NGLQ-based holographic mimo small-scale fading channel discrete modeling method, system and storage medium

Abstract

The application provides a holographic MIMO small-scale fading channel discrete modeling method based on NGLQ, a system and a storage medium, the method projects and truncates a spherical wave number domain into a tight support two-dimensional wave number domain according to an incident angle boundary, and obtains a spatial continuous autocorrelation function. The incident angle boundary and the calculation degree of freedom are combined to adaptively determine the discrete quadrature node number with the least calculation amount. The node and weight are mapped to a physical aperture domain by using a Gauss-Legendre quadrature rule, and a non-uniform two-dimensional quadrature node coordinate set and a weight matrix are generated. Then, by using a high-order Nyström method, a continuous Karhunen-Loeve decomposition integral equation is discretized and a symmetrization matrix is constructed. The matrix is subjected to eigenvalue decomposition and effective eigenvalues are screened, and continuous characteristic functions covering the whole aperture space are obtained by using continuous interpolation. Independent and identically distributed complex Gaussian random weighting coefficients are combined for series summation reconstruction, and spatial continuous HMIMO small-scale fading channel samples strictly satisfying electromagnetic physical constraints are generated.

Description

Technical Field

[0001] This invention relates to the field of communications, and more specifically, to a method and system for discrete modeling of small-scale fading channels in holographic MIMO based on NGLQ. Background Technology

[0002] HMIMO arrays physically exhibit a spatially continuous electromagnetic aperture, integrating high-density antenna elements with near-zero spacing within a compact physical space. In this continuous aperture architecture, the wireless channel no longer represents a traditional set of independent discrete coefficients, but rather a continuous spatial function following the physical laws of electromagnetic wave propagation. To enable the communication system to resolve the available orthogonal spatial channels within the physical space and approach the Shannon capacity limit, it is essential to accurately characterize and reconstruct the electromagnetically constrained channel state information in digital baseband processing and system-level simulation. Therefore, constructing a continuous-to-discrete channel modeling method that combines electromagnetic physical consistency with mathematical computability is a core technological prerequisite for realizing and evaluating HMIMO systems.

[0003] To accurately model the propagation characteristics of electromagnetic waves in physical space, existing techniques first characterize three-dimensional far-field small-scale fading as a zero-mean, spatially stationary, and correlated scalar Gaussian random field. By introducing the physical constraint that this random field must satisfy the Helmholtz equation, a continuous Fourier plane spectrum representation method is derived. Furthermore, since the aforementioned continuous channel model cannot be directly applied to discrete baseband processing and simulation in modern digital communication systems, the closest prior art proposed in this invention is a Nyström discretization method based on Gauss-Legend Quadrature (GLQ) (i.e., the NGLQ method), which serves as a means to achieve discretized modeling of HMIMO channels. This closest prior art employs a fixed physical space degree of freedom (i.e., ... ) plus an empirical constant ( The method statically allocates discrete computing nodes and constructs a discrete kernel matrix accordingly. Subsequently, the method performs standard full eigenvalue decomposition (EVD) on the entire discrete kernel matrix and directly substitutes the extracted full eigenvalue system into the Nyström formula for continuous interpolation reconstruction.

[0004] However, in the actual deployment of complex communication systems, the aforementioned closest existing technology has the following two significant objective technical defects: Defect 1: The node allocation mechanism based on physical degrees of freedom lacks scenario adaptability. Existing technologies rely on the physical spatial degrees of freedom of the antenna (e.g., one-dimensional) to allocate the number of discretized quadrature nodes. This mechanism lacks adaptability to actual electromagnetic propagation environments. In engineering, this directly leads to the following two problems: (1) Inability to handle extreme end-fire scenarios: When an electromagnetic wave is incident from an end-fire direction parallel to the antenna array axis, the spatial phase change reaches its global maximum. At this point, the computational degrees of freedom (cDoF) actually required to ensure the convergence of the numerical quadrature spectrum is significantly reduced. Mathematically, the number of degrees of freedom is strictly greater than that of traditional physical degrees of freedom. Existing technologies that rely on physical degrees of freedom for node allocation will result in undersampling, making it impossible to cross the numerical convergence threshold, and directly causing the channel discretization reconstruction model to fail.

[0005] (2) Causing significant computational redundancy in angle-constrained scenarios: In typical base station sector coverage scenarios (such as beams covering only specific elevation angles), the effective incident angle of electromagnetic waves is strictly limited. Existing technologies perform indiscriminate oversampling of the omnidirectional physical wavenumber domain, resulting in a large number of computing nodes being allocated to spatial directions where no signal energy propagates. Since the computational complexity of subsequent kernel matrix eigenvalue decomposition is increasing... increase( In order to calculate the total number of nodes, this non-environment-aware allocation mechanism inevitably leads to a large amount of wasted computing power and redundant system resources.

[0006] Defect 2: Numerical instability and error margin caused by the coupling between the number of nodes and the number of feature truncations. When the autocorrelation kernel function of a continuous channel possesses... When smoothness is achieved, the eigenvalues ​​of the corresponding integral operator exhibit an exponentially rapid decay. Existing techniques have failed to address the issue of the "total number of quadrature nodes" used for numerical integration. "Number of Feature Modes (Number of Feature Modes)" and "Number of Feature Modes" used for final channel reconstruction Effective decoupling is not possible (i.e., a reasonable feature truncation mechanism is lacking). When the system increases the number of nodes to reduce the quadrature truncation error, the discrete kernel matrix will produce values ​​that fall below the hardware machine accuracy (e.g., less than the required value). The numerical noise eigenvalues ​​of the channel model are used to perform Nyström continuous interpolation. The computation process requires division by these near-zero eigenvalues, which directly leads to a severe amplification of numerical noise. Therefore, existing technologies, in pursuing high-precision channel reconstruction, not only fail to achieve continuous convergence of reconstruction errors but are also limited by a significant error floor, severely impacting the reconstruction accuracy and numerical reliability of the channel model under finite machine precision.

