A robust multipath channel estimation method for antenna array systems

Abstract

This invention relates to a robust multipath channel estimation method for antenna array systems, belonging to the field of signal processing. It includes: establishing a large-scale MIMO signal propagation model with array gain-phase perturbations; designing an antenna array movement scheme; reconstructing the obtained CSI matrix at the receiver to obtain a unified representation of the CSI from multiple observations; extracting data from the CSI covariance matrix based on a joint spatial-frequency smoothing method to obtain a rank-recovered CSI covariance matrix; performing eigenvalue decomposition on the rank-recovered CSI covariance matrix to obtain a noise subspace matrix; and then achieving joint estimation of angle, time delay, and gain-phase perturbations under the constructed one-dimensional angle spectrum, one-dimensional time delay spectrum function, and closed-form solution of array gain-phase perturbations. This invention exhibits robust parameter estimation performance for array gain-phase perturbations, significantly improving parameter estimation accuracy and multipath resolution.

Description

Technical Field

[0001] This invention belongs to the field of signal processing and relates to a channel estimation technique, specifically a parameterized multipath channel estimation method that considers the inconsistency of array channels in a large-scale antenna array system. Background Technology

[0002] Massive multiple-input multiple-output (MIMO) is an emerging wireless communication technology that significantly improves signal transmission efficiency and reliability by adding more antennas at the base station. Due to the large number of antennas and the complexity of the channel state, only through accurate channel estimation and prediction can optimal resource allocation and power control be achieved, thereby improving system performance and user experience. Therefore, channel estimation is an indispensable part of massive MIMO systems and one of the keys to achieving efficient communication.

[0003] Currently, channel estimation methods for large-scale MIMO systems can be broadly categorized into two types: 1) Non-parametric model-based methods: These methods make no assumptions about the channel and directly estimate the channel based on existing observation data. 2) Parametric model-based methods: These methods assume that the characteristic parameters of the channel are known or estimable and describe the channel's variation patterns by establishing mathematical models. The advantage of non-parametric model methods is their adaptability to various channel models, eliminating the need for strict prior assumptions about the channel and offering high flexibility and adaptability. However, their disadvantages are also significant. Firstly, they require a large number of training samples to obtain accurate estimation results, resulting in high computational complexity. Secondly, the performance of these algorithms degrades significantly when dealing with large-dimensional channel state information (CSI) matrices in real-world scenarios. Parametric model-based channel estimation, by making strict prior assumptions about the channel model, reduces the complexity and computational cost of estimation while still yielding more accurate results.

[0004] In previous research, pure angle estimation and pure delay estimation techniques have become mature. However, a single parameter dimension is clearly insufficient to characterize the complete state information of the channel. Therefore, channel models described by multiple parameters are the main trend in the development of parameterized channel estimation. Currently, the mainstream multi-parameter channel estimation model is joint angle and delay estimation (JADE), which achieves a more complete and accurate estimation of the channel state by combining the angle domain and the delay domain.

[0005] It is important to note that the parameterized channel estimation studies mentioned above are all based on the ideal antenna assumption, that is, the steering vector of the antenna array is assumed to be precisely known. However, in reality, there are unknown array perturbations, such as gain-phase perturbations, coupling, and inaccurate array positions, which can cause inconsistencies between the pre-defined array manifold and actual observations, thus significantly affecting the performance of parameter estimation. Although there are many studies on angle or time delay estimation under array perturbations, research on multi-parameter channel estimation considering array perturbation conditions in large-scale MIMO systems remains lacking. Summary of the Invention

[0006] The technical problem to be solved by this invention is:

[0007] To address the problem of parameterized multipath channel estimation in large-scale antenna array systems with inconsistent antenna array channels, this invention provides a robust multipath channel estimation method for antenna array systems. This method primarily improves the accuracy and robustness of parameter estimation by increasing the array degrees of freedom and the virtual array aperture.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0009] A robust multipath channel estimation method for an antenna array system, characterized by comprising:

[0010] Establish a MIMO signal propagation model with array gain-phase perturbation;

[0011] Design an antenna array movement scheme, where the base station receives multiple observation data and reassembles the data to obtain a unified CSI representation of the multiple observations;

[0012] The covariance matrix of the unified CSI is calculated, and the CSI covariance matrix is ​​extracted based on the spatial-frequency joint smoothing method to obtain the rank-recovered CSI covariance matrix;

[0013] The obtained rank-recovered CSI covariance matrix is ​​subjected to eigenvalue decomposition to obtain its corresponding noise subspace matrix; a one-dimensional angle spectrum function is constructed based on the noise subspace matrix, and the incident angle is estimated by peak search; a one-dimensional time delay spectrum function is constructed with the estimated incident angle as support, and the path delay is estimated by peak search; the array gain-phase perturbation is estimated by combining the incident angle and the path delay using the derived closed-form solution.

