An aerial computing method based on polarization steering

Abstract

The application provides an air computing method based on polarization shaping, relates to the technical field of Internet of Things, and comprises the following steps: firstly, an air computing system of a receiving point provided with a polarization reconfigurable antenna and a plurality of transmitting devices is constructed. The transmitting devices transmit data through polarization channels, and the receiving point calculates the mean square error of actual and estimated superposed data. Then, joint optimization is performed on the transmitting phase, the receiving phase and the receiving beam forming vector with the target of minimizing the mean square error. Finally, the optimal parameters are solved by using an alternating optimization algorithm and saved to the air computing system, so that air computing is realized. According to the application, polarization shaping is performed on the receiving point and the transmitting device, and the optimal receiving polarization reconfigurable antenna phase, the receiving beam forming vector and the transmitting device phase are calculated with the target of minimizing the mean square error, so that air computing is realized under the condition of lower cost and power consumption.

Description

Technical Field

[0001] This invention relates to the field of Internet of Things (IoT) technology, and in particular to an aerial computing method based on polarization shaping. Background Technology

[0002] Over-the-air computing (OTA) technology, with its "computation while communicating" transmission paradigm, has become a core research hotspot in 6G edge intelligence, industrial IoT, and large-scale distributed sensor networks. OTA leverages the superposition characteristics of electromagnetic wave waveforms in wireless channels, allowing multiple distributed nodes to synchronously transmit data on the same time-frequency resources. At the receiving point, the objective function is directly calculated through channel-simulated addition, completely overcoming the latency bottleneck and spectrum resource waste problems of the traditional "transmit first, compute later" orthogonal multiple access mode. It possesses irreplaceable technological advantages and industrial application value in scenarios involving the aggregation of massive amounts of low-latency data from multiple nodes. However, the large-scale deployment of OTA faces a core bottleneck that is difficult to overcome: to ensure the accuracy of the aggregation calculation results, the signals of all nodes must be strictly aligned in amplitude and phase at the receiving point. This makes the system's mean square error completely limited by the node with the worst channel conditions, exhibiting a significant "weakest link" effect. When a node is in a deep fading channel scenario, the signal transmission strength of the entire system must be significantly reduced to align its weak signal, directly leading to a sharp decline in the overall system's calculation accuracy. This core challenge poses a major obstacle to the widespread application of OTA in complex wireless environments.

[0003] To alleviate the inherent "weakest link" bottleneck in over-the-air computing, existing research mainly employs power control and multi-receiver polarization reconfigurable antenna beamforming schemes. These schemes compensate for channel fading by adjusting node transmit power and optimizing the beam vector of the multi-receiver polarization reconfigurable antenna at the receiver, thereby improving the equivalent channel gain of the worst-performing node. While these schemes can improve system performance to some extent, in scenarios with severe deep fading, the maximum transmit power limit of IoT terminal nodes restricts the effectiveness of simple power compensation and spatial domain beamforming optimization. To further overcome performance bottlenecks, existing research has proposed intelligent reflector-assisted over-the-air computing schemes. These schemes reconstruct the wireless propagation environment by deploying a large number of passive reflector elements, thereby enhancing the channel gain of the worst-performing node. However, the introduction of intelligent reflectors not only brings extremely high channel estimation overhead and computational complexity to passive beamforming optimization, but also significantly increases system hardware deployment costs and control link burden, making it difficult to adapt to the needs of low-cost, low-power large-scale IoT terminal deployments.

[0004] Against this backdrop, the polarization dimension of electromagnetic waves, as a fourth-dimensional wireless resource independent of time, frequency, and space, represents a largely unexplored technological direction and offers a novel solution to the core challenge of the "worst-case transmitting device" problem in airborne computing. In real-world wireless propagation environments, due to multipath effects such as reflection and scattering, signals often undergo depolarization, leading to a mismatch between the polarization state at the receiver and the transmitter, resulting in significant signal power loss. Traditional fixed-polarization receiver-reconfigurable antennas cannot adapt to the dynamic changes in polarization states in the propagation environment. While dual-polarization receiver-reconfigurable antennas can utilize polarization diversity gain, they require twice the RF link, resulting in high hardware costs and power consumption. Summary of the Invention

[0005] To overcome the limitations of fixed-polarization receive-polarization reconfigurable antennas in adapting to dynamically changing polarization states and the high cost and power consumption of dual-polarization receive-polarization reconfigurable antennas, this invention provides an airborne computing method based on polarization shaping.

