A Holographic MIMO Near-Field Channel Estimation Method Based on Spatial Correlation Matrix

Abstract

This invention discloses a holographic MIMO near-field channel estimation method based on spatial correlation matrix, comprising: modeling the 3D H-MIMO channel based on a non-uniform spherical wave model to establish an H-MIMO near-field channel model; calculating the spatial correlation coefficients between individual antennas at the base station, introducing a generalized single-sphere scatterer model, and deriving the near-field spatial correlation matrix; performing eigenvalue decomposition to construct a low-dimensional signal subspace; designing a pilot matrix, with the number of pilot slots in the pilot matrix set as the rank of the low-dimensional signal subspace; and estimating the coefficients of the low-dimensional signal subspace to obtain a channel estimator for the low-dimensional signal subspace. This invention effectively utilizes prior information on spatial correlation and provides a channel estimation method that significantly reduces pilot overhead and computational complexity.

Description

Technical Field

[0001] This invention relates to the field of channel estimation technology for holographic MIMO systems, and more specifically to a method for estimating the near-field channel of a low-rank subspace in holographic MIMO based on a generalized single-sphere scatterer model and a spatial correlation matrix. Background Technology

[0002] In holographic multiple-input multiple-output (H-MIMO) systems, the dense arrangement of antenna elements and continuous aperture structure lead to a sharp increase in the dimension of channel state information (CSI). Furthermore, since the communication distance is often located in the Fresnel region, electromagnetic waves exhibit spherical wave propagation characteristics, making traditional channel estimation methods based on the plane wave assumption difficult to apply.

[0003] Furthermore, in the millimeter-wave and terahertz bands, H-MIMO system channels exhibit strong near-field spatial correlations. Traditional discrete array channel modeling methods neglect the physical dimensions of antenna elements and the diffraction effect of electromagnetic waves across continuous apertures, resulting in a lack of physical interpretability in the channel model. Existing channel estimation methods, such as the Minimum Mean Square Error (MMSE) estimator, the Least Squares (LS) estimator, and the Orthogonal Matching Pursuit (OMP) algorithm, face problems of high pilot overhead and computational complexity in large-scale antenna systems. Especially in high-dimensional H-MIMO systems, the computational complexity of traditional compressed sensing methods increases exponentially with the antenna size, making practical deployment difficult.

[0004] Furthermore, existing channel models are mostly based on uniform linear arrays (ULAs) and generalized single-ring scattering models, which make it difficult to accurately characterize the spatial correlation characteristics of three-dimensional uniform planar arrays (UPAs) in near-field environments. Although some studies have attempted to estimate parameters using the covariance matrices in the angular and range domains, or to approximate the channel covariance using discrete Fourier transforms, these methods are either only applicable to line-of-sight (LoS) scenarios or difficult to generalize to three-dimensional UPA structures, limiting their application in practical H-MIMO systems.

[0005] Therefore, given the high-dimensionality, strong correlation, and low-rank characteristics of the near-field channel in H-MIMO systems, there is an urgent need for a channel estimation method that can effectively utilize spatial correlation prior information while significantly reducing pilot overhead and computational complexity, in order to support the future 6G communication system's requirements for high spectral efficiency and low-latency communication. Summary of the Invention

[0006] The present invention provides a holographic MIMO near-field channel estimation method based on spatial correlation matrix that can significantly reduce pilot overhead and improve channel estimation accuracy, and can at least solve one of the above-mentioned technical problems.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] A holographic MIMO near-field channel estimation method based on spatial correlation matrix is ​​applied to a 6G downlink H-MIMO system. In this system, the base station deploys a three-dimensional uniform planar array containing N antenna elements to serve a single-antenna user. The method includes the following steps:

[0009] S1. Model the 3D H-MIMO channel based on the non-uniform spherical wave model and establish the H-MIMO near-field channel model.

[0010] S2. Based on the H-MIMO near-field channel model established in S1, calculate the spatial correlation coefficient between each antenna at the base station, introduce the generalized single-sphere scatterer model, and combine it with the scatterer probability distribution function to derive the near-field spatial correlation matrix.

[0011] S3. Perform eigenvalue decomposition on the near-field spatial correlation matrix obtained in S2, select the eigenvectors corresponding to the principal eigenvalues ​​that contain more than 99% of the total energy, and use these eigenvectors to construct a low-dimensional signal subspace.

