Laminated intelligent metasurface-assisted low-altitude holographic MIMO channel optimization fitting method

Abstract

The invention relates to a laminated intelligent metasurface-assisted low-altitude holographic MIMO channel optimization fitting method, and belongs to the technical field of digital communication. The method comprises the following steps: initializing system parameters, and determining beam forming matrixes of TX-SIM and RX-SIM; constructing a spatial correlation matrix of a transmitting and receiving end, and determining a spatial correlation holographic MIMO channel matrix, a singular value matrix and a scaling factor of an end-to-end channel; calculating channel fitting errors corresponding to a plurality of groups of preset super-atom phase shift configurations; and by taking minimization of a channel fitting error as an optimization target, carrying out iterative optimization on the super-atom phase shift by adopting a linear decline particle swarm optimization method, and obtaining and outputting optimal phase shift configuration. According to the method, the optimization problem caused by multilayer coupling and non-convex constraint of the laminated intelligent metasurface in a low-altitude dynamic environment is effectively solved, the global optimization capability is enhanced, the channel fitting error is reduced, and the channel capacity and the communication quality of a holographic MIMO system are improved.

Description

Technical Field

[0001] This invention belongs to the field of digital communication technology, specifically relating to a low-altitude holographic MIMO (HMIMO) channel optimization fitting method assisted by stacked smart metasurfaces (SIM). Background Technology

[0002] The innovative technology of Stacked Intelligent Metasurfaces (SIMs) has recently been demonstrated to enable advanced signal processing directly in the native Electro Magnetic (EM) wave domain. Unlike traditional MIMO systems with only active antennas, SIMs are tightly integrated with the transmitter (TX) and receiver (RX) to enhance Quality of Service (QoS). When applied to low-altitude communication scenarios, this technology provides an innovative solution to challenges such as the high-speed movement of nodes like UAV swarms and aerial platforms, complex channel variations, and the vulnerability of line-of-sight links to congestion. However, the dynamic low-altitude environment and the SIM's own structure present severe optimization challenges: SIMs are composed of complex stacked layers of metasurfaces, whose performance surpasses that of single-layer metasurfaces, but this also introduces highly coupled multi-layer joint control variables; simultaneously, the control of each metaatom must follow non-convex constant mode constraints. In the low-altitude context, the rapidly changing channel and the deep coupling of the SIM's multi-layer adjustable parameters make the overall system optimization problem exhibit strong non-convexity, making traditional algorithms prone to getting trapped in local optima and struggling to achieve the beamforming and intelligent channel reshaping capabilities that SIMs should possess in the dynamic spatial domain. Therefore, exploring new methods that can avoid local optima and efficiently solve this complex non-convex problem has become a key challenge in unleashing the full potential of low-altitude SIM.

[0003] In artificial electromagnetic materials, superatoms are the most basic structural units that make up metasurfaces. These units are typically subwavelength in size and possess specific electromagnetic resonance characteristics (such as electric resonance, magnetic resonance, etc.). By designing the shape, size, material, and surrounding environment of superatoms, their response to incident electromagnetic waves can be precisely controlled, that is, the phase, amplitude, polarization, and frequency of the waves they reflect or transmit can be controlled.

[0004] When optimizing parameters such as beam covariance matrix and SIM phase shift matrix, non-convexity problems that are difficult to solve inevitably arise. Therefore, there is an urgent need for a method that can efficiently and globally optimize SIM phase shift, thereby significantly reducing channel fitting error and improving system capacity. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a low-altitude holographic MIMO channel optimization fitting method assisted by stacked intelligent metasurfaces. This method solves the problems of strong non-convexity, easy getting trapped in local optima, and low computational efficiency in the joint optimization of holographic MIMO channels assisted by stacked intelligent metasurfaces in low-altitude dynamic environments. It can achieve global high-efficiency optimization, significantly reduce channel fitting error, and improve system capacity.

[0006] To achieve the above objectives, the technical solution adopted by this invention is as follows: a low-altitude holographic MIMO channel optimization and fitting method assisted by stacked intelligent metasurfaces, comprising the following steps:

[0007] S1. Initialize system parameters, including wavelength, transmission coefficient of each layer of superatoms in the transmitter-layered smart metasurface TX-SIM, and transmission coefficient of each layer of superatoms in the receiver-layered smart metasurface RX-SIM.

[0008] Based on the system parameters, the same-layer superatomic spacing and beamforming matrix of TX-SIM and RX-SIM are determined.

[0009] S2. Based on the same-layer superatomic spacing and beamforming matrix of TX-SIM and RX-SIM, construct the spatial correlation matrices of TX-SIM and RX-SIM respectively, and then determine the spatial correlation holographic MIMO channel matrix, singular value matrix and scaling factor of end-to-end channel.

[0010] S3. Based on the beamforming matrix of TX-SIM and RX-SIM, as well as the spatially correlated holographic MIMO channel matrix, singular value matrix, and scaling factor of the end-to-end channel, calculate the channel fitting error corresponding to the preset multiple sets of superatomic phase shift configurations respectively.

[0011] S4. With minimizing the channel fitting error as the optimization objective, the linear decreasing particle swarm optimization method is used to iteratively optimize the superatomic phase shifts of TX-SIM and RX-SIM to obtain the optimal phase shift configuration that minimizes the channel fitting error, including the optimized TX-SIM phase shift matrix, RX-SIM phase shift matrix and channel fitting error.

[0012] S5. The final channel fitting error is taken as the optimal channel fitting error, and the corresponding TX-SIM phase shift matrix and RX-SIM phase shift matrix are taken as the optimal phase shift outputs of TX-SIM and RX-SIM, respectively.

[0013] Further, in step S1, determining the same-layer superatomic spacing and beamforming matrix of TX-SIM and RX-SIM specifically includes:

[0014] S1.1 For a holographic MIMO far-field communication system based on stacked smart metasurfaces (SIM), the transmission coefficient of the superatoms is determined based on the phase shift of the superatoms on each layer of the TX-SIM and RX-SIM, and then the transmission coefficient matrix of each layer of the TX-SIM and RX-SIM is determined.