[0006] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: This invention provides an aerial computing method based on polarization shaping, comprising: Construct an airborne computing system based on polarization shaping. The airborne computing system includes a receiving point and several transmitting devices. The receiving point is equipped with M receiving polarization reconfigurable antennas, and each transmitting device is equipped with a transmitting polarization reconfigurable antenna. Each transmitting device forms a polarization channel to the receiving point. Each of the transmitting devices sends sensor data to the receiving point through a corresponding polarization channel. The receiving point receives the sensor data from all the transmitting devices and calculates the actual superimposed data and the estimated superimposed data. Based on the actual superimposed data and the estimated superimposed data, the mean square error is calculated, and the phase of the transmitting device, the phase of the receiving polarization reconfigurable antenna, and the receiving beamforming vector of the receiving point are jointly optimized with the minimization of the mean square error as the optimization objective. The optimization objective is solved using an alternating optimization algorithm to obtain the optimal receiver polarization reconfigurable antenna phase, receiver beamforming vector, and transmitter phase. The optimal receiving polarization reconfigurable antenna phase, receiving beamforming vector, and transmitting device phase are saved to the polarization-based airborne computing system to achieve airborne computing.

[0007] Preferably, each of the transmitting devices is provided with a transmit polarization reconfigurable antenna, and each of the transmitting devices forms a polarization channel to the receiving point, including: The physical channel from the k-th transmitting device to the receiving point is determined by the polarization channel matrix. express:

[0008] in, This represents the polarization sub-channel between the k-th transmitting device and the m-th receiving polarization reconfigurable antenna; The polarization subchannel The model is as follows: ( ⊙ ) in, For large-scale path loss, it is defined as , For path loss, Let k be the distance from the k-th transmitting device to the receiving point. The path loss index; For polarization coupling matrix, Let be the small-scale Rayleigh fading from the k-th transmitting device to the m-th receiving polarized reconfigurable antenna, and ⊙ be the Hadamard product; Each transmitting device is equipped with a polarization-reconfigurable receive polarization-reconfigurable antenna, and the transmit polarization shaping vector for each transmitting device is... The expression is as follows:

[0009] in, Provide the emission polarization shaping vector for the k-th transmitting device; Polarization shaping is performed on the receiving point, and the receiving polarization shaping matrix of the receiving point is obtained. for:

[0010] Where blkdiag is a block diagonal matrix. ; The polarization channel from the k-th transmitting device to the receiving point The expression is as follows:

[0011] in, Let k be the polarization channel from the transmitting device to the receiving point. This indicates the conjugate transpose.

[0012] Preferably, calculating the actual overlay data includes: Let the transmission data of the k-th transmitting device be... The transmitted data Normalization , With zero mean and unity power, each Independent of each other, that is , ,and The actual superimposed data is described as follows: .

[0013] Preferably, calculating the estimated overlay data includes: Let the data transmitted by the k-th transmitting device be... ,in and adopt Power control is performed, whereby satisfy , The preset maximum power; Superimposed signal vector received by the receiving point ∈ for:

[0014] in, It is additive white Gaussian noise; The receiving point utilizes the received beamforming vector and noise reduction factor For the superimposed signal vector After processing, estimated superimposed data of the transmission data from all transmitting devices is obtained: .

[0015] Preferably, the mean square error is calculated based on the actual superimposed data and the estimated superimposed data, including: Based on the actual and estimated superimposed data, the initial mean square error is defined as follows:

[0016] The initial mean square error is derived to obtain a closed-form expression for the mean square error:

[0017] make Signal alignment is performed on the closed-form expression of the mean square error to obtain the aligned closed-form expression:

[0018] Solving the aligned closed equation yields the optimal emission scalar:

[0019] in, For complex conjugate; Due to transmit power constraints ,have

[0020] Under this design, the closed-form mean square error is completely eliminated, and the computational error of the airborne computing system originates from noise, which is addressed by the noise reduction factor. Substituting into the closed-form expression for mean square error, we obtain the final mean square error: .

[0021] Preferably, with minimizing the mean square error as the optimization objective, the phase of the transmitting device, the phase of the receiving polarization reconfigurable antenna, and the receiving beamforming vector of the receiving point are jointly optimized, including: The optimization objective is modeled as follows:

[0022] in, For the phase of the k-th transmitting device, Let U be the phase of the m-th receive polarization reconfigurable antenna, and U be the receive beamforming vector. This represents the Euclidean norm of a vector.

[0023] Preferably, an alternating optimization algorithm is used to solve the optimization objective to obtain the optimal receiver polarization reconfigurable antenna phase, receiver beamforming vector, and transmitter phase, including: The phase of the receiver polarization reconfigurable antenna, the receiver beamforming vector, and the phase of the transmitting device are solved iteratively, respectively: With fixed receiver polarization reconfigurable antenna phase and receiver beamforming vector, phase optimization of transmitting equipment is achieved. With the phase of the fixed transmitting equipment and the receiving beamforming vector unchanged, the phase of the receiving polarization reconfigurable antenna is optimized. With fixed receiver polarization, the reconfigurable antenna phase and the transmitting device phase remain unchanged, thus optimizing the receiver beamforming vector. The optimal phase and optimal receiving beamforming vector for each transmitting device and receiving polarization reconfigurable antenna are obtained until the objective function converges or the preset maximum number of iterations is reached.