[0007] Therefore, there is an urgent need for a stable HMIMO channel reconstruction method based on environmental awareness and prior truncation to solve the problems of wasted quadrature nodes caused by blind node allocation without environmental awareness in the existing NGLQ discretization method, as well as numerical instability and error amplification caused by the lack of feature truncation mechanism in full eigenvalue decomposition. This would enable high-precision, low-complexity, and high-stability continuous aperture channel reconstruction with limited machine accuracy. Summary of the Invention

[0008] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for discrete modeling of small-scale fading channels in holographic MIMO based on NGLQ.

[0009] According to a first aspect of the present invention, a method for discrete modeling of small-scale fading channels in holographic MIMO based on NGLQ includes: Step S1: Obtain the effective incident angle distribution boundary of the current communication environment. Based on the effective incident angle distribution boundary, truncate the traditional omnidirectional spherical wavenumber domain projection into an effective two-dimensional wavenumber domain with a compact support set. Step S2: Obtain the continuous spatial small-scale fading autocorrelation function constrained by the effective two-dimensional wavenumber domain; Step S3: For a preset aperture size, determine the number of discrete quadrature nodes by using the effective incident angle distribution boundary and the calculated degrees of freedom; Step S4: Based on the number of discrete quadrature nodes, using the Gauss-Legend quadrature rule, map the quadrature nodes and weights of the standard interval to the physical aperture domain to generate a two-dimensional quadrature node coordinate set and corresponding weight matrix with non-uniform distribution characteristics. Step S5: Based on the two-dimensional quadrature node coordinate set and the corresponding weight matrix, the continuous Kajunin-Louis decomposition integral equation based on the autocorrelation function is discretized using the higher-order Nyström method to obtain the symmetric matrix. Step S6: Perform eigenvalue decomposition on the symmetric matrix to obtain eigenvalues, and select effective eigenvalues ​​based on a preset precision. Perform Nyström continuous interpolation based on the effective eigenvalues ​​to obtain continuous eigenfunctions covering the entire continuous physical aperture space. Step S7: Based on the effective eigenvalues ​​and continuous eigenfunctions, combine the independent and identically distributed complex Gaussian random weighted coefficients to perform KLD series summation, generating spatially continuous HMIMO small-scale fading channel samples that satisfy the target electromagnetic physical constraints.

[0010] Preferably, the effective incident angle distribution boundary includes the maximum elevation angle and the maximum azimuth angle, that is, the maximum incident angle of the electromagnetic wave in the vertical and horizontal directions.

[0011] Preferably, step S2 includes: Step S2.1: Characterize the 3D far-field small-scale fading of the HMIMO system as a zero-mean, spatially stationary, and correlated scalar Gaussian random field; Step S2.2: Based on the effective incident angle distribution boundary, obtain the continuous autocorrelation function of the scalar Gaussian random field within the finite aperture. ,in, and These represent any two consecutive spatial coordinate vectors within the two-dimensional aperture.

[0012] Preferably, step S3 specifically includes: For size For a two-dimensional rectangular physical aperture, based on the computational degrees of freedom of the aperture in the corresponding directions and the effective incident angle distribution boundary, the number of discrete quadrature nodes (i.e., the number of sampling points) in the X-axis and Y-axis directions are calculated and assigned respectively. and ,in:

[0013]

[0014] in, This indicates the rounding up operation; and These represent the physical lengths of the aperture on the X and Y axes, respectively. and These represent the degrees of freedom for calculating the aperture in two dimensions. The wavelength of electromagnetic waves; These are preset integer-type degree-of-freedom margin parameters; This indicates the maximum pitch angle, which is the maximum angle of incidence of the electromagnetic wave in the vertical direction; This indicates the maximum azimuth angle, which is the maximum incident angle of the electromagnetic wave in the horizontal direction.

[0015] along with As the value increases, the channel reconstruction error decays exponentially (or exponentially).

[0016] Preferably, step S4 includes: Step S4.1: Using the standard Gauss-Legend quadrature algorithm, in the standard interval... Generate one-dimensional integral roots and weights above; Step S4.2: Transform the product root and weights to the physical space domain through linear mapping. In this process, the coordinates of the discrete quadrature nodes within the two-dimensional aperture are obtained. and the corresponding two-dimensional node weights ,in , ; Step S4.3: Flatten the discrete quadrature nodes and their corresponding two-dimensional node weights within the two-dimensional aperture into a one-dimensional sequence according to the preset expansion rules (e.g., lexicographical arrangement); Step S4.4: Create a global one-dimensional index (For example ),get One-dimensional discrete quadrature node coordinates and their corresponding weights Among them, the total number of global nodes ; Step S4.5: Based on the one-dimensional weight sequence, construct a structure with size... diagonal weight matrix .

[0017] Preferably, step S5 includes: Step S5.1: Generate a discrete kernel matrix by sampling the kernel function at the coordinate set of the quadrature nodes. ; Step S5.2: Combine the weight matrix Construct a symmetric matrix .

[0018] The KLD integral equation for a continuous field is defined as follows:

[0019] in, and These are the eigenvalues ​​and eigenfunctions of the continuous integral operator, respectively.

[0020] The above generated Substituting the coordinates of the discrete quadrature nodes into the autocorrelation function In the middle, the construction size is Discrete kernel matrix Its elements are defined as .

