A six-dimensional movable antenna-based air-to-air hybrid beamforming method and system

Abstract

The application relates to the technical field of wireless communication, in particular to a six-dimensional movable antenna air-to-air hybrid beamforming method and system, which has the technical scheme as follows: a multi-level coordinate system mapping model is established; a line-of-sight air-to-air dynamic channel model is constructed; a joint optimization model is established; and an HD-MATD3 algorithm based on data and model hybrid driving is adopted to solve the joint optimization model in real time; the six-dimensional movable antenna is introduced, so that the antenna subarray has three-dimensional displacement and three-dimensional rotation space adjustment capability, thereby compensating for the pointing deviation of a narrow beam in a high dynamic environment, improving the continuity and stability of a communication link, avoiding the multi-layer iteration and large-scale search process in traditional alternating optimization, significantly reducing the single-step optimization calculation time, enhancing the real-time response capability of the system to high dynamic link changes, being more suitable for deployment on a power and energy consumption limited unmanned aerial vehicle platform, and having good engineering implementation value and application promotion prospect.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, specifically to a method and system for air-to-air hybrid beamforming based on a six-dimensional movable antenna. Background Technology

[0002] With the rapid development of integrated air-to-ground networks, UAV swarm collaboration, and low-altitude intelligent communication technologies, air-to-air (A2A) communication has become a key supporting technology for UAV swarm collaborative operations, target perception information exchange, disaster emergency communication, and aerial networking. Especially in the millimeter-wave band, A2A communication links typically possess strong line-of-sight (LoS) characteristics, enabling high-speed data transmission with high spectral efficiency. Therefore, it is widely considered an important development direction for future aerial communication systems.

[0003] However, during actual flight, UAVs are affected by factors such as wind disturbances, airframe vibrations, flight path changes, and attitude adjustments, causing their position, speed, and attitude parameters to continuously change dynamically, resulting in a constant shift in the beam alignment between the transmitter and receiver. For millimeter-wave communication, due to the narrow beam, high directionality, and strong directional characteristics of the beam, even a slight deflection can cause significant array gain loss, leading to a decrease in link speed, increased communication fluctuations, and even link interruptions.

[0004] In existing air-to-air communication systems, most still use fixed-position antennas (FPA) or traditional planar array structures. These structures lack the ability to actively adjust in physical space and cannot dynamically reconfigure the antenna geometry based on the UAV's attitude and link direction. Therefore, they are more sensitive to beam misalignment in highly dynamic flight scenarios and find it difficult to effectively suppress performance degradation caused by position shifts and attitude disturbances.

[0005] On the other hand, while some position optimization or attitude adjustment methods have been proposed in research on mobile antenna-assisted communication, most of them focus on static or quasi-static scenarios and do not fully consider the characteristics of high-speed movement, continuous attitude disturbances, and rapid link changes of UAVs in air-to-air communication. In addition, existing hybrid beamforming optimization methods usually rely on alternating optimization (AO) or other iterative search algorithms for solving the problem. These methods often require multiple nested iterations, resulting in high computational complexity and long solution time, making it difficult to meet the fast beam tracking requirements of UAV platforms under real-time, computing power, and energy consumption constraints.

[0006] Therefore, how to efficiently optimize the antenna position, attitude, and hybrid beamforming parameters in a dynamic air-to-air communication scenario by combining the spatial degrees of freedom of a six-dimensional movable antenna, in order to suppress beam misalignment, improve link speed, and reduce computational overhead, has become a pressing technical problem in this field. To solve the above problems, this application proposes an air-to-air hybrid beamforming method and system based on a six-dimensional movable antenna. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a method and system for air-to-air hybrid beamforming based on a six-dimensional movable antenna, solving the problems mentioned in the background technology.

[0008] The above-mentioned technical objective of the present invention is achieved through the following technical solution: On one hand, this invention proposes an air-to-air hybrid beamforming method based on a six-dimensional movable antenna. This method is applied to UAV-to-UAV communication systems. The six-dimensional movable antenna (6DMA) has three-dimensional positional movement degrees of freedom and three-dimensional attitude rotation degrees of freedom. The method includes the following steps: S1. Establish a multi-level coordinate system mapping model to convert the local coordinates of each antenna in the uniform planar array UPA subarray on the transmitting UAV and the receiving UAV into the absolute physical position in the global coordinate system, so as to characterize the spatial geometric changes caused by the body attitude jitter and the relative motion of the antenna. S2. Construct a line-of-sight air-to-air dynamic channel model, calculate the distance between antennas based on the absolute physical positions of the transmitting and receiving antennas, establish complex channel element expressions, and construct a hybrid beamforming signal transmission model that includes analog beamforming matrix, digital beamforming matrix and receiver combining vector. S3. Establish a joint optimization model with the goal of maximizing the instantaneous achievable rate of the system. Under the constraints of antenna movement area, rotation range, transmit power and analog beam constant mode, jointly optimize the analog beamforming parameters and digital beamforming parameters of the transmitter, the receive combining vector of the receiver, and the three-dimensional position and attitude of each UPA subarray of the transmitter and receiver. S4. The HD-MATD3 algorithm, driven by a hybrid data and model approach, is used to solve the joint optimization model in real time. In this process, a deep reinforcement learning network is used to infer the non-convex geometric optimization parameters and the simulated beamforming parameters in the joint optimization model in real time. The obtained parameters are then input into the closed-loop solution calculation module to directly calculate the digital beamforming parameters and the receiver merging vector parameters.

