A method for optimizing deployment of a UAV group for seamless coverage of ground users

Abstract

This invention discloses an optimization method for UAV swarm deployment to achieve seamless coverage for ground users, relating to the field of communication technology. The method includes: acquiring parameters of the research object and generating signal-to-noise ratio (SNR) data using a predetermined urban emergency communication model. The research object includes ground users, UAVs, and satellites. Based on the SNR data, a UAV swarm deployment optimization problem is constructed, and deployment constraint data is generated. This deployment constraint data includes UAV power limit constraints, minimum decoding SNR constraints, reliable transmission constraints, physical seamless coverage constraints, and flight altitude constraints. Based on the deployment constraint data, the reliable transmission constraints are deterministically processed according to the UAV power limit constraints. This invention achieves seamless ground user coverage, downlink transmission quality, and deployment convergence stability by uniformly transmitting and iteratively constraining the SNR data, deployment constraint data, and simplified deployment constraint data.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and more specifically to an optimized method for the deployment of unmanned aerial vehicle (UAV) swarms to provide seamless coverage for ground users. Background Technology

[0002] As the integrated air-space-ground network evolves towards deeper coverage, unmanned aerial vehicle (UAV) swarms, as key relay nodes connecting satellite ephemeris resources and ground mapping data, play a core role in ensuring emergency communication in urban areas due to their flexible deployment, good line-of-sight conditions, and support for beamforming technology.

[0003] Currently, in the optimization of UAV swarm deployment for seamless coverage of ground users, the focus is usually on configuring the deployment location of UAVs based on geometric coverage range or single reception quality. It is difficult to express the average signal-to-noise ratio of the UAV swarm and the average signal-to-noise ratio of ground users in a unified constraint in the same deployment solution process. This results in a lack of a coherent correlation mechanism between the decoding requirements of the satellite-to-UAV swarm link, the reliable transmission requirements of the UAV swarm to ground user link, and the physical seamless coverage requirements within the target area. In this case, even if some ground users can be included in the coverage area, the lack of a unified transmission relationship between deployment constraint data may lead to problems such as inconsistencies between deployment results and downlink transmission conditions, gaps in coverage boundaries, or deployment status that cannot simultaneously meet multiple constraints.

[0004] Secondly, in solving the problem of drone swarm deployment optimization, directly searching the deployment location and number of drones together is often affected by random transmission conditions, logical coverage relationships, and the coupling of candidate drone activation status. This makes it difficult to further transform the simplified deployment constraint data into a stable iterative solution process. Especially when the location parameters of ground users in the target area are unevenly distributed, the coverage topology needs to be continuously adjusted, and the scheduling variables for candidate drone activation are constantly changing, it is easy to encounter situations such as the initial deployment location being disconnected from the subsequent update process, unstable convergence of the number of drones deployed, and insufficient adaptation between the drone swarm deployment optimization results and the location parameter distribution of ground users. This affects the usability of the drone swarm deployment optimization results in actual emergency communication scenarios. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides an optimized method for drone swarm deployment that provides seamless coverage for ground users.

[0006] An optimized method for drone swarm deployment to provide seamless coverage for ground users, the method comprising:

[0007] S1: Obtain the parameters of the research object and generate signal-to-noise ratio data through a predetermined urban emergency communication model. The research object includes ground users, drones, and satellites.

[0008] S2: Construct an optimization problem for UAV swarm deployment based on signal-to-noise ratio data, and generate deployment constraint data, which includes UAV power limit constraints, minimum decoding signal-to-noise ratio constraints, reliable transmission constraints, physical seamless coverage constraints, and flight altitude constraints;

[0009] S3: Based on the deployment constraint data, the reliable transmission constraint is deterministically processed based on the UAV power limit constraint to generate deterministic transmission constraints, and the physical seamless coverage constraint is relaxed to generate relaxed coverage constraints. Simplified deployment constraint data is generated based on the deterministic transmission constraint and the relaxed coverage constraint.

[0010] S4: Based on the simplified deployment constraint data, generate the initial deployment location and initial number of drones, and iteratively update the drone deployment location and number of drones in the drone swarm deployment optimization problem to generate the drone swarm deployment optimization result.

[0011] Furthermore, the parameters of the research object include the satellite's position parameters, the UAV's position parameters, the ground user's position parameters, the satellite's transmission power, the UAV's transmission power, the UAV's noise power, and the ground user's noise power. The signal-to-noise ratio data includes the average signal-to-noise ratio of the UAV swarm and the average signal-to-noise ratio of the ground user.

[0012] Furthermore, the steps for generating signal-to-noise ratio data are as follows:

[0013] S11: Based on the parameters of the research object, establish spatial location description data;

[0014] S12: Generate the first-stage link channel data from satellite to UAV based on the spatial location description data, and calculate the average signal-to-noise ratio of the UAV swarm;

[0015] S13: Generate the second-stage link channel data from the UAV to the ground user based on the spatial location description data;

[0016] S14: Calculate the average signal-to-noise ratio (SNR) of ground users based on the second-stage link channel data, and combine the average SNR of the UAV swarm and the average SNR of ground users into SNR data.

[0017] Furthermore, the steps for generating deployment constraint data are as follows:

[0018] S21: Based on the signal-to-noise ratio data and the parameters of the research object, construct the objective function for the optimization problem of UAV swarm deployment;

[0019] S22: Generate the minimum decoding signal-to-noise ratio constraint based on the average signal-to-noise ratio of the drone swarm;

[0020] S23: Generate UAV power limit constraints and reliable transmission constraints based on the average signal-to-noise ratio of ground users;

[0021] S24: Generate physical seamless coverage constraints based on the location parameters of ground users and UAVs, and generate flight altitude constraints based on the location parameters of UAVs;

[0022] S25: Combine the minimum decoding signal-to-noise ratio constraint, reliable transmission constraint, physical seamless coverage constraint, and flight altitude constraint into deployment constraint data.

[0023] Furthermore, the steps for generating deterministic transport constraints include:

[0024] S31: Based on the UAV power limit constraints, reliable transmission constraints, and second-stage link channel data, construct the random distribution expression corresponding to the average signal-to-noise ratio of ground users, and determine the probability constraint expression corresponding to the reliable transmission constraints;

[0025] S32: Based on the aforementioned probability constraint expression, perform an equivalent transformation on the probability that the average signal-to-noise ratio of the ground user is greater than the ground user reception threshold, and transform the reliable transmission constraint into a first-order Marcum-Q function constraint.

[0026] S33: Based on the UAV power limit constraints and the second-stage link channel data, construct the beamforming vector corresponding to the ground user using the maximum ratio transmission, and generate the beamforming vector corresponding to the second-stage link channel data.

[0027] S34: Based on the beamforming vector, the first-order Marcum-Q function constraint is rewritten by thresholding to generate a deterministic transmission threshold value, and a deterministic transmission constraint is established based on the deterministic transmission threshold value.

[0028] Furthermore, the steps for generating simplified deployment constraint data include:

[0029] S35: Based on physical seamless coverage constraints, the location parameters of ground users and the location parameters of UAVs, establish a coverage determination expression between ground users and UAVs;

[0030] S36: Based on the coverage determination expression, construct a coverage state variable and generate a variable to represent the coverage state variable. Was the ground user the first The coverage state variables of the drone;

[0031] S37: Based on the coverage state variables and the preset large M constant, relax the logical OR relationship in the physical seamless coverage constraint, and transform the coverage decision expression into the coverage constraint inequality expression.

[0032] S38: Generate relaxed coverage constraints based on the coverage constraint inequality expression, and simplify the deployment constraint data based on deterministic transport constraints and relaxed coverage constraints to generate simplified deployment constraint data.

[0033] Furthermore, the logic for generating the initial deployment location and initial number of drones is as follows:

[0034] S41: Based on the simplified deployment constraint data, the location parameters of ground users, and the physical seamless coverage constraints, establish an initial coverage topology, and based on the initial coverage topology, set the high-altitude formation flight conditions of UAVs, and generate the ground coverage range corresponding to a single UAV.

[0035] S42: Based on the ground coverage area corresponding to a single drone, candidate deployment units are generated using a hexagonal cellular configuration;

[0036] S43: Based on the location parameters of ground users in the candidate deployment units, perform coverage mapping to generate the initial deployment location of the UAV;

[0037] S44: Generate the initial number of drones based on the number of candidate deployment units corresponding to the initial deployment location of the drones.

[0038] Furthermore, the steps for generating the optimized deployment results of the drone swarm are as follows:

[0039] S45: Based on the initial deployment location, the initial number of drones, and the simplified deployment constraint data, construct the iterative solution problem corresponding to the drone swarm deployment optimization problem;

[0040] S46: Based on the iterative solution of the problem, a 0-1 scheduling vector is introduced to transform the number of drones deployed into a candidate drone activation scheduling variable;

[0041] S47: Based on the candidate UAVs corresponding to the 0-1 scheduling vector, enable the scheduling variable, introduce auxiliary variables and construct an iterative subproblem, and perform successive convex approximations on the non-convex constraints in the iterative subproblem to generate a convex optimization update problem;

[0042] S48: Based on the convex optimization update problem, iteratively update the drone deployment location and the number of drones deployed, and generate the drone swarm deployment optimization result when the convergence threshold is met.