[0024] Preferably, the phase of the fixed-receive polarization reconfigurable antenna and the receive beamforming vector remain unchanged, while the phase optimization of the transmitting equipment includes: The original problem is transformed into maximizing the effective power of the transmitting device, and the objective function is as follows:

[0025] Introducing intermediate variables Combining the polarization shaping vector of the launching equipment, the objective function simplifies to:

[0026] According to the property of the modulus of complex numbers, when satisfying The closed-form solution for the optimal transmitting device phase is shown below: .

[0027] Preferably, with the phase of the transmitting device and the receiving beamforming vector fixed, phase optimization of the receiving polarization reconfigurable antenna includes: An element-wise alternating optimization strategy is adopted. In the m-th step, all parameters except the m-th receive-polarized reconfigurable antenna are fixed, and only the phase of the m-th receive-polarized reconfigurable antenna is optimized:

[0028] The received signal of the k-th transmitting device Perform variable separation and expansion:

[0029] make Indicates other The sum of signals from the root antennas and the vertical component in the current antenna that is not phase-controlled:

[0030] make This represents the horizontal component coefficients that are subject to phase modulation in the current antenna:

[0031] The optimization problem for antenna phase can be expressed as follows:

[0032] in, It is a non-convex term; By introducing real variables By utilizing the property of modulus expansion, the optimization problem can be linearized. The linearized optimization problem is as follows:

[0033] make , Construct a semidefinite matrix The linearized optimization problem is relaxed into the following convex semidefinite programming problem:

[0034] Wherein, the coefficient matrix The expression is as follows:

[0035] Solving the convex semidefinite programming problem yields the following results: Then make a judgment: like The optimized antenna phase can be obtained directly through eigenvalue decomposition. like Using Gaussian randomization method from The optimal antenna phase that satisfies the constraints is recovered. .

[0036] Preferably, the phase of the fixed-receive-polarization reconfigurable antenna and the phase of the transmitting device remain unchanged, and the receiving beamforming vector is optimized, including: Under the constraint that the received signals corresponding to each of the transmitting devices meet a preset minimum power threshold, the optimization objective is to minimize the power of the received beamforming vector. The expression for the optimization objective is as follows:

[0037] A semidefinite matrix variable is introduced to handle the nonconvexity of the optimization objective. The expression for the semidefinite matrix variable is as follows:

[0038] The power constraint of the received beamforming vector can be rewritten as regarding The linear form of is expressed as follows:

[0039] The non-convex rank-one constraint is ignored for the linear form. The optimization objective is relaxed into the following convex semidefinite programming problem:

[0040] Solving for the results Afterwards, according to The rank optimization of the receive beamforming vector yields the optimal receive beamforming vector: like ,right Perform eigenvalue decomposition and take the eigenvector corresponding to the largest eigenvalue as the optimal receiving beamforming vector; like The optimal receiving beamforming vector is solved using Gaussian randomization.

[0041] Compared with the prior art, the beneficial effects of the technical solution of the present invention are: This invention provides an airborne computing method based on polarization shaping. First, an airborne computing system based on polarization shaping is constructed. This system includes a receiving point and several transmitting devices. The receiving point is equipped with M receive polarization-reconfigurable antennas, and each transmitting device is equipped with a transmit polarization-reconfigurable antenna. Each transmitting device forms a polarization channel with the receiving point. Each transmitting device transmits sensor data to the receiving point through its corresponding polarization channel. The receiving point receives the sensor data from all transmitting devices and calculates the actual superimposed data and the estimated superimposed data. Based on the actual superimposed data and the estimated superimposed data, a mean square error (MSE) is calculated. Minimizing this MSE is used as the optimization objective to jointly optimize the phase of the transmitting devices, the phase of the receive polarization-reconfigurable antennas, and the receive beamforming vector of the receiving point. An alternating optimization algorithm is used to solve for the optimization objective, obtaining the optimal receive polarization-reconfigurable antenna phase, the receive beamforming vector, and the transmitting device phase. The optimal receive polarization-reconfigurable antenna, the receive beamforming vector, and the transmitting device phase are saved to the polarization-shaping-based airborne computing system to realize airborne computing. This invention achieves over-the-air computing under conditions of lower cost and power consumption by polarizing the receiving point and the transmitting device and minimizing the mean square error, thereby calculating the optimal receiving polarization reconfigurable antenna phase, receiving beamforming vector and transmitting device phase. Attached Figure Description

[0042] Figure 1 This is a flowchart illustrating an aerial computing method based on polarization shaping in Example 1. Figure 2 The figure shows the experimental results of the mean square error of the polarization shaping scheme and the fixed polarization scheme in Example 3 as a function of the number of iterations. Figure 3 This is an experimental result diagram showing the variation of mean square error with different number of transmitting devices for different polarization schemes in Example 3. Detailed Implementation

[0043] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent. To better illustrate this embodiment, some parts in the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions; It will be understood by those skilled in the art that certain well-known structures and their descriptions may be omitted in the accompanying drawings.