[0009] Preferably, the multi-level coordinate system mapping model in step S1 includes a global coordinate system, a full array coordinate system, and a sub-array local coordinate system; At any moment The first transmitter The absolute physical position of each antenna in the global coordinate system Calculate according to the following formula:

[0010] in, Let be the rotation matrix of the transmitter's full array coordinate system relative to the global coordinate system. For the first Rotation matrices of each UPA subarray relative to the full array coordinate system This represents the fixed position of the antenna in the local coordinate system of the subarray. Let be the position of the subarray in the full array coordinate system. The coordinates of the launching UAV in the global coordinate system; Receiver The absolute physical position of each antenna in the global coordinate system is calculated in the same way as that of the transmitter.

[0011] Preferably, in the dynamic channel model of step S2, the transmitting antenna... With receiving antenna At any moment Complex channel elements Represented as:

[0012] in, For transmitting antenna With receiving antenna The Euclidean distance between them The channel gain includes path loss and antenna directivity gain; The hybrid beamforming signal transmission model satisfies the diagonal structure constraint of the sub-connector blocks, and the system's instantaneous achievable rate is [data missing]. Represented as:

[0013] in, To receive the merged vector, For the channel matrix, To simulate the beamforming matrix, For digital beamforming matrix, This represents the noise variance.

[0014] Preferably, the HD-MATD3 algorithm in step S4 adopts a multi-agent, dual-delay, deep deterministic policy gradient architecture, whose state space... Includes channel features compressed using Singular Value Decomposition (SVD). ; The channel features The extraction method is as follows: for the channel matrix Perform truncated singular value decomposition and extract the previous values. The maximum singular values ​​form the energy feature vector, and the corresponding left and right singular vectors are combined to construct the directional feature, so as to compress the high-dimensional complex channel matrix into a low-dimensional real feature vector. The state space includes at least the normalized UAV state characteristics, the geometric position and attitude characteristics of the six-dimensional movable antenna, the simulated beam characteristics, and the channel characteristics.

[0015] Preferably, the action space of the algorithm is a continuous incremental instruction, including simulated phase increment, three-dimensional position increment of the antenna subarray, and three-dimensional attitude angle increment; When interacting with the environment, a forced truncation projection function is introduced to restrict the action commands to a preset physical movable area and rotation range to ensure the physical feasibility of the output action.

[0016] Preferably, the reward function of the algorithm Defined as:

[0017] in, For performance weighting, For instantaneous achievable speed, and These are the boundary penalty weights for antenna movement and rotation, respectively. and These are the penalty terms corresponding to when the antenna position and attitude exceed the preset boundaries.

[0018] Preferably, the closed-form solution calculation module in step S4 is implemented in the following way: After obtaining the geometric state and simulated beam phase of the deep reinforcement learning network output, the equivalent channel is reconstructed.

[0019] The digital beamforming vector is obtained using the maximum ratio transmission MRT and the maximum ratio combining MRC. Combined with Received Vector Closed-form solution:

[0020] in, Represents the equivalent channel matrix. This represents the conjugate transpose of the equivalent channel matrix.

[0021] On the other hand, this invention proposes an air-to-air hybrid beamforming system based on a six-dimensional movable antenna, comprising: The spatial mapping module is used to calculate the absolute physical position of the transmitting and receiving antennas in real time, and to convert the antenna position from the local coordinate system to the absolute physical position in the global coordinate system through multi-level coordinate system mapping. The channel modeling module is used to construct a dynamic line-of-sight channel model and calculate the channel matrix based on the physical location of the transmitting and receiving antennas, and to establish a hybrid beamforming signal transmission model. The joint optimization module is used to execute the HD-MATD3 algorithm based on a hybrid data and model approach. It infers non-convex parameters in real time through an agent network and combines the closed-loop solution calculation module to obtain digital beamforming parameters and receiver merging vector parameters. The closed-form solution calculation module is used to reconstruct the equivalent channel after obtaining the geometric state and simulated beam phase output by the joint optimization module, and to calculate the closed-form solution of the digital beamforming vector and the receiver combining vector based on the maximum ratio transmission (MRT) and maximum ratio combining (MRC).