[0012] S4. Based on the low-dimensional signal subspace constructed in S3, design the pilot matrix. The number of pilot time slots in the pilot matrix is ​​set to the rank of the low-dimensional signal subspace, and ensure that the row space of the pilot matrix and the column space of the low-dimensional signal subspace are orthogonally matched to avoid energy leakage in the low-dimensional signal subspace during projection.

[0013] S5. Based on the pilot matrix designed in S4, the coefficients of the low-dimensional signal subspace are estimated to obtain the channel estimator of the low-dimensional signal subspace.

[0014] Furthermore, the holographic channel matrix from base station to user The Each element is represented as:

[0015]

[0016] in, Represents the complex vector space, and These represent the number of antenna elements along the y-axis and z-axis, respectively. and These represent the arrangement numbers of the antenna elements along the y-axis and z-axis on the array plane, respectively. Represents the first in the holographic channel matrix There are elements, where Q represents the total number of scatterers in the environment, and β... q Let g represent the channel power gain of the q-th scatterer. q For the central element of the uniform planar array UPA The signal amplitude contributed by the q-th scatterer at point , and Representing the scatterer and the central unit, and the scatterer and the central unit, respectively. The distance between units Let λ' represent the distance between the q-th scatterer and the user, and let e' represent the signal wavelength. x Let UPA be the unit normal vector of the uniform planar array. Let j' represent the phase shift caused by the q-th scatterer, and j' represent a complex number.

[0017] Furthermore, in S1, considering the physical dimensions of the antenna element, the antenna element is modeled as a square with an area of ​​A, the spacing between antenna elements is denoted as δ, and the array occupancy ratio is defined. This ratio characterizes the coverage of the antenna element on the uniform planar array UPA panel;

[0018] because ,therefore ,when At that time, the antenna elements are seamlessly and tightly arranged on the uniform planar array UPA panel. At that time, there are gaps between antenna elements, and the gaps change with... Decrease and increase.

[0019] Furthermore, in S2, the integral expression for the near-field spatial correlation matrix R is:

[0020]

[0021]

[0022] Where i and j represent the i-th and j-th antenna elements, respectively. and These are the elevation and azimuth angles between the scatterer and the central element, respectively. Let be the probability distribution function of the scatterer. This represents the array occupancy ratio. and Let these represent the projection direction cosines of the two antenna elements, respectively. , and Represent the scatterer and the central unit, and the (n)th unit, respectively. y ,nz )and The distance between units, e is a natural constant, λ' represents the signal wavelength, and j' represents a complex number.

[0023] Furthermore, in S2, considering the generalized single-sphere scatterer distribution model, let the sphere radius be L and the sphere center coordinates be... Where D≥0, and These represent the distance between the center of the sphere and the central element, the elevation angle, and the azimuth angle, respectively, and T is the matrix transpose;

[0024] Parameterize the scatterer position coordinates in the near-field spatial correlation matrix R as ,in, , The pitch angle, It is the azimuth angle, therefore the distance Parameterized as .

[0025] Furthermore, in S2, the von Mises-Fischer distribution is considered as the probability distribution function of the scatterer. Its spherical distribution perfectly matches the direction of three-dimensional wave propagation space and can flexibly control the direction and diffusion degree. The probability distribution function of the scatterer is expressed as:

[0026]

[0027] Where sinh(·) represents the hyperbolic sine function, The scatterer disperses outwards from its center in the average direction. , is a parameter used to control the degree of distribution concentration, when At that time, the scatterer is uniformly distributed on a sphere with center C and radius L. At that time, the scattering particles are all concentrated in the average direction.

[0028] Furthermore, in S3, the process of extracting the low-dimensional signal subspace is formally expressed as follows:

[0029]

[0030]

[0031] Where R is the near-field spatial correlation matrix, U is the subspace matrix, and Λ is the diagonal matrix. H' is the conjugate transpose, and U1 is the low-dimensional signal subspace. Let N be a complex vector space, where N is the total number of antenna elements and r is the number of principal eigenvalues.

[0032] Let the holographic channel vector Based on the characteristics of the low-dimensional signal subspace, the columns of the low-dimensional signal subspace U1 are used as basis vectors to represent the vectorized channel h, i.e., h = U1v, where vec(·) is the vectorization operation. These are the subspace coefficients of an r-dimensional vector.