[0015] S1.2 Calculate the superatomic spacing on the same layer of the TX-SIM, the superatomic spacing on adjacent layers of the TX-SIM, and the superatomic spacing between the transmitting antenna and the first layer of the TX-SIM, and then determine the electromagnetic wave transmission coefficients between adjacent layers of the TX-SIM and between the transmitting antenna array and the TX-SIM.

[0016] S1.3 Calculate the superatomic spacing on the same layer of the RX-SIM, the superatomic spacing on adjacent layers of the RX-SIM, and the superatomic spacing between the receiving antenna and the first layer of the RX-SIM, and then determine the electromagnetic wave transmission coefficients between adjacent layers of the RX-SIM and between the receiving antenna array and the RX-SIM.

[0017] S1.4 Based on the transmission coefficient matrix of each layer of the TX-SIM metasurface and the electromagnetic wave transmission coefficient between adjacent layers of metasurface and between the transmitting antenna array and the metasurface, the beamforming matrix of the TX-SIM is constructed by cascading the layers.

[0018] Based on the transmission coefficient matrix of each metasurface layer of RX-SIM and the electromagnetic wave transmission coefficients between adjacent metasurface layers and between the receiving antenna array and the metasurface, the beamforming matrix of RX-SIM is constructed by cascading the layers.

[0019] Furthermore, the beamforming matrix of the TX-SIM is expressed as:

[0020]

[0021] in, , , These are respectively the Lth layer and the Lth layer of TX-SIM. Transmission coefficient matrix of the first layer metasurface; , These represent the areas between the (L-1)th and Lth layers of the TX-SIM metasurface, and the... Layer and First Electromagnetic wave transmission coefficient between metasurface layers; is the electromagnetic wave transmission coefficient between the transmitting antenna array and the first layer metasurface;

[0022] The beamforming matrix of the RX-SIM is represented as follows:

[0023]

[0024] in, , , These are respectively the first layer of RX-SIM, the second layer... Transmission coefficient matrix of the first and Kth layer metasurfaces; , For RX-SIM, the first Layer and First Electromagnetic wave transmission coefficients between metasurface layers and between the (K-1)th and Kth metasurface layers; denoted as the electromagnetic wave transmission coefficient between the first-layer metasurface and the receiving antenna array.

[0025] Further, in step S2, the spatial correlation matrices of TX-SIM and RX-SIM are constructed to determine the scaling factor of the prediction channel, the spatially correlated holographic MIMO channel, and the singular value matrix, specifically including:

[0026] S2.1. Based on the same-layer superatomic spacing of TX-SIM and RX-SIM, calculate the spatial correlation matrix of TX-SIM and RX-SIM respectively;

[0027] S2.2. Generate a spatially correlated holographic MIMO channel matrix based on the spatial correlation matrices of TX-SIM and RX-SIM. ,in The Rayleigh fading channel matrix is ​​independent and identically distributed;

[0028] S2.3, Spatial Correlation Holographic MIMO Channel Matrix Perform singular value decomposition to obtain the singular value matrix, and calculate the end-to-end channel matrix;

[0029] S2.4. Based on the least squares relationship between the end-to-end channel matrix and the singular value matrix, the scaling factor of the end-to-end channel is calculated.

[0030] Furthermore, in step S3, for each group of superatomic phase shift configurations, the corresponding channel fitting error is calculated according to the following formula. :

[0031]

[0032] in, This is the scaling factor for the end-to-end channel. For TX-SIM beamforming matrix, For the beamforming matrix of RX-SIM, For spatially correlated holographic MIMO channel matrix, It is a singular value matrix. The Frobenius norm is used to characterize the fitting error of the desired channel fitting problem.

[0033] Furthermore, in step S4, the superatomic phase shifts of TX-SIM and RX-SIM are iteratively optimized using a linear decreasing particle swarm optimization method, specifically including:

[0034] S4.1 Initialize a set of random particles, each particle i is assigned a position. and speed Two attributes; of which, position Representing the superatomic phase shift combination of TX-SIM and RX-SIM, velocity This represents the magnitude of the phase shift change;

[0035] S4.2, calculate the channel fitting error of the multiple sets of superatomic phase shift configurations obtained in step S3. The fitness of each particle is calculated as an input parameter. : ;

[0036] S4.3, Perform iterative optimization:

[0037] Update individual optimal solution and the global optimal solution ;

[0038] Update the particle's velocity and position according to the following formula:

[0039]

[0040]

[0041] in, Indicates the current iteration number. , Let represent the velocities of the particles in the t-th and t+1-th iterations, respectively. , These represent the positions of the particles in the t-th and t+1-th iterations, respectively. For inertial weights, and For learning factors;

[0042] S4.4 Update the inertia weights using a linear decreasing strategy. Learning factors and Then return to step S4.3 and continue iterating until the iteration termination condition is met;

[0043] S4.5 Output the optimized superatomic phase shift combination and channel fitting error, that is, obtain the optimized TX-SIM phase shift matrix, RX-SIM phase shift matrix and channel fitting error.

[0044] Furthermore, a linear decreasing strategy is adopted to update the inertia weights. , means as follows:

[0045]

[0046] in, Let be the inertia weight for the t-th iteration. The maximum number of iterations, and These are the maximum and minimum values ​​set, respectively.

[0047] The learning factor is updated using a linear decreasing strategy. and , means as follows:

[0048]

[0049]

[0050] in, , The learning factors for the t-th iteration are respectively , , , Learning factors The maximum and minimum values, , Learning factors The maximum and minimum values.

[0051] The present invention also provides a computer device, comprising: at least one processor, at least one memory, and computer program instructions stored in the memory, which implement the above-described method when executed by the processor.

[0052] The present invention also provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the above-described method.

