Establish the wave vector from the base station to the low-altitude aircraft at time ;

[0071] ;

[0072] wherein is the wave vector from the base station to the low-altitude aircraft at time , is the carrier wavelength, is the horizontal coordinate of the low-altitude aircraft at time , is the horizontal coordinate of the base station .

[0073] 2) Establish the steering vector from the base station to the movable antenna array at time ;

[0074] ;

[0075] wherein , ; is the two-dimensional coordinate of the antenna in the movable antenna panel local coordinate system, is the range of the movable antenna panel;

[0076] 3) Establish the channel vector between the base station and the low-altitude aircraft at time ;

[0077] ;

[0078] wherein denotes the path loss at a reference distance of 1 meter; is a base station to the low-altitude aircraft Euclidean distance, ;

[0079] is a base station to the low-altitude aircraft channel power gain.

[0080] 4) the connection indication vector of the low-altitude aircraft to the base station ;

[0081] ;

[0082] wherein denotes the association state of the low-altitude aircraft to the base station .

[0083] Specifically, when the low-altitude aircraft establishes a communication link with the base station through the allocated time-frequency resource block at time , , the remaining base stations are then regarded as interfering base stations, wherein ; otherwise, .

[0084] 5) the received signal-to-interference-plus-noise ratio of the low-altitude aircraft at time ;

[0085] ;

[0086] wherein is a set of base stations, denotes the association of the low-altitude aircraft to the base station at time , wherein the remaining base stations except for the base station are regarded as interfering base stations; denotes the beamforming vector of the low-altitude aircraft to the base station for communication, and denotes the conjugate transpose of the vector; is the transmit power of the base station; , denote the channel vectors between the low-altitude aircraft and the base station , the base station at time ; is the additive white Gaussian noise variance.

[0087] Specifically, in step S2, the discretization optimization problem of the model is:

[0088] ,

[0089] ,

[0090] ,

[0091] ,

[0092] ,

[0093] ,

[0094] ,

[0095] ,

[0096] ,

[0097] in , for time Antenna position vectors of each antenna. for Low-altitude aircraft and Beamforming matrix for communication of individual base stations for The location of low-altitude aircraft at all times. for The connection indication vector between the low-altitude aircraft and the base station at any given time; The mission completion time for a low-altitude aircraft from the starting point to the destination; It is the minimum signal-to-interference-plus-noise ratio threshold at which low-altitude aircraft can maintain reliable communication. It is the starting point for low-altitude aircraft flights. It is the destination for low-altitude aircraft. It is the maximum speed of a low-altitude aircraft. It refers to the range of motion of the movable antenna. This is the maximum moving speed of the movable antenna. To exclude the first Any antenna position outside the antenna; It is the minimum antenna spacing required to avoid antenna coupling effects.

[0098] Specifically, in step S3, in the example of discretizing the flight area into a grid,

[0099] Low-altitude aircraft at an altitude of The side length at the level flight altitude is Flying within a square area, in which sufficiently large to cover all possible positions of the low-altitude aircraft during its flight. The region is discretized into grid cells with granularity , where , thus there are discrete points in total. The granularity is small enough to guarantee that the signal-to-interference-and-noise ratio (SINR) is constant within each grid cell. Denote the position of the th grid point as , where . Thus, by the path discretization method, when the trajectory of the low-altitude aircraft is line segments, the low-altitude aircraft visits grid points during its flight.

[0100] In this embodiment, during the process of iteratively expanding nodes on the discrete grid using the selective uniform cost search algorithm, the intermediate nodes set for expansion are:

[0101] ;

[0102] where denotes the index of the visited grid point in the trajectory of the low-altitude aircraft, i.e., the level of the node, , the maximum value of is , the position of the grid point, , the corresponding antenna position, , the low-altitude aircraft-base station association indicator vector, , the history of the trajectory of the low-altitude aircraft up to the th visited grid point.

[0103] Further, during the process of iteratively expanding nodes on the discrete grid using the selective uniform cost search algorithm, for a node , the cost function defined includes:

[0104] flight time cost function , the cumulative flight time from the initial position to the grid point along the trajectory ;

[0105] potential minimum task completion time cost function , the sum of the flight time from the initial position to the grid point and the lower bound of the achievable flight time from to the end point ;

[0106] ;

[0107] wherein, is the first segment flight trajectory time;

[0108] ;

[0109] wherein, and represent the x-axis, y-axis coordinates of the end point respectively, and and represent the x-axis, y-axis coordinates of the grid point respectively.