[0044] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0045] Example 1 This embodiment provides an aerial computing method based on polarization shaping, such as... Figure 1As shown, it includes: Construct an airborne computing system based on polarization shaping. The airborne computing system includes a receiving point and several transmitting devices. The receiving point is equipped with M receiving polarization reconfigurable antennas, and each transmitting device is equipped with a transmitting polarization reconfigurable antenna. Each transmitting device forms a polarization channel to the receiving point. Each of the transmitting devices sends sensor data to the receiving point through a corresponding polarization channel. The receiving point receives the sensor data from all the transmitting devices and calculates the actual superimposed data and the estimated superimposed data. Based on the actual superimposed data and the estimated superimposed data, the mean square error is calculated, and the phase of the transmitting device, the phase of the receiving polarization reconfigurable antenna, and the receiving beamforming vector of the receiving point are jointly optimized with the minimization of the mean square error as the optimization objective. The optimization objective is solved using an alternating optimization algorithm to obtain the optimal receiver polarization reconfigurable antenna phase, receiver beamforming vector, and transmitter phase. The optimal receiving polarization reconfigurable antenna phase, receiving beamforming vector, and transmitting device phase are saved to the polarization-based airborne computing system to achieve airborne computing.

[0046] In its specific implementation, this invention first constructs an airborne computing system based on polarization shaping. This system includes a receiving point and several transmitting devices. The receiving point is equipped with M reconfigurable polarized antennas for receiving, and each transmitting device is equipped with one reconfigurable polarized antenna for transmitting. Each transmitting device forms a polarization channel with the receiving point. Next, each transmitting device sends sensor data to the receiving point through its corresponding polarization channel. The receiving point receives the sensor data from all transmitting devices and calculates the actual superimposed data and the estimated superimposed data. Then, based on the actual superimposed data and the estimated superimposed data, the mean square error is calculated. Minimizing this mean square error is used as the optimization objective to jointly optimize the phase of the transmitting devices, the phase of the reconfigurable polarized antennas for receiving, and the receiving beamforming vector of the receiving point. Next, an alternating optimization algorithm is used to solve for the optimization objective, obtaining the optimal phase of the reconfigurable polarized antennas for receiving, the receiving beamforming vector for receiving, and the phase of the transmitting devices. Finally, the optimal phase of the reconfigurable polarized antennas for receiving, the receiving beamforming vector for receiving, and the phase of the transmitting devices are saved to the polarization-shaped airborne computing system, thus realizing airborne computing. This invention achieves over-the-air computing under conditions of lower cost and power consumption by polarizing the receiving point and the transmitting device and minimizing the mean square error, thereby calculating the optimal receiving polarization reconfigurable antenna phase, receiving beamforming vector and transmitting device phase.

[0047] Example 2 This embodiment provides a method for aerial computing based on polarization shaping, including: Construct an airborne computing system based on polarization shaping. The airborne computing system includes a receiving point and several transmitting devices. The receiving point is equipped with M receiving polarization reconfigurable antennas, and each transmitting device is equipped with a transmitting polarization reconfigurable antenna. Each transmitting device forms a polarization channel to the receiving point. Each of the transmitting devices sends sensor data to the receiving point through a corresponding polarization channel. The receiving point receives the sensor data from all the transmitting devices and calculates the actual superimposed data and the estimated superimposed data. Based on the actual superimposed data and the estimated superimposed data, the mean square error is calculated, and the phase of the transmitting device, the phase of the receiving polarization reconfigurable antenna, and the receiving beamforming vector of the receiving point are jointly optimized with the minimization of the mean square error as the optimization objective. The optimization objective is solved using an alternating optimization algorithm to obtain the optimal receiver polarization reconfigurable antenna phase, receiver beamforming vector, and transmitter phase. The optimal receiving polarization reconfigurable antenna phase, receiving beamforming vector, and transmitting device phase are saved to the polarization-based airborne computing system to achieve airborne computing.

