Spectral efficiency optimization method and system for rotatable continuous aperture array

Abstract

The invention discloses a spectrum efficiency optimization method and system for a rotatable continuous aperture array. According to the method, based on a rotatable CAPA system model, an integral-based spectral efficiency maximization optimization problem model with the rate of the rotatable CAPA system as a target function is constructed, and a precoder and each Rx-CAPA rotation angle are optimized under the constraint of total sending power and the constraint of each Rx-CAPA rotation angle range. And the rotation angle of the precoder and the rotation angle of each Rx-CAPA are respectively optimized by using an alternating optimization method. For optimization of the precoder, related sub-problems are solved by using methods such as a Lagrange duality theory and a variational method (CoV), and a CAPA precoder in a continuous space is obtained. On the basis, the rotation angle of the CAPA at each user is optimized by using a gradient rising method and the like, and the optimal orientation angle of each Rx-CAPA under the current precoder is obtained. A simulation result shows that compared with a traditional static CAPA system, the rotatable CAPA system has the advantage that the spectrum efficiency of the system can be obviously improved.

Description

Technical Field

[0001] This invention relates to the field of Continuous Aperture Array (CAPA) wireless communication, and in particular to CAPA multi-user downlink communication methods and systems. Background Technology

[0002] With the continuous evolution of wireless communication technology and the development of metamaterials technology, traditional communication architectures based on spatial discrete antenna arrays are gradually showing bottlenecks in terms of degree-of-freedom utilization efficiency, array gain improvement, and energy consumption control. Facing the urgent needs of 6G and later 6G wireless systems for ultra-high-speed transmission, ultra-large-scale connectivity, and high-precision spatial control capabilities, the academic community has begun to explore new array forms that break through the physical constraints of discrete arrays. Against this backdrop, Continuous Aperture Arrays (CAPAs) have emerged. Their core idea is to construct a continuous electromagnetic radiation surface within a finite physical aperture, achieving continuous controllability of the electromagnetic field amplitude and phase through precise control of the surface current distribution. Benefiting from the advantages of metamaterials in electromagnetic response modulation and integration, CAPAs demonstrate good feasibility in both theoretical modeling and engineering implementation, providing a new research direction for improving system degrees of freedom, enhancing near- and far-field beamforming capabilities, and supporting future intelligent wireless communication.

[0003] In existing CAPA-related research, most studies focus on deploying CAPAs at the base station side, while user terminals still employ single-antenna or low-dimensional antenna configurations. Even in the few studies that consider CAPAs at both the base station and user terminals, the antenna array is usually assumed to be a static structure with a fixed orientation. This modeling approach, to some extent, ignores the potential advantages of CAPAs as continuous electromagnetic radiation surfaces in terms of spatial orientation and geometric reconfigurability. In fact, in near-field communication and high-frequency transmission scenarios, array orientation has a significant impact on channel characteristics, energy focusing capabilities, and spatial degree-of-freedom utilization efficiency. Therefore, introducing a CAPA architecture with rotatable characteristics and studying its channel modeling, beamforming, and system performance evolution under dynamic orientation adjustment conditions not only helps to compensate for the shortcomings of existing research in array spatial flexibility but also provides new research motivation and theoretical foundation for fully exploring the performance potential of CAPAs in future B6G communication systems. Summary of the Invention

[0004] Purpose of the invention: In view of the above-mentioned research status, the purpose of this invention is to study downlink multi-user communication of rotatable CAPA systems, and to provide a spectral efficiency optimization method and system for rotatable continuous aperture arrays, so as to obtain the pre-encoder with maximum spectral efficiency and the optimal orientation of each receiving CAPA (Rx-CAPA) under a given system configuration.

[0005] Technical Solution: To achieve the above-mentioned objectives, the present invention provides a method for optimizing the spectral efficiency of rotatable continuous aperture arrays, comprising the following steps:

[0006] Based on a rotatable CAPA system model, an integral-based optimization model for maximizing spectral efficiency is constructed with the rotatable CAPA system rate as the objective function. Under the constraints of total transmit power and the rotation angle range of each Rx-CAPA, the pre-encoder and the rotation angle of each Rx-CAPA are optimized. The pre-encoder is a current density function in continuous space. The rotation angle can be continuously varied within a preset range.