[0053] Compared with existing technologies, this invention has the following advantages: The low-altitude holographic MIMO channel optimization and fitting method assisted by stacked intelligent metasurfaces proposed in this invention solves the non-convexity problem that is difficult to solve when optimizing parameters such as beam covariance matrix and SIM phase shift matrix through an iterative optimization swarm intelligent search method. This invention first randomly selects several sets of transceiver hyperatomic phase shifts to obtain the beamforming matrix, then obtains the expected diagonal matrix through staged singular value decomposition based on the spatially correlated channel model, and obtains the scaling factor through the least squares method. Then, it constructs a channel fitting problem model, and finally uses a linear decreasing particle swarm optimization method based on hyperatomic phase shift optimization to obtain the optimal solution for the transceiver transmission phase shift matrix and fitting error. This method has stronger global optimization capabilities, effectively avoids getting trapped in local optima, significantly reduces channel fitting error, improves system capacity, and has relatively low computational cost, thus improving optimization efficiency. Attached Figure Description

[0054] Figure 1 This is a flowchart illustrating the implementation of the low-altitude holographic MIMO channel optimization and fitting method assisted by stacked intelligent metasurfaces provided in this embodiment of the invention.

[0055] Figure 2 This is a model diagram of a SIM-assisted HMIMO communication system in an embodiment of the present invention;

[0056] Figure 3 This is a flowchart of the SIM-assisted wave domain beamforming method in an embodiment of the present invention;

[0057] Figure 4 This is a flowchart of the expected channel scaling factor calculation method in an embodiment of the present invention;

[0058] Figure 5 This is a flowchart of the SIM end-to-end channel fitting error calculation method in an embodiment of the present invention;

[0059] Figure 6 This is a flowchart of the linear decreasing particle swarm optimization method for superatomic phase shift optimization in this embodiment of the invention;

[0060] Figure 7 This is a graph showing the NMSE variation with the number of metasurface layers under different schemes in the embodiments of the present invention;

[0061] Figure 8 This is a graph showing the NMSE variation under different schemes in this invention, where the inertial weight changes. Detailed Implementation

[0062] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0063] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0064] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0065] like Figure 1 As shown in the figure, this embodiment provides a low-altitude holographic MIMO channel optimization fitting method assisted by stacked intelligent metasurfaces, and its specific implementation process is as follows.

[0066] S1. Initialize system parameters, including: wavelength λ, transmittance coefficient of superatoms on the emitter-layered smart metasurface (TX-SIM). and the transmission coefficient of superatoms on the receiver-stacked smart metasurface (RX-SIM) The TX-SIM has S antennas and L metasurfaces, each containing M superatoms arranged in a square uniform arrangement; the RX-SIM has S antennas and K metasurfaces, each containing N superatoms arranged in a square uniform arrangement.

[0067] Transmitter The first layer on the supersurface Transmission coefficient of a superatom It can be represented as:

[0068] (1)

[0069] in, This indicates the phase shift of the superatom, and , .

[0070] Receiver The first layer on the supersurface Transmission coefficient of a superatom It can be represented as:

[0071] (2)

[0072] in, This indicates the phase shift of the superatom, and , .

[0073] Based on the system parameters, i.e. , and Determine the in-layer superatomic spacing of TX-SIM and beamforming matrix and the same-layer superatomic spacing of RX-SIM and beamforming matrix The specific implementation steps are as follows.

[0074] S1.1, For holographic MIMO far-field communication systems based on stacked smart metasurface SIMs (such as...) Figure 2 As shown), both the transceiver and receiver are SIMs, and the TX-SIM and RX-SIM are parallel to each other and perpendicular to each other. Axis; provided A data stream, and These represent the number of metasurface layers at the transmitter and receiver, respectively, with each layer having the same number of superatoms; each metasurface layer at the transmitter has... Each superatom has a receiving end metasurface with [number] superatoms. One superatom, and All greater than or equal to All of them are arranged in a square; the S transmitting antennas are spaced at intervals of A uniform linear array, perpendicular to The plane, whose distance from the first metasurface is equal to Furthermore, the center of the antenna array is aligned with the centers of all metasurface arrays. The TX-SIM's... The first layer on the supersurface The transmission coefficient of each superatom is: .in, , representing the phase shift of the superatom. Then, the TX-SIM... The transmission coefficient vector of the layered metasurface is expressed as: Its matrix form, namely TX-SIM, is... The transmission coefficient matrix of the layered metasurface is Similarly, RX-SIM's... The first layer on the supersurface The transmission coefficient of each superatom is: .in, , representing the phase shift of the superatom. Then, the RX-SIM... The transmission coefficient vector of the layered metasurface is expressed as: Its matrix form, namely RX-SIM, is... The transmission coefficient matrix of the layered metasurface is: . and It can be understood as an exponential phase shift matrix.

[0075] S1.2 and TX-SIM are two concentric superatoms. and distance The following formula can be used for calculation:

[0076] (3)

[0077] in, is a real number representing the distance between two adjacent superatoms; This indicates that TX-SIM superatoms are in Distance index along the axial direction; Indicates the nearest greater than or equal to integers, This indicates that TX-SIM superatoms are in The distance index along the axis, and return Divide by The remainder after that.

[0078] The distance between two adjacent superatoms in TX-SIM The following formula can be used for calculation:

[0079] (4)

[0080] in, is a real number representing the spacing between adjacent layers in TX-SIM.

[0081] Assume the transmitter is used for launching. A data stream The transmitting antennas are arranged at intervals of 1 / 2. A uniform linear array, perpendicular to The plane; its distance from the first metasurface is also equal to Furthermore, the center of the antenna array is aligned with the center of all metasurface arrays.

[0082] Therefore, the s-th antenna at TX-SIM and the th antenna on the first layer of the supersurface The spacing between superatoms The following formula can be used for calculation:

[0083] (5)

[0084] TX-SIM from the first The first layer on the surface of the metasurface From the first superatom to the... The first layer on the surface of the metasurface Electromagnetic wave transmission coefficient of a superatom The following formula can be used for calculation:

[0085] (6)

[0086] in, is a real number representing the area of ​​each superatom; Indicates the direction of signal propagation and the first The angle between the normal directions of the metasurface layers is determined by the superatoms. and The actual physical location is measured and calculated. The electromagnetic wave transmission coefficient between the transmitting antenna and the metasurface is calculated by using equation (6). Replace with This can be calculated.