[0043] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0044] This invention, by linking signal-to-noise ratio (SNR) data, deployment constraint data, and simplified deployment constraint data in urban emergency communication scenarios, enables the average SNR of the UAV swarm and the average SNR of ground users to participate simultaneously in the solution process of the UAV swarm deployment optimization problem. This ensures that the UAV swarm deployment optimization results take into account downlink decoding requirements, reliable transmission requirements, and physical seamless coverage requirements, thereby reducing deployment deviations caused by random transmission fluctuations and coverage boundary gaps, and thus improving deployment feasibility and consistency under the condition of seamless coverage for ground users.

[0045] Furthermore, this invention constructs an iterative update process based on deterministic transmission constraints, relaxed coverage constraints, initial deployment locations, and initial number of UAVs, enabling the deployment locations and number of UAVs to continuously converge on a unified constraint basis. This reduces the search instability when candidate UAVs enable scheduling variables and UAV location parameters are jointly solved, while maintaining the compatibility between the UAV swarm deployment optimization results and the location parameter distribution of ground users within the target area. This improves the convergence stability and practical application effectiveness of the UAV swarm deployment optimization results under emergency communication conditions.

[0046] In summary, this invention achieves optimal UAV swarm deployment by uniformly transmitting and iteratively constraining signal-to-noise ratio data, deployment constraint data, and simplified deployment constraint data, thus simultaneously ensuring seamless coverage for ground users, downlink transmission quality, and deployment convergence stability. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0048] Figure 1 This is a flowchart illustrating an optimized method for seamless drone swarm deployment to ground users, provided as an embodiment of the present invention. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] Please see Figure 1As shown in the figure, this embodiment discloses an optimized method for drone swarm deployment to provide seamless coverage for ground users. The method includes:

[0051] S1: Obtain the parameters of the research object and generate signal-to-noise ratio data through a predetermined urban emergency communication model. The research object includes ground users, drones, and satellites.

[0052] The purpose of step S1 is to first perform a unified modeling of the two-hop downlink between satellites, drones and ground users in emergency communication scenarios, and then generate signal-to-noise ratio data that can characterize communication quality based on the unified modeling results, thereby providing input data with a source basis for the subsequent deployment constraint construction.

[0053] The established urban emergency communication model is a computational model based on input-output mapping of spatial geometric parameters, link loss parameters, and power parameters. Its input consists of the parameters of the research object, and its output is signal-to-noise ratio data. The urban emergency communication model employs a decoding-forwarding protocol for two-stage downlink transmission: the first stage is the satellite-to-UAV swarm link, and the second stage is the UAV swarm-to-ground user link.

[0054] This can be understood as the first stage and the second stage each having their corresponding mathematical calculation functions.

[0055] Specifically, the parameters of the research object include the satellite's position parameters, the UAV's position parameters, the ground user's position parameters, the satellite's transmission power, the UAV's transmission power, the UAV's noise power, and the ground user's noise power;

[0056] The signal-to-noise ratio (SNR) data includes the average SNR of the drone swarm and the average SNR of ground users.

[0057] The position parameters of the satellite, the UAV, and the ground user together determine the link geometry and link direction angle. The satellite's transmission power and the UAV's noise power together determine the signal reception quality of the first-stage link. The UAV's transmission power and the ground user's noise power together determine the signal reception quality of the second-stage link.

[0058] To facilitate subsequent unified calculations, this embodiment pre-writes the above parameters into a link parameter table within the same calculation period. The link parameter table can be jointly provided by the emergency communication command platform, satellite ephemeris interface, UAV navigation system, and ground user positioning terminal.

[0059] Specifically, the steps for generating signal-to-noise ratio data are as follows:

[0060] S11: Based on the parameters of the research object, establish spatial location description data;

[0061] In one specific embodiment, the satellite's position parameters are represented in three-dimensional coordinate form as follows:

[0062]

[0063] in, This refers to the lateral coordinates of the satellite within the pre-defined urban emergency communication area. The vertical coordinates of the satellite within the pre-defined urban emergency communication area. This represents the satellite's altitude relative to the ground reference plane.

[0064] In one specific embodiment, the first The position parameters of the UAV are represented in three-dimensional coordinate form as follows:

[0065]

[0066] in, For the first The lateral coordinates of the drone within the pre-defined urban emergency communication area. For the first The longitudinal coordinates of the drone within the pre-defined urban emergency communication area. For the first The altitude of the drone relative to the ground reference plane. Index the number of drones. ∈ , A set of drone ID numbers;

[0067] In one specific embodiment, the first The location parameters of each ground user are represented in three-dimensional coordinate form as follows:

[0068]

[0069] in, For the first The horizontal coordinates of a ground user within a pre-defined urban emergency communication area. For the first The vertical coordinates of a ground user within a pre-defined urban emergency communication area. Index the ground users. ∈ , For ground users;

[0070] It should be noted that: since ground users are located on a ground reference plane, their height values ​​are taken as... .

[0071] In one specific embodiment, the satellite's position parameters can be read from the satellite orbit parameters and ephemeris interface, the UAV's position parameters can be jointly output by the UAV's onboard global navigation satellite system receiving module and airborne inertial navigation module, and the ground user's position parameters can be provided by the emergency terminal positioning module, ground mapping data, or a preset user coordinate table.

[0072] To avoid coordinate system differences in multi-source location data at the same time, this embodiment maps the satellite position parameters, UAV position parameters, and ground user position parameters to the same ground reference coordinate system.

[0073] S12: Generate the first-stage link channel data from satellite to UAV based on the spatial location description data, and calculate the average signal-to-noise ratio of the UAV swarm;

[0074] In one specific embodiment, based on the spatial position description data in S11, the distance and angle between the satellite and each UAV are calculated respectively;

[0075] Among them, the satellite to the The formula for calculating the distance between drones is:

[0076]

[0077] In the formula, For satellites and the The spatial Euclidean distance between drones. For satellites and the The squared distance term of the drone in the horizontal coordinate direction. For satellites and the The squared distance term of the drone along the longitudinal coordinate direction. For satellites and the The square of the distance in the altitude direction for the drone;

[0078] It should be noted that: Chinese characters It is an abbreviation of the English name of the satellite, Satellite.

[0079] Satellite and the The formula for calculating the angle between two drones is:

[0080]

[0081] In the formula, For satellites and the The geometric angle between the drones It is an inverse cosine function. This indicates that the distance between the satellite and the nth UAV in the altitude direction accounts for a portion of the total spatial distance. The ratio;

[0082] Based on satellite and The distance and angle between the drones were calculated to obtain the distance between the satellite and the first drone. The line-of-sight channel coefficient of a UAV is expressed as:

[0083]

[0084] In the formula, For the satellite to the The line-of-sight channel coefficient of the drone, This is a preset reference channel gain constant related to the channel environment. For a given reference distance, The path loss coefficient for the satellite-to-UAV link. It is an exponential function. The imaginary unit, Pi Indicates that it is composed of satellites and the first The phase term caused by the geometric angle between the drones.

[0085] It should be noted that: , , The link budget parameters can be preset based on the satellite carrier frequency, the urban airspace propagation environment, and the antenna deployment method.

[0086] The line-of-sight channel coefficients corresponding to each UAV are combined into a line-of-sight channel vector from the satellite to the UAV swarm, expressed as:

[0087]

[0088] in, This represents the line-of-sight channel vector from the satellite to the UAV swarm. For drone collection The number of drones in the country For the transpose operation, the line-of-sight channel vector is output as the first-stage link channel data.

[0089] Based on satellite transmission power The noise power of the drone Line-of-sight channel vector Based on the mathematical calculation function of the first stage of the established urban emergency communication model, the average signal-to-noise ratio of the drone swarm is generated. The mathematical calculation function of the first stage of the established urban emergency communication model is expressed as follows:

[0090]

[0091] In the formula, The average signal-to-noise ratio of the drone swarm. Line-of-sight channel vector The conjugate transpose of . The sum of squared magnitudes of the line-of-sight channel vectors from the satellite to the UAV swarm, and the noise power of the UAV. The superscript 2 indicates that the noise power is represented in variance form.

[0092] It should be noted that the average signal-to-noise ratio of the drone swarm represents the average reception quality of the downlink signal transmitted by the satellite at the drone swarm receiver, and is used to characterize whether the drone swarm can correctly decode the information transmitted by the satellite.