[0110] As shown in Figure 3 , the planning process in step S3 includes:

[0111] Step S301, initialization; check whether the starting point satisfies the signal-to-interference-and-noise ratio constraint, if yes, generate an initial node and add it to the node set;

[0112] that is, when the signal-to-interference-and-noise ratio of the starting point is greater than the minimum signal-to-interference-and-noise ratio threshold value at which the low-altitude aircraft can maintain reliable communication; generate an initial node and add it to the node set ; is the antenna position of the starting point, is the low-altitude aircraft-base station association indication vector of the starting point, is the low-altitude aircraft trajectory history of the 0th visited grid point.

[0113] Step S302, when the node set is not empty, perform hierarchical screening, from the first node subset in the node set, which is the low-altitude aircraft potential minimum task completion time minimum, further screen out the second node subset which is the low-altitude aircraft cumulative flight time maximum, randomly select a node in the second node subset for expansion, and delete the node in the node set;

[0114] the first node subset ; the second node subset , randomly select a node in the second node subset for expansion, and delete the node in the node set .

[0115] Step S303, judge whether the grid point position of the selected node is the end point , if yes, find the minimum feasible low-altitude aircraft path; otherwise, proceed to the next step;

[0116] Step S304: For the grid point position of the selected node For all neighboring grid points, perform joint optimization of the beamforming vector, antenna position vector, and association between the low-altitude aircraft and the base station to obtain the maximum signal-to-interference-plus-noise ratio (SIR). Neighboring grid points that satisfy the SIR constraint of the low-altitude aircraft are considered as feasible neighboring grid points.

[0117] Step S305: The next layer of nodes consists of each feasible neighboring grid point. With node set The nodes that already exist in the network, have the same grid point location, antenna location, and association between the low-altitude aircraft and the base station, are compared, and the nodes with the smaller potential minimum task completion time are retained as candidate nodes and added to the node set.

[0118] Step S306: Limit the number of candidate nodes stored in each trajectory level of the node set to a fixed value c;

[0119] ;

[0120] Step S307: When the node set is empty and no destination has been found. If the set of nodes is empty, then there is no low-altitude aircraft trajectory that meets the constraints in this scenario; if the set of nodes is not empty, then return to step 302.

[0121] Specifically, in the joint optimization in step S304, the beamforming vector of the neighboring grid points is solved by the minimum mean square error method; the antenna position vector is solved by the continuous optimization method; and in the association between the low-altitude aircraft and the base station, the low-altitude aircraft is always connected only to the base station that can bring the maximum signal-to-interference-plus-noise ratio.

[0122] More specifically, in the calculation of beamforming vectors for neighboring grid points,

[0123] For the A low-altitude aircraft trajectory point, beamforming vector The closed-form solution is calculated using the least mean square error method as follows:

[0124] ;

[0125] in, It is the identity matrix. The low-altitude aircraft is located at the Each trajectory point is related to the base station. The channel vector, .

[0126] More specifically, in the calculation of the antenna position vector of neighboring grid points,

[0127] Given the beamforming vector and the antenna position vector of this grid point, the optimization problem of the antenna position vectors of neighboring grid points can be simplified to:

[0128] ;

[0129] ;

[0130] ;

[0131] ;

[0132] This optimization problem can be solved using a continuous optimization algorithm.

[0133] Since the second constraint is a non-convex constraint, it can be relaxed using the Cauchy-Schwarz inequality as follows:

[0134] ;

[0135] in, For the continuous optimization algorithm Antenna position vector during the step-by-step iteration process.

[0136] At this point, all constraints in the optimization problem are convex. Therefore, in each iteration, we can first solve the following ascending direction to find the problem:

[0137] ,

[0138] ,

[0139] ,

[0140] ,

[0141] in, for exist The gradient at point can be obtained by the following formula:

[0142] ;

[0143] in, It is A dimensional vector, whose dimensional vector is the first dimensional vector. One element is 1, and the rest are 0. This is a convex optimization problem, which can be solved efficiently using the standard optimization toolbox.

[0144] Then, the step size in the ascending direction is obtained using a one-dimensional search method. for:

[0145] ;

[0146] Finally, may be updated as:

[0147] ;

[0148] The iteration of the continuous optimization algorithm stops when the increase of the objective function is less than a threshold . .