[0033] Furthermore, in S3, the number of principal eigenvalues ​​r is determined as follows:

[0034] The diagonal matrix Λ contains all eigenvalues ​​sorted in descending order. The number of principal eigenvalues ​​r is defined as the number of eigenvalues ​​containing more than 99% of the total channel energy, expressed as:

[0035]

[0036] in, , is a parameter used to control the degree of distribution concentration. λ is a positive integer, N is the total number of antenna elements, and n is the nth antenna element.

[0037] Furthermore, in S4, the pilot matrix is ​​designed as follows: Where U1 is the low-dimensional signal subspace, Given a normalized T-dimensional orthogonal pilot matrix, the signal received by the user is:

[0038]

[0039] Where y is the user-received signal, ρ is the pilot signal-to-noise ratio, H' is the conjugate transpose, and h is the holographic channel vector. It is normalized Gaussian additive white noise;

[0040] Substituting h=U1v into the above equation, we obtain the user received signal. ,in, These are the subspace coefficients of an r-dimensional vector;

[0041] Let the equivalent observation matrix be defined. Then the user received signal is obtained. .

[0042] Furthermore, in S5, the MMSE estimator estimates the coefficients v of the low-dimensional signal subspace as follows:

[0043]

[0044] in, Here are the subspace coefficients of the MMSE estimator, and Λ1 is a diagonal matrix composed of principal eigenvalues. W is the equivalent observation matrix, H' is the conjugate transpose, ρ is the pilot signal-to-noise ratio, and I... T Let y be the identity matrix, and y be the user-received signal.

[0045] The low-dimensional signal subspace MMSE channel estimator MMSE-sub is then:

[0046]

[0047] in, U1 is the estimated value of the MMSE channel estimator in the low-dimensional signal subspace, where U1 is the low-dimensional signal subspace.

[0048] If we directly perform least squares estimation on the coefficients V of the low-dimensional signal subspace, the expression is:

[0049]

[0050] in, For the subspace coefficients of the low-dimensional signal subspace LS channel estimator, The normalized T-dimensional orthogonal pilot matrix;

[0051] The low-dimensional signal subspace LS channel estimator, LS-sub, is:

[0052]

[0053] in, The value is the estimate of the LS channel estimator for the low-dimensional signal subspace.

[0054] The beneficial effects of this invention are reflected in:

[0055] The low-rank subspace near-field channel estimation method based on the generalized single-sphere scatterer model and spatial correlation matrix provided by this invention provides the same channel estimation accuracy as traditional channel estimation while significantly reducing pilot overhead. It can not only effectively utilize spatial correlation prior information, but also significantly reduce pilot overhead and computational complexity, meeting the requirements of future 6G communication systems for high spectral efficiency and low latency communication. Attached Figure Description

[0056] The accompanying drawings, which are provided to further illustrate this application and form part of this application, illustrate exemplary embodiments of this application and are used to explain this application, but do not constitute an undue limitation of this application.

[0057] Figure 1 This is a schematic diagram of the overall process of the channel estimation method according to an embodiment of the present invention.

[0058] Figure 2 The channel estimation method of this embodiment of the invention differs from other channel estimation methods in that the antenna element side length is... The degree of polymerization of the scatterer is A diagram showing the performance comparison under different signal-to-noise ratio environments.

[0059] Figure 3 The channel estimation method of this embodiment of the invention differs from other channel estimation methods in that the antenna element side length is... The degree of polymerization of the scatterer is A diagram showing the performance comparison under different signal-to-noise ratio environments.

[0060] Figure 4 This is a schematic diagram comparing the performance of the channel estimation method of this invention with other channel estimation methods under different antenna spacings in an embodiment of the present invention.

[0061] Figure 5 This is a structural block diagram of a computer device according to an embodiment of the present invention. Detailed Implementation

[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] It should be noted that the meaning of "and / or" throughout the text includes three parallel solutions. Taking "A and / or B" as an example, it includes solution A, solution B, or a solution that simultaneously satisfies A and B. Furthermore, "multiple" refers to two or more. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0064] See Figure 1 This invention provides a holographic MIMO near-field channel estimation method based on spatial correlation matrix, applied to a 6G downlink H-MIMO system. In this system, the base station (BS) deploys a three-dimensional uniform planar array containing N antenna elements to serve a single-antenna user (UE). The method includes the following steps:

[0065] S1. Model the 3D H-MIMO channel based on the non-uniform spherical wave model and establish the H-MIMO near-field channel model.