[0021] Using the Gauss-Legend quadrature rule, the above continuous integral equation can be approximated as the following discrete matrix eigenvalue decomposition problem:

[0022] Preferably, step S6 includes: Step S6.1: Symmetricize the matrix Eigenvalue decomposition is performed to obtain a set of discrete eigenvalues. and the corresponding discrete feature vectors That is, the value defined on the quadrature node.

[0023] Step S6.2: Based on the preset precision threshold Truncation and extraction of values ​​greater than the precision threshold The effective feature values ​​and their corresponding feature vectors are defined as the total number of effective feature patterns. Each effective feature pattern includes a set of effective feature values ​​and its corresponding feature vector; Step S6.3: For the extracted Using the Nyström continuous interpolation formula, the discrete feature vectors are analytically extended to cover any spatial location within the entire aperture, based on the effective feature patterns. Continuous characteristic function at point :

[0024] In the formula, Indicates the index of the Gauss-Legend quadrature node; Indicates the first Coordinates of the Gauss-Legend quadrature nodes; Indicates the first The Gauss-Legend de Gauss product weights.

[0025] Preferably, step S7 includes: Based on continuous characteristic function and their corresponding eigenvalues , combined A set of independent and identically distributed standard complex Gaussian random variables The spatially continuous HMIMO small-scale fading random channel is reconstructed using the following finite-term truncated series summation formula. : .

[0026] According to a second aspect of the present invention, a discrete modeling system for small-scale fading channels of holographic MIMO based on NGLQ includes: Module M1: Obtain the effective incident angle distribution boundary of the current communication environment, and based on the effective incident angle distribution boundary, truncate the traditional omnidirectional spherical wavenumber domain projection into an effective two-dimensional wavenumber domain with a compact support set; Module M2: Obtains the continuous spatial small-scale fading autocorrelation function limited by the effective two-dimensional wavenumber domain through the effective two-dimensional wavenumber domain; Module M3: For a preset aperture size, the number of discrete quadrature nodes is determined by the effective incident angle distribution boundary and the computational degrees of freedom; Module M4: Based on the number of discrete quadrature nodes, using the Gauss-Legend quadrature rule, the quadrature nodes and weights of the standard interval are mapped to the physical aperture domain, generating a two-dimensional quadrature node coordinate set and corresponding weight matrix with non-uniform distribution characteristics. Module M5: Based on the two-dimensional quadrature node coordinate set and the corresponding weight matrix, the high-order Nyström method is used to discretize the continuous Kajunin-Louis decomposition integral equation based on the autocorrelation function to obtain the symmetric matrix. Module M6: Performs eigenvalue decomposition on the symmetric matrix to obtain eigenvalues, filters valid eigenvalues ​​based on a preset precision, performs Nyström continuous interpolation based on the valid eigenvalues, and obtains continuous eigenfunctions covering the entire continuous physical aperture space. Module M7: Based on effective eigenvalues ​​and continuous eigenfunctions, and combined with independent and identically distributed complex Gaussian random weighted coefficients, KLD series summation is performed to generate spatially continuous HMIMO small-scale fading channel samples that satisfy the target electromagnetic physical constraints.

[0027] According to a third aspect of the present invention, a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the steps of a discrete modeling method for small-scale fading channels of holographic MIMO based on NGLQ are provided.

[0028] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention integrates computational degrees of freedom with the spatial boundaries of the communication environment, establishing an adaptive GLQ node allocation rule. This method can handle extreme end-fire scenarios that previous methods could not address, and effectively reduces the number of nodes required for GLQ by considering the limited angular range of the incident wave's vertical and horizontal dimensions. Specifically, considering the typical vertical angular coverage range of base stations in current cellular networks... and the angular coverage of the horizontal dimension The upper limit of the number of points required for the x-axis and y-axis will be constrained as follows:

[0029]

[0030] Compared to non-environment-aware node allocation mechanisms, the required number of GLQ points is reduced. Level. Because the computational complexity of subsequent kernel moment EVD is increasing. This exponential reduction in dimensionality effectively reduces computational complexity and significantly improves the computational efficiency of HMIMO system-level simulations.

[0031] 2. This invention innovatively uses the total number of quadrature nodes for numerical integration. Number of feature modes truncations used for channel reconstruction Decoupling is achieved by introducing a preset machine accuracy threshold for control. The extraction of this feature avoids the noise floor amplification effect caused by dividing by near-zero eigenvalues ​​during Nyström continuous interpolation. This dual independent control rule ensures high accuracy and numerical stability of channel reconstruction under limited hardware precision.

[0032] 3. For directional scattering environments lacking analytical closed-form solutions in practical communication (such as vMF mixing models), this invention proposes a numerical preprocessing framework based on NUIDFT. Compared to the method of "numerical IDFT + zero-padding + continuous interpolation", directly performing NUIDFT can eliminate the error margin introduced by continuous interpolation, thereby achieving near-machine accuracy (e.g., MSRE reaching a certain level). The channel reconstruction requirements (on a scale of several orders of magnitude) have broadened the physical and mathematical boundaries of channel simulation.

[0033] 4. Based on the aforementioned high-fidelity, adaptive, and physically universally applicable discretized framework, this invention can be directly integrated as a bottom-level module into system-level wireless communication simulation platforms or hardware channel emulators. The introduction of this model effectively reduces cascade verification errors caused by distortion in the bottom-level channel modeling, affecting upper-level precoding design, channel estimation, and capacity assessment. This provides rigorous model support for the technical evaluation of next-generation continuous aperture antenna systems. Attached Figure Description

[0034] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a schematic diagram of the effective wavenumber domain range and NGLQ sampling range in an embodiment of the present invention.