[0149] More specifically, in the low-altitude aerial vehicle-base station association indication vector calculation of the neighbor grid points,

[0150] the low-altitude aerial vehicle-base station association indication value is , where is the index of the base station with the maximum signal-to-interference-and-noise ratio for the low-altitude aerial vehicle.

[0151] Steps S305 and S306 reduce the complexity of the path planning algorithm by reducing the number of expandable nodes. Step S307 indicates that when the node set is empty, the low-altitude aerial vehicle trajectory that meets the condition cannot be obtained.

[0152] When the trajectory planning result is obtained, in step S4, the aerial vehicle flies along the planned optimal path and adjusts the antenna position and beamforming in real time to maintain the link quality and achieve communication coverage enhancement.

[0153] As shown in Figure 4 , the embodiment also gives a comparison of trajectory planning of low-altitude aerial vehicles equipped with movable antennas, low-altitude aerial vehicles equipped with traditional fixed antennas, and low-altitude aerial vehicles equipped with sparse antennas in the communication coverage enhanced low-altitude aerial vehicle path planning method. The low-altitude aerial vehicle scheme equipped with movable antennas allows the aerial vehicle to fly along a straighter and shorter trajectory, significantly compressing the task time, and verifying the communication coverage enhancement effect in the embodiment.

[0154] In summary, the communication coverage enhanced low-altitude aerial vehicle path planning method disclosed in the embodiment significantly suppresses the strong line-of-sight interference of non-associated base stations by means of movable antenna arrays and joint optimization beamforming, maintains a high signal-to-interference-and-noise ratio throughout the journey, and guarantees stable connection of low-altitude aerial vehicles in a cellular network; minimizes the task completion time of low-altitude aerial vehicles under the condition of meeting the communication link quality, significantly improves the trajectory planning efficiency of low-altitude aerial vehicles; and provides a new and effective design mode beyond the traditional antenna architecture for future air communication networks.

[0155] The above describes only the preferred embodiments of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical scope disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A path planning method for low-altitude aircraft with enhanced communication coverage, characterized in that, include: Model a communication system consisting of a low-altitude aircraft equipped with a movable antenna and at least one base station; A joint state model is obtained, which includes the aircraft trajectory, antenna position, beamforming vector, and base station association. The model is established as a discretized optimization problem; the problem is constrained by signal-to-interference-plus-noise ratio, maximum speed of the aircraft, antenna movement range and speed, minimum antenna spacing, and base station correlation, with the optimization objective being to minimize the mission completion time of the aircraft from the starting point to the ending point. A selective consistent cost search algorithm is used to iteratively expand nodes on a discrete grid. During each expansion, beamforming, antenna position and base station association are jointly optimized to retain nodes that meet the signal-to-interference-plus-noise ratio and have a small potential task time. The optimal path is output at the destination. The aircraft flies along the optimal path and adjusts the antenna position and beamforming in real time to maintain link quality; The discretization optimization problem for establishing the model is as follows: ， ， ， ， ， ， ， ， ， in , for time Antenna position vectors of each antenna. for Low-altitude aircraft and Beamforming matrix for communication of individual base stations for The location of low-altitude aircraft at all times. for The connection indication vector between the low-altitude aircraft and the base station at any given time; The mission completion time for a low-altitude aircraft from the starting point to the destination; It is the minimum signal-to-interference-plus-noise ratio threshold at which low-altitude aircraft can maintain reliable communication. It is the starting point for low-altitude aircraft flights. It is the destination for low-altitude aircraft. It is the maximum speed of a low-altitude aircraft. It refers to the range of motion of the movable antenna. This is the maximum moving speed of the movable antenna. To exclude the first Any antenna position outside the antenna; It is the minimum antenna spacing required to avoid antenna coupling effects.

2. The communication coverage enhancement path planning method for low-altitude aircraft according to claim 1, characterized in that, The bottom of the low-altitude aircraft is equipped with a A two-dimensional array consisting of movable antennas; low-altitude aircraft deployed at a fixed altitude in a uniformly distributed manner. When flying within the area of ​​a base station, the aircraft and the base station form a cellular network communication system.