[0007] The rotation angles of the pre-encoder and each Rx-CAPA are optimized using an alternating optimization method until convergence, wherein:

[0008] The optimization of the preencoder includes: fixing the positions of each Rx-CAPA, performing a Lagrangian dual transformation on the objective problem after introducing a first set of auxiliary variables to obtain an unconstrained optimization problem, and then alternately optimizing the first set of auxiliary variables and the preencoder. Specifically, when optimizing the first set of auxiliary variables with the preencoder fixed, the optimal solution of the first set of auxiliary variables is obtained by differentiating the objective function. When optimizing the preencoder with the first set of auxiliary variables fixed, a second set of auxiliary variables is introduced and a quadratic transformation is performed on the sub-objective function at this time. The optimal solution of the second set of auxiliary variables is obtained by differentiating the transformed sub-objective function. The preencoder is then solved directly in continuous space using the variational method (CoV).

[0009] The optimization of the rotation angle of each Rx-CAPA includes: fixing the precoder, performing a second transformation on the objective problem by introducing a third set of auxiliary variables, obtaining the optimal solution of the third set of auxiliary variables by differentiating the objective function, and using the gradient ascent method to obtain the optimal rotation angle of each Rx-CAPA.

[0010] Furthermore, in the rotatable CAPA system model, both the base station and each user are equipped with CAPAs, and the Rx-CAPA at the user's location can rotate within a preset angle range; the transmitting CAPA (Tx-CAPA) at the base station maintains a fixed position in space, and the main coordinate system in the system model is constructed with the center of the Tx-CAPA as the origin; an auxiliary coordinate system is constructed with the center of each Rx-CAPA as the origin, and each Rx-CAPA can rotate around one of the coordinate axes in the main coordinate system; the coordinates of any point on the plane where the Rx-CAPA is located in the main coordinate system are determined jointly by the rotation matrix and the coordinates of the center point of the Rx-CAPA in the main coordinate system.

[0011] Furthermore, the system rate , For the number of users, , For the first Rx-CAPA around the principal coordinate system Axis rotation angle, , To carry and send to the Pre-encoder of user data For user collection, The plane containing Tx-CAPA Let Tx-CAPA be the coordinates of any point. For noise power, This is the equivalent channel function after considering the receiver function.

[0012] Furthermore, the spectral effectiveness maximization optimization problem is expressed as:

[0013]

[0014] in, , For transmit power constraints.

[0015] Furthermore, the first set of auxiliary variables is obtained by differentiating the objective function. In the optimal solution, the optimal Represented as: .

[0016] Furthermore, the set of second auxiliary variables is obtained by differentiating the objective function. In the optimal solution, the optimal Represented as: .

[0017] Furthermore, the variational method is used to directly solve the precoder in continuous space. Calculate using the following formula: ;in, , , , , , , It is the identity matrix. This indicates that the elements are arranged in a diagonal matrix.

[0018] Furthermore, the set of third auxiliary variables is obtained by differentiating the objective function. In the optimal solution, the optimal Represented as:

[0019] ;for , ;in, For the first The set of points of an Rx-CAPA in its auxiliary coordinate system. for The coordinates of any point on, To take rotation angle into account The receiving function, To take rotation angle into account The equivalent channel function after that.

[0020] Furthermore, the gradient ascent method is used to obtain the optimal rotation angle for each Rx-CAPA, the th... Rx-CAPA rotation angle at each user location The relevant gradient is represented as: ;in, Describe the objective function. Indicates taking the real part, for , about The gradient is:

[0021] .

[0022] The present invention also provides a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when loaded onto the processor, implements the precoding method for maximizing the spectral effectiveness of the rotatable continuous aperture antenna system.

[0023] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0024] 1. This invention conducts in-depth research on the problem of maximizing the spectral efficiency of rotatable CAPA systems, introduces a rotatable CAPA system model with variable array orientation, and incorporates the spatial orientation of the antenna array as an optimizable degree of freedom into the overall precoding design framework, thereby breaking through the limitations of existing CAPA precoding schemes that generally assume the antenna array is statically fixed and only optimize in the signal domain or beam domain.

[0025] 2. This invention employs a variational method to model and solve the CAPA precoder in a continuous spatial domain. This not only avoids the degree-of-freedom truncation and approximation errors introduced by traditional methods relying on discrete Fourier series expansions, but also more accurately characterizes the electromagnetic field distribution and signal propagation characteristics. Therefore, the optimized results obtained are significantly superior to approximation schemes based on discrete expansions in terms of accuracy, stability, and physical interpretability, effectively improving the system's precoding performance and communication efficiency.