[0093] S13: Generate the second-stage link channel data from the UAV to the ground user based on the spatial location description data;

[0094] In one specific embodiment, based on the spatial location description data in S11, the first... drones and the first The distance and angle between each ground user are calculated separately;

[0095] Among them, the drones and the first The distance between each ground user is:

[0096]

[0097] In the formula, For the first drones and the first Spatial Euclidean distance between ground users For the first drones and the first The squared distance of a ground user in the horizontal coordinate direction. For the first drones and the first The squared distance term of each ground user in the longitudinal coordinate direction. For the first The squared distance between the drone and the ground user in the altitude direction.

[0098] According to the drones and the first Distance calculation between ground users. drones and the first The angle between ground users is represented as:

[0099]

[0100] In the formula, For the first drones and the first The geometric angle between ground users For the first drones and the first The distance between ground users in the vertical direction accounts for the total spatial distance. The ratio of .

[0101] In one specific embodiment, the second-stage link is modeled using a Ricean channel, which consists of both line-of-sight and non-line-of-sight channel components, based on the... drones and the first Calculate the distance and angle between each ground user, and calculate the i-th... The drone to the The line-of-sight channel components for each ground user are represented as follows:

[0102]

[0103] In the formula, For the first The drone to the Line-of-sight channel components for each ground user This represents the path loss coefficient for the link from the UAV to the ground user; the physical meanings of the other symbols are consistent with the aforementioned definitions.

[0104] No. The drone to the Non-line-of-sight channel components for each ground user It can be written as:

[0105]

[0106] This indicates that the mean is 0 and the variance is 0. The complex Gaussian random distribution, The power variance of the non-line-of-sight channel components;

[0107] It should be noted that the non-line-of-sight channel components correspond to the small-scale fading components between the UAV and the ground user caused by building obstruction, scattering and reflection. In implementation, they can be generated directly according to the scenario channel model or generated according to the random channel module in the simulation platform.

[0108] Based on the The drone to the Calculate the line-of-sight channel components and non-line-of-sight channel components of the ground user, and calculate the _th _ ... The drone to the The combined channel coefficients for a ground user are expressed as follows:

[0109]

[0110] In the formula, For the first The drone to the The overall channel coefficients for each ground user This is the weighting factor for the line-of-sight channel components. For the weighting factors of the non-line-of-sight channel components, , satisfy ;

[0111] It should be noted that: , The channel environment is pre-set based on urban emergency communication scenarios, specifically according to the line-of-sight conditions in urban emergency communication scenarios. , Used to reflect the proportion of line-of-sight propagation paths and non-line-of-sight propagation paths in the integrated channel;

[0112] For example, when the drone flies at a high altitude and line-of-sight propagation is dominant, Value greater than When high-rise buildings have a large amount of obstruction and reflection, It can be increased accordingly.

[0113] To bring all drones to the The combined channel coefficients of each ground user constitute the combined channel vector from the UAV to the ground user, expressed as:

[0114]

[0115] in, For drone swarms to the first The integrated channel vector of each ground user is output as the link channel data for the second stage.

[0116] S14: Calculate the average signal-to-noise ratio of ground users based on the second-stage link channel data, and combine the average signal-to-noise ratio of the UAV swarm and the average signal-to-noise ratio of ground users into signal-to-noise ratio data;

[0117] In one specific embodiment, based on the synthesized channel vector generated in S13 The transmit power of the drone and the noise power of the ground user. , No. Beamforming vector for each ground user And the mathematical calculation function for the second stage of the established urban emergency communication model, to calculate and generate the first... The average signal-to-noise ratio for each ground user, expressed mathematically in the second stage of a given urban emergency communication model, is as follows:

[0118]

[0119] In the formula, For the first Average signal-to-noise ratio for each ground user For drone swarms to the first The combined channel vector of a ground user The conjugate transpose of . For the first Beamforming vectors corresponding to each ground user This is the signal power term resulting from the combined effect of the channel vector and the beamforming vector.

[0120] It should be noted that the beamforming vector It can be obtained in the following way:

[0121] No. A ground user transmits pilot signals to the UAV swarm in the pilot time slot. Each UAV performs channel estimation on the pilot signals to obtain the first... The ground user's integrated channel vector is then used by the computing chip to perform normalized conjugate weighting based on the integrated channel vector to generate the first... The beamforming vector corresponding to each ground user can be processed using the maximum ratio transmission criterion or an equivalent conjugate beamforming criterion, and its output is a complex weight vector consistent with the dimension of the synthesized channel vector.

[0122] In a specific embodiment, the average signal-to-noise ratio of the drone swarm obtained in S12 is... The average signal-to-noise ratio of ground users obtained in this step Together they serve as the output of step S1 and are combined to define the signal-to-noise ratio data.

[0123] It should be noted that the signal-to-noise ratio data indicates whether the satellite-to-UAV swarm link meets the decoding requirements, and whether the UAV swarm-to-ground user link meets the downlink reception quality requirements.

[0124] In subsequent steps, the minimum decoding signal-to-noise ratio constraint corresponds to the average signal-to-noise ratio of the referenced drone swarm, and the reliable transmission constraint corresponds to the average signal-to-noise ratio of the referenced ground users.

[0125] S2: Construct an optimization problem for UAV swarm deployment based on signal-to-noise ratio data, and generate deployment constraint data, which includes UAV power limit constraints, minimum decoding signal-to-noise ratio constraints, reliable transmission constraints, physical seamless coverage constraints, and flight altitude constraints;

[0126] The purpose of step S2 is to transform the communication quality requirements, coverage requirements, and flight requirements in the integrated air-space-ground downlink into solvable deployment constraints based on the signal-to-noise ratio data generated in step S1, thereby constructing a drone swarm deployment optimization problem with the drone deployment location and number as the optimization objects.

[0127] The input to the UAV swarm deployment optimization problem is the signal-to-noise ratio data output in step S1 and the parameters of the research object obtained in step S1. The output of the UAV swarm deployment optimization problem is the deployment constraint data.

[0128] Specifically, the steps for generating deployment constraint data are as follows:

[0129] S21: Based on the signal-to-noise ratio data and the parameters of the research object, construct the objective function for the optimization problem of UAV swarm deployment;

[0130] In one specific embodiment, based on the signal-to-noise ratio data generated in step S1 and the parameters of the research object, the number of drones deployed and their deployment locations are taken as variables to be optimized.

[0131] The number of deployments corresponds to the number of drones. The deployment location corresponds to the position parameters of each drone. ;

[0132] Based on the deployment requirement of "minimizing the number of drones deployed while meeting communication quality and area coverage requirements" in emergency communication scenarios, the objective function of the drone swarm deployment optimization problem is set as minimizing the number of drones, expressed as:

[0133]

[0134] In the formula, Number of drones;

[0135] It should be noted that the number of drones is set as the objective function because in urban emergency communication scenarios, the fewer drones there are, the lower the deployment cost, collaborative control overhead, and energy consumption. Therefore, this objective function is consistent with the engineering requirements of emergency communication scenarios.

[0136] Secondly, the objective function does not constitute a complete deployment optimization problem on its own, but together with the various constraints generated in S22 to S24, it constitutes a drone swarm deployment optimization problem.

[0137] S22: Generate the minimum decoding signal-to-noise ratio constraint based on the average signal-to-noise ratio of the drone swarm;

[0138] In one specific embodiment, step S1 has generated the average signal-to-noise ratio of the drone swarm, which represents the average reception quality of the downlink signal transmitted by the satellite at the drone swarm receiver.

[0139] To ensure that the drone swarm can successfully decode the information transmitted by the satellite, a minimum threshold requirement needs to be set for the average signal-to-noise ratio of the drone swarm. The minimum decoding signal-to-noise ratio constraint is expressed as:

[0140]

[0141] In the formula, The average signal-to-noise ratio of the drone swarm generated in step S1. This is the minimum decoding signal-to-noise ratio threshold.

[0142] It should be noted that: It can be preset according to the modulation and coding scheme used in the satellite downlink and the decoding performance of the UAV swarm receiver;

[0143] in, Less than This indicates that the drone swarm was unable to reliably decode the satellite downlink signal. Greater than or equal to When this occurs, it indicates that the drone swarm meets the minimum decoding requirements of the first-stage link. Therefore, the average signal-to-noise ratio of the drone swarm output in step S1 is transformed into a minimum decoding signal-to-noise ratio constraint.

[0144] S23: Generate UAV power limit constraints and reliable transmission constraints based on the average signal-to-noise ratio of ground users;

[0145] In a specific embodiment, the first generated in step S1 Beamforming vector for each ground user The drone's transmit power needs to be met, and the transmit power limit is expressed as follows:

[0146]

[0147] In the formula, Beamforming vector The conjugate transpose of . Beamforming vector The square of the second norm.

[0148] It should be noted that the transmit power limit is used to constrain the beamforming vector. Make the beamforming vector The square of the L2 norm is equal to 1. Selecting 1 indicates that it has been normalized and no additional power dimension is required.