[0066] In S1, unlike traditional array modeling which treats antenna elements as point sources without physical dimensions, this invention considers the physical dimensions of antenna elements, models them as squares with area A, denotes the spacing between antenna elements as δ, and defines the array occupancy ratio. This ratio characterizes the coverage of the antenna element on the uniform planar array (UPA) panel;

[0067] because ,therefore ,when At that time, the antenna elements are seamlessly and tightly arranged on the UPA panel. At that time, there are gaps between antenna elements, and the gaps change with... Decrease and increase.

[0068] Therefore, by adjusting the unit size and unit spacing The model, which unifies the modeling of continuous holographic surfaces to discrete antenna arrays, considers the relationship between the sizes of the surfaces. It establishes a three-dimensional Cartesian coordinate system, assuming the UPA center of the BS is located at the origin, with the UPA plane coinciding with the yz plane. y and N z Let N be the number of antenna elements along the y-axis and z-axis, respectively, then N = N y ×N z For simplicity, assume N y and N z It is an odd number. (BS is the first...) The center position of each antenna element is ,in, , .

[0069] This embodiment models the 3D H-MIMO channel and calculates its spatial correlation matrix based on the Non-Uniform Spherical Wave (NUSW) model. It assumes there are Q scatterers in the environment, and the position of the q-th scatterer is denoted as... , where r q θ q and Let q represent the distance from the scattering object to the array center, its elevation angle, and its azimuth angle, respectively. Therefore, the q-th scattering object and the scattering object... The distance between array cells is Then, the holographic channel matrix from BS to UE. The Each element is represented as:

[0070]

[0071] in, Represents the complex vector space, and These represent the number of antenna elements along the y-axis and z-axis, respectively. and These represent the arrangement numbers of the antenna elements along the y-axis and z-axis on the array plane, respectively. Represents the first in the holographic channel matrix There are elements, where Q represents the total number of scatterers in the environment, and β... q Let g represent the channel power gain of the q-th scatterer. q For UPA central unit The signal amplitude contributed by the q-th scatterer is such that, to avoid power calculation errors due to the number of scatterers or individual differences, this random variable satisfies... , and Representing the scatterer and the central unit, and the scatterer and the central unit, respectively. The distance between units Let λ' represent the distance between the q-th scatterer and the user, and let e' represent the signal wavelength. x Let UPA be the unit normal vector of the uniform planar array. Let j' represent the phase shift caused by the q-th scatterer, and j' represent a complex number.

[0072] Let the holographic channel vector And the distance between all antenna elements and the q-th scatterer is denoted as Then equation (1) can be rewritten as follows:

[0073] (2)

[0074] in, 0 Let represent the Hadamard product. Based on the NUSW channel model described above, the spatial correlation characteristics of the H-MIMO system can be obtained analytically by representing the second-order statistics of the channel vector h. It is worth noting that in the traditional far-field model, spatial correlation is dominated only by the angular domain statistics, while the near-field propagation characteristics of H-MIMO make the scatterer distance fluctuation and antenna element projection effect the key factors affecting the correlation. In order to quantify this coupling effect and to provide support for subsequent channel estimation, the BS needs to obtain prior knowledge of the spatial covariance matrix of the UE. Therefore, the following will derive its spatial correlation matrix starting from the channel structure of equation (2). The integral expression for .

[0075] S2. Based on the H-MIMO near-field channel model established in S1, calculate the spatial correlation coefficient between each antenna at the base station, introduce the generalized single-sphere scatterer model, and combine it with the scatterer probability distribution function to derive the near-field spatial correlation matrix.

[0076] In S2, based on the modeling of accurate distance and projection attenuation using the NUSW model, this embodiment proposes an analytical framework for constructing a three-dimensional spatial correlation matrix in the joint angle-distance domain. Furthermore, based on the above equation (2), the integral expression for the near-field spatial correlation matrix R is derived as follows:

[0077]

[0078]

[0079] Where i and j represent the i-th and j-th antenna elements, respectively. and These are the elevation and azimuth angles between the scatterer and the central element, respectively. Let be the probability distribution function of the scatterer. This represents the array occupancy ratio. and Let these represent the projection direction cosines of the two antenna elements, respectively. , and Represent the scatterer and the central unit, and the (n)th unit, respectively. y ,n z )and The distance between units, e is a natural constant, λ' represents the signal wavelength, and j' represents a complex number.

[0080] In S2, a generalized single-sphere scatterer distribution model is considered, with the sphere radius being L and the sphere center coordinates being... Where D≥0, and These represent the distance between the center of the sphere and the central element, the elevation angle, and the azimuth angle, respectively, and T is the matrix transpose;

[0081] Parameterize the scatterer position coordinates in the near-field spatial correlation matrix R as ,in, , The pitch angle, It is the azimuth angle, therefore the distance Parameterized as .