[0048] It should be noted that, in this embodiment, each transmitting device is equipped with a transmit polarization reconfigurable antenna, and each transmitting device forms a polarization channel to the receiving point, including: The physical channel from the k-th transmitting device to the receiving point is determined by the polarization channel matrix. express:

[0049] in, This represents the polarization sub-channel between the k-th transmitting device and the m-th receiving polarization reconfigurable antenna; The polarization subchannel The model is as follows: ( ⊙ ) in, For large-scale path loss, it is defined as , For path loss, Let k be the distance from the k-th transmitting device to the receiving point. The path loss index; For polarization coupling matrix, Let be the small-scale Rayleigh fading from the k-th transmitting device to the m-th receiving polarized reconfigurable antenna, and ⊙ be the Hadamard product; Each transmitting device is equipped with a polarization-reconfigurable receive polarization-reconfigurable antenna, and the transmit polarization shaping vector for each transmitting device is... The expression is as follows:

[0050] in, Provide the emission polarization shaping vector for the k-th transmitting device; Polarization shaping is performed on the receiving point, and the receiving polarization shaping matrix of the receiving point is obtained. for:

[0051] Where blkdiag is a block diagonal matrix. ; The polarization channel from the k-th transmitting device to the receiving point The expression is as follows:

[0052] in, Let k be the polarization channel from the transmitting device to the receiving point. This indicates the conjugate transpose.

[0053] It should be noted that, in this embodiment, calculating the actual overlay data includes: Let the transmission data of the k-th transmitting device be... The transmitted data Normalization , With zero mean and unity power, each Independent of each other, that is , ,and The actual superimposed data is described as follows: .

[0054] It should be noted that, in this embodiment, the calculation of the estimated overlay data includes: Let the data transmitted by the k-th transmitting device be... ,in and adopt Power control is performed, whereby satisfy , The preset maximum power; Superimposed signal vector received by the receiving point ∈ for:

[0055] in, It is additive white Gaussian noise; The receiving point utilizes the received beamforming vector and noise reduction factor For the superimposed signal vector After processing, estimated superimposed data of the transmission data from all transmitting devices is obtained: .

[0056] It should be noted that, in this embodiment, the mean square error is calculated based on the actual superimposed data and the estimated superimposed data, including: Based on the actual and estimated superimposed data, the initial mean square error is defined as follows:

[0057] The initial mean square error is derived to obtain a closed-form expression for the mean square error:

[0058] make Signal alignment is performed on the closed-form expression of the mean square error to obtain the aligned closed-form expression:

[0059] Solving the aligned closed equation yields the optimal emission scalar:

[0060] in, For complex conjugate; Due to transmit power constraints ,have

[0061] Under this design, the closed-form mean square error is completely eliminated, and the computational error of the airborne computing system originates from noise, which is addressed by the noise reduction factor. Substituting into the closed-form expression for mean square error, we obtain the final mean square error: .

[0062] It should be noted that, in this embodiment, the optimization objective is to minimize the mean square error, and the phase of the transmitting device, the phase of the receiving polarization reconfigurable antenna, and the receiving beamforming vector of the receiving point are jointly optimized, including: The optimization objective is modeled as follows:

[0063] in, For the phase of the k-th transmitting device, Let U be the phase of the m-th receive polarization reconfigurable antenna, and U be the receive beamforming vector. This represents the Euclidean norm of a vector.

[0064] It should be noted that, in this embodiment, an alternating optimization algorithm is used to solve the optimization objective to obtain the optimal receiver polarization reconfigurable antenna phase, receiver beamforming vector, and transmitter phase, including: The phase of the receiver polarization reconfigurable antenna, the receiver beamforming vector, and the phase of the transmitting device are solved iteratively, respectively: With fixed receiver polarization reconfigurable antenna phase and receiver beamforming vector, phase optimization of transmitting equipment is achieved. With the phase of the fixed transmitting equipment and the receiving beamforming vector unchanged, the phase of the receiving polarization reconfigurable antenna is optimized. With fixed receiver polarization, the reconfigurable antenna phase and the transmitting device phase remain unchanged, thus optimizing the receiver beamforming vector. The optimal phase and optimal receiving beamforming vector for each transmitting device and receiving polarization reconfigurable antenna are obtained until the objective function converges or the preset maximum number of iterations is reached.

[0065] It should be noted that in this embodiment, the phase of the fixed-receive polarization reconfigurable antenna and the receive beamforming vector remain unchanged, while the phase optimization of the transmitting device includes: The original problem is transformed into maximizing the effective power of the transmitting device, and the objective function is as follows:

[0066] Introducing intermediate variables Combining the polarization shaping vector of the launching equipment, the objective function simplifies to:

[0067] According to the property of the modulus of complex numbers, when satisfying The closed-form solution for the optimal transmitting device phase is shown below: .