[0149] Furthermore, the first The average signal-to-noise ratio for each ground user is The average signal-to-noise ratio of the ground users represents the downlink signal after being relayed by the UAV swarm in the 1st... Average reception quality of each ground user receiver;

[0150] Since the second-stage link contains non-line-of-sight channel components, the link reception quality fluctuates randomly. Therefore, in this embodiment, instead of directly using a single-shot determination method with an average signal-to-noise ratio greater than a threshold, a reliable transmission constraint that meets probability requirements is adopted.

[0151] Specifically, the reception threshold for ground users is set as follows: Set the reliable transmission probability threshold as Then the first The reliable transmission constraints for each ground user are written as follows:

[0152]

[0153] In the formula, For the first Average signal-to-noise ratio of ground users Greater than or equal to the ground user reception threshold The probability, A set of ground user IDs;

[0154] It should be noted that: Used to characterize the minimum signal quality required for a ground user to maintain stable reception under the current service type. To characterize the probability requirement for a link to meet a reception threshold under random fading conditions, the above probability constraints are established for all ground users, forming a complete set of reliable transmission constraints; when the probability corresponding to any ground user does not meet the threshold... If the current drone deployment status cannot meet the service access requirements of the ground user, then the average signal-to-noise ratio of the ground user output in step S1 can be converted into a reliable transmission constraint.

[0155] S24: Generate physical seamless coverage constraints based on the location parameters of ground users and UAVs, and generate flight altitude constraints based on the location parameters of UAVs;

[0156] In a specific embodiment, in addition to meeting the link signal-to-noise ratio requirements, it is also necessary to ensure that ground users in the target area are always within the effective coverage range of the drone swarm, and to avoid intermittent areas at the coverage boundary after deployment.

[0157] Based on this, physical seamless coverage constraints are established according to the location parameters of ground users and the location parameters of UAVs;

[0158] Let the first The drone at its current flight altitude The ground projection coverage radius is Then the first The coverage radius corresponding to a drone can be expressed as:

[0159]

[0160] In the formula, Given the predetermined elevation angle parameters of the drone to the ground, Indicates the first A drone at high altitude The corresponding ground coverage radius.

[0161] It should be noted that: the given elevation angle parameters Based on the pre-set ground terminal reception conditions in urban emergency communication scenarios; when the drone flies at an altitude... Once confirmed, the first The effective ground coverage area corresponding to a drone can be approximated as being based on With the center, and A circular coverage area with radius [missing information] .

[0162] Furthermore, regarding the first A ground user, if its planar coordinates Satisfy the following formula:

[0163]

[0164] Then it means the first The ground user is in the first Within the coverage area of ​​the drone.

[0165] To ensure uninterrupted coverage for ground users, the basic requirement for physical seamless coverage is that all ground users must be within the coverage area of ​​at least one drone.

[0166] At the same time, overlapping coverage areas are preserved at the boundaries of adjacent drone coverage areas to ensure that there are no discontinuities between adjacent coverage circles;

[0167] Correspondingly, the physical seamless coverage constraint can be expressed as: each ground user in the target area satisfies the coverage determination at least once, and there are no coverage gaps between adjacent drone coverage areas;

[0168] Represented as:

[0169]

[0170] In practice, the absence of a gap between the coverage areas of adjacent drones can be determined by comparing the horizontal distance between the two drones with their respective coverage radii. When the horizontal distance between the two drones is not greater than the sum of their corresponding coverage radii, it indicates that there is no gap between their coverage boundaries.

[0171] In one specific embodiment, based on the altitude value in the drone's position parameters. Furthermore, it is necessary to set upper and lower limits for the drone's flight altitude to avoid insufficient coverage due to deployment altitude being too low, or excessive link loss due to deployment altitude being too high.

[0172] Specifically, the lower limit of the drone's flight altitude is set as follows: The upper limit of flight altitude is Then the flight altitude constraint is written as:

[0173]

[0174] In the formula, For the first The altitude value in the position parameters of the drone;

[0175] It should be noted that: , The settings are pre-defined based on urban low-altitude airspace management requirements, UAV flight performance, and emergency communication coverage needs.

[0176] Through the above processing, physical seamless coverage constraints and flight altitude constraints can be obtained respectively.

[0177] S25: Combine minimum decoding signal-to-noise ratio constraints, reliable transmission constraints, physical seamless coverage constraints, and flight altitude constraints into deployment constraint data;

[0178] In a specific embodiment, the minimum decoding signal-to-noise ratio constraint generated in S22, the UAV power limit constraint and reliable transmission constraint generated in S23, and the physical seamless coverage constraint and flight altitude constraint generated in S24 are written into the same constraint expression system, and together with the objective function established in S21, they form the UAV swarm deployment optimization problem.

[0179] Specifically, the drone swarm deployment optimization problem can be written as:

[0180] The objective function is:

[0181]

[0182] The constraints are:

[0183]

[0184]

[0185]

[0186]

[0187]

[0188] In a specific embodiment, the above five types of constraints are combined to form deployment constraint data, which is then used as the output of step S2.

[0189] S3: Based on the deployment constraint data, the reliable transmission constraint is deterministically processed based on the UAV power limit constraint to generate deterministic transmission constraints, and the physical seamless coverage constraint is relaxed to generate relaxed coverage constraints. Simplified deployment constraint data is generated based on the deterministic transmission constraint and the relaxed coverage constraint.

[0190] The purpose of step S3 is to transform the deployment constraint data, which still contains random probability form and logical "OR" form in step S2, into a constraint expression that can directly participate in the initial deployment and iterative solution. Among them, reliable transmission constraints are transformed into deterministic transmission constraints through deterministic processing, and physical seamless coverage constraints are transformed into relaxed coverage constraints through relaxation processing, thus jointly constituting simplified deployment constraint data.

[0191] It should be noted that the deployment constraint data generated in step S2 includes UAV power limit constraints, minimum decoding signal-to-noise ratio constraints, reliable transmission constraints, physical seamless coverage constraints, and flight altitude constraints. This step only further processes the reliable transmission constraints and physical seamless coverage constraints.

[0192] The minimum decoding signal-to-noise ratio constraint and flight altitude constraint are retained in this step and do not participate in the representation transformation.

[0193] Specifically, the steps for generating deterministic transport constraints include:

[0194] S31: Based on the UAV power limit constraints, reliable transmission constraints, and second-stage link channel data, construct the random distribution expression corresponding to the average signal-to-noise ratio of ground users, and determine the probability constraint expression corresponding to the reliable transmission constraints;

[0195] In one specific embodiment, step S14 of step S1 has generated the second stage link channel data, the UAV's transmit power, the ground user's noise power, and the beamforming vector. Average signal-to-noise ratio for each ground user;

[0196] Since reliable transmission constraints have been established based on the average signal-to-noise ratio of ground users in step S23 of S2, this step expands on the source of the random term in the reliable transmission constraints based on the above.

[0197] In a specific embodiment, the second-stage link channel data is generated by step S13 of step S1, and the second-stage link channel data is represented by a synthesized channel vector as follows:

[0198]

[0199] in, For drone swarms to the first The integrated channel vector of a ground user; according to S13 of step S1, the integrated channel coefficient is composed of line-of-sight channel components and non-line-of-sight channel components weighted together. Therefore, the integrated channel vector can be written as a combination of line-of-sight channel components and non-line-of-sight channel components.

[0200] Furthermore, the average signal-to-noise ratio of ground users is expressed in step S14 as follows: ;

[0201] Synthetic channel vector The conjugate transpose of . For the first Beamforming vectors corresponding to each ground user Noise power for ground users.

[0202] Since the non-line-of-sight channel components in the second-stage link channel data follow a complex Gaussian random distribution, the signal power term in the average signal-to-noise ratio of ground users... It belongs to random variables, thus making the reliable transmission constraint established in step S23 of S2 possible. This belongs to the category of probabilistic constraint expressions.

[0203] In one specific embodiment, after substituting the line-of-sight channel component and the non-line-of-sight channel component in the integrated channel vector respectively, a random distribution expression corresponding to the average signal-to-noise ratio of the ground user is constructed.

[0204] Among them, the line-of-sight channel components correspond to deterministic terms, and the non-line-of-sight channel components correspond to random terms. Therefore This is an integrated form of the deterministic mean term and the complex Gaussian random perturbation term, and based on this, the probabilistic constraint expression corresponding to the reliable transmission constraint is determined.

[0205] It should be noted that this step does not redefine the reliable transmission constraints, but rather expands the reliable transmission constraints already generated in step S2 to the level of random distribution expression.

[0206] S32: Based on the aforementioned probability constraint expression, perform an equivalent transformation on the probability that the average signal-to-noise ratio of the ground user is greater than the ground user reception threshold, and transform the reliable transmission constraint into a first-order Marcum-Q function constraint.