[0087] S1.3 and RX-SIM are two concentric superatoms. and distance The following formula can be used for calculation:

[0088] (7)

[0089] in, The digit is a real number, representing the distance between two adjacent superatoms in the RX-SIM. This represents the distance exponent of the RX-SIM superatoms along the z-axis. This indicates that RX-SIM superatoms are in Distance index along the axis.

[0090] Therefore, the distance between two adjacent superatoms in RX-SIM The following formula can be used for calculation:

[0091] (8)

[0092] in, is a real number representing the spacing between adjacent layers in the RX-SIM.

[0093] Therefore, at RX-SIM, the s-th receiving antenna and the th antenna on the first layer of the metasurface... Superatomic spacing , can be represented as:

[0094] (9)

[0095] RX-SIM from the first The first layer on the surface of the metasurface From the first superatom to the... The first layer on the surface of the metasurface Electromagnetic wave transmission coefficient of a superatom The following formula can be used for calculation:

[0096] (10)

[0097] in, Let be a real number representing the area of ​​each superatom. Indicates the direction of signal propagation and the first The angle between the normal directions of the metasurface layers is determined by the superatoms. and The actual physical location is measured and calculated. The electromagnetic wave transmission coefficient between the receiving antenna and the metasurface is calculated by using equation (6). Replace with This can be calculated.

[0098] S1.4. Based on the transmission coefficient matrix of each metasurface layer of TX-SIM and the electromagnetic wave transmission coefficients between adjacent metasurface layers and between the transmitting antenna array and the metasurface, construct a wave domain-based TX-SIM by cascading layer-by-layer. 3D beamforming matrix , can be represented as:

[0099] (11)

[0100] in, It is an integer, and its value range is 1. ; for A complex matrix of dimension 1, representing the TX-SIM 1-th dimension. The exponential phase shift of the layered metasurface, i.e., the transmission coefficient matrix of TX-SIM; for A complex matrix of dimension 1, representing the TX-SIM 1st dimension. Layer and First Electromagnetic wave transmission coefficient between metasurface layers; for The 3D complex matrix represents the electromagnetic wave transmission coefficient between the transmitting antenna array and the first layer of the transmitter metasurface.

[0101] Based on the transmission coefficient matrix of each metasurface layer of RX-SIM and the electromagnetic wave transmission coefficients between adjacent metasurface layers and between the receiving antenna array and the metasurface, a wave domain-based RX-SIM is constructed by cascading the layers. 3D beamforming matrix , can be represented as:

[0102] (12)

[0103] in, It is an integer, and its value range is 1. ; for A complex matrix of dimension 1, representing the RX-SIM 1-th dimension. The exponential phase shift of the layered metasurface, i.e., the transmission coefficient matrix of RX-SIM; for A complex matrix of dimension 1, representing the RX-SIM 1-th dimension. Layer and First Electromagnetic wave transmission coefficient between metasurface layers; for The 3D complex matrix represents the electromagnetic wave transmission coefficient between the first layer of the receiver metasurface and the receiving antenna array.

[0104] S1.5, Output , , , and .

[0105] Figure 3 The implementation flow of the SIM-assisted wave domain beamforming method in this embodiment is shown. It can be seen that it is mainly achieved through the following steps: First, the wavelength is initialized. TX-SIM superatomic transmission coefficient RX-SIM superatomic transmission coefficient Next, the transmissivity of the superatomic layer is calculated. , Then, the superatomic physical positions are calculated using TX-SIM. , , Next, the physical positions of the superatoms are calculated using RX-SIM. , , Subsequently, the TX-SIM based wave domain was calculated. 3D beamforming matrix RX-SIM is based on the wave domain. 3D beamforming matrix Finally, output , , , , .

[0106] S2, based on wavelength In-slice superatomic spacing of TX-SIM and beamforming matrix Superatomic spacing in the same layer as RX-SIM and beamforming matrix Construct the spatial correlation matrix of TX-SIM respectively. ( Spatial correlation matrix of 1D and RX-SIM ( dimension).

[0107] S2.1. Based on the same-layer superatomic spacing of TX-SIM and RX-SIM, calculate the spatial correlation matrix of TX-SIM and RX-SIM respectively.

[0108] Spatial correlation matrix of TX-SIM It can be represented as:

[0109] (13)

[0110] Spatial correlation matrix of RX-SIM It can be represented as:

[0111] (14)

[0112] in, This is the Singer function.

[0113] based on , , , and Calculations yielded 3D spatial correlation holographic MIMO channel , Vickers Matrix Scaling factor of end-to-end channel The specific implementation steps are as follows.

[0114] S2.2, Generate the metasurface from the TX-SIM output metasurface to the RX-SIM input metasurface. 3D spatial correlation holographic MIMO channel matrix , can be represented as:

[0115] (15)

[0116] in, for The Rayleigh fading channel matrix is ​​an independent and identically distributed matrix. and They represent TX-SIM and Spatial correlation matrix at RX-SIM; spatial correlation matrices of TX-SIM and RX-SIM for far-field propagation in an isotropic scattering environment. and It can be obtained from equations (13) and (14).

[0117] The path loss between transceivers can be expressed as:

[0118] (16)

[0119] The first item represents the reference distance. Free space path loss, Represents the path loss index. The standard deviation is A zero-mean Gaussian random variable is used to characterize large-scale signal fluctuations in shadow fading. This refers to the actual distance between the transceivers.

[0120] S2.3, Given a wireless channel and a fixed number of data streams Optimal holographic MIMO transmission is achieved by applying the truncated singular value decomposition (SVD) method. Truncated SVD is a low-rank approximation of SVD, which preserves the first rank of the singular value decomposition (SVD) while maintaining the first rank. The largest singular value and its corresponding singular vector are taken, and the rest are discarded, thus obtaining a new original matrix. (The rank may be very high) It is approximated as a rank of matrix .