3. The communication coverage enhancement path planning method for low-altitude aircraft according to claim 2, characterized in that, The signal-to-interference-plus-noise ratio of low-altitude aircraft at any given time for: ； in, for A collection of base stations ,express Low-altitude aircraft and base stations The association, excluding base stations The remaining base stations are used as interference base stations; Indicates low-altitude aircraft and base stations Beamforming vectors for communication, " denotes the conjugate transpose of a vector; This refers to the base station's transmission power. , Representing time respectively base station Base stations Channel vector between the aircraft and low-altitude aircraft; The variance is the additive white Gaussian noise.

4. The communication coverage enhancement path planning method for low-altitude aircraft according to claim 3, characterized in that, time base station Channel vector between low-altitude aircraft Represented as: ； in, This indicates the path loss when the reference distance is 1 meter. For base stations European distance to low-altitude aircraft; It is the carrier wavelength; Indicates time From base station A steering vector pointing towards a movable antenna array; ； in, , For antenna Two-dimensional coordinates in the local coordinate system of the movable antenna panel; For base stations To low-altitude aircraft Waves in time.

5. The communication coverage enhancement path planning method for low-altitude aircraft according to any one of claims 1-4, characterized in that, During the iterative expansion of nodes on a discrete grid using the selective consistent cost search algorithm, the intermediate expansion nodes are set as follows: ； in, This indicates the index of a visited grid point in the trajectory of a low-altitude aircraft. For grid point locations, For the corresponding antenna position, This is the low-altitude aircraft-base station association indication vector. As of the date The history of low-altitude aircraft trajectories at each access grid point.

6. The communication coverage enhancement path planning method for low-altitude aircraft according to claim 5, characterized in that, During the iterative expansion of nodes on a discrete grid using the selective consistent cost search algorithm, for nodes... The defined cost functions include: Flight time cost function , for the initial position Along the trajectory Reaching the grid point The cumulative flight time; Potential minimum task completion time cost function , for the initial position To grid point Flight time and from To the finish line The sum of the lower bounds of achievable flight times; ； in, For the first The time taken for a segment of the flight path; ； in, and They represent the endpoints respectively. The x-axis and y-axis coordinates, and and Representing grid points respectively The x-axis and y-axis coordinates.

7. The communication coverage enhancement path planning method for low-altitude aircraft according to claim 6, characterized in that, The planning process includes: Step S301: Initialization; Check if the starting point meets the signal-to-interference-plus-noise ratio constraint. If it does, generate the initial node and add it to the node set. Step S302: When the node set is not empty, perform hierarchical filtering. From the first node subset with the smallest potential minimum task completion time of the low-altitude aircraft, filter out the second node subset with the largest cumulative flight time of the low-altitude aircraft. Randomly select a node from the second node subset for expansion and delete the node from the node set. Step S303: Determine whether the grid point position of the selected node is the endpoint. If yes, find the smallest feasible low-altitude aircraft path; otherwise, proceed to the next step. Step S304: For all neighboring grid points of the selected node's grid point location, perform joint optimization of the neighboring grid point's beamforming vector, antenna position vector, and association between the low-altitude aircraft and the base station to obtain the maximum signal-to-interference-plus-noise ratio (SIR). The neighboring grid points that satisfy the SIR constraints of the low-altitude aircraft are taken as feasible neighboring grid points. Step S305: Compare the next-layer nodes composed of each feasible neighbor grid point with the nodes already existing in the node set that have the same grid point location, antenna location, and association between the low-altitude aircraft and the base station. Retain the nodes with the smaller potential minimum task completion time and add them to the node set as candidate nodes. Step S306: Limit the number of candidate nodes stored in each trajectory level of the node set to a fixed value; Step S307: If the node set is empty and no node reaching the destination is found, then there is no low-altitude aircraft trajectory that meets the constraints; if the node set is not empty, return to step S302.

8. The communication coverage enhancement path planning method for low-altitude aircraft according to claim 7, characterized in that, In the joint optimization in step 304, the beamforming vector of the neighboring grid points is solved by the minimum mean square error method; the antenna position vector is solved by the continuous optimization method; in the association between the low-altitude aircraft and the base station, the low-altitude aircraft is always connected only to the base station that can bring the maximum signal-to-interference-plus-noise ratio.

9. The communication coverage enhancement path planning method for low-altitude aircraft according to claim 8, characterized in that, In the calculation of beamforming vectors for neighboring grid points, For the A low-altitude aircraft trajectory point, beamforming vector The closed-form solution is calculated using the least mean square error method as follows: ； in, It is the identity matrix. The low-altitude aircraft is located at the Each trajectory point is related to the base station. The channel vector, .

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