[0026] 3. This invention utilizes an alternating optimization method to optimize the precoder and the rotation angles of each Rx-CAPA until convergence. First, assuming a fixed orientation for each Rx-CAPA, the precoder is optimized using methods such as Lagrange dual transformation, sub-target quadratic transformation, and variational methods. Then, with the precoder fixed, the rotation angles of each Rx-CAPA are optimized using quadratic transformation and gradient ascent methods. Numerical results show that the rotatable CAPA precoder with flexible array orientation achieves higher spectral efficiency compared to traditional static array precoders. It significantly improves the system's spatial adaptability and spectral efficiency in complex propagation environments, effectively compensating for the shortcomings of traditional CAPA systems in terms of spatial flexibility and environmental adaptability, and providing a new feasible approach and optimization dimension for CAPA precoding design. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating the overall process of an embodiment of the present invention.

[0028] Figure 2 This is a schematic diagram of downlink transmission of the rotatable CAPA system in an embodiment of the present invention.

[0029] Figure 3 This is a comparison of the system spectral efficiency obtained under three schemes: the rotatable CAPA system pre-encoder, the static CAPA system pre-encoder, and the rotatable CAPA system with only optimization of the rotation angle of each Rx-CAPA. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0031] This invention discloses a spectral efficiency optimization method for rotatable continuous aperture arrays, wherein the base station is equipped with a CAPA on which the current density distribution can be arbitrarily designed; and the user side is equipped with a CAPA with a variable orientation angle. Therefore, when designing to maximize the system's spectral efficiency, the pre-encoder function in the continuous space and the rotation angle of each Rx-CAPA are both optimization variables.

[0032] like Figure 1 As shown in the figure, the spectral efficiency optimization method for rotatable continuous aperture arrays described in this embodiment mainly includes the following steps:

[0033] S1. Based on the rotatable CAPA system model, an integral-based optimization model for maximizing spectral efficiency is constructed with the rotatable CAPA system rate as the objective function. Under the constraints of total transmit power and the rotation angle range of each Rx-CAPA, the pre-encoder and the rotation angle of each Rx-CAPA are optimized. The pre-encoder is a current density function in continuous space. The rotation angle can be continuously varied within a preset range.

[0034] S2. Optimize the pre-encoder and the rotation angles of each Rx-CAPA using an alternating optimization method until convergence, including:

[0035] S21. The optimization of the pre-encoder includes: fixing the positions of each Rx-CAPA, performing a Lagrangian dual transformation on the objective problem after introducing a first set of auxiliary variables to obtain an unconstrained optimization problem, and then alternately optimizing the first set of auxiliary variables and the pre-encoder. Specifically, when optimizing the first set of auxiliary variables with the pre-encoder fixed, the optimal solution of the first set of auxiliary variables is obtained by differentiating the objective function. When optimizing the pre-encoder with the first set of auxiliary variables fixed, a second set of auxiliary variables is introduced and a quadratic transformation is performed on the sub-objective function at this time. The optimal solution of the second set of auxiliary variables is obtained by differentiating the transformed sub-objective function. The pre-encoder is then solved directly in continuous space using a variational method.

[0036] S22. The optimization of the rotation angle of each Rx-CAPA includes: fixing the precoder, performing a second transformation on the objective problem by introducing a third set of auxiliary variables, obtaining the optimal solution of the third set of auxiliary variables by taking the derivative of the objective function, and obtaining the optimal rotation angle of each Rx-CAPA by using the gradient ascent method.

[0037] In this embodiment, the base station is equipped with a CAPA to send different data to N users. Each user is equipped with a CAPA that can rotate within a certain angle range. In the rotatable CAPA system model, both the base station and each user are equipped with a CAPA, and the Rx-CAPA at each user can rotate within a preset angle range. The Tx-CAPA at the base station maintains a fixed position in space. The main coordinate system in the system model is constructed with the center of the Tx-CAPA as the origin. An auxiliary coordinate system is constructed with the center of each Rx-CAPA as the origin, and each Rx-CAPA can rotate around one of the coordinate axes in the main coordinate system. The coordinates of any point on the plane where the Rx-CAPA is located in the main coordinate system are determined jointly by the rotation matrix and the coordinates of the center point of the Rx-CAPA in the main coordinate system.

[0038] The following is combined with Figure 2 The specific scenario shown will be used to provide a more detailed explanation of the method in this embodiment.

[0039] First, the spectral efficiency model and problem construction of the rotatable CAPA system are explained.