[0035] Figure 2 This is a geometrical diagram of the end-fire and broadside incident scenarios in an embodiment of the present invention.

[0036] Figure 3 The high-frequency kernel function component in the end-fire scenario of this invention embodiment. A schematic diagram of numerical integration error convergence under different GLQ node numbers.

[0037] Figure 4 This is a schematic diagram of the cumulative distribution function (CDF) curves of mean square reconstruction error (MSRE) for different antenna aperture sizes in an anisotropic scattering scenario according to an embodiment of the present invention (wherein, the continuous spatial autocorrelation function is constructed based on NUIDFT). Detailed Implementation

[0038] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0039] For ease of understanding, the abbreviations and key terms involved in this invention are defined as follows: Holographic Multiple-input Multiple-output (HMIMO) The Nyström Method with Gauss-Legendre Quadrature (NGLQ) Fourier series expansion (FSE) Karhunen-Loève Decomposition (KLD) Feng Mises-Fisher Distribution (vMF); Autocorrelation Function (ACF) Power Spectral Density (PSD) Eigenvalue Decomposition (EVD) Cumulative Distribution Function (CDF) Inverse Discrete Fourier Transform (IDFT) Inverse Fast Fourier Transform (IFFT); Reconstruction Error (RE) Mean Squared Reconstruction Error (MSRE) Degrees of Freedom: Degrees of Freedom, DoF; Non-uniform inverse discrete Fourier transform (NUIDFT). Example 1: This embodiment provides a discrete modeling method for small-scale fading channels in holographic MIMO based on NGLQ. This method, based on high-order NGLQ and prior environmental information, achieves high-precision channel reconstruction by calculating the degree-of-freedom constrained mathematical nodes. Specifically, this embodiment takes a two-dimensional (2D) rectangular antenna aperture as an example, assuming the physical dimensions of the aperture are... The electromagnetic wave wavelength corresponding to the system carrier wave is... .

[0040] This method specifically includes the following steps: Step S1: Obtain the effective incident angle distribution boundary of the current communication environment. Based on the effective incident angle distribution boundary, truncate the traditional omnidirectional spherical wavenumber domain projection into an effective two-dimensional wavenumber domain with a compact support set. The effective incident angle distribution boundary includes the maximum elevation angle and the maximum azimuth angle, which are the maximum incident angles of electromagnetic waves in the vertical and horizontal directions.

[0041] Based on the above scheme, the aperture of the 2D rectangular antenna is set at... - Plane, where - The axis corresponds to the side-firing direction. Definition and This corresponds to the angle of incidence of the electromagnetic wave in the vertical and horizontal directions. Assuming... and Limited to the following specific scope , ,in This is the maximum angle of incidence.

[0042] It should be noted that the above-mentioned limits on the vertical and horizontal incident angles correspond to the physical scenario of base station sector coverage in actual cellular mobile networks. Under these angle limitations, the effective range of small-scale fading channels in the wavenumber domain is as follows: Figure 1 As shown.

[0043] Step S2: Obtain the continuous spatial small-scale fading autocorrelation function constrained by the effective two-dimensional wavenumber domain.

[0044] It is understood that step S2 includes: Step S2.1: Characterize the 3D far-field small-scale fading of the HMIMO system as a zero-mean, spatially stationary, and correlated scalar Gaussian random field.

[0045] Step S2.2: Based on the effective incident angle distribution boundary, obtain the continuous autocorrelation function of the scalar Gaussian random field within the finite aperture. ,in, and These represent any two consecutive spatial coordinate vectors within the two-dimensional aperture.

[0046] Based on the above scheme, and using the constraints of electromagnetic wave propagation theory and the Paley-Wiener theorem, the autocorrelation function possesses the following properties in the spatial domain: Smoothing properties.

[0047] Step S3: For a preset aperture size, determine the number of discrete quadrature nodes by using the effective incident angle distribution boundary and the calculated degrees of freedom; Understandably, in order to offset the residual quadrature error during the discretization process and achieve spectral convergence of MSRE, the number of discrete quadrature nodes (i.e., the number of sampling points) in the X-axis and Y-axis directions are calculated and allocated based on the computational degrees of freedom of the aperture in the corresponding direction and the effective incident angle distribution boundary. and ,in:

[0048]

[0049] in, This indicates the rounding up operation; and These represent the physical lengths of the aperture on the X and Y axes, respectively. and These represent the degrees of freedom for calculating the aperture in two dimensions. The wavelength of electromagnetic waves; The preset integer degree-of-freedom margin parameters, as As the value increases, the channel reconstruction error decays exponentially (or more exponentially). This indicates the maximum pitch angle, which is the maximum angle of incidence of the electromagnetic wave in the vertical direction; This indicates the maximum azimuth angle, which is the maximum incident angle of the electromagnetic wave in the horizontal direction.

[0050] Step S4: Based on the number of discrete quadrature nodes, using the Gauss-Legend quadrature rule, map the quadrature nodes and weights of the standard interval to the physical aperture domain to generate a two-dimensional quadrature node coordinate set and corresponding weight matrix with non-uniform distribution characteristics. It is understandable that step S4 specifically includes: Step S4.1: Using the standard Gauss-Legend quadrature algorithm, in the standard interval... Generate one-dimensional integral roots and weights above; Step S4.2: Transform the product root and weights to the physical space domain through linear mapping. In this process, the coordinates of the discrete quadrature nodes within the two-dimensional aperture are obtained. and the corresponding two-dimensional node weights ,in ， ; Step S4.3: In order to construct the subsequent one-dimensional discrete matrix equation, according to the preset expansion rules (e.g., lexicographical arrangement), the discrete quadrature nodes in the two-dimensional aperture and the corresponding two-dimensional node weights are flattened into a one-dimensional sequence. Step S4.4: Create a global one-dimensional index (For example ),get One-dimensional discrete quadrature node coordinates and their corresponding weights Among them, the total number of global nodes ; Step S4.5: Based on the one-dimensional weight sequence, construct a structure with size... diagonal weight matrix .

