A method for optimizing the layout of airborne antennas for unmanned aerial vehicles (UAVs)

Abstract

This invention provides a method for optimizing the layout of airborne antennas for unmanned aerial vehicles (UAVs), relating to the field of UAV communication technology. Based on mission requirements, this invention obtains time series of attitude angles, including typical attitudes such as level flight, climb, descent, turn, and hover. The pitch and roll angles are discretized into multiple attitude units. Historical data is used to statistically analyze the duration of each attitude unit and calculate its comprehensive weight. Subsequently, multiple alternative antenna layout schemes are generated under geometric, engineering, and dynamic constraints. Electromagnetic simulation is used to obtain communication performance evaluation values ​​for each attitude unit, and the overall communication performance of the scheme is obtained by weighting the attitude unit values. Finally, with the goal of maximizing overall communication performance and minimizing engineering complexity, the TOPSIS method is used for multi-objective ranking, and the optimal antenna layout scheme is determined by combining Pareto solutions. This achieves synergistic optimization of communication performance and engineering feasibility for UAVs in dynamic flight missions.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) communication technology, specifically to a method for optimizing the layout of UAV onboard antennas. Background Technology

[0002] When performing diverse missions, unmanned aerial vehicles (UAVs) often face problems such as unstable communication links and susceptibility to interference. The root cause lies in the fact that antenna layout design often relies on experience or static conditions, failing to fully consider the impact of dynamic attitude changes during actual flight on communication performance. Traditional layout methods are mostly optimized based on a single typical attitude or simplified model, lacking quantitative analysis of multi-attitude weights throughout the entire mission cycle, leading to decreased communication performance under complex flight conditions. Furthermore, existing solutions often neglect the synergistic optimization between engineering feasibility, structural constraints, and communication performance, making it difficult to balance reliability, lightweight design, and high performance requirements in practical applications. Therefore, there is an urgent need for an antenna layout method that can integrate flight attitude temporal characteristics, multiple constraints, and multi-objective optimization to improve the communication robustness and engineering applicability of UAVs in dynamic missions.

[0003] In the prior art, CN105281016A discloses a method for designing and verifying the layout of an airborne antenna for a UAV, including: optimizing the antenna position layout based on the antenna isolation; after the antenna is installed, performing radiation pattern performance simulation analysis, aerodynamic performance analysis, isolation baseline test, radiation pattern baseline test, scaled-down model wind test, antenna coupling level test, and mutual interference check between transceiver pairs in sequence, thereby optimizing the antenna installation position through the above steps.

[0004] The main problems with the above-mentioned solutions are: the flight attitude sequence of the UAV in actual missions is not included in the layout optimization, and only static isolation is used as the core constraint, which may lead to a decrease in the communication performance of the antenna during dynamic flight, especially in high-maneuverability or continuous attitude change scenarios, which may easily lead to link instability; the separation of layout optimization and verification requires a large number of field tests and wind tunnel tests after installation, resulting in a long design cycle, high cost, and difficulty in predicting conflicts between communication performance and engineering constraints in the early stage. Repeated modifications will increase development risks and resource consumption; the optimization process involves iterating on multiple objectives in sequence, failing to take multiple objectives into account at the same time, and making it difficult to guarantee global optimality.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a method for optimizing the layout of airborne antennas for unmanned aerial vehicles (UAVs) to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for optimizing the layout of an airborne antenna for a drone, comprising the following steps: Step 1: Before each work task is executed, determine the typical flight attitudes involved in the work task and obtain the attitude angle time series of the work task; the typical flight attitudes include level flight, climb, descent, turn and hover; the attitude angles include pitch angle and roll angle. Step 2: Discretize the pitch and roll angles within their respective ranges to generate several discrete attitude units. Map the time series of attitude angles of the task to the discrete attitude units. Calculate the duration of the UAV in each attitude unit while performing the task, and then calculate the time basis weight of each attitude unit. Calculate the comprehensive weight based on the time basis weight of the attitude unit and the typical flight attitude types. Step 3: Using geometric constraints, engineering constraints, and dynamic constraints as constraints, generate multiple alternative antenna layout schemes. For any alternative antenna layout scheme and any attitude unit, obtain the communication performance evaluation value of the alternative antenna layout scheme under that attitude unit. Based on the attitude units included in the task and their respective comprehensive weights, calculate the comprehensive communication performance of the alternative antenna layout schemes. Step 4: Calculate the fitness value with the goal of maximizing overall communication performance and minimizing engineering complexity. Calculate the information entropy of the two objectives and perform TOPSIS ranking. Construct a Pareto solution set based on the fitness values ​​of all candidate antenna layout schemes. Determine the optimal antenna layout scheme based on the TOPSIS ranking results and the Pareto solution set.

[0008] Furthermore, the principle of obtaining the attitude angle time series of the work task is as follows: From the historical flight data, multiple task execution segments that are the same as the work task to be performed are selected. In each selected task execution segment, a sampling point is set with a sampling frequency of 1Hz. The pitch angle and roll angle of each sampling point are obtained, and pitch angle sequence and roll angle sequence are generated respectively. The two sequences are integrated to generate the attitude angle time series.

[0009] Furthermore, the principle underlying the generation of discrete attitude units is as follows: The pitch angle ranges from -90° to 90°, and the roll angle ranges from -180° to 180°. The discretization step size is set to 15°. The number of discrete pitch angles is the ratio of the difference between the maximum and minimum pitch angle values ​​to the discretization step size plus one, and the number of discrete roll angles is the ratio of the difference between the maximum and minimum roll angle values ​​to the discretization step size plus one. Starting from the minimum pitch angle value, a discrete pitch angle is generated every discretization step size until the maximum pitch angle value is reached. All these discrete pitch angles constitute a discrete pitch angle set. Similarly, a discrete roll angle set is generated. A discrete pitch angle and a discrete roll angle are selected from the discrete pitch angle set and the discrete roll angle set, and they are arranged and combined to form several discrete attitude units. The number of attitude units is the product of the number of discrete pitch angles and the number of discrete roll angles.