[0040] like Figure 2 As shown, each base station and user site is equipped with a CAPA, and the Rx-CAPA at each user site can rotate within a certain angle range; N auxiliary coordinate systems are constructed with the center of each Rx-CAPA as the origin, and each Rx-CAPA can rotate around the center of the main coordinate system. The axis is rotated, and the rotation angle is denoted as the optimization variable. ,in, For user collection, For the first Rx-CAPA winding The angle of axis rotation; the CAPA (Tx-CAPA) transmitted at the base station maintains a fixed position in space, and a principal coordinate system xoyz is constructed with the center of Tx-CAPA as the origin, such that the coordinates of any point on Tx-CAPA are... satisfy ,in, and Tx-CAPA along and Dimensions of the axes. Principal coordinate system and the first... The transformation to the auxiliary coordinate system where each Rx-CAPA resides is:

[0041]

[0042] in, For the first The plane containing each Rx-CAPA; for Any point on the th Coordinate description in an auxiliary coordinate system; for The coordinate description of any point in the principal coordinate system; for Around The rotation matrix of the axis; for The coordinates of the center point in the principal coordinate system.

[0043] No. The signal received at each user location is:

[0044]

[0045] in, To carry signals The pre-encoder is a function of the current density in continuous space. Let Tx-CAPA be the coordinates of any point. The coordinates of any point on Rx-CAPA at the user's location; The plane containing Tx-CAPA To send to the The data for each user satisfies the following independent zero-mean condition: ; The noise field function of the user Rx-CAPA satisfies the following Gaussian noise field condition:

[0046]

[0047] in, For noise power, For Dirac function, superscript Indicates conjugate; To consider the equivalent channel function after polarized reception, its expression is: , To send the polarization vector, For the first The coordinates of the received polarization vector at each user location in the principal coordinate system are described, where... For the received polarization vector at the th Coordinate description in an auxiliary coordinate system; For the dyadic Green's function, considering only the radiation term, its expression can be approximated as: ,in, represents an imaginary number, For free space wave impedance, For wavelength, For wave number, For normalized coordinates, For any coordinate vector in space, The identity matrix is ​​used; the optimization objective is the system speed. ,in For the first The signal-to-interference-to-noise ratio (SINR) when demodulating a signal at a user location is expressed as follows:

[0048]

[0049] in, To consider the equivalent channel function after considering the receiver function, since a uniformly distributed receiver function is taken into account, It can be considered as the distribution area A constant on, and satisfying ; This is the set of pre-encoder functions that need to be designed.

[0050] Based on the above system model, the spectral effectiveness maximization problem constructed in step S1 is as follows:

[0051]

[0052] in, For transmit power constraints; Can be bypassed Axis in Rotate within the range.

[0053] Based on step S2, the alternating optimization method is used to... and The optimization is performed separately: First, the precoder is optimized while keeping each Rx-CAPA fixed; then, based on the current precoder, the orientation angle of each Rx-CAPA is optimized, and this process is repeated until the algorithm converges.

[0054] According to step S21, the positions of each Rx-CAPA are fixed. After introducing the first set of auxiliary variables, a Lagrangian dual transformation is performed on the target problem to obtain an unconstrained optimization problem. Then, the first set of auxiliary variables and the pre-encoder are alternately optimized. Specifically, in this embodiment, the pre-encoder optimization problem can be solved by introducing the first set of auxiliary variables. And using the Lagrange dual transformation, it is transformed into the following subproblem:

[0055] ,

[0056] in,

[0057]

[0058] It can be further proven that the optimal precoder must satisfy the following full-power transmission condition: The subproblem is solved iteratively using alternating optimization. With variables fixed... Under the premise of, the optimal The following solution can be obtained by differentiating the objective function:

[0059]

[0060] According to step S21, in the fixed Under the premise of this, a second set of auxiliary variables is introduced and a second transformation is performed on the sub-objective function at this time. Specifically, in this embodiment, a second set of auxiliary variables is introduced. Further The subproblem is transformed into the following subproblem using a quadratic transformation:

[0061] ,

[0062] in,

[0063]

[0064] in, This indicates taking the real part.

[0065] For optimization variables ,exist{ When fixed, by adjusting the objective function The optimal solution obtained by differentiation is:

[0066]

[0067] According to step S21, for the optimization variables Using the CoV theory, it can be obtained When fixed, its optimal solution is:

[0068]

[0069] in, , , , , , , It is the identity matrix. This indicates that the elements are arranged in a diagonal matrix.