[0068] It should be noted that in this embodiment, the phase of the fixed transmitting device and the receiving beamforming vector remain unchanged, while the phase optimization of the receiving polarization reconfigurable antenna includes: An element-wise alternating optimization strategy is adopted. In the m-th step, all parameters except the m-th receive-polarized reconfigurable antenna are fixed, and only the phase of the m-th receive-polarized reconfigurable antenna is optimized:

[0069] The received signal of the k-th transmitting device Perform variable separation and expansion:

[0070] make Indicates other The sum of signals from the root antennas and the vertical component in the current antenna that is not phase-controlled:

[0071] make This represents the horizontal component coefficients that are subject to phase modulation in the current antenna:

[0072] The optimization problem for antenna phase can be expressed as follows:

[0073] in, It is a non-convex term; By introducing real variables By utilizing the property of modulus expansion, the optimization problem can be linearized. The linearized optimization problem is as follows:

[0074] make , Construct a semidefinite matrix The linearized optimization problem is relaxed into the following convex semidefinite programming problem:

[0075] Wherein, the coefficient matrix The expression is as follows:

[0076] Solving the convex semidefinite programming problem yields the following results: Then make a judgment: like The optimized antenna phase can be obtained directly through eigenvalue decomposition. like Using Gaussian randomization method from The optimal antenna phase that satisfies the constraints is recovered. .

[0077] It should be noted that in this embodiment, the phase of the fixed-receive polarization reconfigurable antenna and the phase of the transmitting device remain unchanged. The optimization of the receive beamforming vector includes: Under the constraint that the received signals corresponding to each of the transmitting devices meet a preset minimum power threshold, the optimization objective is to minimize the power of the received beamforming vector. The expression for the optimization objective is as follows:

[0078] A semidefinite matrix variable is introduced to handle the nonconvexity of the optimization objective. The expression for the semidefinite matrix variable is as follows:

[0079] The power constraint of the received beamforming vector can be rewritten as regarding The linear form of is expressed as follows:

[0080] The non-convex rank-one constraint is ignored for the linear form. The optimization objective is relaxed into the following convex semidefinite programming problem:

[0081] Solving for the results Afterwards, according to The rank optimization of the receive beamforming vector yields the optimal receive beamforming vector: like ,right Perform eigenvalue decomposition and take the eigenvector corresponding to the largest eigenvalue as the optimal receiving beamforming vector; like The optimal receiving beamforming vector is solved using Gaussian randomization.

[0082] Example 3 This embodiment provides an aerial computing method based on polarization shaping, including: Construct an airborne computing system based on polarization shaping. The airborne computing system includes a receiving point and several transmitting devices. The receiving point is equipped with M receiving polarization reconfigurable antennas, and each transmitting device is equipped with a transmitting polarization reconfigurable antenna. Each transmitting device forms a polarization channel to the receiving point. Each of the transmitting devices sends sensor data to the receiving point through a corresponding polarization channel. The receiving point receives the sensor data from all the transmitting devices and calculates the actual superimposed data and the estimated superimposed data. Based on the actual superimposed data and the estimated superimposed data, the mean square error is calculated, and the phase of the transmitting device, the phase of the receiving polarization reconfigurable antenna, and the receiving beamforming vector of the receiving point are jointly optimized with the minimization of the mean square error as the optimization objective. The optimization objective is solved using an alternating optimization algorithm to obtain the optimal receiver polarization reconfigurable antenna phase, receiver beamforming vector, and transmitter phase. The optimal receiving polarization reconfigurable antenna phase, receiving beamforming vector, and transmitting device phase are saved to the polarization-based airborne computing system to achieve airborne computing.

[0083] In this embodiment, an experiment was conducted to compare the performance of the mean square error (MSE) of the traditional fixed polarization scheme and the polarization shaping scheme provided by this invention with the number of iterations. In this experiment, the number of transmitting devices was set to 10. The experimental results are as follows: Figure 2 As shown, through analysis Figure 2 Based on the simulation data, the following technical conclusions can be drawn: (1) Algorithm convergence analysis: As the number of iterations increases, the mean square error of the system under the above two schemes shows a gradual decreasing trend and eventually tends to stabilize and converge. This shows that the alternating optimization algorithm proposed in this invention has good convergence performance. (2) Convergence speed comparison: Compared with the traditional fixed polarization scheme, the polarization shaping scheme adopted in this embodiment of the invention shows a better convergence rate. Specifically, the scheme of this invention can quickly reach a stable convergence state after experiencing fewer iterations (about 3 iterations). (3) Comparison of computational accuracy: The lower bound of the MSE of the scheme proposed in this embodiment of the invention is significantly lower than the lower bound of the MSE of the fixed polarization scheme. In summary, the simulation results fully demonstrate that by introducing polarization shaping technology into the air computing system and combining it with the proposed alternating optimization algorithm, this invention can achieve lower computational errors with a faster convergence speed, thereby significantly improving the accuracy of data aggregation and the robustness of the system in complex wireless environments.