[0207] In a specific embodiment, based on the random distribution expression obtained in step S31, the random signal power term involved in the average signal-to-noise ratio of ground users follows a non-central chi-square distribution with 2 degrees of freedom. Therefore, the probability constraint expression in step S31 can be transformed into a first-order Marcum-Q function form.

[0208] Specifically, the average signal-to-noise ratio of ground users is greater than the ground user reception threshold. The probability can be expressed in terms of the signal power term, and combined with the existing derivation of the squared modulus distribution of complex Gaussian random variables, we get:

[0209]

[0210] In the formula, It is a first-order Marcum-Q function. The standard deviation of the non-line-of-sight channel components;

[0211] The vector composed of the line-of-sight channel components in the second-stage link channel data is represented as:

[0212]

[0213] Since the UAV power limit constraint in step S2 has already been given ,therefore, ;

[0214] Therefore, the above formula can be further simplified to only with , First-order Marcum-Q function constraints related to ground user reception thresholds and link parameters;

[0215] In a specific embodiment, after the above equivalent transformation, the reliable transmission constraint in step S2 is transformed into a first-order Marcum-Q function constraint. This processing result is used to further perform thresholding rewriting in combination with the maximum ratio transmission construction result.

[0216] It should be noted that the first-order Marcum-Q function constraint is not the final deterministic transport constraint, but it has completed the formal transformation from probabilistic constraint to functional threshold constraint.

[0217] S33: Based on the UAV power limit constraints and the second-stage link channel data, construct the beamforming vector corresponding to the ground user using the maximum ratio transmission, and generate the beamforming vector corresponding to the second-stage link channel data.

[0218] The UAV power constraint in step S2 requires the beamforming vector to satisfy the unit norm constraint. Therefore, under the condition of satisfying this constraint, it is necessary to select a beamforming method that maximizes the signal power received by ground users.

[0219] In one specific embodiment, the maximum ratio transmission is used to construct the first Beamforming vectors corresponding to each ground user; the maximum transmission ratio processing method is:

[0220] The line-of-sight channel component vectors in the second-stage link channel data are conjugate and normalized to obtain a beamforming vector consistent with the line-of-sight propagation direction, expressed as:

[0221]

[0222] In the formula, The first one is constructed based on the maximum ratio transmission. Beamforming vectors corresponding to each ground user The conjugate of the line-of-sight channel vector. It is the L2 norm of the line-of-sight channel vector.

[0223] It should be noted that the maximum ratio transmission used in this step is not an additional introduction of a new control object, but rather a specific construction method for the beamforming vector already used in S14 of step S1; this construction method corresponds item by item with the link channel data of the second stage, which can ensure that the dimension of the beamforming vector is consistent with the dimension of the integrated channel vector.

[0224] The beamforming vector constructed in the above manner is used as the input in the subsequent step S34 to rewrite the first-order Marcum-Q function constraint obtained in step S32 by thresholding.

[0225] S34: Based on the beamforming vector, the first-order Marcum-Q function constraint is rewritten by thresholding to generate a deterministic transmission threshold value, and a deterministic transmission constraint is established based on the deterministic transmission threshold value.

[0226] In a specific embodiment, the beamforming vector constructed in step S33 is substituted into the first-order Marcum-Q function constraint in step S32.

[0227] It should be noted that the inverse value of the first-order Marcum-Q function can be obtained through a preset numerical calculation program, a lookup table method, or a special function calculation module in a communication simulation platform.

[0228] Because the maximum ratio transmission configuration aligns the beamforming vector with the line-of-sight channel vector, the original constraints... It can be simplified to The corresponding modulus form allows us to rewrite the first-order Marcum-Q function constraint as a constraint expression only concerning the line-of-sight channel vector norm threshold, as follows:

[0229]

[0230] Since the first-order Marcum-Q function is monotonically increasing with respect to the first independent variable, the above constraint can be further written in the form of a norm lower bound, i.e., generating a deterministic transmission threshold value, expressed as:

[0231]

[0232] In the formula, This is a constant determined jointly by the line-of-sight channel component weighting factor, the non-line-of-sight channel component weighting factor, and the non-line-of-sight channel component standard deviation, and ;

[0233] In a specific embodiment, the entire right side above is defined as a deterministic transmission threshold, that is: the deterministic transmission threshold represents the minimum line-of-sight channel vector norm threshold that must be satisfied to ensure the downlink reception quality of the ground user under given ground user reception threshold and reliable transmission probability threshold.

[0234] Furthermore, a deterministic transmission constraint is established based on the deterministic transmission threshold value. That is, when the line-of-sight channel vector norm corresponding to any ground user is not less than the deterministic transmission threshold value, it indicates that the current deployment state meets the reliable transmission requirements of the ground user.

[0235] When the line-of-sight channel vector norm corresponding to any ground user is less than the deterministic transmission threshold, it indicates that the current deployment state does not meet the reliable transmission requirements of that ground user.

[0236] Thus, the reliable transport constraints originally given in probabilistic form in step S2 are processed into deterministic transport constraints that can be directly used in the optimization solution.

[0237] Specifically, the steps for generating simplified deployment constraint data include:

[0238] S35: Based on physical seamless coverage constraints, the location parameters of ground users and the location parameters of UAVs, establish a coverage determination expression between ground users and UAVs;

[0239] In a specific embodiment, step S24 has already established a physical seamless coverage constraint based on the location parameters of the ground user and the location parameters of the UAV, and represented the coverage area corresponding to a single UAV as the ground projection coverage area. Based on this, this step establishes a user-by-user and UAV-by-UAV coverage determination expression for "whether the ground user falls into the coverage area".

[0240] In one specific embodiment, the first... The position parameters of the drone , No. The location parameters of each ground user are According to the coverage radius expression given in step S24, the ground coverage area corresponding to a single UAV is determined by the coverage radius and the horizontal projection position of the UAV.

[0241] Furthermore, if the first The ground user and the first The horizontal distance between the drones meets the following requirements:

[0242]

[0243] Then it means the first The ground user is in the first Within the coverage area of ​​the drone, among which, Given the predetermined elevation angle parameters of the drone to the ground, Indicates the first A drone at high altitude The corresponding ground coverage radius;

[0244] It should be noted that the above coverage determination expression is essentially an item-by-item expansion of the physical seamless coverage constraint in step S2, which is used to subsequently construct the coverage state variables and perform relaxation processing; this expression preserves the geometric correspondence between the UAV's position parameters and the ground user's position parameters.

[0245] S36: Based on the coverage determination expression, construct a coverage state variable and generate a variable to represent the coverage state variable. Was the ground user the first The coverage state variables of the drone;

[0246] In a specific embodiment, to express the geometric coverage determination in step S35 in a discrete form that facilitates unified solution, a coverage state variable is introduced. This coverage state variable is represented in binary form and is defined as follows:

[0247]

[0248] In the formula, To cover state variables;

[0249] In a specific embodiment, the coverage state variables correspond one by one with the coverage determination expression in step S35;

[0250] When the The ground user was the first When a drone is deployed for coverage, the corresponding coverage state variable is assigned a value of 1. The ground user was not included. When a drone is deployed for coverage, the corresponding coverage status variable is set to 0.

[0251] It should be noted that the covering state variable is used to transform the covering decision expression, which is only characterized by geometric relations, into a discrete representation result that can participate in constraint relaxation processing and subsequent constraint rewriting, thereby providing a variable basis for the subsequent introduction of a preset large M constant to construct the covering constraint inequality expression.

[0252] S37: Based on the coverage state variables and the preset large M constant, relax the logical OR relationship in the physical seamless coverage constraint, and transform the coverage decision expression into the coverage constraint inequality expression.

[0253] In a specific embodiment, the physical seamless coverage constraint given in step S24 can be summarized as follows:

[0254] Each ground user is covered by at least one drone, meaning that for any ground user, at least one of the following conditions is met: "covered by the first drone", "covered by the second drone", "covered by the third drone", etc.

[0255] Since this logic is a nonlinear discrete logic relationship, it cannot be directly used for subsequent convex optimization solutions. Therefore, this step uses a preset large M constant to relax it.

[0256] The cover decision expression in step S35 is rewritten as a cover constraint inequality expression, as follows:

[0257]

[0258] In the formula, The value of M is a preset large constant, which is greater than the upper limit of the maximum horizontal distance that may occur between any ground user and any candidate UAV horizontal projection position within the target area. The upper limit of the maximum horizontal distance is determined jointly based on the horizontal dimension of the target area, the vertical dimension of the target area, and the deployment range of the candidate UAV.

[0259] When covering state variables When =1, the above expression degenerates into a true coverage determination expression;

[0260] When covering state variables When =0, the right side of the above equation is relaxed due to the introduction of a large M constant, thus no longer constraining the coverage of the corresponding UAV and ground user pair.