[0010] Furthermore, the principle for calculating the overall weight is as follows: The principle of mapping the time series of attitude angles of a task to discrete attitude units is as follows: For each sampling point in the attitude angle time series, find the discrete pitch angle and discrete roll angle that are closest to the pitch angle and roll angle of the sampling point from the discrete set of pitch angle and the discrete set of roll angle, respectively; classify the sampling point into the attitude unit, which is considered to complete the mapping of this sampling point; traverse all sampling points in the attitude angle time series according to the above steps. The number of times each attitude unit is mapped is counted. The product of the time interval between adjacent sampling points and the number of times the attitude unit is mapped is used as the duration of the attitude unit. The ratio of the duration of the attitude unit to the total time of the task is used as the time basis weight of the attitude unit in this task. Based on the impact of different typical flight attitudes on antenna communication performance in historical flight data, the attitude type weights of different typical flight attitudes are determined by expert scoring. The comprehensive weight of the attitude unit is obtained by multiplying the time-based weight of the attitude unit by the attitude type weight of the corresponding typical flight attitude.

[0011] Furthermore, the principle for generating multiple alternative antenna layout schemes is as follows: The geometric constraints include: the antenna is mounted on the outer surface of the UAV and avoids the carbon fiber structure; the omnidirectional antenna is mounted on the upper part of the UAV and the directional antenna is pointed in the direction of the signal source; the installation attitude of the antenna on the UAV is consistent with its polarization direction; the distance between the airborne antennas meets the isolation requirements. The engineering constraints include: the antenna mounting point should be located in a region with high rigidity and low vibration; the antenna and its support should meet the structural strength requirements of the UAV under typical flight attitudes; and the antenna installation should not disrupt the aerodynamic shape of the UAV. The dynamic constraints include: the center of gravity of the UAV after the antenna is installed meets the requirements of the flight mission; Based on geometric constraints, several sets of antenna mounting points are generated on the outer surface of the UAV. Based on the sets of antenna mounting points, several installation schemes are generated. These installation schemes are verified by engineering constraints and dynamic constraints respectively. The installation schemes that satisfy the three constraints are retained as alternative antenna layout schemes.

[0012] Furthermore, the principle underlying the calculation of the overall communication performance of alternative antenna layout schemes is as follows: The UAV is modeled in electromagnetic simulation software, and alternative antenna layout schemes are assigned to the UAV. The UAV model is rotated in space so that its attitude is consistent with the center value of a given attitude unit. For each communication link that needs to be guaranteed, the received power and interference power of the antenna are obtained. The received power is subtracted from the interference power to obtain the simulated signal-to-noise ratio of the communication link. The simulated signal-to-noise ratio of each communication link is divided by the minimum required signal-to-noise ratio for the communication link to work normally to generate the signal-to-noise ratio margin of each communication link. The average value of the signal-to-noise ratio margins of all communication links is calculated to obtain the communication performance evaluation value of the given alternative antenna layout scheme under a given attitude unit. For a complete task, the communication performance evaluation values ​​of the attitude units included in the task are weighted and added together with the comprehensive weight of the attitude units to obtain the comprehensive communication performance of the alternative antenna layout scheme under the task.

[0013] Furthermore, the principle for calculating the fitness value is as follows: The logic for calculating the engineering complexity is as follows: obtain the number of antenna mounting points, the total length of the antenna, and the total mass of the antenna; normalize the above parameters and add them together with weights to obtain the engineering complexity. The fitness value is obtained by adding the overall communication performance to the reciprocal of the engineering complexity.

[0014] Furthermore, the principle underlying the determination of the optimal antenna layout scheme is as follows: Based on M alternative antenna layout schemes and their corresponding engineering complexity and overall communication performance, an M×2 matrix is ​​constructed. For each alternative antenna layout scheme, maximum and minimum normalization are applied to both the overall communication performance and engineering complexity. Then, the contribution ratio of each alternative antenna layout scheme under different targets is calculated. The calculation logic is to divide the normalized value of one alternative antenna layout scheme under a target by the sum of the normalized values ​​of all alternative antenna layout schemes under the corresponding target. The product of the contribution ratio of all alternative control schemes and the logarithm of the contribution ratio to the base e is summed and divided by the negative reciprocal of the logarithm of M to the base e to obtain the information entropy corresponding to a target. Then, the information entropy is calculated. The entropy weight of the same target is calculated as follows: subtract the information entropy of a target from 1, and then divide by the sum of the information entropies of all targets minus 1. Multiply the target's entropy weight by the normalized value of the target under different alternative antenna layout schemes to weight the normalized value of the target, construct a weighted decision matrix, generate a positive ideal solution based on the maximum value of each target in the weighted decision matrix, and generate a negative ideal solution based on the minimum value of each target. Calculate the Euclidean distance from the target weighted value of each alternative antenna layout scheme to the positive and negative ideal solutions, and then generate the proximity score. The logic for calculating the proximity score is: the ratio of the Euclidean distance to the negative ideal solution to the sum of the Euclidean distances to the positive and negative ideal solutions. Find the Pareto front solution from all the alternative antenna layout schemes to construct the Pareto solution set. Sort the schemes in the Pareto solution set from largest to smallest proximity and select the alternative antenna layout scheme with the largest proximity as the optimal antenna layout scheme.

[0015] Compared with the prior art, the beneficial effects of the present invention are: This invention incorporates dynamic changes in attitude during flight into the optimization process by acquiring attitude angle time series, making the antenna layout more aligned with the actual flight mission requirements. By acquiring the attitude sequence, it is possible to identify which attitudes occur frequently and last for a long time during the mission, thereby assigning them higher weights in subsequent steps and ensuring optimal communication performance under these key attitudes.