[0051] Step S5: Based on the two-dimensional quadrature node coordinate set and the corresponding weight matrix, the continuous Kahunen-Louis decomposition integral equation based on the autocorrelation function is discretized using the higher-order Nyström method to obtain the symmetric matrix.

[0052] Understandably, step S5 includes: Step S5.1: Generate a discrete kernel matrix by sampling the kernel function at the coordinate set of the quadrature nodes. ; Step S5.2: Combine the weight matrix Construct a symmetric matrix .

[0053] Specifically, the KLD integral equation for a continuous field is defined as:

[0054] in, For the eigenvalues ​​of the continuous integral operator, and To calculate the coordinates of the product nodes, the coordinates are respectively and The characteristic function of the continuous integral operator at time .

[0055] The product generated in step S4 Substituting the coordinates of the discrete quadrature nodes into the autocorrelation function In the middle, the construction size is Discrete kernel matrix Its elements are defined as .

[0056] Using the Gauss-Legend quadrature rule, the above continuous integral equation can be approximated as the following discrete matrix eigenvalue decomposition problem:

[0057] and These are the eigenvalues ​​and eigenvectors of the eigenvalue decomposition problem described above.

[0058] Step S6: Perform eigenvalue decomposition on the symmetric matrix to obtain eigenvalues, and select effective eigenvalues ​​based on a preset precision. Perform Nyström continuous interpolation based on the effective eigenvalues ​​to obtain continuous eigenfunctions covering the entire continuous physical aperture space. Specifically, step S6 includes: Step S6.1: Symmetricize the matrix Eigenvalue decomposition is performed to obtain a set of discrete eigenvalues. and the corresponding discrete feature vectors (i.e., the value defined on the quadrature node).

[0059] Step S6.2: To eliminate the numerical instability caused by feature values ​​being lower than the hardware precision, a preset precision threshold is used. (For example ), truncate and extract if the precision threshold is exceeded The effective feature values ​​and their corresponding feature vectors are defined as the total number of effective feature patterns. Each effective feature pattern includes a set of effective feature values ​​and its corresponding feature vector; Step S6.3: For the extracted Using the Nyström continuous interpolation formula, the effective feature patterns are analytically extended from feature vectors defined only on discrete quadrature nodes to cover any spatial location within the entire aperture. Continuous characteristic function at point :

[0060] In the formula, Indicates the index of the Gauss-Legend quadrature node; Indicates the first The spatial coordinates of the quadrature nodes (i.e.) ); Indicates the first The Gauss-Legend de Gauss product weights.

[0061] Step S7: Based on the effective eigenvalues ​​and continuous eigenfunctions, combine the independent and identically distributed complex Gaussian random weighted coefficients to perform KLD series summation, generating spatially continuous HMIMO small-scale fading channel samples that satisfy the target electromagnetic physical constraints.

[0062] Specifically, based on continuous feature functions and their corresponding eigenvalues , combined A set of independent and identically distributed standard complex Gaussian random variables The spatially continuous HMIMO small-scale fading random channel is reconstructed using the following finite-term truncated series summation formula. : .

[0063] Understandably, this generated channel model It can be directly used as underlying physical parameters or input data and integrated into communication system-level simulators or test instruments to evaluate the spatial channel characteristics and transmission performance of baseband transmission algorithms under different terminal apertures.

[0064] Example 2: Evaluation of numerical integration error in a linear antenna aperture end-fire scenario: This embodiment, as one of the specific application scenarios of Embodiment 1 above, elaborates in detail the end-fire scenario of a linear antenna aperture (such as...). Figure 2 As shown, this invention demonstrates the necessity and technical advantages of using the effective wavenumber domain range and computational degrees of freedom to determine the number of discrete quadrature nodes.

[0065] 1. Physical settings and kernel function substitution in linear antenna aperture end-fire scenario In such Figure 2 In the environment shown, the electromagnetic wave multipath components reaching the target physical aperture are concentrated in the end-fire direction. At this time, the continuous spatial small-scale fading autocorrelation function obtained in step S2, after mapping, takes the following form:

[0066] in, , ; and These represent mappings to the standard integration interval. Normalized dimensionless spatial coordinates of two independent observation points on the antenna (which correspond to any two spatial positions on the one-dimensional linear physical antenna aperture); The normalized maximum spatial angular frequency (or cutoff spatial frequency) is represented by the physical aperture length. With system carrier wavelength The ratio of is determined by , which physically characterizes the maximum spatial phase deflection rate that can be generated when electromagnetic waves propagate along the antenna aperture in an end-fire scenario.

[0067] The above-specific kernel function Substituting steps S3 to S7 of Embodiment 1, the computer device can perform reconstruction to generate a small-scale fading random channel for that specific physical scenario.