[0014] A further technical solution of the present invention: The large-scale MIMO signal propagation model under array gain-phase perturbation is as follows:

[0015] Assume the base station (BS) is equipped with a uniform linear array of M antenna elements, and the user communicates with the BS in the far field. Assume there are K propagation paths between the user's transmitted signal and the BS, including one line-of-sight path and K-1 non-line-of-sight paths. Therefore, considering array gain-phase perturbations, the BS received signal model can be expressed as follows:

[0016] Y=ΓAPF T B+W

[0017] in It is a diagonal matrix whose diagonal elements γ m m = 1, 2, ..., M-1 corresponds to the complex gain-phase perturbation of the (m+1)th array element; For array space response, This is the guide vector corresponding to the k-th path; It is a diagonal matrix whose diagonal elements consist of the fading factors of K paths; The time delay response for all N subcarriers is defined. It contains the delay information of the nth subcarrier of all paths; It is a diagonal matrix composed of binary phase shift keying symbols, b n The BPSK symbol for the nth subcarrier is defined in {-1,1}; It is an additive noise matrix;

[0018] Therefore, the CSI matrix obtained from the BS end can be represented as

[0019]

[0020] Z = WB can be considered as the estimation error of the CSI matrix C. A column straightening operation is performed on the CSI matrix C to obtain the CSI vector.

[0021]

[0022] in Defined as an array manifold with gain-phase perturbation. Defined as path fading vector, Defined as a new additive noise vector, which is assumed to conform to a variance of σ. 2 It follows a zero-mean complex Gaussian distribution.

[0023] A further technical solution of the present invention: the antenna array movement scheme and data recombination method are as follows:

[0024] The total observation time of BS is evenly divided into L time slots, with starting times t1, t2, and t3, t4, t5, t6, t7, t8, t9, t1, t2, ...1, t2, t3, t4, t ll = 1, 2, ..., L; the antenna array of BS remains stationary in each time slot, but at each time t l By moving a fixed distance Δd, BS can collect L observation signals, corresponding to L CSI vectors, denoted as...

[0025]

[0026] Will Divide the unit into N uniform units, and define the nth unit as... Represented as

[0027]

[0028] Where F n,: This represents the nth row of F; the recombined CSI vector is defined in advance as... Similarly, it is divided into N units, and the nth unit is represented as... Therefore,

[0029]

[0030] in This represents the actual array manifold with an L-order observation expansion having gain-phase perturbations. Thus, the reconstructed CSI vector It can be represented as

[0031]

[0032] in Represents the equivalent channel response.

[0033] A further technical solution of the present invention: The method of extracting data from the CSI covariance matrix based on the spatial-frequency domain joint smoothing method to obtain the rank-recovered CSI covariance matrix is ​​specifically as follows:

[0034] Reconstructed CSI vector covariance matrix It can be represented as

[0035]

[0036] in Denotes the covariance matrix of ρ;

[0037] In the constructed selection matrix and Below, the CSI covariance matrix Perform data extraction operations, i.e.

[0038]

[0039] Where p = 1, 2, ..., P and q = 1, 2, ..., Q; thus, the rank-recovered CSI covariance matrix R is obtained. CSI :

[0040]

[0041] in

[0042] A further technical solution of the present invention: the eigenvalue decomposition of the obtained rank-recovered CSI covariance matrix to obtain its corresponding noise subspace matrix specifically involves:

[0043] For the rank-restored CSI covariance matrix R CSI Its equivalent channel response is Ψ1=F1⊙E1, which can be expressed as

[0044]

[0045]

[0046] in Indicates the first The second observation has a steering vector with gain-phase perturbation; additionally,

[0047]

[0048] in

[0049]

[0050]

[0051]

[0052] For R CSI By performing eigenvalue decomposition, its noise subspace matrix can be obtained.