[0022] In summary, the present invention has the following main beneficial effects: 1. This invention introduces a six-dimensional movable antenna, enabling the antenna subarray to have spatial adjustment capabilities of three-dimensional displacement and three-dimensional rotation. It can actively reconstruct the array geometry based on the real-time position and attitude changes of the UAV, thereby compensating for the pointing deviation caused by narrow beams in high dynamic environments, effectively reducing rate oscillations and link fading caused by beam misalignment, and improving the continuity and stability of the communication link. This invention combines the six-dimensional movable antenna with hybrid beamforming design, making full use of spatial degrees of freedom and array gain resources in line-of-sight air-to-air links, enabling the transmitter and receiver to more accurately align with the effective propagation direction, thereby increasing the effective signal reception power, enhancing the link's anti-disturbance capability, and ultimately improving the system's instantaneous achievable rate and overall transmission performance.

[0023] 2. This invention employs the HD-MATD3 algorithm, driven by a hybrid data and model approach. It delegates the inefficient solution of non-convex geometric optimization and analog beamforming problems, which are difficult to solve efficiently in traditional methods, to a deep reinforcement learning network for real-time inference. Meanwhile, the digital beamforming and receiver merging parts, which possess closed-form solution characteristics, are directly solved analytically using mathematical methods. This avoids the multi-layered iterations and large-scale search processes inherent in traditional alternating optimization, significantly reducing single-step optimization computation time and enhancing the system's real-time response to highly dynamic link changes. While ensuring optimization results approaching those of high-quality iterative algorithms, this invention reduces reliance on complex online searches, making it more suitable for deployment on UAV platforms with limited computing power and energy consumption. It possesses significant engineering implementation value and promising application prospects. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of a specific embodiment of the present invention.

[0025] Figure 2This is the normalized beam pattern used in this specific embodiment.

[0026] Figure 3 The reward convergence curve of HD-MATD3 trained in this specific embodiment is shown.

[0027] Figure 4 This is a comparison of the achievable rates of 6DMA and FPA under different schemes in this specific embodiment as a function of simulation time.

[0028] Figure 5 The percentage increase in achievable speed for 6DMA-MATD3 in this specific embodiment varies with distance.

[0029] Figure 6 This document compares the achievable rate CDF curves of 6DMA and FPA for different schemes in this specific embodiment. Detailed Implementation

[0030] 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 some embodiments of the present invention, but not all embodiments. Based on the described 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.

[0031] The following embodiments are used to illustrate the present invention, but should not be used to limit the scope of protection of the present invention. The conditions in the embodiments can be further adjusted according to specific conditions, and simple improvements to the method of the present invention under the premise of the concept of the present invention are all within the scope of protection claimed by the present invention.

[0032] Example 1

[0033] Scenario: Consider a UAV-to-UAV communication system in an integrated air-ground scenario.

[0034] Unmanned Aerial Vehicle-Transmitter (UAV-T) equipped with Each UPA subarray contains independently movable and rotatable uniform planar array (UPA) subarrays. One fixed antenna, total number of antennas Sub-connection One RF link.

[0035] Unmanned Aerial Vehicle-Receiver (UAV-R) equipped with Each subarray of UPA can be moved and rotated independently, and each subarray contains One fixed antenna, total number of antennas .

[0036] Assumptions: The two communicating parties conduct line-of-sight transmission at high altitude, and a time-varying channel model is established based on the principle of ray tracing; perfect channel state information (CSI) can be obtained at both the transmitting and receiving ends; the UAV can obtain its latest position and attitude information through the Global Positioning System (GPS) and inertial navigation equipment.

[0037] 1. UAV 6DMA Position and Attitude Space Mapping Module: This module defines a unified multi-level coordinate system, converting the local coordinates of each antenna in the UPA subarray into its absolute physical position in the global coordinate system. This accurately represents the spatial geometric changes caused by UAV body jitter and relative antenna motion. Specifically, it includes three levels of coordinate system definition: Global coordinate system: As the absolute spatial reference benchmark of the communication system, it is used to uniformly describe the absolute position coordinates and dynamic flight trajectory of the transmitting and receiving UAVs in three-dimensional physical space.

[0038] Full array coordinate system (body axis system): A local reference system bound to the UAV platform (or center of mass) to characterize the dynamic attitude changes (such as yaw angle, pitch angle, and roll angle) of the UAV caused by external environmental influences during flight. To simplify spatial transformation calculations, the antenna full array coordinate system can be set to maintain a fixed rotational displacement relationship with the UAV body axis system or directly coincide with it.

[0039] Subarray local coordinate system: A relative coordinate system established with the center of each independent movable and rotatable UPA subarray as the reference, used to accurately preset and describe the relative spatial geometric topology of each fixed antenna element inside each subarray.

[0040] exist At time , the global position of the UAV-T is recorded as The rotation matrix of its full array coordinate system relative to the global coordinate system Depend on Pitch angle, Roll angle, The yaw angle is obtained.

[0041] No. UPA subarray In the full array coordinate system The three-dimensional position at time is ,in For the first The UPA subarray moving region, the first Rotation matrices of each UPA subarray relative to the full array coordinate system Depend on Pitch angle, Roll angle, The yaw angle is obtained, and the attitude angle vector is obtained. ,in The range of rotation is defined.