[0068] 2. Numerical integration error assessment Based on the resolvability in the end-fire scenario, the numerical integration error using M GLQ nodes in this scenario can be directly evaluated. Its definition is as follows:

[0069] Where, integrand Defined as a kernel function that maps to a standard interval. Its corresponding characteristic function The product of: , represents the entity mapped by the integrand in a continuous integral equation; This represents the specific integrand expression mapped onto the standard region [-1,1], and its physical essence is the product of the spatial autocorrelation kernel function and the spatial response of the feature pattern; Indicates the first The discrete quadrature weight of each Gauss-Legend quadrature node physically represents the integral proportion of that discrete sampling node in the total spatial energy; Indicates that it is defined in the standard interval. The first The coordinates of each Gauss-Legend discretized quadrature node physically correspond to a specific discrete sampling position on the linear antenna aperture. It represents the continuous characteristic function corresponding to the autocorrelation kernel function in the end-fire scenario, which physically characterizes the spatial characteristic patterns that are orthogonal to each other in the confined space channel; In the above formula .

[0070] Based on the definition of the KLD integral equation in step S5, the equation for the end-fire scenario can be derived. The two corresponding characteristic equations are:

[0071]

[0072] In the formula, and These represent two mutually orthogonal continuous feature functions corresponding to the spatial autocorrelation kernel function in the end-fire scenario.

[0073] because and With only a phase difference, this embodiment extracts the integrand. The evaluation is performed using the following expression:

[0074] In the formula, The specific integrand expansion corresponding to the first feature pattern.

[0075] To quantify numerical integration error, this embodiment extracts... Mid-to-high frequency components To evaluate its numerical integration error, the simulation results are as follows: Figure 3 As shown.

[0076] It is important to note that, in Figure 1 In the scenario shown, where the projectile is fired from the end, Therefore, the number of points selected by GLQ on the X-axis must follow the following rules:

[0077] Figure 3 Statistical results show that under normalized different antenna aperture sizes (i.e. The numerical integration errors are all within approximately [missing information]. It begins to converge at a super-exponential rate. L This represents the physical length of the linear antenna aperture.

[0078] The simulation results objectively verify the accuracy and necessity of the GLQ point selection criterion proposed in this invention under extreme end-fire scenarios. Since the existing methods use the following GLQ point selection rules... This method mathematically leads to undersampling problems, making it unsuitable for extreme end-fire scenarios and unable to adaptively adjust based on the vertical and horizontal ranges of the incident wave. This, in turn, proves the irreplaceable nature of the core truncation mechanism of this invention.

[0079] Example 3: Channel Discretization Reconstruction and Accuracy Verification Based on Anisotropic Scattering Scenarios: This embodiment, as another preferred implementation of Embodiment 1 above, elaborates in detail the implementation details and numerical stability of the method of the present invention in a three-dimensional anisotropic scattering scenario that is closer to a real complex communication environment.

[0080] 1. Physical modeling and kernel function numerical acquisition in non-isotropic scenarios: Unlike linear end-fire scenarios with closed-form solutions, the spatial autocorrelation function in anisotropic scattering scenarios typically cannot be expressed analytically. Therefore, this embodiment employs the widely used vMF mixing model in engineering to characterize the spatial angular power spectrum.

[0081] In a preferred embodiment, the system distributes the spherical angular power. Modeling as The weighted summation of independent scattering clusters is expressed as follows:

[0082] in, For the first Positive real-valued normalized weights for scattering clusters (satisfying) ); For the first The vMF distribution function of each cluster is defined as follows:

[0083] In this distribution, and They represent the first The modal elevation and modal azimuth angles of each scattering cluster; The concentration parameter is used to physically characterize the extent of angular power spread of scattered energy around the modal direction.

[0084] Although the power spectral density (PSD) in anisotropic conditions exhibits boundary singularities, it remains strictly integrable and compactly supported in the wavenumber domain. According to the Paley-Wiener theorem, this physical property mathematically guarantees the corresponding spatial autocorrelation function. Still possess The smoothing properties provide a solid theoretical foundation for applying the NGLQ method. Due to the lack of a closed-form solution, this embodiment performs the following numerical preprocessing steps using a computing device to obtain the continuous kernel function required in Example 1: Step A, Wavenumber Domain Mapping and Numerical Sampling: To obtain a continuous kernel function, it is first necessary to construct the angular power distribution defined on a three-dimensional unit sphere based on the aforementioned vMF mixture model. Transform it into an expression on the two-dimensional wavenumber field plane.

[0085] Specifically, the system first introduces a mapping relationship from standard spherical coordinates to Cartesian wavenumber coordinates (i.e., mapping). correspond , correspond , correspond , Let X, Y, and Z represent the wavenumber components of the electromagnetic wave vector along the three orthogonal dimensions (X, Y, and Z) in a three-dimensional Cartesian coordinate system. Then, since actual physical scattering is typically modeled as an upper hemisphere in front of the receiver, this method utilizes the symmetry of the physical field and integral identities to represent the vertical components in the three-dimensional wavenumber domain. Integration along the projection direction eliminates the inconsistencies. This spatial dimension reduction projection operation, which involves mapping first and then integrating, transforms the original three-dimensional spherical model into one that relies solely on two-dimensional Cartesian wavenumber coordinates. The expression is obtained, thus constructing a two-dimensional integral form that defines the continuous autocorrelation function.

[0086] In this expression, the free space wavenumber is introduced. This defines the physical boundary of the propagation spectrum in the wavenumber domain. The integrand of the reduced integral is composed of the vMF wavenumber domain distribution term after coordinate mapping and the geometric attenuation denominator term resulting from the spherical projection onto the two-dimensional disk (i.e., proportional to...). Subsequently, the wavenumber domain of the specific two-dimensional integrand after dimensionality reduction is performed. ) Grid sampling.