[0082] In S2, because To ensure a high geometric fit with the generalized single-sphere scatterer model, this invention considers using the von Mises-Fischer distribution as the scatterer probability distribution function. Its spherical distribution perfectly matches the direction of three-dimensional wave propagation and allows for flexible control of direction and diffusion. This scatterer probability distribution function is expressed as:

[0083]

[0084] Where sinh(·) represents the hyperbolic sine function, The scatterer disperses outwards from its center in the average direction. , is a parameter used to control the degree of distribution concentration, when At that time, the scatterer is uniformly distributed on a sphere with center C and radius L. At that time, the scattering particles are all concentrated in the average direction.

[0085] For downlink communication, assume that the BS sends mutually orthogonal pilot matrices X∈L to the UE. N×T Where T is the number of pilot time slots, and the signal received by the UE within T time slots is:

[0086] (5)

[0087] in, For pilot signal-to-noise ratio, It is normalized Gaussian additive white noise.

[0088] If the spatial correlation matrix in equation (3) above is known, then the MMSE estimator can be used to estimate h, and the estimated value is:

[0089] (6)

[0090] Here, R contains N×N elements. In practice, obtaining the complete R is very difficult when the BS only sends small data packets or when N is large. In this case, the Least Squares (LS) estimator can be considered as an alternative. This method only requires the pilot matrix and the LS estimates of ρ and h:

[0091] (7)

[0092] However, the LS estimator does not use any prior information and therefore performs poorly. Therefore, this invention aims to find a method that can guarantee estimation accuracy while saving pilot overhead by studying the structural characteristics of the spatial correlation matrix of 3D H-MIMO.

[0093] See Figures 2-3 In this embodiment, the antenna array is set as a 65×65 UPA, and the side length of the antenna element is... ,consider and Two antenna spacing options are used, with a carrier frequency of 30 GHz. For the generalized single-sphere model, the following settings are provided. , , , Furthermore, in equation (3) We compared the changes in the eigenvalues ​​of the spatial correlation matrix under matching conditions of 0 and 50, respectively. We can observe that the rate of eigenvalue descent is related to... Proportional to, with Inversely proportional. When , The eigenvalue decreases fastest at time, followed by , sometimes , The slowest. Near-field communication in H-MIMO inherently leads to energy concentration in the spatial correlation matrix, resulting in a low-rank channel. Furthermore, when the antenna spacing is small and the scatterer aggregation is high, the correlation between antennas is strong, leading to a stronger rank deficiency effect in the spatial correlation matrix. Therefore, this embodiment considers projecting the channel onto the principal component space of the spatial correlation matrix, extracting the principal eigenvectors through eigenvalue decomposition—that is, the eigenvectors corresponding to the eigenvalues ​​containing more than 99% of the total energy—and constructing a low-dimensional subspace for channel estimation.

[0094] To understand how MMSE utilizes the low-rank spatial correlation matrix, the following steps are taken:

[0095] S3. Perform eigenvalue decomposition on the near-field spatial correlation matrix obtained in S2, select the eigenvectors corresponding to the principal eigenvalues ​​containing more than 99% of the total energy, and use these eigenvectors to construct a low-dimensional signal subspace.

[0096] In S3, the process of extracting the low-dimensional signal subspace is formally expressed as follows:

[0097]

[0098]

[0099] Where R is the near-field spatial correlation matrix, U is the subspace matrix, and Λ is the diagonal matrix. H' is the conjugate transpose, and U1 is the low-dimensional signal subspace. Let N be a complex vector space, where N is the total number of antenna elements and r is the number of principal eigenvalues.

[0100] Let the holographic channel vector Based on the characteristics of the low-dimensional signal subspace, the columns of the low-dimensional signal subspace U1 are used as basis vectors to represent the vectorized channel h, i.e., h = U1v, where vec(·) is the vectorization operation. These are the subspace coefficients of an r-dimensional vector.

[0101] In S3, the number of principal eigenvalues ​​r is determined as follows:

[0102] The diagonal matrix Λ contains all eigenvalues ​​sorted in descending order. The number of principal eigenvalues ​​r is defined as the number of eigenvalues ​​containing more than 99% of the total channel energy, expressed as:

[0103]

[0104] in, , is a parameter used to control the degree of distribution concentration. λ is a positive integer, N is the total number of antenna elements, and n is the nth antenna element.