[0053] A further technical solution of the present invention: the construction of a one-dimensional angle spectrum function based on the noise subspace matrix, and the estimation of the incident angle through spectral peak search, specifically involves:

[0054] Construct a function with the incident angle θ as the variable. Where θ∈[-90°,90°]; thus, the following one-dimensional angle spectrum function is given:

[0055]

[0056] Where det{·} represents the determinant of the matrix, theoretically, χ θ (θ kThe angles k = 1, 2, ..., K have local maxima in the angle spectrum; therefore, the angle value corresponding to the local maxima in the angle spectrum is the estimated incident angle, expressed as:

[0057] A further technical solution of the present invention: the construction of a one-dimensional time delay spectrum function supported by the estimated incident angle, and the estimation of path delay through spectral peak search, specifically involves:

[0058] Using the time delay τ as a variable, construct the following function corresponding to the k-th path.

[0059]

[0060] in The incident angle is estimated, and from this, the following one-dimensional time delay spectrum function corresponding to the k-th path is constructed:

[0061]

[0062] Obviously, χ τ,k (τ k The path should have a maximum value in the k-th delay spectrum. Therefore, the delay value corresponding to the maximum value in the k-th delay spectrum is the estimated delay value of the k-th path, expressed as:

[0063] A further technical solution of the present invention: the estimation of array gain-phase perturbation using the derived closed-form solution by combining the incident angle and path delay specifically involves:

[0064] definition Therefore, Ωγ=0, where Define ω as the first column of Ω. Composed of the columns of Ω except for ω, The array gain-phase perturbation vector can be estimated using the following formula.

[0065]

[0066] in This indicates the Moore-Penrose inverse operation.

[0067] A computer system is characterized by comprising: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method described above.

[0068] A computer-readable storage medium is characterized by storing computer-executable instructions, which, when executed, are used to implement the above-described method.

[0069] The beneficial effects of this invention are as follows:

[0070] This invention provides a robust parameterized multipath channel estimation method for large-scale antenna array systems. It proposes a novel spatial-frequency joint smoothing method that can effectively recover the rank of the covariance matrix of the coherent signal, thereby achieving multipath signal resolution. Under the given one-dimensional angle and time delay spectrum function, the algorithm still has accurate and robust parameter estimation performance under the condition of uncalibrated array gain-phase perturbation, which significantly improves the parameter estimation accuracy and multipath resolution capability compared with existing algorithms. Attached Figure Description

[0071] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0072] Figure 1 This is a flowchart of the algorithm of the present invention.

[0073] Figure 2 This is a schematic diagram of the antenna array movement scheme designed for this invention.

[0074] Figure 3 This is a scatter plot of the estimated angle and time delay values ​​from 500 Monte Carlo tests conducted according to the present invention.

[0075] Figure 4 This is a schematic diagram illustrating the relationship between the root mean square error and the signal-to-noise ratio for angle estimation in this invention.

[0076] Figure 5 This is a schematic diagram illustrating the relationship between the root mean square error and the signal-to-noise ratio for time delay estimation in this invention.

[0077] Figure 6 This is a schematic diagram illustrating the relationship between the root mean square error and signal-to-noise ratio for the gain-phase perturbation estimation of this invention. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0079] To address the problem that traditional parameterized channel estimation algorithms cannot effectively estimate parameters when there are inconsistencies in antenna array channels, this invention proposes a parameterized channel estimation method for large-scale antenna array systems. This method utilizes a designed spatial-frequency domain joint smoothing method to perform joint angle and time delay estimation under array gain and phase perturbations. It exhibits robust parameter estimation performance for array gain and phase perturbations and significantly improves parameter estimation accuracy and multipath resolution compared to existing algorithms.

[0080] This invention provides a parameterized channel estimation method for joint angle and time delay using a designed spatial-frequency joint smoothing method under array gain phase perturbation, specifically including the following steps:

[0081] Step 1: Establish a large-scale MIMO signal propagation model with array gain-phase perturbation;

[0082] Step 2: Under the designed antenna array movement scheme, the obtained CSI matrix is ​​reassembled at the receiving end to achieve a unified representation of CSI from multiple observations;

[0083] Step 3: Calculate the covariance matrix of the unified CSI obtained in Step 2, and extract data from the CSI covariance matrix using the designed spatial-frequency joint smoothing method to obtain the rank-recovered CSI covariance matrix.

[0084] Step 4: Perform eigenvalue decomposition on the rank-recovered CSI covariance matrix obtained in Step 3 to obtain its corresponding noise subspace matrix. Then, under the constructed one-dimensional angle spectrum, one-dimensional time delay spectrum function and closed-form solution of array gain phase perturbation, the joint estimation of angle, time delay and gain phase perturbation is realized.