[0087] Step B, Inverse Discrete Transform in the Spatial Domain and Mapping to Continuous Kernel Functions: Based on the wavenumber domain sampling points from step A, the discrete autocorrelation function is obtained using the IDFT method. To ensure a high-precision interpolation basis, in and A relatively large number of sampling points are configured on each axis (e.g., preferably set). This involves introducing zero-padding to improve spatial resolution. By performing the inverse fast Fourier transform (IFFT), the generated spatial range is limited by... The discrete kernel function data points are obtained. Continuous interpolation (such as cubic interpolation) is performed on the obtained discrete data points to reconstruct the kernel function defined on the continuous displacement coordinates. and Difference autocorrelation function on Considering the size of the target physical aperture is (i.e., absolute coordinates) ,at the same time Its corresponding relative displacement range naturally covers the interval and Therefore, the system will extract the interpolated function from its original generated sampling range (e.g., ...). Strictly truncate to the displacement region of interest. .

[0088] To adapt to the general discretization framework in Implementation Example 1, based on the principle of spatial stationarity, a system is established from absolute coordinate pairs... To the truncated difference autocorrelation function The mapping relationship is as follows:

[0089] in, and Defined in the physical aperture region Any two spatial locations within the range. 、 、 Let X and Y represent the absolute spatial coordinates of any two independent observation points on the surface of the target physical aperture along the X-axis in a two-dimensional Cartesian rectangular coordinate system. and ) and absolute spatial coordinates along the Y-axis ( and ).

[0090] After the above mapping transformation, the obtained This is the continuous autocorrelation function required in step S2 of Example 1. Subsequently, following steps S3 to S7 of Example 1, the Gauss-Legendary quadrature node pairs are used... Discretization is performed to ultimately complete channel reconstruction in non-isotropic scenarios.

[0091] It should be noted that the kernel function obtained above The method has the low complexity of IFFT, but the interpolation operation introduces interpolation error. To eliminate this error, the NUIDFT method can be directly applied to the sampling points in the wavenumber domain to obtain the differential autocorrelation function. Its corresponding The value of directly corresponds to the value of the non-uniformly distributed GLQ quadrature nodes. Subsequently, channel reconstruction in the non-isotropic scenario is completed according to steps S5 to S7 of Example 1. The spatial computational complexity of the NUIDFT-based method is higher than that of the "IFFT + zero-padding + interpolation method," therefore it is more suitable for high-precision channel reconstruction requirements with small antenna aperture sizes.

[0092] 2. Reconstruction accuracy verification and numerical stability To verify the reconstruction accuracy and numerical stability of the proposed algorithm under highly random environments, the system generated 1000 random channel implementations based on the vMF model, and the CDF of the MSRE was statistically analyzed. In the simulation configuration, the number of scattering clusters... obey Discrete uniform distribution, modal elevation angle With azimuth In respectively and A uniformly distributed concentration parameter describing the angular power spread. exist Uniformly distributed within, with each cluster having a weight. Normalized after uniform sampling. Numerical precision was set to... .

[0093] Figure 4 The statistical results show that, when the NUIDFT method is applied and the numerical precision is set to 1, In this scenario, MSRE can stably reach level (i.e.) (The square of the result). This result fully demonstrates the stability and ultra-high accuracy of the proposed method in numerical reconstruction. On the other hand, in simulation scenarios of very large-scale antenna apertures (i.e., large electrical size) that allow for moderate errors, the application of the IFFT-based and continuous interpolation method can significantly reduce computational complexity, thereby enabling the system to achieve a flexible trade-off between reconstruction accuracy and computational efficiency.

[0094] This invention also provides a discrete modeling system for small-scale fading channels of holographic MIMO based on NGLQ. The discrete modeling system for small-scale fading channels of holographic MIMO based on NGLQ can be implemented by executing the process steps of the discrete modeling method for small-scale fading channels of holographic MIMO based on NGLQ. That is, those skilled in the art can understand the discrete modeling method for small-scale fading channels of holographic MIMO based on NGLQ as a preferred embodiment of the discrete modeling system for small-scale fading channels of holographic MIMO based on NGLQ.

[0095] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0096] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A discrete modeling method for small-scale fading channels of holographic MIMO based on NGLQ, characterized in that, include: Step S1: Obtain the effective incident angle distribution boundary of the current communication environment. Based on the effective incident angle distribution boundary, truncate the traditional omnidirectional spherical wavenumber domain projection into an effective two-dimensional wavenumber domain with a compact support set. Step S2: Obtain the continuous spatial small-scale fading autocorrelation function constrained by the effective two-dimensional wavenumber domain; Step S3: For a preset aperture size, determine the number of discrete quadrature nodes by using the effective incident angle distribution boundary and the calculated degrees of freedom; Step S4: Based on the number of discrete quadrature nodes, using the Gauss-Legend quadrature rule, map the quadrature nodes and weights of the standard interval to the physical aperture domain to generate a two-dimensional quadrature node coordinate set and corresponding weight matrix with non-uniform distribution characteristics. Step S5: Based on the two-dimensional quadrature node coordinate set and the corresponding weight matrix, the continuous Kajunin-Louis decomposition integral equation based on the autocorrelation function is discretized using the higher-order Nyström method to obtain the symmetric matrix. Step S6: Perform eigenvalue decomposition on the symmetric matrix to obtain eigenvalues, and select effective eigenvalues ​​based on a preset precision. Perform Nyström continuous interpolation based on the effective eigenvalues ​​to obtain continuous eigenfunctions covering the entire continuous physical aperture space. Step S7: Based on the effective eigenvalues ​​and continuous eigenfunctions, combine the independent and identically distributed complex Gaussian random weighted coefficients to perform KLD series summation, generating spatially continuous HMIMO small-scale fading channel samples that satisfy the target electromagnetic physical constraints.