[0042] No. Within the UPA subarray, the first One fixed antenna, with , That is, the first The fixed positions of the antennas in their local coordinate system are: Further, based on coordinate system transformation, the first... The antennas are in the global coordinate system The position at that time is:

[0043] Similarly, UAV-R's first The antennas are in the global coordinate system. The position of the moment is Therefore, the accuracy of any transmitting antenna can be calculated in real time. With receiving antenna Euclidean distance between .

[0044] 2. Line-of-sight air-to-air dynamic channel and signal modeling module: Based on the determined absolute coordinates of the transmitting and receiving antennas, a time-varying line-of-sight channel matrix including spatial directivity gain and a hybrid beamforming signal transmission model are constructed.

[0045] Specifically, based on the principle of ray tracing, time 3D line-of-sight channel matrix The first in The complex channel elements are represented as follows:

[0046] in, For the first The channel gain of a complex number of channel elements includes large-scale attenuation factors (such as path loss) and antenna directivity gain.

[0047] Furthermore, a single-stream signal is transmitted at the transmitting end. At that time, the received signal after hybrid beamforming and receiving merging Represented as:

[0048] in, For the UAV-R receive combining vector, To satisfy the diagonal structure of the sub-connector block and the unit modulus constraint of the UAV-T The simulated beamforming matrix; Digital beamforming matrix for UAV-T; It is an additive white Gaussian noise vector. , Let V be the noise scalar variance. The maximum transmit power is... Then there is a power constraint.

[0049] Therefore, the instantaneous achievable rate of the system The model is as follows: .

[0050] 3. Hybrid Beamforming Joint Optimization Problem Modeling Module: The overall system optimization objective is to jointly optimize the digital beamforming and analog beamforming on the UAV-T side, the receive combining vector on the UAV-R side, and the three-dimensional position and orientation of the 6DMA subarrays on both sides, under constraints such as antenna movement area, rotation range, transmit power, and analog beam constant mode, in order to maximize the instantaneous achievable data rate.

[0051] in The set of locations for all UPA subarray antennas of UAV-T and UAV-R: The attitude set of all UPA subarray antennas for UAV-T and UAV-R: .

[0052] 4. Hybrid-driven multi-agent dual-delay deep deterministic policy gradient (HD-MATD3) joint optimization module: The original non-convex, high-dimensional complex geometry and beam joint optimization problem is modeled as a Markov Decision Process (MDP). The non-convex part that is difficult to solve is separated and handed over to the deep reinforcement learning (RL) network for inference, while the convex optimization part with closed-form solution is obtained from the mathematical closed-form solution, realizing joint decision-making driven by data and model.

[0053] Specifically, the MDP process design of this joint optimization module is as follows: 4.1 Global State Space : Global state fusion and normalization of transmit and receive UAV states 6DMA geometric position and attitude state Simulated phase state of the transmitter after sine and cosine encoding And the channel state after singular value decomposition compression and dimensionality reduction. .

[0054] Channel feature compression by means of Before truncation extraction The maximal singular values ​​constitute the normalized energy eigenvector. And extract the left and right singular vectors corresponding to the maximum singular value to construct directional features. and This compresses highly complex matrices into real eigenvectors, thus avoiding the curse of dimensionality.

[0055] The final global state is represented as .

[0056] 4.2 Local Observation Space : Agent 1 (responsible for TX simulation beamforming): Local observation state includes , and the achievable speed at the previous moment ,Right now

[0057] Agent 2 (responsible for 6DMA position and attitude): Local observation state includes , , and ,Right now .

[0058] 4.3 Motion Space The Actor network outputs a dimensionless action range. continuous increment instructions within Agent-1 outputs the simulated phase increment and maps it back to the actual physical phase based on periodicity; Agent-2 outputs the three-dimensional position increment and attitude angle increment of the antenna subarray. .

[0059] When interacting with the environment, a forced truncation projection function is introduced to strictly project any actions that attempt to cross the boundary to the physically movable area and rotation range, ensuring the feasibility of the solution.

[0060] 4.4 Reward Function : The primary reward is the instantaneous achievable speed, supplemented by penalties for exceeding the limits:

[0061] in Performance weights reflect the importance of achievable speeds. and These are the boundary penalty weights for antenna movement and rotation, respectively.

[0062] and The physical distance / angle error of the agent's attempts to move and rotate beyond the hard boundary is quantified separately. The further the agent tries to move out of the boundary, the greater the penalty.