[0016] This invention further divides the continuous attitude space into finite attitude units by discretizing pitch and roll angles, statistically analyzes the duration of each attitude unit, and calculates its time-based weight. The time-based weight reflects the frequency and duration of attitude occurrences, while the attitude type weight reflects the sensitivity of different flight phases to communication performance. The combination of these two weights forms a comprehensive weight, making the optimization more aligned with actual mission requirements. Multiple alternative antenna layout schemes are generated under geometric, engineering, and dynamic constraints. Electromagnetic simulation is performed on each attitude unit to obtain the communication performance evaluation value under that attitude. This value is then weighted using the comprehensive weight to obtain the comprehensive communication performance over the entire mission cycle, making the communication performance evaluation more comprehensive and realistic. By combining information entropy to determine objective weights, performing TOPSIS ranking, and filtering non-dominated solutions using Pareto solution sets, global optimization is performed on conflicting optimization objectives to find the engineering optimal solution that achieves the best balance between performance and complexity. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the method flow of an embodiment of the present invention; Figure 2 This is a schematic diagram of the attitude angle time series change according to an embodiment of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0019] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0020] Example: Please see Figures 1 to 2 The present invention provides a technical solution: A method for optimizing the layout of an airborne antenna for a drone, comprising the following steps: Step 1: Before each work task is executed, determine the typical flight attitudes involved in the work task and obtain the attitude angle time series of the work task; the typical flight attitudes include level flight, climb, descent, turn and hover; the attitude angles include pitch angle and roll angle. In this embodiment, the principle of obtaining the attitude angle time series of the work task is as follows: From the historical flight data, multiple task execution segments that are the same as the work task to be performed are selected. In each selected task execution segment, a sampling point is set with a sampling frequency of 1Hz. The pitch angle and roll angle of each sampling point are obtained, and pitch angle sequence and roll angle sequence are generated respectively. The two sequences are integrated to generate the attitude angle time series.

[0021] Typical flight attitudes include level flight, climb, descent, turn, and hovering. Level flight means that both pitch and roll angles are close to 0°, and the flight altitude remains basically constant. Climb means that the pitch angle is positive, the roll angle changes slightly, and the flight altitude increases. Descent means that the pitch angle is negative, the roll angle changes slightly, and the flight altitude decreases. When turning, the roll angle changes significantly, while the pitch angle changes very little. Hovering means that both pitch and roll angles are close to 0°, and the airspeed is almost zero. From historical flight data, mission execution segments that are identical to the task at hand in the following dimensions are retrieved: altitude change trend, speed change trend, maneuver sequence, and environmental conditions. The maneuver sequence represents the order of flight attitude changes, and environmental conditions include terrain and weather conditions. Within the retrieved mission execution segments, sampling is performed at a frequency of 1Hz to obtain the pitch and roll angles at each sampling point, generating a pitch angle sequence, specifically: , ,in, Represents the pitch angle sequence. Indicates the first The pitch angle of each sampling point Indicates the index of the sampling point, and , Indicates the number of sampling points. Indicates the roll angle sequence. Indicates the first The roll angle at each sampling point; the pitch angle sequence and roll angle sequence are aligned according to the sampling point time series and merged into an attitude angle time series: ,in, This represents the time series of attitude angles.

[0022] Table 1 shows the changes in pitch and roll angles over time during a task. From 0 to 6 seconds, the pitch angle gradually increases from negative to positive as the UAV takes off and climbs. From 7 to 12 seconds, the roll angle changes from 0 to 10° as the UAV makes a right turn. From 13 to 16 seconds, the pitch angle is 0 and the roll angle approaches 0, indicating level flight. From 17 to 24 seconds, the roll angle changes negatively and the pitch angle increases negatively as the UAV makes a left turn and descends. From 25 to 30 seconds, both the pitch and roll angles are 0, indicating hovering.

[0023] Table 1. Schematic diagram of attitude angle change over time

[0024] Step 2: Discretize the pitch and roll angles within their respective ranges to generate several discrete attitude units. Map the time series of attitude angles of the task to the discrete attitude units. Calculate the duration of the UAV in each attitude unit while performing the task, and then calculate the time basis weight of each attitude unit. Calculate the comprehensive weight based on the time basis weight of the attitude unit and the typical flight attitude types. In this embodiment, the principle underlying the generation of discrete attitude units is as follows: The pitch angle ranges from -90° to 90°, and the roll angle ranges from -180° to 180°. The discretization step size is set to 15°. The number of discrete pitch angles is the ratio of the difference between the maximum and minimum pitch angle values ​​to the discretization step size plus one, and the number of discrete roll angles is the ratio of the difference between the maximum and minimum roll angle values ​​to the discretization step size plus one. Starting from the minimum pitch angle value, a discrete pitch angle is generated every discretization step size until the maximum pitch angle value is reached. All these discrete pitch angles constitute a discrete pitch angle set. Similarly, a discrete roll angle set is generated. A discrete pitch angle and a discrete roll angle are selected from the discrete pitch angle set and the discrete roll angle set, and they are arranged and combined to form several discrete attitude units. The number of attitude units is the product of the number of discrete pitch angles and the number of discrete roll angles.

[0025] The formula for calculating the number of discrete pitch angles is: ,in, Represents the number of discrete pitch angles. This represents the maximum value of the pitch angle. This represents the minimum value of the pitch angle. Indicates the discretization step size; The formula for calculating the discrete roll angle is: ,in, Indicates the number of discrete roll angles. This indicates the maximum value of the roll angle. This indicates the minimum value of the roll angle; The discrete set of pitch angles is: ; The discrete set of roll angles is: ; Discrete attitude units are: ,in, Indicates the first A discrete pitch angle, The index represents the discrete pitch angle, and , Indicates the first A discrete roll angle, The index representing the discrete roll angle, and , Indicates the first The discrete pitch angles and the first An attitude unit constructed from discrete roll angles. Indicates the index of the attitude unit; The attitude unit divides the continuous UAV flight attitude into a finite number of discrete attitude combinations, with each attitude unit corresponding to a specific attitude combination. Continuous attitude angle data is difficult to use directly for optimization calculations. If electromagnetic simulation is performed for each sampling point, computational redundancy will occur. After discretization, only representative attitude units need to be simulated. By statistically analyzing the mapping between attitude angle time series and attitude units, the frequency and duration of the UAV in each attitude range during the flight mission can be determined.