2. The method according to claim 1, characterized in that, The effective incident angle distribution boundary includes the maximum elevation angle and the maximum azimuth angle, which are the maximum incident angles of electromagnetic waves in the vertical and horizontal directions.

3. The method according to claim 2, characterized in that, Step S2 includes: Step S2.1: Characterize the 3D far-field small-scale fading of the HMIMO system as a zero-mean, spatially stationary, and correlated scalar Gaussian random field; Step S2.2: Based on the effective incident angle distribution boundary, obtain the continuous autocorrelation function of the scalar Gaussian random field within the finite aperture. ,in, and These represent any two consecutive spatial coordinate vectors within the two-dimensional aperture.

4. The method according to claim 3, characterized in that, Step S3 specifically includes: For size For a two-dimensional rectangular physical aperture, based on the computational degrees of freedom of the aperture in the corresponding directions and the effective incident angle distribution boundary, the number of discrete quadrature nodes in the X-axis and Y-axis directions are calculated and assigned respectively. and ,in: in, This indicates the rounding up operation; and These represent the physical lengths of the aperture on the X and Y axes, respectively. and These represent the degrees of freedom for calculating the aperture in two dimensions. The wavelength of electromagnetic waves; These are preset integer-type degree-of-freedom margin parameters; This indicates the maximum pitch angle, which is the maximum angle of incidence of the electromagnetic wave in the vertical direction; This indicates the maximum azimuth angle, which is the maximum incident angle of the electromagnetic wave in the horizontal direction.

5. The method according to claim 4, characterized in that, Step S4 includes: Step S4.1: Using the standard Gauss-Legend quadrature algorithm, in the standard interval... Generate one-dimensional integral roots and weights above; Step S4.2: Transform the product root and weights to the physical space domain through linear mapping. In this process, the coordinates of the discrete quadrature nodes within the two-dimensional aperture are obtained. and the corresponding two-dimensional node weights ,in , ; Step S4.3: According to the preset unfolding rules, flatten the discrete quadrature nodes and corresponding two-dimensional node weights within the two-dimensional aperture into a one-dimensional sequence; Step S4.4: Create a global one-dimensional index ,get One-dimensional discrete quadrature node coordinates and their corresponding weights Among them, the total number of global nodes ; Step S4.5: Based on the one-dimensional weight sequence, construct a structure with size... diagonal weight matrix .

6. The method according to claim 5, characterized in that, Step S5 includes: Step S5.1: Generate a discrete kernel matrix by sampling the kernel function at the coordinate set of the quadrature nodes. ; Step S5.2: Combine the weight matrix Construct a symmetric matrix .

7. The method according to claim 6, characterized in that, Step S6 includes: Step S6.1: Symmetricize the matrix Eigenvalue decomposition is performed to obtain a set of discrete eigenvalues. and the corresponding discrete feature vectors ; Step S6.2: Based on the preset precision threshold Truncation and extraction of values ​​greater than the precision threshold The effective feature values ​​and their corresponding feature vectors are defined as the total number of effective feature patterns. Each effective feature pattern includes a set of effective feature values ​​and its corresponding feature vector; Step S6.3: For the extracted Using the Nyström continuous interpolation formula, the discrete feature vectors are analytically extended to cover any spatial location within the entire aperture, based on the effective feature patterns. Continuous characteristic function at point : In the formula, Indicates the index of the Gauss-Legend quadrature node; Indicates the first Coordinates of Gauss-Legend quadrature nodes; Indicates the first The Gauss-Legend de Gauss product weights.

8. The method according to claim 7, characterized in that, Step S7 includes: Based on continuous characteristic function and their corresponding eigenvalues , combined A set of independent and identically distributed standard complex Gaussian random variables The spatially continuous HMIMO small-scale fading random channel is reconstructed using the following finite-term truncated series summation formula. : .

9. A discrete modeling system for small-scale fading channels of holographic MIMO based on NGLQ, characterized in that, include: Module M1: Obtain the effective incident angle distribution boundary of the current communication environment, and based on the effective incident angle distribution boundary, truncate the traditional omnidirectional spherical wavenumber domain projection into an effective two-dimensional wavenumber domain with a compact support set; Module M2: Obtains the continuous spatial small-scale fading autocorrelation function limited by the effective two-dimensional wavenumber domain through the effective two-dimensional wavenumber domain; Module M3: For a preset aperture size, the number of discrete quadrature nodes is determined by the effective incident angle distribution boundary and the computational degrees of freedom; Module M4: Based on the number of discrete quadrature nodes, using the Gauss-Legend quadrature rule, the quadrature nodes and weights of the standard interval are mapped to the physical aperture domain, generating a two-dimensional quadrature node coordinate set and corresponding weight matrix with non-uniform distribution characteristics. Module M5: Based on the two-dimensional quadrature node coordinate set and the corresponding weight matrix, the high-order Nyström method is used to discretize the continuous Kajunin-Louis decomposition integral equation based on the autocorrelation function to obtain the symmetric matrix. Module M6: Performs eigenvalue decomposition on the symmetric matrix to obtain eigenvalues, filters valid eigenvalues ​​based on a preset precision, performs Nyström continuous interpolation based on the valid eigenvalues, and obtains continuous eigenfunctions covering the entire continuous physical aperture space. Module M7: Based on effective eigenvalues ​​and continuous eigenfunctions, and combined with independent and identically distributed complex Gaussian random weighted coefficients, KLD series summation is performed to generate spatially continuous HMIMO small-scale fading channel samples that satisfy the target electromagnetic physical constraints.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the NGLQ-based holographic MIMO small-scale fading channel discrete modeling method as described in any one of claims 1 to 8.

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