[0063] 4.5. Deterministic Subroutine Modules within the Environment: After acquiring the physical geometry state and simulated beam phase output by the agent, the system reconstructs an effective equivalent channel. For digital domain variables, closed-form solutions can be obtained directly using Maximum Ratio Transmission (MRT) and Maximum Ratio Combining (MRC):

[0064] Specifically, the HD MATD3 algorithm steps of this joint optimization module are as follows: After obtaining the above MDP process, the steps of the joint optimization algorithm based on HD MATD3 and 6DMA are as follows: Initialization Phase: Construct and initialize the multi-agent Actor network, the dual-Critic network, and the corresponding target network parameters. Clear the experience replay pool. The environment is reset and an initial global state is constructed using the initial optimized physical state obtained from the traditional alternating optimization algorithm. .

[0065] Execution interaction phase (for each time step) ): Step 1: Based on current local observations The two Actor networks generate joint normalized action vectors with exploration noise. .

[0066] Step 2: Perform environment projection and physical truncation, and... Decode the phase, position, and attitude increments, and update the transmitter's analog beamforming matrix. And 6DMA physical structure parameters, forcibly truncate illegal out-of-bounds values.

[0067] Step 3: Start the deterministic subroutine within the environment to reconstruct the line-of-sight channel. Digital beamforming is obtained through rapid iteration of MRT / MRC. and receive merged vector And perform power normalization.

[0068] Step 4: Calculate the instantaneous achievable rate under the current physical configuration and beam as the basic feedback, and subtract the out-of-bounds penalty to obtain the total reward. Acquire UAV status, 6DMA geometric position and attitude, simulate phase state at the transmitter, extract and compress channel features, and generate the global state for the next time step. Transfer records Store in playback pool .

[0069] Network update phase: Step 5: When When the sample size meets the batch size requirement, small batches of data are randomly sampled. The target action with truncated smoothed noise is calculated, the target Q-value is evaluated, and the Critic network is updated by minimizing the error loss function.

[0070] Step 6: Use a delayed update mechanism (e.g., every two steps) to update the Actor network parameters by fixing the Critic network based on the deterministic policy gradient theorem.

[0071] Step 7: Use the soft update rate to smoothly update the network parameters of the target Actor and the target Critic, and proceed to the next time step loop until convergence at the end of the round.

[0072] This algorithm employs a data- and model-driven multi-agent architecture, combining a dual-crit network, delay policy updates, and target policy smoothing mechanisms to establish interaction between multiple agents and a highly dynamic environment, achieving dynamic policy optimization. The algorithm entrusts the difficult-to-optimize non-convex geometric position and attitude problem and simulated beamforming to reinforcement learning agents for real-time inference. Simultaneously, it directly calculates digital beamforming and the receive merging vector using mathematical closed-form optimal solutions. Under hard constraints such as 6DMA movement area and rotation range, maximum transmit power, and simulated beamforming unit modulus, it achieves low-complexity real-time joint optimization of antenna 3D position, attitude, and hybrid beamforming. This method not only completely overcomes the high computational complexity and inference delay bottlenecks of traditional AO algorithms but also actively reconstructs the channel environment to compensate for beam alignment deviations caused by changes in UAV position and attitude, thereby significantly improving the real-time reachability in air-to-air dynamic line-of-sight scenarios.

[0073] Example 2

[0074] The scenario in this embodiment is as follows: Figure 1The diagram illustrates a UAV-to-UAV communication scenario within an integrated air-to-ground or high-altitude communication network. Two UAVs (transmitter UAV-T and receiver UAV-R) fly at constant speeds along their respective predetermined paths. Over a period of time... During the communication cycle, the UAV-T's speed is 22.9 m / s, and the UAV-R's speed is 15 m / s. The communication distance between the two aircraft increases uniformly from an initial 50 m to 1028 m over time. Affected by the actual wind field and fuselage vibration, the UAV experiences continuous attitude disturbances (including random jitters such as yaw, pitch, and roll) and positional shifts during flight. Both the UAV-T and UAV-R operate in the 30 GHz millimeter-wave band and have identical transceiver antenna configurations, consisting of four independently movable and rotatable 2×2 uniform planar arrays, for a total of 16 antennas per end. The system employs a sub-connected hybrid beamforming architecture, with four RF links configured at both ends, each independently connecting to and driving a 2×2 uniform planar sub-array. Furthermore, due to the physical limitations and channel attributes of this specific embodiment, directional antennas are used for communication, with a half-power beamwidth of 30°. The normalized beam pattern is shown below. Figure 2 As shown. System maximum transmit power. Limited to 30dBm, receiver background noise power -80dBm. Each UPA subarray in the 6DMA has a maximum of 10 in the XY plane of the full array coordinate system. ×10 Two-dimensional translation region (in (for carrier wavelength), and also has a continuous rotation adjustment range of [-60°, 60°] in the three Euler angle dimensions of yaw, pitch, and roll. .

[0075] Assumptions: The two parties in the UAV communication are conducting line-of-sight transmission at high altitude; both the transmitting and receiving ends can obtain perfect CSI; and they can obtain their own latest position and attitude information in real time.