[0084] This embodiment also includes an experiment to compare the differences in mean square error (MSE) with the number of transmitting devices for 10 polarization-reconfigurable antennas under various polarization schemes. These various polarization schemes include the polarization shaping, left-hand and right-hand circular polarization, dynamic linear polarization, fixed left-hand circular polarization, fixed vertical polarization, and fixed receiver polarization of this invention. The experimental results are as follows: Figure 3 As shown, through analysis Figure 3 As shown in the curve, the polarization shaping scheme proposed in this invention consistently maintains the lowest calculation error throughout the entire range of varying transmitter numbers. Particularly when the number of transmitters is large, the MSE growth rate of this invention's scheme is significantly faster and more gradual than other traditional schemes. Therefore, it can be concluded that this invention's scheme exhibits superior scalability and robustness in massively connected IoT scenarios.

[0085] The same or similar labels correspond to the same or similar parts; The terms used to describe positional relationships in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent. Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for aerial computation based on polarization shaping, characterized in that, include: Construct an airborne computing system based on polarization shaping. The airborne computing system includes a receiving point and several transmitting devices. The receiving point is equipped with M receiving polarization reconfigurable antennas, and each transmitting device is equipped with a transmitting polarization reconfigurable antenna. Each transmitting device forms a polarization channel to the receiving point. Each of the transmitting devices sends sensor data to the receiving point through a corresponding polarization channel. The receiving point receives the sensor data from all the transmitting devices and calculates the actual superimposed data and the estimated superimposed data. Based on the actual superimposed data and the estimated superimposed data, the mean square error is calculated, and the phase of the transmitting device, the phase of the receiving polarization reconfigurable antenna, and the receiving beamforming vector of the receiving point are jointly optimized with the minimization of the mean square error as the optimization objective. The optimization objective is solved using an alternating optimization algorithm to obtain the optimal receiver polarization reconfigurable antenna phase, receiver beamforming vector, and transmitter phase. The optimal receiving polarization reconfigurable antenna phase, receiving beamforming vector, and transmitting device phase are saved to the polarization-based airborne computing system to achieve airborne computing.

2. The aerial computing method based on polarization shaping according to claim 1, characterized in that, Each of the transmitting devices is equipped with a transmit polarization reconfigurable antenna, and each of the transmitting devices forms a polarization channel to the receiving point, including: The physical channel from the k-th transmitting device to the receiving point is determined by the polarization channel matrix. express: in, This represents the polarization sub-channel between the k-th transmitting device and the m-th receiving polarization reconfigurable antenna; The polarization subchannel The model is as follows: ( ⊙ ) in, For large-scale path loss, it is defined as , For path loss, Let k be the distance from the k-th transmitting device to the receiving point. The path loss index; The polarization coupling matrix, Let be the small-scale Rayleigh fading from the k-th transmitting device to the m-th receiving polarized reconfigurable antenna, and ⊙ be the Hadamard product; Each transmitting device is equipped with a polarization-reconfigurable receive polarization-reconfigurable antenna, and the transmit polarization shaping vector for each transmitting device is... The expression is as follows: in, Provide the emission polarization shaping vector for the k-th transmitting device; Polarization shaping is performed on the receiving point, and the receiving polarization shaping matrix of the receiving point is obtained. for: Where blkdiag is a block diagonal matrix. ; The polarization channel from the k-th transmitting device to the receiving point The expression is as follows: in, Let k be the polarization channel from the transmitting device to the receiving point. This indicates the conjugate transpose.

3. The aerial computing method based on polarization shaping according to claim 2, characterized in that, Calculate the actual overlay data, including: Let the transmission data of the k-th transmitting device be... The transmitted data Normalization , With zero mean and unity power, each Independent of each other, that is , ,and The actual superimposed data is described as follows: 。 4. The aerial computing method based on polarization shaping according to claim 3, characterized in that, Calculate the estimated overlay data, including: Let the data transmitted by the k-th transmitting device be... ,in and adopt Power control is performed, where, satisfy , The preset maximum power; Superimposed signal vector received by the receiving point ∈ for: in, It is additive white Gaussian noise; The receiving point utilizes the received beamforming vector and noise reduction factor For the superimposed signal vector After processing, estimated superimposed data of the transmission data from all transmitting devices is obtained: 。 5. The aerial computing method based on polarization shaping according to claim 4, characterized in that, Based on the actual superimposed data and the estimated superimposed data, the mean square error is calculated, including: Based on the actual and estimated superimposed data, the initial mean square error is defined as follows: The initial mean square error is derived to obtain a closed-form expression for the mean square error: make Signal alignment is performed on the closed-form expression of the mean square error to obtain the aligned closed-form expression: Solving the aligned closed equation yields the optimal emission scalar: in, For complex conjugate; Due to transmit power constraints ,have Under this design, the closed-form mean square error is completely eliminated, and the computational error of the airborne computing system originates from noise, which is addressed by the noise reduction factor. Substituting into the closed-form expression for mean square error, we obtain the final mean square error: 。 6. The aerial computing method based on polarization shaping according to claim 5, characterized in that, With minimizing the mean square error as the optimization objective, the phase of the transmitting device, the phase of the receiving polarization reconfigurable antenna, and the receiving beamforming vector of the receiving point are jointly optimized, including: The optimization objective is modeled as follows: in, For the phase of the k-th transmitting device, Let U be the phase of the m-th receive polarization reconfigurable antenna, and U be the receive beamforming vector. This represents the Euclidean norm of a vector.