[0261] Furthermore, to ensure that each ground user is covered by at least one drone, constraints also need to be established:

[0262]

[0263] This constraint means that for any ground user, at least one of the corresponding coverage state variables must have a value of 1 across all UAV IDs.

[0264] It should be noted that after the above relaxation process, the original physical seamless coverage constraint is transformed into two types of coverage constraint inequalities; one type is used to constrain the geometric coverage condition, and the other type is used to constrain the at least one coverage condition.

[0265] S38: Generate relaxed coverage constraints based on the coverage constraint inequality expression, and simplify the deployment constraint data based on deterministic transport constraints and relaxed coverage constraints to generate simplified deployment constraint data.

[0266] In a specific embodiment, the covering constraint inequality expression obtained in step S37 is written as a relaxed covering constraint, which is used to characterize the covering constraint expression after processing the covering state variables and the preset large M constant.

[0267] The deterministic transport constraints generated in step S34 and the relaxed coverage constraints generated in this step are used together to replace the reliable transport constraints and physical seamless coverage constraints in step S2.

[0268] The minimum decoding signal-to-noise ratio constraint, UAV power limit constraint, and flight altitude constraint are retained in this step, and together with the newly generated deterministic transmission constraint and relaxed coverage constraint, they form a new constraint expression system.

[0269] After replacement and reorganization, simplified deployment constraint data is obtained;

[0270] The simplified deployment constraint data includes: UAV power limit constraint, minimum decoding signal-to-noise ratio constraint, deterministic transmission constraint, relaxed coverage constraint, and flight altitude constraint.

[0271] S4: Based on the simplified deployment constraint data, generate the initial deployment location and initial number of drones, and iteratively update the drone deployment location and number of drones in the drone swarm deployment optimization problem to generate the drone swarm deployment optimization result;

[0272] The purpose of step S4 is to generate the initial deployment location and initial number of UAVs based on the simplified deployment constraint data generated in step S3, using the initial coverage topology with regular geometric structure, so as to reduce the search dimension and initial infeasibility risk in the subsequent solution process.

[0273] Based on the initial deployment location and the initial number of drones, the deployment location and number of drones in the drone swarm deployment optimization problem are iteratively updated to generate drone swarm deployment optimization results that satisfy the simplified deployment constraints.

[0274] It should be noted that the simplified deployment constraint data generated in step S3 includes UAV power limit constraints, minimum decoding signal-to-noise ratio constraints, deterministic transmission constraints, relaxed coverage constraints, and flight altitude constraints.

[0275] This step performs initial deployment and iterative updates based on the simplified deployment constraint data mentioned above. It does not change the types of constraints in the simplified deployment constraint data, but only solves for the drone deployment location and the number of drones deployed.

[0276] Specifically, the initial deployment location and initial number of drones include:

[0277] Specifically, the logic for generating the initial deployment location and initial number of drones is as follows:

[0278] S41: Based on the simplified deployment constraint data, the location parameters of ground users, and the physical seamless coverage constraints, establish an initial coverage topology, and based on the initial coverage topology, set the high-altitude formation flight conditions of UAVs, and generate the ground coverage range corresponding to a single UAV.

[0279] In a specific embodiment, step S3 has transformed the physical seamless coverage constraint into a relaxed coverage constraint. However, the geometric coverage essence corresponding to the relaxed coverage constraint still originates from the physical seamless coverage constraint established in step S2. Therefore, when establishing the initial coverage topology, this step simultaneously references the simplified deployment constraint data, the location parameters of ground users, and the physical seamless coverage constraint.

[0280] The purpose of establishing the initial coverage topology is to generate an feasible initial layout for the deployment locations and number of UAVs without directly entering the high-dimensional non-convex iterative solution, so that subsequent iterative updates can start from the vicinity of the initial solution that meets the coverage requirements.

[0281] Specifically, based on the flight altitude constraints in the simplified deployment constraint data: ;

[0282] To facilitate unified calculations and reduce the degrees of freedom in the initial coverage topology, this embodiment sets the condition for UAVs to fly in formation at the same altitude, that is, all UAVs fly at the same altitude during the initial deployment phase, expressed as:

[0283]

[0284] In the formula, The uniform flight altitude under the initial coverage topology, and satisfying ;

[0285] It should be noted that the drone formation flight condition is used to eliminate the additional variable caused by the inconsistency of the altitude values ​​of each drone in the initial deployment stage, so that the calculation of the ground coverage area is uniformly controlled by a single flight altitude parameter. In the subsequent iterative update process of step S48, the drone deployment location and the number of drones deployed can continue to be adjusted according to the convex optimization update problem.

[0286] Based on the coverage radius expression used in the physical seamless coverage constraint in step S2, at a uniform flight altitude The ground coverage area corresponding to a single UAV can be determined by the ground coverage radius; if we continue using the coverage expression related to elevation angle in step S2 above, the ground coverage radius corresponding to a single UAV is expressed as:

[0287]

[0288] In the formula, This refers to the ground coverage radius of a single drone. The given elevation angle parameters for the UAV to the ground;

[0289] Based on this, the ground coverage area corresponding to a single drone can be represented as: the horizontal projection coordinates of the drone. With the center as the radius of the ground coverage A circular region with a radius of is used to generate candidate deployment units in the subsequent step S42.

[0290] It should be noted that the ground coverage area corresponding to a single drone output in this step is not the final deployment result, but rather an initial geometric coverage basis generated based on a uniform flight altitude, used to support the subsequent generation of candidate deployment units for hexagonal cellular configuration.

[0291] S42: Based on the ground coverage area corresponding to a single drone, candidate deployment units are generated using a hexagonal cellular configuration;

[0292] To reduce the overlap of coverage between adjacent UAVs in the target area and to ensure continuous coverage of the location parameters of ground users, this step uses a hexagonal cellular configuration to generate candidate deployment units.

[0293] Based on the ground coverage range of a single drone generated in step S41, and using the ground coverage radius of a single drone as a basis, the target area is divided into multiple hexagonal regions arranged according to rules, with each hexagonal region corresponding to a candidate deployment unit.

[0294] In a specific embodiment, the hexagonal cell configuration satisfies the following: the center point of each candidate deployment unit can be used as a candidate horizontal deployment position for a drone, and adjacent candidate deployment units are arranged in a side-connected manner, such that the distance from the center point of any candidate deployment unit to the center point of its adjacent candidate deployment unit is set according to the ground coverage radius corresponding to a single drone, thereby ensuring that there are no coverage breaks between adjacent candidate deployment units.

[0295] It should be noted that the hexagonal cell configuration is adopted because, under the same ground coverage radius, the hexagonal cell configuration can form a continuous paving of the planar area and reduce the area of ​​repeated coverage. Therefore, the candidate deployment units generated in this step can not only meet the geometric coverage requirements corresponding to the physical seamless coverage constraint in step S2, but also help to reduce the number of drones deployed in subsequent iterations.

[0296] The number of candidate deployment units is determined by the size of the target area, the ground coverage area corresponding to a single UAV, and the distribution of location parameters of ground users.

[0297] For scenarios where the location parameters of ground users are relatively dispersed, the candidate deployment unit can cover a larger area on the plane;

[0298] For scenarios where the location parameters of ground users are relatively concentrated, candidate deployment units are concentrated in the vicinity of the areas where the location parameters of ground users are dense.

[0299] S43: Based on the location parameters of ground users in the candidate deployment units, perform coverage mapping to generate the initial deployment location of the UAV;

[0300] In one specific embodiment, step S42 has already generated multiple candidate deployment units. Based on this, this step maps the location parameters of the ground users to the coverage area of ​​the candidate deployment units one by one to determine which candidate deployment units need to be retained as the actual initial deployment locations.

[0301] Specifically, for any candidate deployment unit, determine whether its corresponding ground coverage area covers the location parameters of at least one ground user;

[0302] If the ground coverage area corresponding to a candidate deployment unit covers the location parameters of at least one ground user, then the location parameters corresponding to the center point of the candidate deployment unit are retained as the initial deployment location.

[0303] If the ground coverage area corresponding to a candidate deployment unit does not cover the location parameters of any ground users, then the location parameters corresponding to that candidate deployment unit will not be included in the initial deployment location.

[0304] In a specific embodiment, after performing the above coverage mapping on all candidate deployment units, an initial deployment location set for the UAV can be generated. Each element in the initial deployment location set is determined by the center point of a candidate deployment unit, which can be represented as:

[0305]

[0306] In the formula, For the first An initial deployment location, This represents the initial number of deployment locations. The uniform flight altitude set in step S41.

[0307] It should be noted that the initial deployment location of the drones obtained in this step is not the final optimized deployment result of the drone swarm, but rather the initial point for subsequent iterations and updates.

[0308] This initial point simultaneously satisfies the geometric distribution rules of candidate deployment units and the location parameter coverage mapping requirements of ground users.