[0121] First of all, Performing singular value decomposition, we have:

[0122] (17)

[0123] Therefore, we obtain Vickers Matrix , Left-dimensional singular matrix as well as 3D right singular matrix superscript This represents the calculation of the conjugate matrix; where, , ,and .

[0124] Then, take the left singular matrix. The former The line is used as the receiver's receiving matrix Take the right singular matrix The former The column serves as the encoding matrix of the transmitter pre-encoder. The end-to-end channel matrix can be calculated. as follows:

[0125] (18)

[0126] S2.4 To maximize channel capacity, resource allocation can be performed using information-theoretic water-filling calculations. This involves allocating higher power to channels with better quality and lower power to channels with poorer quality, and allocating power to each data stream accordingly. as follows:

[0127] (19)

[0128] in, is a real number, representing the decision threshold set to satisfy the total power constraint, and can be obtained by the bisection method; is a real number representing the average noise power at the receiver; For the first Individual channel singular values.

[0129] Information-theoretic water-filling is a classic resource allocation strategy. Given a limited total power, it allocates more power to sub-channels with good channel conditions and less or no power to sub-channels with poor channel conditions, thereby maximizing the total system capacity. The optimal power allocation solution of the water-filling method is: .in, This represents the equivalent noise height of the sub-channel; a smaller value indicates better channel conditions. It is the "water level line," whose value is adjusted iteratively to ensure that the allocated sub-channel power meets the total power constraint. .

[0130] The bisection method is used to solve for the optimal water level in water injection power allocation. It is an important numerical tool. It utilizes power and the function about By exploiting the monotonicity of the binary search algorithm, and through continuous binary guessing and verification, the "water level" that perfectly satisfies the total power constraint is quickly and accurately found, thus achieving optimal power allocation. The binary search iterative process is as follows: Initialize the lower bound of the iteration interval. and the Upper Realm Take the midpoint of the current interval. ;Will Substituting into the water injection formula, the power of each channel is calculated. If at this time Then let Conversely, then let Repeated updates Until the difference between the two reaches the expected value.

[0131] Therefore, the channel capacity C of holographic MIMO communication with a finite data stream can be expressed as:

[0132] (20)

[0133] Then, the end-to-end channel matrix is ​​minimized by optimizing the phase shifts of TX-SIM and RX-SIM. With singular value matrix The error between the two is characterized by the Frobenius norm, which represents the fitting error of the desired channel fitting problem. The channel fitting error is then expressed as:

[0134] (twenty one)

[0135] in, is a real number representing the scaling factor of the end-to-end channel.

[0136] In the field of matrices, the Frobenius norm is a very important metric used to measure the size or complexity of a matrix. For a given matrix... dimensional matrix The Frobenius norm (also known as the F-norm or Hilbert-Schmidt norm) of a matrix is ​​defined as the square root of the sum of the squares of the absolute values ​​of all its elements. Mathematically, it is expressed as: .in, It is a matrix No. Line 1 The elements of the column.

[0137] For matrix and Vectorization converts the matrix form into vectors, yielding the following results: dimensional vector and ;right and And it is calculated and updated by the least squares method. .

[0138] S2.5, Output , and .

[0139] Least squares (LS) is an optimization method that best fits a data model by minimizing the sum of squared errors between predicted and observed values. Its solutions have clear geometric meaning and good statistical properties, making it a cornerstone tool for data analysis and parameter estimation in science and engineering. It assumes the model is a linear function of the parameters: The matrix form is: .in, yes 3D observation vector, yes 3D design matrix yes The parameter vector to be determined yes The error vector is dimensional. Then the least squares objective function (sum of squared residuals) is: .

[0140] Figure 4 The implementation flow of the expected channel scaling factor calculation method in this embodiment is shown. It can be seen that it is mainly implemented through the following steps: First, initialization... , , , , Then, calculate the channel matrix. ,right Perform truncated singular value decomposition to obtain Vickers Matrix , Left-dimensional singular matrix ,and 3D right singular matrix And calculate the end-to-end matrix. Next, the power allocation is achieved using a water injection method; subsequently, the scaling factor is updated using a least squares method. Finally, output , , .

[0141] S3. Beamforming matrix based on TX-SIM obtained in step S1 Beamforming matrix of RX-SIM and the scaling factor obtained in step S2 Spatial correlation holographic MIMO channel matrix and singular value matrix Calculate the first Channel fitting error corresponding to group phase shift .like Then let If the condition is not met, proceed to step S1; otherwise, proceed to step S4, thereby obtaining the channel fitting errors corresponding to the preset multiple sets of superatomic phase shift configurations. A positive integer, representing the current phase shift group number. The total number of phase shift groups is preset. The specific implementation steps are as follows.

[0142] S3.1, Externally input parameters: TX-SIM beamforming matrix RX-SIM beamforming matrix Scaling factor for prediction channel , 3D spatial correlation holographic MIMO channel and Vickers Matrix .

[0143] S3.2 Minimize the end-to-end channel matrix by optimizing the phase shifts of TX-SIM and RX-SIM. With singular value matrix The error between these values ​​is characterized by the Frobenius norm, which represents the fitting error of the desired channel fitting problem. For each set of superatomic phase shift configurations, the corresponding channel fitting error is calculated according to the following formula. :

[0144]

[0145] in, This is the scaling factor for the end-to-end channel. For TX-SIM beamforming matrix, For the beamforming matrix of RX-SIM, For spatially correlated holographic MIMO channel matrix, It is a singular value matrix. The Frobenius norm is used to characterize the fitting error of the desired channel fitting problem.