[0026] The principle for calculating the overall weight is as follows: The principle of mapping the time series of attitude angles of a task to discrete attitude units is as follows: For each sampling point in the attitude angle time series, find the discrete pitch angle and discrete roll angle that are closest to the pitch angle and roll angle of the sampling point from the discrete set of pitch angle and the discrete set of roll angle, respectively; classify the sampling point into the attitude unit, which is considered to complete the mapping of this sampling point; traverse all sampling points in the attitude angle time series according to the above steps. For attitude angle time series For each sampling point, query the nearest discrete pitch angle and discrete roll angle, respectively: , ,in, Indicates and The closest discrete pitch angle, Indicates and The closest discrete roll angle will be used to sample the points. Mapped to attitude unit ; Iterate through all sampling points in the attitude angle time series until all sampling points have been mapped to attitude units; The number of times each attitude unit is mapped is counted. The product of the time interval between adjacent sampling points and the number of times the attitude unit is mapped is used as the duration of the attitude unit. The ratio of the duration of the attitude unit to the total time of the task is used as the time basis weight of the attitude unit in this task. The formula for calculating the duration of an attitude unit is: ,in, Indicates the first The duration of each pose unit, Indicates the first The number of times each pose unit is mapped; the total task time is: Then the attitude unit The time-based weights are: ; The time-based weight reflects the proportion of time a UAV spends in a particular attitude unit during mission execution. The time-based weight directly reflects the length of time a UAV spends in a particular attitude unit during a single mission; a larger time-based weight indicates a longer flight time in that attitude. By calculating the time-based weight of each attitude unit, we can identify attitudes that occur frequently and last for a long time during the mission. These attitudes have a greater impact on communication performance and therefore have higher weights in communication performance evaluation. To ensure communication performance, the antenna layout needs to perform well in these high-weight attitudes. Without discretization and weight calculation, electromagnetic simulation is required for each sampling point, resulting in redundant computation. By discretizing into a finite number of attitude units and calculating their time-based weights, simulation is performed only on representative attitude units, reducing computational costs. Furthermore, the time-based weight makes the optimization process more closely reflect the actual flight mission's time distribution, rather than assuming all attitudes are equally important. This ensures that the antenna layout performs better in attitudes that occur frequently during the mission, improving the overall reliability of the communication system. By weighting the communication performance evaluation values ​​of each attitude unit according to the time-based weight, we can obtain an evaluation index reflecting the comprehensive communication performance throughout the entire mission cycle. This makes antenna layout optimization no longer based on a single attitude, but on a dynamic process across the entire mission.

[0027] Based on the impact of different typical flight attitudes on antenna communication performance in historical flight data, the attitude type weights of different typical flight attitudes are determined by expert scoring. The comprehensive weight of the attitude unit is obtained by multiplying the time-based weight of the attitude unit by the attitude type weight of the corresponding typical flight attitude.

[0028] Attitude type weights reflect the impact of different flight attitudes on antenna communication performance. Their values ​​are related to the rate and magnitude of change of the attitude angle. A larger rate of change in the attitude angle indicates a faster change in the UAV's attitude, leading to rapid antenna pointing deviation and communication link instability. A larger magnitude of change in the attitude angle may cause signal blockage or polarization mismatch. When the UAV is climbing or descending, the pitch angle changes significantly, resulting in a noticeable change in antenna pointing, which may lead to signal attenuation or link interruption; these two attitudes have the highest attitude type weights. When the UAV is hovering, its attitude is relatively stable, but there may be an impact of fuselage rotation on the directional antenna; this attitude has a medium attitude type weight. The degree of attitude change during turning is between climbing and hovering. Between stops, there are usually significant roll angle changes. When the UAV is in level flight, its attitude is the most stable and the communication environment is the most predictable. The attitude type weight corresponding to this attitude is the smallest. For the five attitudes of climb, descent, turn, hover, and level flight, the attitude type weights are 1.2, 1.2, 1.1, 1.0, and 0.8, respectively. The higher the attitude type weight, the greater the impact of the attitude on the antenna communication performance. A better antenna layout is needed to ensure communication quality. During critical phases such as climb and descent, communication interruption may lead to mission failure. Therefore, these attitudes are given higher weights. By assigning different weights to different attitudes, the optimization process focuses more on those attitudes that have a significant impact on communication performance, thereby improving the communication robustness of the UAV in dynamic missions.

[0029] The formula for calculating the overall weight is: ;in, Indicates the first The overall weight of each pose unit, This represents the attitude type weights corresponding to typical flight attitudes for the attitude unit; The comprehensive weight takes into account the time spent by the UAV in different attitudes when performing a specific task, as well as the severity of the impact of the attitude on communication performance. It guides which attitudes should be prioritized for ensuring communication performance. The comprehensive weight is proportional to the time-based weight and the attitude type weight, which means that the longer the UAV is in a certain attitude, the more severe the impact of that attitude on communication performance, and the higher its comprehensive weight, and the more it should be considered in optimization.

[0030] Step 3: Using geometric constraints, engineering constraints, and dynamic constraints as constraints, generate multiple alternative antenna layout schemes. For any alternative antenna layout scheme and any attitude unit, obtain the communication performance evaluation value of the alternative antenna layout scheme under that attitude unit. Based on the attitude units included in the task and their respective comprehensive weights, calculate the comprehensive communication performance of the alternative antenna layout schemes. In this embodiment, the principle for generating multiple alternative antenna layout schemes is as follows: The geometric constraints include: the antenna is mounted on the outer surface of the UAV and avoids the carbon fiber structure; the omnidirectional antenna is mounted on the upper part of the UAV and the directional antenna is pointed in the direction of the signal source; the installation attitude of the antenna on the UAV is consistent with its polarization direction; the distance between the airborne antennas meets the isolation requirements. When installing drone antennas, all antennas must be mounted on the outer surface of the drone to ensure that the signal is not blocked or shielded by the fuselage. Carbon fiber has shielding and absorption properties for electromagnetic waves, which can severely affect antenna radiation efficiency and communication distance; therefore, antenna installation points should avoid areas of carbon fiber composite materials on the drone. Omnidirectional antennas should be preferentially installed on the upper part of the drone, such as the top of the fuselage or the top of the vertical tail, to maximize their radiation range and reduce obstruction of omnidirectional coverage by the fuselage and wings. Directional antennas, such as parabolic antennas and flat panel antennas, should be installed in a position that points in the main direction of the signal source, such as forward, sideways, or downward from the drone; the specific location depends on the orientation of the ground station or relay platform during the flight mission. The physical orientation of the antenna must be consistent with its designed polarization to avoid signal attenuation due to polarization mismatch. For adjustable-pointing directional antennas, their installation position must ensure effective alignment with the signal source within the mission attitude range to avoid mechanical dead zones. A certain physical distance must be maintained between multiple airborne antennas to reduce mutual coupling interference; this physical distance should not be less than half a wavelength. The isolation between antennas typically meets the following requirements. .