[0105] S4. Design the pilot matrix based on the low-dimensional signal subspace constructed in S3.

[0106] Since channel estimation in the subspace only needs to be performed within the subspace, the number of pilot slots T is set to the rank r of the subspace. However, the number of pilot slots is reduced only to... This is insufficient to guarantee estimation accuracy. If the pilot matrix fails to effectively cover the column space of U1, the observation equation will be unable to fully capture the channel energy distribution, leading to irreversible information loss in the subspace coefficient estimation. Therefore, the number of pilot slots in the pilot matrix is ​​designed to be the rank of the low-dimensional signal subspace, and the row space of the pilot matrix is ​​orthogonally matched with the column space of the low-dimensional signal subspace to avoid energy leakage in the low-dimensional signal subspace during projection.

[0107] In S4, the pilot matrix is ​​designed as follows: Where U1 is the low-dimensional signal subspace, Given a normalized T-dimensional orthogonal pilot matrix, the signal received by the UE is:

[0108]

[0109] Where y is the user-received signal, ρ is the pilot signal-to-noise ratio, H' is the conjugate transpose, and h is the holographic channel vector. It is normalized Gaussian additive white noise;

[0110] Substituting h=U1v into the above equation, we obtain the user received signal. ,in, These are the subspace coefficients of an r-dimensional vector;

[0111] Let the equivalent observation matrix be defined. Then the user received signal is obtained. .

[0112] S5. Based on the pilot matrix designed in S4, the coefficients of the low-dimensional signal subspace are estimated to obtain the channel estimator of the low-dimensional signal subspace.

[0113] See Figure 4In S5, when the signal-to-noise ratio is high, the noise component can be ignored, and the MMSE estimator estimates the low-dimensional signal subspace coefficients v as follows:

[0114]

[0115] in, Here are the subspace coefficients of the MMSE estimator, and Λ1 is a diagonal matrix composed of principal eigenvalues. W is the equivalent observation matrix, H' is the conjugate transpose, ρ is the pilot signal-to-noise ratio, and I... T Let y be the identity matrix, and y be the user-received signal.

[0116] The low-dimensional signal subspace MMSE channel estimator MMSE-sub is then:

[0117]

[0118] in, U1 is the estimated value of the MMSE channel estimator in the low-dimensional signal subspace, where U1 is the low-dimensional signal subspace.

[0119] If we directly perform least squares estimation on the coefficients V of the low-dimensional signal subspace, the expression is:

[0120]

[0121] in, For the subspace coefficients of the low-dimensional signal subspace LS channel estimator, The normalized T-dimensional orthogonal pilot matrix;

[0122] The low-dimensional signal subspace LS channel estimator LS-sub is then:

[0123]

[0124] in, The value is the estimate of the LS channel estimator for the low-dimensional signal subspace.

[0125] Therefore, theoretically, as the signal-to-noise ratio increases, noise becomes negligible, and relying solely on observed data, the performance of LS-sub will continuously approach that of MMSE-sub. However, in low-noise conditions, MMSE-sub utilizes prior information... It suppresses noise and outperforms LS-sub.

[0126] This invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the holographic MIMO near-field channel estimation method based on the spatial correlation matrix described above.

[0127] See Figure 5 The present invention also provides a computer device, including a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the holographic MIMO near-field channel estimation method based on the spatial correlation matrix described above.

[0128] This invention also provides a computer program product containing instructions that, when run on a computer, cause the computer to perform the steps of the holographic MIMO near-field channel estimation method based on the spatial correlation matrix described above.

[0129] It is understood that the systems, devices, and storage media provided in the embodiments of the present invention correspond to the methods provided in the embodiments of the present invention, and the explanations, examples, and beneficial effects of the relevant content can be referred to the corresponding parts of the above-described holographic MIMO near-field channel estimation method based on spatial correlation matrix.

[0130] It should be noted that those skilled in the art will understand that all or part of the steps implemented in the embodiments of the present invention can be implemented entirely or partially by software, hardware, firmware, or any combination thereof. When implemented in hardware, it can be implemented entirely or partially by purchasing standard parts or modifications. When implemented in software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available media may be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid state disks (SSDs)).