[0309] For example, if the target area is an emergency communication area of ​​a city, and the location parameters of ground users are mainly concentrated near several rescue stations, road intersections and temporary resettlement points, then after the location parameters of ground users are mapped by candidate deployment units, the initial deployment position of the UAV can be generated at the center point of the candidate deployment unit covering the above-mentioned locations, thereby reducing the repeated deployment of UAVs in the ground area.

[0310] S44: Generate the initial number of drones based on the number of candidate deployment units corresponding to the initial deployment location of the drones;

[0311] In a specific embodiment, step S43 has generated the initial deployment location of the drone; since each initial deployment location uniquely corresponds to a reserved candidate deployment unit, the initial number of drones can be directly generated based on the number of candidate deployment units corresponding to the initial deployment location of the drone.

[0312] Specifically, the number of candidate deployment units corresponding to the initial deployment locations retained in step S43 is defined as the initial number of drones, denoted as . ;

[0313] It should be noted that the initial number of drones in this step is used to characterize the number of drones that need to be activated in the initial stage under the condition of satisfying the initial coverage topology and candidate deployment unit coverage mapping results. This number is the starting value for optimizing the number of drones deployed in subsequent steps S45 to S48.

[0314] The initial number of drones output in this step, together with the initial deployment location of the drones output in step S43, constitutes the initialization condition for subsequent iterative solutions to the problem.

[0315] Specifically, the steps to generate optimized drone swarm deployment results are as follows:

[0316] S45: Based on the initial deployment location, the initial number of drones, and the simplified deployment constraint data, construct the iterative solution problem corresponding to the drone swarm deployment optimization problem;

[0317] In a specific embodiment, steps S43 and S44 have already generated the initial deployment location and initial number of drones, respectively. Based on this, this step writes the simplified deployment constraint data into a unified solution framework to construct an iterative solution problem corresponding to the drone swarm deployment optimization problem.

[0318] Specifically, the optimization objects of the iterative problem include the deployment location of the drones and the number of drones deployed;

[0319] The initial value for the drone deployment location is the initial deployment location of the drone generated in step S43, and the initial value for the number of drones deployed is the initial number of drones generated in step S44.

[0320] The objective of the iterative solution remains consistent with the UAV swarm deployment optimization problem in step S2, namely, to minimize the number of UAVs deployed while satisfying the simplified deployment constraints.

[0321] Simultaneously, the deployment locations of drones are updated in a coordinated manner, ensuring that the updated deployment locations and the updated number of drones together satisfy the minimum decoding signal-to-noise ratio constraint, drone power limit constraint, deterministic transmission constraint, relaxed coverage constraint, and flight altitude constraint.

[0322] It should be noted that this step does not directly obtain the final optimization result of the drone swarm deployment. Instead, it transforms the initial deployment location of the drones, the initial number of drones, and the simplified deployment constraint data into an iterative problem expression, providing a foundation for the subsequent introduction of 0-1 scheduling vectors and auxiliary variables.

[0323] S46: Based on the iterative solution of the problem, a 0-1 scheduling vector is introduced to transform the number of drones deployed into a candidate drone activation scheduling variable;

[0324] In a specific embodiment, the iterative problem constructed in step S45 still directly includes the number of drones deployed. However, the number of drones deployed is a discrete variable, which is not convenient to directly perform continuous optimization in conjunction with the drone deployment location. Therefore, this step introduces a 0-1 scheduling vector to transform the number of drones deployed into a candidate drone activation scheduling variable.

[0325] Specifically, the range of candidate drone numbers corresponding to the initial number of drones obtained in step S44 is represented as follows:

[0326]

[0327] Then, after introducing the 0-1 scheduling vector, it can be represented as:

[0328]

[0329] in, For the first The candidate drones corresponding to each candidate drone enable scheduling variables, and satisfy the following conditions: ;

[0330] After the above variable transformation, the number of deployed drones can be equivalently converted into the sum of the scheduling variables for all candidate drones, which is: ;

[0331] It should be noted that this step is used to transform the optimization of the number of drone deployments from the original counting problem into a candidate drone activation scheduling problem. This allows for discrete optimization of whether each candidate drone should be activated on a fixed set of candidate drones, and the solution is jointly solved with the continuous update of the drone deployment location.

[0332] S47: Based on the candidate UAVs corresponding to the 0-1 scheduling vector, enable the scheduling variable, introduce auxiliary variables and construct an iterative subproblem, and perform successive convex approximations on the non-convex constraints in the iterative subproblem to generate a convex optimization update problem;

[0333] In one specific embodiment, step S46 has introduced a 0-1 scheduling vector and transformed the number of drone deployments into a candidate drone activation scheduling variable;

[0334] At this point, the minimum decoding signal-to-noise ratio constraint and the deterministic transmission constraint still contain nonlinear coupling terms between the candidate UAV activation scheduling variable and the UAV's position parameters. Therefore, this step reconstructs the relevant constraints by introducing auxiliary variables.

[0335] Specifically, for the satellite-to-UAV link, the satellite's position parameters are: , No. The position parameters of the candidate drones are: ;

[0336] For the first The first auxiliary variable is introduced for each candidate drone. and establish:

[0337]

[0338] The path loss coefficient for the satellite-to-UAV link;

[0339] For the drone-to-ground user link, the first The candidate drone and the first A second auxiliary variable is introduced into the link between ground users. and establish:

[0340]

[0341] In the formula, the first The location parameters of each ground user are , This represents the path loss coefficient for the link from the drone to the ground user.

[0342] In a specific embodiment, since the first auxiliary variable and the second auxiliary variable respectively replace the upper bound of the distance loss term of the satellite-to-candidate UAV link and the distance loss term of the candidate UAV-to-ground user link, after the candidate UAV enables the participation of the scheduling variable, the corresponding link gain term can be written as a fractional combination of the candidate UAV enabling scheduling variable and the auxiliary variable.

[0343] The core term in the minimum decoding signal-to-noise ratio constraint is written as:

[0344]

[0345] In deterministic transport constraints, the first The core item corresponding to each ground user is written as:

[0346]

[0347] In the formula, For the first The scheduling variables are enabled for each candidate drone. This represents the initial number of drones;

[0348] Furthermore, the above fractional expressions are substituted into the minimum decoding signal-to-noise ratio constraint and the deterministic transmission constraint, and together with the relaxed coverage constraint and the flight altitude constraint, they form an iterative subproblem; the optimization variables of the iterative subproblem include the candidate UAV activation scheduling variable, the UAV's position parameters, the first auxiliary variable, and the second auxiliary variable.

[0349] In a specific embodiment, to transform the fractional coupling terms in the iterative subproblem into a solvable convex expression, the values ​​of the candidate UAV activation scheduling variable, the first auxiliary variable, and the second auxiliary variable in the current iteration are used as the expansion base; let the value of the candidate UAV activation scheduling variable in the current iteration be... The first auxiliary variable takes the value of The second auxiliary variable takes the value of Then for and Perform successive convex approximations separately.

[0350] Specifically, by performing a first-order Taylor approximation on the fractional terms in the minimum decoding signal-to-noise ratio constraint, we obtain:

[0351]

[0352] Applying a first-order Taylor approximation to the fractional terms in the deterministic transport constraints, we obtain:

[0353]

[0354] In a specific embodiment, the minimum decoding signal-to-noise ratio constraint, deterministic transmission constraint, relaxed coverage constraint, and flight altitude constraint after successive convex approximation are jointly written into a unified solution framework to generate a convex optimization update problem.

[0355] The objective function of the convex optimization update problem is the sum of the candidate UAV activation scheduling variables, expressed as:

[0356]

[0357] The objective function of the convex optimization update problem is used to reduce the number of candidate drones that are activated while satisfying the constraints.

[0358] It should be noted that the convex optimization update problem output in this step includes the objective function under the current round, the approximate minimum decoding signal-to-noise ratio constraint, the approximate deterministic transmission constraint, the relaxed coverage constraint, and the flight altitude constraint, and serves as the input for updating the UAV deployment location and the number of UAVs in step S48.

[0359] S48: Based on the convex optimization update problem, iteratively update the drone deployment location and the number of drones deployed, and generate the drone swarm deployment optimization result when the convergence threshold is met;

[0360] Step S47 has generated a convex optimization update problem. This step obtains the update values ​​of the candidate UAV activation scheduling variable, the UAV position parameter update value, the first auxiliary variable update value, and the second auxiliary variable update value corresponding to the current iteration by solving the convex optimization update problem.

[0361] In a specific embodiment, let the first... After rounds of iterative solving, the th The update value of the candidate drone scheduling variable corresponding to each candidate drone is [value]. The corresponding position parameter update value is ;

[0362] Based on the updated values ​​of the scheduling variables for all candidate drones, the number of candidate drones activated in the current round is counted, and the corresponding number of drones deployed in the current round is generated, represented as:

[0363]

[0364] In one specific embodiment, the following will be satisfied Position parameters corresponding to candidate drones Remove from the current round of deployment results.