[0031] The engineering constraints include: the antenna mounting point should be located in a region with high rigidity and low vibration; the antenna and its support should meet the structural strength requirements of the UAV under typical flight attitudes; and the antenna installation should not disrupt the aerodynamic shape of the UAV. The antenna should be installed in the main load-bearing structural areas of the fuselage, wings, or tail, such as rigid parts like wingplates, ribs, and bulkheads, avoiding installation in flexible areas like skin and fairings. The antenna and its support must be able to withstand the inertial load of the UAV under maximum maneuvering overload. Under continuous vibration environments such as continuous engine operation and atmospheric turbulence, the antenna mounting structure should not loosen, shift, or experience fatigue-induced disconnection of connectors. The antenna layout should not significantly alter the UAV's aerodynamic shape, affecting longitudinal stability. The aerodynamic center is typically located at one-quarter of the wing's average aerodynamic chord length, with permissible aerodynamic center displacements of: longitudinal displacement not exceeding 2% of the average aerodynamic chord length, and vertical displacement not exceeding 1% of the fuselage length.

[0032] The dynamic constraints include: the center of gravity of the UAV after the antenna is installed meets the requirements of the flight mission; The installation of the antenna must not compromise the flight stability and maneuverability of the UAV throughout the entire mission, from takeoff to landing. The center of gravity is a key factor affecting all of this; the original design of the UAV specifies an allowable range for the center of gravity, typically between 25% and 35% of the mean aerodynamic chord. The closer to 25%, the more stable the UAV, but the worse its maneuverability and maneuverability, requiring a larger rudder deflection angle to change attitude; the closer to 30%, the weaker the UAV's stability, but the more sensitive its maneuverability. After installing the antenna, the UAV's center of gravity will change, and the maneuverability and stability of the UAV after the change in the center of gravity must meet the requirements of the flight mission.

[0033] Based on geometric constraints, several sets of antenna mounting points are generated on the outer surface of the UAV. Based on the sets of antenna mounting points, several installation schemes are generated. These installation schemes are verified by engineering constraints and dynamic constraints respectively. The installation schemes that satisfy the three constraints are retained as alternative antenna layout schemes.

[0034] A series of candidate mounting points are predefined on the outer surface of the UAV. Based on geometric constraints, mounting points that meet the requirements are initially screened. From these selected mounting points, multiple preliminary antenna mounting schemes are generated through permutation and combination. Each preliminary antenna mounting scheme is verified by engineering constraints, specifically checking whether the mounting point is in a rigid region, determining through simulation whether the UAV can withstand the vibration of the flight mission, and evaluating whether the aerodynamic shape changes are within the allowable range. Dynamic analysis is performed on the schemes that pass the engineering constraints to calculate the change in the center of gravity position after antenna installation, and schemes that do not meet the dynamic constraints are eliminated. All schemes that pass the triple verification of geometric constraints, engineering constraints, and dynamic constraints are retained as alternative antenna layout schemes.

[0035] The principle underlying the calculation of the overall communication performance of alternative antenna layout schemes is as follows: The UAV is modeled in electromagnetic simulation software, and alternative antenna layout schemes are assigned to the UAV. The UAV model is rotated in space so that its attitude is consistent with the center value of a given attitude unit. For each communication link that needs to be guaranteed, the received power and interference power of the antenna are obtained. The received power is subtracted from the interference power to obtain the simulated signal-to-noise ratio of the communication link. The simulated signal-to-noise ratio of each communication link is divided by the minimum required signal-to-noise ratio for the communication link to work normally to generate the signal-to-noise ratio margin of each communication link. The average value of the signal-to-noise ratio margins of all communication links is calculated to obtain the communication performance evaluation value of the given alternative antenna layout scheme under a given attitude unit. The formula for generating the signal-to-noise ratio margin of a communication link is: ; ; in, Indicates the first Simulated signal-to-noise ratio of the communication links Indicates the index of the communication link, and , Indicates the number of communication links. Indicates the first The received power of each communication link, Indicates the first Interference power of the communication link This indicates the minimum required signal-to-noise ratio. Indicates the first The signal-to-noise ratio margin of each communication link; The formula for generating communication performance evaluation values ​​is: ; in, This represents the communication performance evaluation value of a given alternative antenna layout scheme under a given attitude unit.

[0036] For a complete task, the communication performance evaluation values ​​of the attitude units included in the task are weighted and added together with the comprehensive weight of the attitude units to obtain the comprehensive communication performance of the alternative antenna layout scheme under the task.

[0037] Signal-to-noise ratio (SNR) represents the ratio of signal power to interference power. SNR margin reflects the margin of the current simulated SNR relative to the minimum required SNR; a larger value indicates better communication performance and stronger anti-interference capability. Received power represents the signal power received by the antenna in a certain attitude, while interference power represents the interference power received on the same link, which may come from other antennas, environmental noise, etc. The unit of power is W. The difference between the two powers needs to be converted to dB. A larger SNR margin indicates that the link can still work stably in noisy and interference environments, and the risk of communication interruption is lower. Under different attitudes, antenna pointing, obstruction, polarization matching, etc., will affect the received power. A larger SNR margin indicates stronger adaptability of the fire unit layout to attitude and higher tolerance to environmental changes. Since UAVs may maintain multiple communication links simultaneously, it is necessary to comprehensively evaluate the performance of all links and average the communication performance evaluation values ​​of each link to obtain the overall communication performance under a given attitude unit.