[0070] Based on step S22, with the pre-encoder fixed, the optimal rotation angle for each receiver CAPA is obtained using the gradient ascent method. The relevant sub-problem is expressed as follows:

[0071]

[0072] in, ,

[0073]

[0074] For the first The set of points of an Rx-CAPA in its auxiliary coordinate system. To take rotation angle into account The receiving function, in this embodiment, is a uniformly distributed function on the receiving plane; To take rotation angle into account The equivalent channel function after that is expressed as follows: , .

[0075] According to step S22, the precoder is fixed, and a second transformation is performed on the target problem after introducing a third set of auxiliary variables. The optimal solution of the third set of auxiliary variables is obtained by differentiating the objective function, and the optimal rotation angle of each Rx-CAPA is obtained using the gradient ascent method. Specifically, in this embodiment, a third set of auxiliary variables is introduced. The optimization subproblem related to the rotation angle can be further transformed into the following equivalent problem:

[0076]

[0077] According to step S22, in the fixed Under the premise, The optimal solution is:

[0078]

[0079] And fixed Under the premise, The optimal solution is given by the gradient ascent method, and the objective function is given by... The gradient is:

[0080]

[0081] in,

[0082]

[0083] in, The equivalent channel function with respect to the rotation angle gradient, For receiving functions with respect to rotation angle The gradient of the receiver function is 0 in this embodiment, since the receiver function is a uniformly distributed function.

[0084] The gradient update formula during gradient ascent is: ,in, To update the step size.

[0085] Repeat the pre-encoder optimization and Rx-CAPA rotation angle update process until the alternating optimization algorithm converges.

[0086] Figure 3 The proposed rotatable CAPA precoder is compared with the precoder in a traditional static CAPA system and a scheme that only considers mechanical rotation angle optimization in terms of system spectral efficiency (SE). Simulation results show that, compared with the CAPA precoding scheme with fixed array orientation and the method that only optimizes the CAPA rotation angle at the receiver, the proposed rotatable CAPA precoder can significantly improve the system spectral efficiency performance.

[0087] In summary, this invention discloses a method for optimizing the spectral efficiency of a rotatable continuous aperture array (CAPA). The base station is equipped with a CAPA, and each user is equipped with a rotatable CAPA. First, an integral-based spectral efficiency maximization problem model is constructed for this rotatable CAPA system. In this problem, the pre-encoder is a function in a continuous space, and the rotation angle of each Rx-CAPA is continuously variable within a certain range. Considering the form of the optimization variables in this problem, alternating optimization is chosen to solve the problem. Within this framework, firstly, the orientation angle of each Rx-CAPA is fixed, and the pre-encoder is solved using methods such as CoV; then, the pre-encoder is fixed again, and the rotation angle of each Rx-CAPA is optimized using methods such as gradient ascent, thus obtaining the optimal orientation angle of each Rx-CAPA under the current pre-encoder.

[0088] Based on the same inventive concept, an embodiment of the present invention discloses a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded onto the processor, it implements the steps of the multi-group multicast energy efficiency maximization precoding method for the continuous aperture antenna system.

[0089] All aspects of this invention not described in detail are well-known to those skilled in the art. The preferred embodiments of this invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of this invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of this invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for optimizing the spectral efficiency of rotatable continuous aperture arrays, characterized in that, Includes the following steps: Based on a rotatable CAPA system model, an integral-based optimization model for maximizing spectral efficiency is constructed with the rotatable CAPA system rate as the objective function. Under the constraints of total transmit power and the rotation angle range of each receive CAPA (Rx-CAPA), the pre-encoder and the rotation angle of each Rx-CAPA are optimized. The pre-encoder is a current density function in continuous space. The rotation angle can be continuously varied within a preset range. The rotation angles of the pre-encoder and each Rx-CAPA are optimized using an alternating optimization method until convergence, wherein: The optimization of the preencoder includes: fixing the positions of each Rx-CAPA, performing a Lagrangian dual transformation on the objective problem after introducing a first set of auxiliary variables to obtain an unconstrained optimization problem, and then alternately optimizing the first set of auxiliary variables and the preencoder. Specifically, when optimizing the first set of auxiliary variables with the preencoder fixed, the optimal solution of the first set of auxiliary variables is obtained by differentiating the objective function. When optimizing the preencoder with the first set of auxiliary variables fixed, a second set of auxiliary variables is introduced and a quadratic transformation is performed on the sub-objective function at this time. The optimal solution of the second set of auxiliary variables is obtained by differentiating the transformed sub-objective function. The preencoder is then solved directly in continuous space using a variational method. The optimization of the rotation angle of each Rx-CAPA includes: fixing the precoder, performing a second transformation on the objective problem by introducing a third set of auxiliary variables, obtaining the optimal solution of the third set of auxiliary variables by differentiating the objective function, and using the gradient ascent method to obtain the optimal rotation angle of each Rx-CAPA.