7. The aerial computing method based on polarization shaping according to claim 6, characterized in that, The optimization objective is solved using an alternating optimization algorithm to obtain the optimal receiver polarization reconfigurable antenna phase, receiver beamforming vector, and transmitter phase, including: The phase of the receiver polarization reconfigurable antenna, the receiver beamforming vector, and the phase of the transmitting device are solved iteratively, respectively: With fixed receiver polarization reconfigurable antenna phase and receiver beamforming vector, phase optimization of transmitting equipment is achieved. With the phase of the fixed transmitting equipment and the receiving beamforming vector unchanged, the phase of the receiving polarization reconfigurable antenna is optimized. With fixed receiver polarization, the reconfigurable antenna phase and the transmitting device phase remain unchanged, thus optimizing the receiver beamforming vector. The optimal phase and optimal receiving beamforming vector for each transmitting device and receiving polarization reconfigurable antenna are obtained until the objective function converges or the preset maximum number of iterations is reached.

8. The aerial computing method based on polarization shaping according to claim 7, characterized in that, With the phase of the fixed-receive-polarization reconfigurable antenna and the receive beamforming vector remaining unchanged, phase optimization of the transmitting equipment is performed, including: The original problem is transformed into maximizing the effective power of the transmitting device, and the objective function is as follows: Introducing intermediate variables Combining the polarization shaping vector of the launching equipment, the objective function simplifies to: According to the property of the modulus of complex numbers, when satisfying The closed-form solution for the optimal transmitting device phase is shown below: 。 9. The aerial computing method based on polarization shaping according to claim 7, characterized in that, With the transmitting equipment phase and receiving beamforming vector fixed, phase optimization is performed on the receiving polarization reconfigurable antenna, including: An element-wise alternating optimization strategy is adopted. In the m-th step, all parameters except the m-th receive-polarized reconfigurable antenna are fixed, and only the phase of the m-th receive-polarized reconfigurable antenna is optimized: The received signal of the k-th transmitting device Perform variable separation and expansion: make Indicates other The sum of signals from the root antennas and the vertical component in the current antenna that is not phase-controlled: make This represents the horizontal component coefficients that are subject to phase modulation in the current antenna: The optimization problem for antenna phase can be expressed as follows: in, It is a non-convex term; By introducing real variables By utilizing the property of modulus expansion, the optimization problem can be linearized. The linearized optimization problem is as follows: make , Construct a semidefinite matrix The linearized optimization problem is relaxed into the following convex semidefinite programming problem: Wherein, the coefficient matrix The expression is as follows: Solving the convex semidefinite programming problem yields the following results: Then make a judgment: like The optimized antenna phase can be obtained directly through eigenvalue decomposition. like Using Gaussian randomization method from The optimal antenna phase that satisfies the constraints is recovered. .

10. The aerial computing method based on polarization shaping according to claim 7, characterized in that, With the phase of the fixed-receive-polarization reconfigurable antenna and the phase of the transmitting equipment remaining unchanged, the receiver beamforming vector is optimized, including: Under the constraint that the received signals corresponding to each of the transmitting devices meet a preset minimum power threshold, the optimization objective is to minimize the power of the received beamforming vector. The expression for the optimization objective is as follows: A semidefinite matrix variable is introduced to handle the nonconvexity of the optimization objective. The expression for the semidefinite matrix variable is as follows: The power constraint of the received beamforming vector can be rewritten as regarding The linear form of is expressed as follows: The non-convex rank-one constraint is ignored for the linear form. The optimization objective is relaxed into the following convex semidefinite programming problem: Solving for the results Afterwards, according to The rank optimization of the receive beamforming vector yields the optimal receive beamforming vector: like ,right Perform eigenvalue decomposition and take the eigenvector corresponding to the largest eigenvalue as the optimal receiving beamforming vector; like The optimal receiving beamforming vector is solved using Gaussian randomization.

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