[0038] The formula for calculating overall communication performance is: ; in, This represents the overall communication performance of a given alternative antenna layout scheme. Indicates the given alternative antenna layout scheme in the th... Communication performance evaluation values ​​for each attitude unit. Indicates the total number of attitude units; Overall communication performance reflects the overall communication stability of the mission. A higher value indicates better average communication performance of the antenna layout throughout the entire mission cycle, a more stable link, better performance in critical attitudes, and a lower risk of communication interruption. UAV flight is a dynamic process; different attitudes occur at different frequencies and have varying impacts on communication. If the same evaluation is applied to all attitudes, an antenna layout scheme might be excellent in some attitudes but only moderately effective in most. Therefore, the communication performance evaluation value is multiplied by a comprehensive weight to obtain the communication performance of a given antenna layout scheme in a specific attitude. This also considers the duration of this attitude throughout the entire flight mission and its impact on communication performance. Different attitudes occur at different frequencies and for different durations during the mission, resulting in varying impacts on communication performance. By assigning different weights, the optimization process focuses more on frequently occurring or communication-sensitive attitudes. Since the attitude of a UAV changes dynamically during missions, the optimal layout for a single attitude may not be applicable to all missions. This formula integrates the performance under multiple attitudes into a comprehensive evaluation index through weighted summation, making the optimization results more closely reflect the actual flight process.

[0039] Step 4: Calculate the fitness value with the goal of maximizing overall communication performance and minimizing engineering complexity. Calculate the information entropy of the two objectives and perform TOPSIS ranking. Construct a Pareto solution set based on the fitness values ​​of all candidate antenna layout schemes. Determine the optimal antenna layout scheme based on the TOPSIS ranking results and the Pareto solution set.

[0040] In this embodiment, the principle for calculating the fitness value is as follows: The logic for calculating the engineering complexity is as follows: obtain the number of antenna mounting points, the total length of the antenna, and the total mass of the antenna; normalize the above parameters and add them together with weights to obtain the engineering complexity. The fitness value is obtained by adding the overall communication performance to the reciprocal of the engineering complexity.

[0041] The formula for calculating project complexity is: ,in, Indicates the first The engineering complexity of the alternative antenna layout schemes, Indicates the index of alternative antenna layout schemes. This represents the number of normalized antenna mounting points. This represents the normalized total antenna length. This represents the normalized total antenna mass. These represent the weighting coefficients for the number of antenna mounting points, the total antenna length, and the total antenna mass, respectively. ; The formula for calculating the fitness value is: ; ; in, Indicates the first The fitness value of each alternative antenna layout scheme. Indicates the first The overall communication performance of the alternative antenna layout schemes. The reciprocal of the complexity of the project; The fitness value reflects both the communication performance and the ease of engineering implementation of the alternative antenna layout scheme. The larger the fitness value, the better the communication stability, signal-to-noise ratio margin, and anti-interference capability of the scheme in the whole mission. The scheme has fewer installation points, lighter antennas, simpler structure, and is easier to implement and maintain.

[0042] The principle underlying the determination of the optimal antenna layout scheme is as follows: Based on M alternative antenna layout schemes and their corresponding engineering complexity and overall communication performance, an M×2 matrix is ​​constructed. For each alternative antenna layout scheme, maximum and minimum normalization are applied to both the overall communication performance and engineering complexity. Then, the contribution ratio of each alternative antenna layout scheme under different targets is calculated. The calculation logic is to divide the normalized value of one alternative antenna layout scheme under a target by the sum of the normalized values ​​of all alternative antenna layout schemes under the corresponding target. The product of the contribution ratio of all alternative control schemes and the logarithm of the contribution ratio to the base e is summed and divided by the negative reciprocal of the logarithm of M to the base e to obtain the information entropy corresponding to a target. Then, the information entropy is calculated. The entropy weight of the same target is calculated as follows: subtract the information entropy of a target from 1, and then divide by the sum of the information entropies of all targets minus 1. Multiply the target's entropy weight by the normalized value of the target under different alternative antenna layout schemes to weight the normalized value of the target, construct a weighted decision matrix, generate a positive ideal solution based on the maximum value of each target in the weighted decision matrix, and generate a negative ideal solution based on the minimum value of each target. Calculate the Euclidean distance from the target weighted value of each alternative antenna layout scheme to the positive and negative ideal solutions, and then generate the proximity score. The logic for calculating the proximity score is: the ratio of the Euclidean distance to the negative ideal solution to the sum of the Euclidean distances to the positive and negative ideal solutions. The formula for calculating the contribution ratio is: ; ; in, Indicates the first The contribution of each alternative antenna layout scheme to the overall communication performance Indicates the first The normalized overall communication performance of the alternative antenna layout schemes Indicates the number of alternative antenna layout options. Indicates the first The proportion of engineering complexity contributed by each alternative antenna layout scheme Indicates the first The normalized engineering complexity of each alternative antenna layout scheme; The contribution ratio reflects the first The proportion of each alternative antenna layout scheme for different objectives after normalization of all schemes. For the first The larger the value of the normalized overall communication performance of each alternative antenna layout scheme relative to the normalized overall communication performance of all schemes, the better the communication performance of that scheme. For the first The larger the proportion of the normalized engineering complexity of a candidate antenna layout scheme relative to the normalized engineering complexity of all schemes, the better the scheme is in terms of engineering implementation. The contribution ratio is calculated by the proportion of the normalized value of a certain scheme to the normalized sum of all schemes. It is essentially a measure of relative proportion or relative importance. If a scheme performs well in a certain objective, its contribution ratio is large, indicating that the scheme is relatively better in that objective.

[0043] The formula for calculating information entropy is: ; ; in, Indicates the first The comprehensive communication performance information entropy of the alternative antenna layout schemes. Indicates the first Information entropy of the engineering complexity of one alternative antenna layout scheme; Information entropy reflects the uniformity of the evaluation results of various alternative antenna layout schemes under a certain objective. If the contribution proportion of all schemes under a certain objective is very uniformly distributed, the information entropy value is large, indicating that the objective has a weak ability to distinguish between schemes and that different schemes do not differ much from each other under that objective. If the distribution is very concentrated, that is, the proportion of one or a few schemes is much higher than that of other schemes, the information entropy value is small, indicating that the objective has a strong ability to distinguish between schemes and can clearly distinguish between superior and inferior ones. The smaller the information entropy, the more obvious the difference between the schemes under that objective, and the greater the weight of that objective in the decision-making process should be. The larger the information entropy, the less obvious the difference between the schemes under that objective, and the smaller the weight of that objective in the decision-making process should be.