2. The spectral efficiency optimization method for rotatable continuous aperture arrays according to claim 1, characterized in that, In the rotatable CAPA system model, both the base station and each user are equipped with CAPAs, and the Rx-CAPA at the user's location can rotate within a preset angle range; the transmitting CAPA (Tx-CAPA) at the base station maintains a fixed position in space, and the main coordinate system in the system model is constructed with the center of the Tx-CAPA as the origin; an auxiliary coordinate system is constructed with the center of each Rx-CAPA as the origin, and each Rx-CAPA can rotate around one of the coordinate axes in the main coordinate system; the coordinates of any point on the plane where the Rx-CAPA is located in the main coordinate system are determined by the rotation matrix and the coordinates of the center point of the Rx-CAPA in the main coordinate system.

3. The spectral efficiency optimization method for rotatable continuous aperture arrays according to claim 1, characterized in that, The system rate , For the number of users, , For the first Rx-CAPA around the principal coordinate system Axis rotation angle, , To carry and send to the Pre-encoder of user data For user collection, The plane containing Tx-CAPA Let Tx-CAPA be the coordinates of any point. For noise power, This is the equivalent channel function after considering the receiver function.

4. The spectral efficiency optimization method for rotatable continuous aperture arrays according to claim 3, characterized in that, The spectral effect maximization optimization problem is expressed as: ； in, , For transmit power constraints.

5. The spectral efficiency optimization method for rotatable continuous aperture arrays according to claim 1, characterized in that, The first set of auxiliary variables is obtained by taking the derivative of the objective function. In the optimal solution, the optimal Represented as: ;in, For the number of users, The plane containing Tx-CAPA Let Tx-CAPA be the coordinates of any point. To carry and send to the Pre-encoder of user data To consider the equivalent channel function after the receiver function, For transmit power constraints, This represents noise power.

6. The spectral efficiency optimization method for rotatable continuous aperture arrays according to claim 1, characterized in that, The set of second auxiliary variables is obtained by taking the derivative of the objective function. In the optimal solution, the optimal Represented as: ;in, For the number of users, The plane containing Tx-CAPA Let Tx-CAPA be the coordinates of any point. To carry and send to the Pre-encoder of user data To consider the equivalent channel function after the receiver function, For transmit power constraints, For noise power, This is the optimal first auxiliary variable obtained.

7. The spectral efficiency optimization method for rotatable continuous aperture arrays according to claim 1, characterized in that, In the process of directly solving the precoder in continuous space using the variational method, the data is sent to the first... Precoder of user data Calculate using the following formula: ;in, , , , , , , It is the identity matrix. This indicates that the elements are arranged in a diagonal matrix. For the number of users, The plane containing Tx-CAPA Let Tx-CAPA be the coordinates of any point. To consider the equivalent channel function after the receiver function, For transmit power constraints, For noise power, The optimal first auxiliary variable obtained is... This is the optimal second auxiliary variable obtained.

8. The spectral efficiency optimization method for rotatable continuous aperture arrays according to claim 1, characterized in that, The set of third auxiliary variables is obtained by differentiating the objective function. In the optimal solution, the optimal Represented as: ;for , ;in, For user collection, For the number of users, The plane containing Tx-CAPA Let Tx-CAPA be the coordinates of any point. For the first The set of points of an Rx-CAPA in its auxiliary coordinate system. for The coordinates of any point on, To take rotation angle into account The receiving function, To take rotation angle into account The equivalent channel function after that, This represents noise power.

9. The spectral efficiency optimization method for rotatable continuous aperture arrays according to claim 8, characterized in that, Among the optimal rotation angles of each Rx-CAPA obtained using the gradient ascent method, the th... Rx-CAPA rotation angle at each user location The relevant gradient is represented as: ;in, Describe the objective function. Indicates taking the real part, for , about The gradient is: 。 10. A computer system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is loaded into the processor, it implements the spectral efficiency maximization precoding method for a rotatable continuous aperture antenna system according to any one of claims 1-9.

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