[0076] 1. Three coordinate systems are defined based on the UAV 6DMA position and attitude space mapping module. Specifically, the three coordinate systems are defined as follows: Global coordinate system: The East-North-Up (ENU) coordinate system is adopted. A reference point is selected as the origin. The X-axis points due east along the local latitude tangent, the Y-axis points due north along the local longitude tangent, and the Z-axis is perpendicular to the local horizontal plane and points to the zenith, serving as the absolute spatial reference.

[0077] Full array coordinate system (body axis system): The origin is located at the UAV's center of mass, the Z-axis is perpendicular to the full array plane and faces outwards, and the X-axis and Y-axis follow the right-hand rule. It is assumed that the UPA full array plane coincides with the UAV's body axis system.

[0078] Subarray local coordinate system: Defines the relative positions of the fixed antennas within each UPA subarray. The Z-axis of each subarray is perpendicular to the subarray plane and points outwards, while the X and Y axes follow the right-hand rule.

[0079] Therefore, the UAV-T number is obtained. The antennas are in the global coordinate system. The position of the moment is Similarly, the UAV-R's first... The antennas are in the global coordinate system. The position of the moment is , Therefore, the accuracy of any transmitting antenna can be calculated in real time. With receiving antenna Euclidean distance between .

[0080] 2. Based on the line-of-sight air-to-air dynamic channel and signal modeling module, a corresponding channel model is established to obtain the achievable rate expression. Specifically, based on the principle of ray tracing, 16×16 dimensional line-of-sight channel matrix The first in The complex channel elements are represented as follows:

[0081] in For the first Channel gain of a complex number of channel elements; For the first The transmitting antenna points to the first The unit direction vector of each receiving antenna; For the first The transmitting antenna to the first The directional gain of each receiving antenna; It is a pattern factor, and its value range is... It describes the energy distribution; For the first The normal vector of each subarray is determined by the array's rotational orientation. Decide; This is the peak gain of the antenna; similarly, the directional gain of the receiving antenna element can be obtained. .

[0082] Furthermore, a single-stream signal is transmitted at the transmitting end. At the same time, the received signal after hybrid beamforming and receiving is combined. Represented as:

[0083] Unit module constraint , , , The noise scalar variance is -80 dBm. The maximum transmit power is... If the value is 30 dBm, then there is a power constraint.

[0084] Assuming receive merge vector normalization The instantaneous achievable rate of the system The model is as follows:

[0085] 3. The final optimization problem is obtained based on the hybrid beamforming joint optimization problem modeling module. The overall system optimization objective is to jointly optimize the digital beamforming and analog beamforming on the UAV-T side, the receive combining vector on the UAV-R side, and the three-dimensional position and orientation of the 6DMA subarrays on both sides, under constraints such as antenna movement area, rotation range, transmit power, and analog beam constant mode, in order to maximize the instantaneous achievable data rate.

[0086] 4. Real-time solution of the above optimization problems based on the HD-MATD3 joint optimization module. Specifically, for the above optimization problems, the transceiver UAV dynamically adjusts the position and attitude of its respective 6DMA antennas and performs hybrid beamforming based on the HD-MATD3 hybrid beamforming and 6DMA joint optimization algorithm to obtain the real-time maximum achievable data rate.

[0087] 5. Simulation Results

[0088] Specifically, HD-MATD3 needs to be trained before simulation. The specific hyperparameter settings for HD-MATD3 training are shown in Table 1. Figure 3 As shown, the reward convergence graph of the training process was obtained. It can be observed that the reward gradually stabilizes after about 800 rounds, eventually converging and becoming stable.

[0089] Table 1

[0090] This specific embodiment simulates simple airflow turbulence during flight. Sinusoidal attitude disturbances are introduced on both the UAV-T and UAV-R sides to simulate the impact of wind field or fuselage vibration on antenna orientation. The trained HD-MATD3 model is applied to the scenario described in this embodiment to simulate the change in achievable rate under changes in UAV position and attitude, and the achievable rates are compared with those of the FPA scheme and the AO-based 6DMA scheme.

[0091] The final simulation results of this specific embodiment are as follows: Figure 4 and Figure 5 As shown, the achievable rates of the three schemes during simulation and the percentage improvement in achievable rate of the HD-MATD3-based 6DMA scheme as a function of communication distance are illustrated. The results show that although the rates of all schemes decrease due to spatial path loss, both 6DMA schemes consistently outperform the traditional FPA scheme. Compared to the severe rate oscillations caused by attitude disturbances in FPA, the 6DMA scheme maintains extremely high smoothness and stability by flexibly adjusting the array to compensate for beam alignment errors. Compared to the FPA scheme, the AO-based 6DMA scheme and the HD-MATD3-based 6DMA scheme achieve maximum achievable rate improvements of 171.2% (2.71 times) and 166.8% (2.67 times), respectively, and average rate improvements of 29.9% and 27.9%, respectively. Furthermore, the 6DMA curves based on HD-MATD3 and AO-based 6DMA closely match, with an average gain difference of only 1.4%, demonstrating that this reinforcement learning algorithm significantly reduces inference computational complexity while simultaneously meeting the communication performance and real-time requirements of highly dynamic scenarios.