[0044] The formula for calculating entropy weight is: ; ; in, express Entropy weight, express Entropy weight; Entropy weight reflects the objective importance or influence of a certain objective in the final decision. It is calculated based on information entropy and measures the ability of each objective to distinguish between alternatives. The larger the entropy weight, the more obvious the difference in the evaluation value of each alternative under that objective. The objective has a stronger ability to distinguish between alternatives and therefore should be given a higher weight in the final decision. The smaller the entropy weight, the closer the evaluation value of each alternative under that objective is. The objective has a weaker ability to distinguish between alternatives and should be given a lower weight in the decision.

[0045] The formula for weighting is: ; ; in, express The weighted value, express The weighted value; By weighting the planning values ​​with entropy weights, important targets with high entropy weights are amplified. The weighted values ​​are adjusted after the target importance is determined. The weighted values ​​of targets with high entropy weights are further amplified, and their impact on the final ranking is greater. The weighted values ​​of targets with low entropy weights are compressed, and their impact on the final ranking is smaller. Through weighting, the two originally incomparable targets, communication performance and engineering complexity, are transformed into comparable targets.

[0046] The ideal solution is: ; The negative ideal solution is: ; in, This represents the ideal solution. express The maximum value in, express The maximum value in, This represents a negative ideal solution. express The minimum value in, express The minimum value in; The formula for generating the similarity score is: ; ; ; in, express Euclidean distance to the ideal solution express Euclidean distance to the negative ideal solution Indicates the first The closeness of the alternative antenna layout schemes; The positive ideal solution is the set of maximum values ​​among the weighted values ​​of each objective, representing the ideal optimal solution. The negative ideal solution is the set of minimum values ​​among the weighted values ​​of each objective, representing the ideal worst solution. The smaller the distance to the positive ideal solution, the better, indicating that the solution is closer to the optimal solution. The larger the distance to the negative ideal solution, the better, indicating that the solution is further away from the worst solution. The proximity reflects how close the solution is to the ideal solution. The higher the proximity, the closer the solution is to the ideal optimal state, and the more balanced and excellent its performance is across all objectives. All solutions are sorted from high to low proximity, which can intuitively show the relative order of the solutions and provide a direct basis for the final selection.

[0047] Find the Pareto front solution from all the alternative antenna layout schemes to construct the Pareto solution set. Sort the schemes in the Pareto solution set from largest to smallest proximity and select the alternative antenna layout scheme with the largest proximity as the optimal antenna layout scheme.

[0048] In UAV antenna layout, maximizing communication performance and minimizing engineering complexity are often contradictory. After performing TOPSIS ranking, some solutions that perform well in a balanced manner across multiple targets but are not extreme may be underestimated. The solution with the highest TOPSIS score may perform extremely well on one target but poorly on another, which may not be feasible in actual engineering. Therefore, we first find the Pareto front solution. The solutions in the Pareto solution set mean that these solutions are already the optimal candidate solutions among multiple targets and there is no situation where they are significantly surpassed by other solutions. From these candidate solutions, we filter them from the closest to the target and determine the solution that is most suitable for the actual engineering situation based on the target weight. This is the optimal antenna layout solution.

[0049] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0050] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0051] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0052] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for optimizing the layout of an airborne antenna for an unmanned aerial vehicle (UAV), characterized in that, The specific steps include: Step 1: Before each work task is executed, determine the typical flight attitudes involved in the work task and obtain the attitude angle time series of the work task; the typical flight attitudes include level flight, climb, descent, turn and hover; the attitude angles include pitch angle and roll angle. Step 2: Discretize the pitch and roll angles within their respective ranges to generate several discrete attitude units. Map the time series of attitude angles of the task to the discrete attitude units. Calculate the duration of the UAV in each attitude unit while performing the task, and then calculate the time basis weight of each attitude unit. Calculate the comprehensive weight based on the time basis weight of the attitude unit and the typical flight attitude types. Step 3: Using geometric constraints, engineering constraints, and dynamic constraints as constraints, generate multiple alternative antenna layout schemes. For any alternative antenna layout scheme and any attitude unit, obtain the communication performance evaluation value of the alternative antenna layout scheme under that attitude unit. Based on the attitude units included in the task and their respective comprehensive weights, calculate the comprehensive communication performance of the alternative antenna layout schemes. Step 4: Calculate the fitness value with the goal of maximizing overall communication performance and minimizing engineering complexity. Calculate the information entropy of the two objectives and perform TOPSIS ranking. Construct a Pareto solution set based on the fitness values ​​of all candidate antenna layout schemes. Determine the optimal antenna layout scheme based on the TOPSIS ranking results and the Pareto solution set.

2. The method for optimizing the layout of an airborne antenna for a UAV according to claim 1, characterized in that: The principle of obtaining the attitude angle time series of the work task in step 1 is as follows: From the historical flight data, multiple task execution segments that are the same as the work task to be executed are selected. In each selected task execution segment, a sampling point is set with a sampling frequency of 1Hz. The pitch angle and roll angle of each sampling point are obtained, and pitch angle sequence and roll angle sequence are generated respectively. The two sequences are integrated to generate the attitude angle time series.

3. The method for optimizing the layout of an airborne antenna for a UAV according to claim 1, characterized in that: The principle underlying the generation of discrete attitude units in step 2 is as follows: The pitch angle ranges from -90° to 90°, and the roll angle ranges from -180° to 180°. The discretization step size is set to 15°. The number of discrete pitch angles is the ratio of the difference between the maximum and minimum pitch angle values ​​to the discretization step size plus one, and the number of discrete roll angles is the ratio of the difference between the maximum and minimum roll angle values ​​to the discretization step size plus one. Starting from the minimum pitch angle value, a discrete pitch angle is generated every discretization step size until the maximum pitch angle value is reached. All these discrete pitch angles constitute a discrete pitch angle set. Similarly, a discrete roll angle set is generated. A discrete pitch angle and a discrete roll angle are selected from the discrete pitch angle set and the discrete roll angle set, and they are arranged and combined to form several discrete attitude units. The number of attitude units is the product of the number of discrete pitch angles and the number of discrete roll angles.