[0131] In summary, this invention addresses the high-dimensionality, strong correlation, and low-rank characteristics of near-field channels in H-MIMO systems by providing a low-rank subspace near-field channel estimation method based on a generalized single-sphere scatterer model and a spatial correlation matrix. First, the expression for the 3D H-MIMO near-field channel spatial correlation matrix is ​​derived based on a generalized single-sphere scatterer distribution model that allows flexible sphere center positioning. Second, based on the density of antenna element deployment and scatterer distribution, the strong rank deficiency characteristic of the spatial correlation matrix is ​​revealed. Third, based on the high correlation and low-rank characteristics of the spatial correlation matrix, a subspace-based channel estimation method is proposed, combining it with traditional MMSE and LS estimators to form low-dimensional subspace-based MMSE-sub estimators and LS-sub estimators, and designing orthogonal pilot sequences for channel estimation. Finally, simulation experiments demonstrate that, under the premise of significantly reducing pilot overhead, the performance of the MMSE-sub estimator remains consistent with that of the traditional MMSE estimator, while the performance of the LS-sub estimator is superior to that of the traditional LS estimator. Thus, while significantly reducing pilot overhead, it provides the same channel estimation accuracy as traditional channel estimation methods.

[0132] It should be understood that the examples and embodiments described herein are for illustrative purposes only and are not intended to limit the invention. Those skilled in the art can make various modifications or changes based on them. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the protection scope of the invention.

Claims

1. A holographic MIMO near-field channel estimation method based on spatial correlation matrix, applied to a 6G downlink H-MIMO system, characterized in that, In the system, the base station deploys a three-dimensional uniform planar array containing N antenna elements to serve a single-antenna user. The method includes the following steps: S1. Model the 3D H-MIMO channel based on the non-uniform spherical wave model and establish the H-MIMO near-field channel model; S2. Based on the H-MIMO near-field channel model established in S1, calculate the spatial correlation coefficient between each antenna element at the base station, introduce the generalized single-sphere scatterer model, and derive the near-field spatial correlation matrix by combining the scatterer probability distribution function. S3. Perform eigenvalue decomposition on the near-field spatial correlation matrix obtained in S2, select the eigenvectors corresponding to the principal eigenvalues ​​that contain more than 99% of the total energy, and use these eigenvectors to construct a low-dimensional signal subspace. S4. Based on the low-dimensional signal subspace constructed in S3, design the pilot matrix. The number of pilot time slots in the pilot matrix is ​​set to the rank of the low-dimensional signal subspace, and ensure that the row space of the pilot matrix and the column space of the low-dimensional signal subspace are orthogonally matched to avoid energy leakage in the low-dimensional signal subspace during projection. S5. Based on the pilot matrix designed in S4, the coefficients of the low-dimensional signal subspace are estimated to obtain the channel estimator of the low-dimensional signal subspace. In S2, considering the generalized single-sphere scatterer distribution model, let the sphere radius be L and the sphere center coordinates be... Where D≥0, and These represent the distance between the center of the sphere and the central element, the elevation angle, and the azimuth angle, respectively, and T is the matrix transpose; Parameterize the scatterer position coordinates in the near-field spatial correlation matrix R as ,in, , The pitch angle, It is the azimuth angle, therefore the distance Parameterized as ; In S2, the von Mises-Fischer distribution is considered as the probability distribution function of the scatterer. Its spherical distribution perfectly matches the direction of three-dimensional wave propagation space and can flexibly control the direction and diffusion degree. The probability distribution function of the scatterer is expressed as: Where sinh(·) represents the hyperbolic sine function, The scatterer disperses outwards from its center in the average direction. , is a parameter used to control the degree of distribution concentration, when At that time, the scatterer is uniformly distributed on a sphere with center C and radius L. At that time, the scattering particles are all concentrated in the average direction.

2. The holographic MIMO near-field channel estimation method based on spatial correlation matrix as described in claim 1, characterized in that, In S1, the holographic channel matrix from the base station to the user The Each element is represented as: in, Represents the complex vector space, and These represent the number of antenna elements along the y-axis and z-axis, respectively. and These represent the arrangement numbers of the antenna elements along the y-axis and z-axis on the array plane, respectively. Represents the first in the holographic channel matrix There are elements, where Q represents the total number of scatterers in the environment, and β... q Let g represent the channel power gain of the q-th scatterer. q For the central element of the uniform planar array UPA The signal amplitude contributed by the q-th scatterer at point , and Representing the scatterer and the central unit, and the scatterer and the central unit, respectively. The distance between units Let λ' represent the distance between the q-th scatterer and the user, and let e' represent the signal wavelength. x Let UPA be the unit normal vector of the uniform planar array. Let j' represent the phase shift caused by the q-th scatterer, and j' represent a complex number.