[0092] Figure 6 The Cumulative Distribution Function (CDF) curves for achievable rates further demonstrate that the CDF curves of the HD-MATD3-based 6DMA scheme and the AO-based 6DMA scheme highly overlap, and are generally located to the right of the traditional FPA scheme. Particularly in the low-rate range (e.g., at a 10% outage probability), both 6DMA schemes significantly improve the lower bound of the rate, greatly reducing the risk of deep fading and outages in the link. Furthermore, compared to the traditional FPA scheme, the rate fluctuations of both 6DMA schemes are significantly reduced throughout the process, thus demonstrating stronger robustness. This is fundamentally because 6DMA actively mitigates beam alignment errors caused by changes in fuselage attitude and position by utilizing additional position and rotation degrees of freedom. In addition, simulation results verify that the proposed HD-MATD3 algorithm can achieve a robust performance distribution highly consistent with traditional high-quality AO algorithms in dynamic and complex environments with extremely low inference complexity.

[0093] To further verify the advantages of low time complexity and high real-time performance of the proposed scheme, 50,000 Monte Carlo simulation tests were conducted on a simulation platform configured with an NVIDIA GeForce RTX 4060 GPU and an AMD Ryzen 7 7745HX CPU, based on the PyTorch 1.12 deep learning programming framework. Table 2 shows a comparison of the theoretical derivation of the time complexity and the average time taken for single-step optimization between the HD-MATD3-based 6DMA scheme and the AO-based 6DMA scheme. The AO-based 6DMA scheme decomposes the original problem into four sub-problems: 6DMA position and attitude optimization based on a genetic algorithm, analog beamforming optimization based on element-wise coordinate descent, digital beamforming based on MRT, and receiver merging optimization iteratively solved based on MRC. For simulation of the AO iteration count, setting it to 10 iterations is sufficient for convergence. The internal iteration count for alternating optimization of digital beamforming and receiver merging is set to convergence in 5 iterations in the simulation. The internal iteration count for simulated beamforming optimization was set to 10 iterations for convergence. Set the population size to 1000. Set the number of generations to 100. The hidden layer dimension of the network is 512, as shown in Table 1.

[0094] Table 2

[0095] Based on the theoretical derivation of time complexity and the comparison of the average time taken for single-step optimization in 50,000 Monte Carlo simulations, the 6DMA scheme based on HD-MATD3 shows an overwhelming advantage in terms of computational efficiency and real-time performance.

[0096] First, from the perspective of time complexity models, the AO-based 6DMA scheme relies on multiple alternating iterations and a large amount of search overhead during the solution process, resulting in high computational complexity. In contrast, the HD-MATD3-based 6DMA scheme only requires forward inference of the neural network and a small number of closed matrix operations in practical applications, eliminating the search iteration overhead and significantly reducing its time complexity compared to the AO scheme.

[0097] Secondly, in terms of actual execution time, the AO-based solution has an average single-step optimization time of up to 4625.31ms, resulting in excessive optimization calculation latency, which cannot meet the requirements of highly dynamic air-to-air communication scenarios with millisecond-level changes; while the HD-MATD3-based solution has an average single-step optimization time of only 19.82ms.

[0098] The HD-MATD3-based 6DMA scheme achieves communication performance highly close to that of a high-quality AO-based 6DMA scheme, but its average single-step optimization time is significantly reduced by approximately 233.4 times. This result fully demonstrates that the system and method proposed in this invention can adapt to the real-time joint optimization of beam and antenna geometry parameters in highly dynamic scenarios, significantly improving the achievable data rate compared to FPA, and significantly reducing the time complexity of optimization computation compared to the traditional AO 6DMA scheme.

[0099] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that, unless otherwise defined, the technical or scientific terms used in this invention should be understood in the ordinary sense by those skilled in the art to which this invention pertains, and the terms "comprising" or "including" or similar terms used in this invention mean that the element or object preceding the word covers the element or object listed after the word and its equivalents.

[0100] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for air-to-air hybrid beamforming based on a six-dimensional movable antenna, characterized in that, The method is applied to a UAV-to-UAV communication system, wherein the six-dimensional movable antenna (6DMA) has three-dimensional positional movement degrees of freedom and three-dimensional attitude rotation degrees of freedom, and includes the following steps: S1. Establish a multi-level coordinate system mapping model to convert the local coordinates of each antenna in the uniform planar array UPA subarray on the transmitting UAV and the receiving UAV into the absolute physical position in the global coordinate system, so as to characterize the spatial geometric changes caused by the body attitude jitter and the relative motion of the antenna. S2. Construct a line-of-sight air-to-air dynamic channel model, calculate the distance between antennas based on the absolute physical positions of the transmitting and receiving antennas, establish complex channel element expressions, and construct a hybrid beamforming signal transmission model that includes analog beamforming matrix, digital beamforming matrix and receiver combining vector. S3. Establish a joint optimization model with the goal of maximizing the instantaneous achievable rate of the system. Under the constraints of antenna movement area, rotation range, transmit power and analog beam constant mode, jointly optimize the analog beamforming parameters and digital beamforming parameters of the transmitter, the receive combining vector of the receiver, and the three-dimensional position and attitude of each UPA subarray of the transmitter and receiver. S4. The HD-MATD3 algorithm, driven by a hybrid data and model approach, is used to solve the joint optimization model in real time. In this process, a deep reinforcement learning network is used to infer the non-convex geometric optimization parameters and the simulated beamforming parameters in the joint optimization model in real time. The obtained parameters are then input into the closed-loop solution calculation module to directly calculate the digital beamforming parameters and the receiver merging vector parameters.