[0146] The optimization problem can then be modeled as:

[0147] (twenty two)

[0148] Among them, (a) Indicates the channel fitting error. The scaling factor compensated by SIM. The expected diagonal matrix has values ​​that are... The diagonal matrix obtained after performing singular value decomposition and sorting the eigenvalues ​​from largest to smallest; (b) and (c) represent the channel responses of TX-SIM and RX-SIM, respectively; in (d) , indicating the first transmitter The first layer on the supersurface The transmission coefficient of each superatom, and Indicates the corresponding phase shift; in (e) , indicating the receiving end The first layer on the supersurface The transmission coefficient of each superatom, and The corresponding phase shift is represented by (f) and (g), which are constant mode constraints.

[0149] S3.3 Calculate and output the channel fitting errors corresponding to the preset multiple sets of superatomic phase shift configurations.

[0150] Figure 5The implementation flow of the SIM end-to-end channel fitting error calculation method in this embodiment is shown. It can be seen that it is mainly implemented through the following steps: First, in the initial iteration, the data passed in the previous step is used to calculate the corresponding beamforming matrix for each group of phase shifts. and At the same time, the scaling factor is obtained. Spatial-dependent HMIMO channels and singular value matrix Next, the end-to-end channel is minimized by optimizing the phase shifts of TX-SIM and RX-SIM. With the expected diagonal matrix The error between the phase shift parameters is characterized by the Frobenius norm to represent the fitting error of the desired channel fitting problem. Finally, the fitting error of each set of phase shift parameters is calculated and compared with the fitting error of that set. Output as an output parameter.

[0151] S4. Obtained from step S1 , , and and the result obtained in step S3 Using the input parameters and minimizing the channel fitting error as the optimization objective, a linear decreasing particle swarm optimization method is employed to iteratively optimize the superatomic phase shifts of TX-SIM and RX-SIM, obtaining the optimal phase shift configuration that minimizes the channel fitting error, including the optimized TX-SIM phase shift matrix. RX-SIM phase shift matrix and channel fitting error This achieves phase optimization. If the current iteration number... If yes, proceed to step S5; otherwise, let... And jump to step S1; where, This is the preset maximum number of iterations. To preset the maximum number of iterations, For positive integers, the minimum mean square error is achieved. exist The following convergence requirements are outlined, and their specific implementation steps are as follows.

[0152] S4.1, Externally input parameters: TX-SIM beamforming matrix RX-SIM beamforming matrix TX-SIM superatomic transmission coefficient RX-SIM superatomic transmission coefficient and channel fitting error .

[0153] Initialize a set of random particles, and assign a position to each particle i. and speed Two attributes; one of which is the particle position. The superatomic phase shift combination representing TX-SIM and RX-SIM, while particle velocity Represents the magnitude of phase shift change; particles exist The position in 3D space can be represented by a vector:

[0154] (twenty three)

[0155] in, Indicates the first The emitter of the first particle The transmission coefficient vector of the layered metasurface. Indicates the first The receiver of the particle The transmission coefficient vector of the metasurface layer; and the particle velocity vector is expressed as:

[0156] (twenty four)

[0157] S4.2, calculate the channel fitting error of the multiple sets of superatomic phase shift configurations obtained in step S3. The fitness of each particle is calculated as an input parameter. :

[0158] (25)

[0159] S4.3, Perform iterative optimization.

[0160] Update individual optimal solution and the global optimal solution .

[0161] Update the particle's velocity and position.

[0162] In the first iteration, the particle velocity obtained in step S4.1 is... and location The updated values ​​are used as input parameters in subsequent iterations; each particle finds its own optimal solution by tracking itself. and the current optimal solution for each individual in the entire population This is used to update its speed and position.

[0163] The particle velocity is updated using the following formula:

[0164] (26)

[0165] in, Indicates the current iteration number. , Let represent the velocities of the particles in the t-th and t+1-th iterations, respectively. For inertial weights, and These are learning factors, all of which were initialized during the first iteration.

[0166] The particle's position is updated using the following formula:

[0167] (27)

[0168] in, , These represent the positions of the particles in the t-th and t+1-th iterations, respectively.

[0169] From particle position The iterative updates derive the optimized phase shift of the superatoms. The optimization process terminates when the convergence condition is met or the maximum iteration count is reached; typically, the obtained phase configuration needs to be combined with power allocation to determine the achievable channel capacity.

[0170] S4.4, Update Variables , and The inertia coefficient controls the contribution of the current particle velocity to the next velocity, balancing the algorithm's exploration and development capabilities; given a relatively large... As particles continue to move at high speeds, they tend to explore new regions, enhancing their global search capabilities, but they are prone to missing local optima; conversely, when... When the particle velocity is small, the particle velocity decays rapidly and tends towards a local fine-grained search to accelerate convergence, but it is prone to getting trapped in local optima; typically, dynamic... This approach achieves better results than using a fixed value. Therefore, a linear decreasing strategy is adopted to update the inertia weights. , means as follows:

[0171] (28)

[0172] in, Let be the inertia weight for the t-th iteration. The maximum number of iterations, and These are the maximum and minimum values ​​set, respectively.

[0173] Similarly, adoption and updating Using the same linear decreasing strategy, update the calculated learning factor. and , means as follows:

[0174] (29)

[0175] (30)

[0176] in, , The learning factors for the t-th iteration are respectively , , , Learning factors The maximum and minimum values, , Learning factors The maximum and minimum values.

[0177] By adjusting the inertia weights and learning factors, the linearly decreasing inertia weight method effectively avoids oscillations and premature convergence caused by excessively large or small inertia weights, thereby improving the robustness of the method.

[0178] Repeat steps S4.3-S4.4 until the iteration termination condition is met, then stop the iteration optimization.

[0179] S4.5 Output the optimized superatomic phase shift combination and channel fitting error This yields the optimized TX-SIM phase shift matrix, RX-SIM phase shift matrix, and channel fitting error.

[0180] S5. The channel fitting error finally obtained in step S4 is... As the optimal channel fitting error and the corresponding TX-SIM phase shift matrix and RX-SIM phase shift matrix These are used as the optimal phase shift outputs for TX-SIM and RX-SIM, respectively.