[0365] To determine whether the current iteration meets the stopping condition, the number of drones deployed and the change in drone deployment location between two consecutive iterations are compared.

[0366] If satisfied Furthermore, the change in the deployment location of the drone is less than the convergence threshold. If the current iteration process satisfies the convergence condition, then it is determined that the current iteration process meets the convergence condition.

[0367] The change in the deployment location of the drone is determined by satisfying all conditions in two consecutive iterations. The maximum Euclidean distance corresponding to the position parameter variation of the candidate UAV is expressed as:

[0368]

[0369] In the formula, Changes in the deployment location of the drone;

[0370] when When the time is less than the convergence threshold, it means that the change in the deployment location of the drones between the current round and the previous round has been less than the convergence threshold.

[0371] If the above convergence conditions are met, the drone deployment location and the number of drones deployed in the current round will be jointly determined as the drone swarm deployment optimization result.

[0372] The optimization results for drone swarm deployment include the final drone deployment location and the final number of drones deployed.

[0373] If the above convergence conditions are not met, the updated values ​​of the candidate UAV activation scheduling variable, the first auxiliary variable, and the second auxiliary variable obtained in the current round will be used as the expansion base points of the next round of successive convex approximation, and the process will return to step S47 to regenerate a new convex optimization update problem until the convergence threshold is met.

[0374] It should be noted that: convergence threshold The pre-set position change judgment parameter is determined based on the spatial scale of the target area, the upper bound of the UAV navigation and positioning error, and the deployment solution accuracy requirements. It is used to determine whether the change in the UAV deployment position between two consecutive iterations is less than the allowable error range.

[0375] The final UAV deployment location is used to characterize the deployment coordinates of each activated UAV in the target area under the conditions of minimum decoding signal-to-noise ratio constraint, UAV power limit constraint, deterministic transmission constraint, relaxed coverage constraint, and flight altitude constraint; the final UAV deployment number is used to characterize the number of UAVs required to be activated under the above constraints.

[0376] The above embodiments are only used to illustrate the technical methods of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical methods of the present invention without departing from the spirit and scope of the technical methods of the present invention.

Claims

1. An optimized method for deploying unmanned aerial vehicle (UAV) swarms to provide seamless coverage for ground users, characterized in that: The method includes: S1: Obtain the parameters of the research object and generate signal-to-noise ratio data through a predetermined urban emergency communication model. The research object includes ground users, drones, and satellites. S2: Construct an optimization problem for UAV swarm deployment based on signal-to-noise ratio data, and generate deployment constraint data, which includes UAV power limit constraints, minimum decoding signal-to-noise ratio constraints, reliable transmission constraints, physical seamless coverage constraints, and flight altitude constraints; S3: Based on the deployment constraint data, the reliable transmission constraint is deterministically processed based on the UAV power limit constraint to generate deterministic transmission constraints, and the physical seamless coverage constraint is relaxed to generate relaxed coverage constraints. Simplified deployment constraint data is generated based on the deterministic transmission constraint and the relaxed coverage constraint. S4: Based on the simplified deployment constraint data, generate the initial deployment location and initial number of drones, and iteratively update the drone deployment location and number of drones in the drone swarm deployment optimization problem to generate the drone swarm deployment optimization result.

2. The method for optimizing the deployment of unmanned aerial vehicle (UAV) swarms to provide seamless coverage for ground users according to claim 1, characterized in that, The parameters of the research objects include satellite position parameters, UAV position parameters, ground user position parameters, satellite transmission power, UAV transmission power, UAV noise power, and ground user noise power. The signal-to-noise ratio (SNR) data includes the average SNR of the UAV swarm and the average SNR of the ground users.

3. The method for optimizing the deployment of unmanned aerial vehicle (UAV) swarms to provide seamless coverage for ground users according to claim 2, characterized in that, The steps to generate signal-to-noise ratio data are as follows: S11: Based on the parameters of the research object, establish spatial location description data; S12: Generate the first-stage link channel data from satellite to UAV based on the spatial location description data, and calculate the average signal-to-noise ratio of the UAV swarm; S13: Generate the second-stage link channel data from the UAV to the ground user based on the spatial location description data; S14: Calculate the average signal-to-noise ratio (SNR) of ground users based on the second-stage link channel data, and combine the average SNR of the UAV swarm and the average SNR of ground users into SNR data.

4. The method for optimizing the deployment of unmanned aerial vehicle (UAV) swarms to provide seamless coverage for ground users according to claim 3, characterized in that, The steps to generate deployment constraint data are as follows: S21: Based on the signal-to-noise ratio data and the parameters of the research object, construct the objective function for the optimization problem of UAV swarm deployment; S22: Generate the minimum decoding signal-to-noise ratio constraint based on the average signal-to-noise ratio of the drone swarm; S23: Generate UAV power limit constraints and reliable transmission constraints based on the average signal-to-noise ratio of ground users; S24: Generate physical seamless coverage constraints based on the location parameters of ground users and UAVs, and generate flight altitude constraints based on the location parameters of UAVs; S25: Combine the minimum decoding signal-to-noise ratio constraint, reliable transmission constraint, physical seamless coverage constraint, and flight altitude constraint into deployment constraint data.

5. The method for optimizing the deployment of unmanned aerial vehicle (UAV) swarms to provide seamless coverage for ground users according to claim 4, characterized in that, The steps for generating deterministic transport constraints include: S31: Based on the UAV power limit constraints, reliable transmission constraints, and second-stage link channel data, construct the random distribution expression corresponding to the average signal-to-noise ratio of ground users, and determine the probability constraint expression corresponding to the reliable transmission constraints; S32: Based on the aforementioned probability constraint expression, perform an equivalent transformation on the probability that the average signal-to-noise ratio of the ground user is greater than the ground user reception threshold, and transform the reliable transmission constraint into a first-order Marcum-Q function constraint. S33: Based on the UAV power limit constraints and the second-stage link channel data, construct the beamforming vector corresponding to the ground user using the maximum ratio transmission, and generate the beamforming vector corresponding to the second-stage link channel data. S34: Based on the beamforming vector, the first-order Marcum-Q function constraint is rewritten by thresholding to generate a deterministic transmission threshold value, and a deterministic transmission constraint is established based on the deterministic transmission threshold value.

6. The method for optimizing the deployment of unmanned aerial vehicle (UAV) swarms to provide seamless coverage for ground users according to claim 5, characterized in that, The steps for generating simplified deployment constraint data include: S35: Based on physical seamless coverage constraints, the location parameters of ground users and the location parameters of UAVs, establish a coverage determination expression between ground users and UAVs; S36: Based on the coverage determination expression, construct a coverage state variable and generate a variable to represent the coverage state variable. Was the ground user the first The coverage state variables of the drone; S37: Based on the coverage state variables and the preset large M constant, relax the logical OR relationship in the physical seamless coverage constraint, and transform the coverage decision expression into the coverage constraint inequality expression. S38: Generate relaxed coverage constraints based on the coverage constraint inequality expression, and simplify the deployment constraint data based on deterministic transport constraints and relaxed coverage constraints to generate simplified deployment constraint data.

7. The method for optimizing the deployment of unmanned aerial vehicle (UAV) swarms to provide seamless coverage for ground users according to claim 6, characterized in that, The logic for generating the initial deployment location and initial number of drones is as follows: S41: Based on the simplified deployment constraint data, the location parameters of ground users, and the physical seamless coverage constraints, establish an initial coverage topology, and based on the initial coverage topology, set the high-altitude formation flight conditions of UAVs, and generate the ground coverage range corresponding to a single UAV. S42: Based on the ground coverage area corresponding to a single drone, candidate deployment units are generated using a hexagonal cellular configuration; S43: Based on the location parameters of ground users in the candidate deployment units, perform coverage mapping to generate the initial deployment location of the UAV; S44: Generate the initial number of drones based on the number of candidate deployment units corresponding to the initial deployment location of the drones.

8. The method for optimizing the deployment of unmanned aerial vehicle (UAV) swarms to provide seamless coverage for ground users according to claim 7, characterized in that, The steps to generate the optimized deployment results of drone swarms are as follows: S45: Based on the initial deployment location, the initial number of drones, and the simplified deployment constraint data, construct the iterative solution problem corresponding to the drone swarm deployment optimization problem; S46: Based on the iterative solution of the problem, a 0-1 scheduling vector is introduced to transform the number of drones deployed into a candidate drone activation scheduling variable; S47: Based on the candidate UAVs corresponding to the 0-1 scheduling vector, enable the scheduling variable, introduce auxiliary variables and construct an iterative subproblem, and perform successive convex approximations on the non-convex constraints in the iterative subproblem to generate a convex optimization update problem; S48: Based on the convex optimization update problem, iteratively update the drone deployment location and the number of drones deployed, and generate the drone swarm deployment optimization result when the convergence threshold is met.

Images