3. The holographic MIMO near-field channel estimation method based on spatial correlation matrix as described in claim 1, characterized in that, In step S1, considering the physical dimensions of the antenna elements, the antenna element is modeled as a square with an area of ​​A, the spacing between antenna elements is denoted as δ, and the array occupancy ratio is defined. The array occupancy ratio characterizes the coverage of the antenna element on the uniform planar array UPA panel; because ,therefore ,when At that time, the antenna elements are seamlessly and tightly arranged on the uniform planar array UPA panel. At that time, there are gaps between antenna elements, and the gaps change with... Decrease and increase.

4. The holographic MIMO near-field channel estimation method based on spatial correlation matrix as described in claim 1, characterized in that, In S2, the integral expression of the near-field spatial correlation matrix R is: Where i and j represent the i-th and j-th antenna elements, respectively. and These are the elevation and azimuth angles between the scatterer and the central element, respectively. Let be the probability distribution function of the scatterer. This represents the array occupancy ratio. and Let these represent the projection direction cosines of the two antenna elements, respectively. , and Represent the scatterer and the central unit, and the (n)th unit, respectively. y ,n z )and The distance between units, e is a natural constant, λ' represents the signal wavelength, and j' represents a complex number.

5. The holographic MIMO near-field channel estimation method based on spatial correlation matrix as described in claim 1, characterized in that, In S3, the process of extracting the low-dimensional signal subspace is formally expressed as follows: Where R is the near-field spatial correlation matrix, U is the subspace matrix, and Λ is the diagonal matrix. H' is the conjugate transpose, and U1 is the low-dimensional signal subspace. Let N be a complex vector space, where N is the total number of antenna elements and r is the number of principal eigenvalues. Let the holographic channel vector Based on the characteristics of the low-dimensional signal subspace, the columns of the low-dimensional signal subspace U1 are used as basis vectors to represent the vectorized channel h, i.e., h = U1v, where vec(·) is the vectorization operation. These are the subspace coefficients of an r-dimensional vector.

6. The holographic MIMO near-field channel estimation method based on spatial correlation matrix as described in claim 5, characterized in that, In S3, the number of principal eigenvalues ​​r is determined as follows: The diagonal matrix Λ contains all eigenvalues ​​sorted in descending order. The number of principal eigenvalues ​​r is defined as the number of eigenvalues ​​containing more than 99% of the total channel energy, expressed as: in, , is a parameter used to control the degree of distribution concentration. λ is a positive integer, N is the total number of antenna elements, and n is the nth antenna element.

7. The holographic MIMO near-field channel estimation method based on spatial correlation matrix as described in claim 1, characterized in that, In S4, the pilot matrix is ​​designed as follows: Where U1 is the low-dimensional signal subspace, Given a normalized T-dimensional orthogonal pilot matrix, the signal received by the user is: Where y is the user-received signal, ρ is the pilot signal-to-noise ratio, H' is the conjugate transpose, and h is the holographic channel vector. It is normalized Gaussian additive white noise; Substituting h=U1v into the above equation, we obtain the user received signal. ,in, These are the subspace coefficients of an r-dimensional vector; Let the equivalent observation matrix be defined. Then the user received signal is obtained. .

8. The holographic MIMO near-field channel estimation method based on spatial correlation matrix as described in claim 1, characterized in that, In S5, the MMSE estimator estimates the coefficients v of the low-dimensional signal subspace as follows: in, Here are the subspace coefficients of the MMSE estimator, and Λ1 is a diagonal matrix composed of principal eigenvalues. W is the equivalent observation matrix. For the conjugate transpose, ρ is the pilot signal-to-noise ratio, and I is... T Let y be the identity matrix, and y be the user-received signal. The low-dimensional signal subspace MMSE channel estimator MMSE-sub is then: in, U1 is the estimated value of the MMSE channel estimator in the low-dimensional signal subspace, where U1 is the low-dimensional signal subspace. If we directly perform least squares estimation on the coefficients V of the low-dimensional signal subspace, the expression is: in, For the subspace coefficients of the low-dimensional signal subspace LS channel estimator, The normalized T-dimensional orthogonal pilot matrix; The low-dimensional signal subspace LS channel estimator LS-sub is then: in, The value is the estimate of the LS channel estimator for the low-dimensional signal subspace.

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