[0181] Figure 6 The implementation flow of the linear decreasing particle swarm optimization method for superatomic phase shift optimization in this embodiment is shown. It can be seen that it is mainly implemented through the following steps: First, in the initial iteration, the phase shifts obtained from TX-SIM and RX-SIM are initialized into a set of random particles, and the position and velocity attributes of each particle are initialized. At this time, the particle position is understood as a combination of phase shifts, while the velocity represents the magnitude of the phase shift change. exist The position in 3D space is represented by a vector. Next, the fitting error for each set of phase shifts is obtained. As an input parameter, the fitness is assigned to each particle. ,Right now Next, each particle finds its own optimal solution by tracking itself. and the current optimal solution for each individual in the entire population This updates its position and velocity. Then, the inertia weights are updated according to a linearly decreasing strategy. and learning factors , Output the updated fitting error Phase shift , .

[0182] Figure 1 This embodiment illustrates the implementation flow of the low-altitude holographic MIMO channel optimization and fitting method assisted by stacked intelligent metasurfaces. It can be seen that it is mainly implemented through the following steps: First, the TX-SIM antenna transmits a signal, which undergoes phase changes through each layer of metasurfaces. After propagating in free space, the signal is processed by the metasurface layer at the RX-SIM end and then received. and The beamforming matrices for the transceiver end are defined in the wave domain. Then, based on the spatially correlated channel model, the expected diagonal matrix is ​​calculated using stage singular value decomposition. Finally, the scaling factor is updated using the least squares criterion. Subsequently, several sets of transmit and receive phase shifts are randomly initialized, and the parameters required for the error calculation method are obtained according to the above steps, thereby obtaining the first... Channel fitting error for each phase shift Next, , and As input parameters, a linear decreasing particle swarm optimization method combined with superatomic phase shift optimization is used to perform the phase optimization process, and the loss function value is calculated. As fitness, the TX-SIM phase shift matrix at this time is... and TX-SIM phase shift matrix Return to step one; finally, if the convergence condition is met, output the optimal value of the fitting error based on the results of the previous step. and the optimal phase shift matrix , .

[0183] Figure 7 This is a comparison chart showing the variation of NMSE with the number of metasurface layers under different schemes in this embodiment. Figure 7 In the middle, the curves corresponding to the three algorithms are for Significant differences were observed, especially for Due to its complex algorithm and significantly increased computational load, Adam-GD... This significantly reduces NMSE. However, as the number of TX-SIM metasurface layers increases, its performance cannot surpass the method proposed in this invention, LD-PSO. Furthermore, the proposed method LD-PSO, due to its lower computational cost, is significantly superior to the GD algorithm. Especially... At that time, the mean squared error of the two algorithms differed by 8.54 dB. This also indicates that the method proposed in this invention has a stronger global optimization capability.

[0184] Figure 8 In this embodiment, NMSE varies with inertia weight under different schemes. A comparison chart of changes. Figure 8 In the middle, we obtain (28) The algorithm performance is significantly better than the fixed one. This is due to the fact that when the number of superatoms is small, given a larger... Particles tend to explore new regions, enhancing global search capabilities. However, when the number of superatoms is large, given a smaller... Particles tend to engage in localized, fine-grained searches. When When fixed at 0.01 and 0.05, the mean square error gradually decreases until... Then, due to the increase in the number of TX-SIM layers, the dimension of the particles simultaneously increases, and the fixed... While a better channel fit cannot be achieved, selecting an appropriate dropout range can significantly reduce the impact. This can be achieved by fixing the channel in the later stages. This strategy increases NMSE, but also reduces achievable channel capacity. compared to, It maintains a more stable positive gain in terms of channel capacity.

[0185] This embodiment also provides a computer device, including: at least one processor, at least one memory, and computer program instructions stored in the memory, which implement the above-described method when executed by the processor.

[0186] This embodiment also provides a computer-readable storage medium storing computer program instructions that, when executed by a processor, implement the above-described method.

[0187] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0188] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0189] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0190] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0191] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for optimizing and fitting low-altitude holographic MIMO channels assisted by stacked intelligent metasurfaces, characterized in that, Includes the following steps: S1. Initialize system parameters, including wavelength, transmission coefficient of each layer of superatoms in the transmitter-layered smart metasurface TX-SIM, and transmission coefficient of each layer of superatoms in the receiver-layered smart metasurface RX-SIM. Based on the system parameters, the same-layer superatomic spacing and beamforming matrix of TX-SIM and RX-SIM are determined. S2. Based on the same-layer superatomic spacing and beamforming matrix of TX-SIM and RX-SIM, construct the spatial correlation matrices of TX-SIM and RX-SIM respectively, and then determine the spatial correlation holographic MIMO channel matrix, singular value matrix and scaling factor of end-to-end channel. S3. Based on the beamforming matrix of TX-SIM and RX-SIM, as well as the spatially correlated holographic MIMO channel matrix, singular value matrix, and scaling factor of the end-to-end channel, calculate the channel fitting error corresponding to the preset multiple sets of superatomic phase shift configurations respectively. S4. With minimizing the channel fitting error as the optimization objective, the linear decreasing particle swarm optimization method is used to iteratively optimize the superatomic phase shifts of TX-SIM and RX-SIM to obtain the optimal phase shift configuration that minimizes the channel fitting error, including the optimized TX-SIM phase shift matrix, RX-SIM phase shift matrix and channel fitting error. S5. The final channel fitting error is taken as the optimal channel fitting error, and the corresponding TX-SIM phase shift matrix and RX-SIM phase shift matrix are taken as the optimal phase shift outputs of TX-SIM and RX-SIM, respectively.