4. The method for optimizing the layout of an airborne antenna for a UAV according to claim 3, characterized in that: The principle behind calculating the overall weight in step 2 is as follows: The principle of mapping the time series of attitude angles of a task to discrete attitude units is as follows: For each sampling point in the attitude angle time series, find the discrete pitch angle and discrete roll angle that are closest to the sampling point from the discrete sets of pitch angle and roll angle respectively; classify the sampling point into the attitude unit, which is regarded as completing the mapping of this sampling point. Follow the steps described above to iterate through all sampling points in the attitude angle time series; The number of times each attitude unit is mapped is counted. The product of the time interval between adjacent sampling points and the number of times the attitude unit is mapped is used as the duration of the attitude unit. The ratio of the duration of the attitude unit to the total time of the task is used as the time basis weight of the attitude unit in this task. Based on the impact of different typical flight attitudes on antenna communication performance in historical flight data, the attitude type weights of different typical flight attitudes are determined by expert scoring. The comprehensive weight of the attitude unit is obtained by multiplying the time-based weight of the attitude unit by the attitude type weight of the corresponding typical flight attitude.

5. The method for optimizing the layout of an airborne antenna for a UAV according to claim 1, characterized in that: The principle behind generating multiple alternative antenna layout schemes in step 3 is as follows: The geometric constraints include: the antenna is mounted on the outer surface of the UAV and avoids the carbon fiber structure; the omnidirectional antenna is mounted on the upper part of the UAV and the directional antenna is pointed in the direction of the signal source; the installation attitude of the antenna on the UAV is consistent with its polarization direction; the distance between the airborne antennas meets the isolation requirements. The engineering constraints include: the antenna mounting point should be located in a region with high rigidity and low vibration; the antenna and its support should meet the structural strength requirements of the UAV under typical flight attitudes; and the antenna installation should not disrupt the aerodynamic shape of the UAV. The dynamic constraints include: the center of gravity of the UAV after the antenna is installed meets the requirements of the flight mission; Based on geometric constraints, several sets of antenna mounting points are generated on the outer surface of the UAV. Based on the sets of antenna mounting points, several installation schemes are generated. These installation schemes are verified by engineering constraints and dynamic constraints respectively. The installation schemes that satisfy the three constraints are retained as alternative antenna layout schemes.

6. The method for optimizing the layout of an airborne antenna for a UAV according to claim 5, characterized in that: The principle underlying the calculation of the overall communication performance of the candidate antenna layout schemes in step 3 is as follows: The UAV is modeled in electromagnetic simulation software, and alternative antenna layout schemes are assigned to the UAV. The UAV model is rotated in space so that its attitude is consistent with the center value of a given attitude unit. For each communication link that needs to be guaranteed, the received power and interference power of the antenna are obtained. The received power is subtracted from the interference power to obtain the simulated signal-to-noise ratio of the communication link. The simulated signal-to-noise ratio of each communication link is divided by the minimum required signal-to-noise ratio for the communication link to work normally to generate the signal-to-noise ratio margin of each communication link. The average value of the signal-to-noise ratio margins of all communication links is calculated to obtain the communication performance evaluation value of the given alternative antenna layout scheme under a given attitude unit. For a complete task, the communication performance evaluation values ​​of the attitude units included in the task are weighted and added together with the comprehensive weight of the attitude units to obtain the comprehensive communication performance of the alternative antenna layout scheme under the task.

7. The method for optimizing the layout of an airborne antenna for a UAV according to claim 6, characterized in that: The principle behind calculating the fitness value in step 4 is as follows: The logic for calculating the engineering complexity is as follows: obtain the number of antenna mounting points, the total length of the antenna, and the total mass of the antenna; normalize the above parameters and add them together with weights to obtain the engineering complexity. The fitness value is obtained by adding the overall communication performance to the reciprocal of the engineering complexity.

8. The method for optimizing the layout of an airborne antenna for a UAV according to claim 7, characterized in that: The principle underlying the determination of the optimal antenna layout scheme in step 4 is as follows: Based on M alternative antenna layout schemes and their corresponding engineering complexity and overall communication performance, an M×2 matrix is ​​constructed. Among all alternative antenna layout schemes, the overall communication performance and engineering complexity are normalized by maximum and minimum respectively. Then, the contribution ratio of each alternative antenna layout scheme under different objectives is calculated. The calculation logic is to divide the normalized value of an alternative antenna layout scheme under an objective by the sum of the normalized values ​​of all alternative antenna layout schemes under the corresponding objective. The product of the contribution proportions of all alternative control schemes and the logarithm of the contribution proportions to the base e is summed and divided by the negative reciprocal of the logarithm of the base e M to obtain the information entropy corresponding to a target. Then, the entropy weights of different targets are calculated. The calculation logic of the entropy weight is: subtract the information entropy of a target from 1, and then divide by the sum of 1 minus the information entropy of all targets. The entropy weight of the target is multiplied by the normalized value of the target under different alternative antenna layout schemes to weight the normalized value of the target, and a weighted decision matrix is ​​constructed. A positive ideal solution is generated based on the maximum value of each target in the weighted decision matrix, and a negative ideal solution is generated based on the minimum value of each target. The Euclidean distance from the target weighted value of each alternative antenna layout scheme to the positive ideal solution and the negative ideal solution is calculated, and then the proximity is generated. The logic of calculating the proximity is: the ratio of the Euclidean distance to the negative ideal solution to the sum of the Euclidean distances to the positive ideal solution and the negative ideal solution. Find the Pareto front solution from all the alternative antenna layout schemes to construct the Pareto solution set. Sort the schemes in the Pareto solution set from largest to smallest proximity and select the alternative antenna layout scheme with the largest proximity as the optimal antenna layout scheme.

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