2. The method according to claim 1, characterized in that, The multi-level coordinate system mapping model in step S1 includes a global coordinate system, a full array coordinate system, and a sub-array local coordinate system. At any moment The first transmitter The absolute physical position of each antenna in the global coordinate system Calculate according to the following formula: in, Let be the rotation matrix of the transmitter's full array coordinate system relative to the global coordinate system. For the first Rotation matrices of each UPA subarray relative to the full array coordinate system. This represents the fixed position of the antenna in the local coordinate system of the subarray. Let be the position of the subarray in the full array coordinate system. The coordinates of the launching UAV in the global coordinate system; Receiver The absolute physical position of each antenna in the global coordinate system is calculated in the same way as that of the transmitter.

3. The method according to claim 1, characterized in that, In the dynamic channel model of step S2, the transmitting antenna With receiving antenna At any moment Complex channel elements Represented as: in, For transmitting antenna With receiving antenna The Euclidean distance between them The channel gain includes path loss and antenna directivity gain; The hybrid beamforming signal transmission model satisfies the diagonal structure constraint of the sub-connector blocks, and the system's instantaneous achievable rate is [data missing]. Represented as: in, To receive the merged vector, For the channel matrix, To simulate the beamforming matrix, For digital beamforming matrix, This represents the noise variance.

4. The method according to claim 1, characterized in that, The HD-MATD3 algorithm in step S4 employs a multi-agent, dual-delay, deep deterministic policy gradient architecture, whose state space... Includes channel features compressed using Singular Value Decomposition (SVD). ; The channel features The extraction method is as follows: for the channel matrix Perform truncated singular value decomposition and extract the previous values. The maximum singular values ​​form the energy feature vector, and the corresponding left and right singular vectors are combined to construct the directional feature, so as to compress the high-dimensional complex channel matrix into a low-dimensional real feature vector. The state space includes at least the normalized UAV state characteristics, the geometric position and attitude characteristics of the six-dimensional movable antenna, the simulated beam characteristics, and the channel characteristics.

5. The method according to claim 4, characterized in that, The algorithm's action space consists of continuous incremental instructions, including simulated phase increments, three-dimensional position increments of the antenna subarray, and three-dimensional attitude angle increments. When interacting with the environment, a forced truncation projection function is introduced to restrict the action commands to a preset physical movable area and rotation range to ensure the physical feasibility of the output action.

6. The method according to claim 4, characterized in that, The reward function of the algorithm Defined as: in, For performance weighting, For instantaneous achievable speed, and These are the boundary penalty weights for antenna movement and rotation, respectively. and These are the penalty terms corresponding to when the antenna position and attitude exceed the preset boundaries.

7. The method according to claim 1, characterized in that, The closed-form solution calculation module in step S4 is implemented in the following way: After obtaining the geometric state and simulated beam phase of the deep reinforcement learning network output, the equivalent channel is reconstructed. The digital beamforming vector is obtained using the maximum ratio transmission MRT and the maximum ratio combining MRC. Combined with Received Vector Closed-form solution: in, Represents the equivalent channel matrix. This represents the conjugate transpose of the equivalent channel matrix.

8. A hybrid air-to-air beamforming system based on a six-dimensional movable antenna, characterized in that, include: The spatial mapping module is used to calculate the absolute physical position of the transmitting and receiving antennas in real time, and to convert the antenna position from the local coordinate system to the absolute physical position in the global coordinate system through multi-level coordinate system mapping. The channel modeling module is used to construct a dynamic line-of-sight channel model and calculate the channel matrix based on the physical location of the transmitting and receiving antennas, and to establish a hybrid beamforming signal transmission model. The joint optimization module is used to execute the HD-MATD3 algorithm based on a hybrid data and model approach. It infers non-convex parameters in real time through an agent network and combines the closed-loop solution calculation module to obtain digital beamforming parameters and receiver merging vector parameters. The closed-form solution calculation module is used to reconstruct the equivalent channel after obtaining the geometric state and simulated beam phase output by the joint optimization module, and to calculate the closed-form solution of the digital beamforming vector and the receiver combining vector based on the maximum ratio transmission (MRT) and maximum ratio combining (MRC).

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