2. The low-altitude holographic MIMO channel optimization and fitting method assisted by stacked intelligent metasurfaces according to claim 1, characterized in that, In step S1, the same-layer superatomic spacing and beamforming matrix of TX-SIM and RX-SIM are determined, specifically including: S1.1 For a holographic MIMO far-field communication system based on stacked smart metasurfaces (SIM), the transmission coefficient of the superatoms is determined based on the phase shift of the superatoms on each layer of the TX-SIM and RX-SIM, and then the transmission coefficient matrix of each layer of the TX-SIM and RX-SIM is determined. S1.2 Calculate the superatomic spacing on the same layer of the TX-SIM, the superatomic spacing on adjacent layers of the TX-SIM, and the superatomic spacing between the transmitting antenna and the first layer of the TX-SIM, and then determine the electromagnetic wave transmission coefficients between adjacent layers of the TX-SIM and between the transmitting antenna array and the TX-SIM. S1.3 Calculate the superatomic spacing on the same layer of the RX-SIM, the superatomic spacing on adjacent layers of the RX-SIM, and the superatomic spacing between the receiving antenna and the first layer of the RX-SIM, and then determine the electromagnetic wave transmission coefficients between adjacent layers of the RX-SIM and between the receiving antenna array and the RX-SIM. S1.4 Based on the transmission coefficient matrix of each layer of the TX-SIM metasurface and the electromagnetic wave transmission coefficient between adjacent layers of metasurface and between the transmitting antenna array and the metasurface, the beamforming matrix of the TX-SIM is constructed by cascading the layers. Based on the transmission coefficient matrix of each metasurface layer of RX-SIM and the electromagnetic wave transmission coefficients between adjacent metasurface layers and between the receiving antenna array and the metasurface, the beamforming matrix of RX-SIM is constructed by cascading the layers.

3. The low-altitude holographic MIMO channel optimization and fitting method assisted by stacked intelligent metasurfaces according to claim 2, characterized in that, The beamforming matrix of the TX-SIM is represented as follows: in, , , These are respectively the Lth layer and the Lth layer of TX-SIM. Transmission coefficient matrix of the first layer metasurface; , These represent the areas between the (L-1)th and Lth layers of the TX-SIM metasurface, and the... Layer and First Electromagnetic wave transmission coefficient between metasurface layers; is the electromagnetic wave transmission coefficient between the transmitting antenna array and the first layer metasurface; The beamforming matrix of the RX-SIM is represented as follows: in, , , These are respectively the first layer of RX-SIM, the second layer... Transmission coefficient matrix of the first and Kth layer metasurfaces; , For RX-SIM, the first Layer and First Electromagnetic wave transmission coefficients between metasurface layers and between the (K-1)th and Kth metasurface layers; denoted as the electromagnetic wave transmission coefficient between the first-layer metasurface and the receiving antenna array.

4. The low-altitude holographic MIMO channel optimization and fitting method assisted by stacked intelligent metasurfaces according to claim 1, characterized in that, In step S2, the spatial correlation matrices of TX-SIM and RX-SIM are constructed to determine the scaling factor of the prediction channel, the spatially correlated holographic MIMO channel, and the singular value matrix. Specifically, this includes: S2.

1. Based on the same-layer superatomic spacing of TX-SIM and RX-SIM, calculate the spatial correlation matrix of TX-SIM and RX-SIM respectively; S2.

2. Generate a spatially correlated holographic MIMO channel matrix based on the spatial correlation matrices of TX-SIM and RX-SIM. ,in The Rayleigh fading channel matrix is ​​independent and identically distributed; S2.3, Spatial Correlation Holographic MIMO Channel Matrix Perform singular value decomposition to obtain the singular value matrix, and calculate the end-to-end channel matrix; S2.

4. Based on the least squares relationship between the end-to-end channel matrix and the singular value matrix, the scaling factor of the end-to-end channel is calculated.

5. The low-altitude holographic MIMO channel optimization and fitting method assisted by stacked intelligent metasurfaces according to claim 1, characterized in that, In step S3, for each group of superatomic phase shift configurations, the corresponding channel fitting error is calculated according to the following formula. : in, This is the scaling factor for the end-to-end channel. For TX-SIM beamforming matrix, For the beamforming matrix of RX-SIM, For spatially correlated holographic MIMO channel matrix, It is a singular value matrix. The Frobenius norm is used to characterize the fitting error of the desired channel fitting problem.

6. The low-altitude holographic MIMO channel optimization and fitting method assisted by stacked intelligent metasurfaces according to claim 1, characterized in that, In step S4, the superatomic phase shifts of TX-SIM and RX-SIM are iteratively optimized using a linear decreasing particle swarm optimization method, specifically including: S4.1 Initialize a set of random particles, each particle i is assigned a position. and speed Two attributes; of which, position Representing the superatomic phase shift combination of TX-SIM and RX-SIM, velocity This represents the magnitude of the phase shift change; S4.2, calculate the channel fitting error of the multiple sets of superatomic phase shift configurations obtained in step S3. The fitness of each particle is calculated as an input parameter. : ; S4.3, Perform iterative optimization: Update individual optimal solution and the global optimal solution ; Update the particle's velocity and position according to the following formula: in, Indicates the current iteration number. , Let represent the velocities of the particles in the t-th and t+1-th iterations, respectively. , These represent the positions of the particles in the t-th and t+1-th iterations, respectively. For inertial weights, and For learning factors; S4.4 Update the inertia weights using a linear decreasing strategy. Learning factors and Then return to step S4.3 and continue iterating until the iteration termination condition is met; S4.5 Output the optimized superatomic phase shift combination and channel fitting error, that is, obtain the optimized TX-SIM phase shift matrix, RX-SIM phase shift matrix and channel fitting error.

7. The low-altitude holographic MIMO channel optimization and fitting method assisted by stacked intelligent metasurfaces according to claim 6, characterized in that, The inertia weights are updated using a linear decreasing strategy. , means as follows: in, Let be the inertia weight for the t-th iteration. The maximum number of iterations, and These are the maximum and minimum values ​​set, respectively. The learning factor is updated using a linear decreasing strategy. and , means as follows: in, , The learning factors for the t-th iteration are respectively , , , Learning factors The maximum and minimum values, , Learning factors The maximum and minimum values.

8. A computer device, characterized in that, include: At least one processor, at least one memory, and computer program instructions stored in the memory, which, when executed by the processor, implement the method as described in any one of claims 1-7.

9. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by a processor, the method described in any one of claims 1-7 is implemented.

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