[0085] The above steps are as follows:

[0086] The large-scale MIMO signal propagation model under array gain-phase perturbation described in step 1 is as follows:

[0087] Assume the base station (BS) is equipped with a uniform linear array of M antenna elements, and the user communicates with the BS in the far field. Assume there are K propagation paths between the user's transmitted signal and the BS, including one line-of-sight (LOS) path and K-1 non-line-of-sight (NLOS) paths. Therefore, considering array gain-phase perturbations, the BS received signal model can be expressed as:

[0088] Y=ΓAPF T B+W

[0089] in It is a diagonal matrix whose diagonal elements γ m m = 1, 2, ..., M-1 corresponds to the complex gain-phase perturbation of the (m+1)th array element (with the first array element as a reference); For array space response, This is the guide vector corresponding to the k-th path; It is a diagonal matrix whose diagonal elements consist of the fading factors of K paths; The time delay response for all N subcarriers is defined. It contains the delay information of the nth subcarrier of all paths; It is a diagonal matrix composed of binary phase shift keying (BPSK) symbols, b n The BPSK symbol for the nth subcarrier is defined in {-1,1}; It is an additive noise matrix.

[0090] Without loss of generality, the BPSK symbol sequence b = [b1, b2, ..., b N ] T Since the training or pilot signals are known in advance for the BS, the CSI matrix obtained at the BS can be expressed as follows:

[0091]

[0092] Z = WB can be considered as the estimation error of the CSI matrix C. We perform column straightening on the CSI matrix C to obtain the CSI vector.

[0093]

[0094] in Defined as an array manifold with gain-phase perturbation. Defined as path fading vector, Defined as a new additive noise vector, which is assumed to conform to a variance of v. 2 It follows a zero-mean complex Gaussian distribution.

[0095] The antenna array movement scheme and data reassembly method described in step 2 are as follows:

[0096] The total observation time of BS is evenly divided into L time slots, with starting times t1, t2, and t3, t4, t5, t6, t7, t8, t9, t1, t2, ...1, t2, t3, t4, t l l = 1, 2, ..., L. The antenna array of BS remains stationary within each time slot, but at each time t... l By moving a fixed distance Δd, BS can collect L observation signals, corresponding to L CSI vectors, denoted as...

[0097]

[0098] Considering the minute motion of the antenna array, the path attenuation factor, time delay, and incident angle for all observations can be considered constant, i.e., ρ l =ρ,F l =F, and

[0099]

[0100] in This represents a rotation-invariant matrix in space; it is a diagonal matrix.

[0101] Will Divide the unit into N uniform units, and define the nth unit as... Represented as

[0102]

[0103] Where F n,: Let F represent the nth row. Therefore, the recombined CSI vector is predefined as... Similarly, it is divided into N units, and the nth unit is represented as... Therefore,

[0104]

[0105] in This represents the actual array manifold with an L-order observation expansion having gain-phase perturbations. Thus, the reconstructed CSI vector It can be represented as

[0106]

[0107] in Represents the equivalent channel response.

[0108] The spatial-frequency joint smoothing method described in step 3 and the method for obtaining the rank-recovered CSI covariance matrix are as follows:

[0109] Reconstructed CSI vector covariance matrix It can be represented as

[0110]

[0111] in Let R be the covariance matrix of ρ. Obviously, R ρ Its rank is 1.

[0112] The perturbation array manifold corresponding to the l-th observation As the smallest unit, Q parts are extracted from it, where the q-th part is represented as...

[0113]

[0114] in Define the selection matrix It is represented as

[0115]

[0116] Obviously, there are

[0117] Noting that F also possesses the rotational invariance property, we extract P parts from F, each part... All with Each subcarrier is associated, that is

[0118]

[0119] in And there are This represents a frequency rotation invariant matrix. F1 is derived from the previous... Line composition, represented as

[0120] F1=[f(τ1),f(τ2),...,f(τ K )]

[0121] in Similarly, define the selection matrix. Represented as

[0122]

[0123] Obviously, there is F p =G F,p F.

[0124] Using the selection matrix G constructed above E,q and G F,p The following is an analysis of the CSI covariance matrix. Perform data extraction operations, i.e.

[0125]

[0126] Where p = 1, 2, ..., P and q = 1, 2, ..., Q, and

[0127]

[0128]

[0129]

[0130] Therefore, the rank-recovered CSI covariance matrix R CSI It can be represented as

[0131]

[0132] in

[0133] The closed-form solutions for the one-dimensional angle spectrum, one-dimensional time delay spectrum function, and array gain phase perturbation constructed in step 4 are as follows:

[0134] After the joint spatial-frequency smoothing operation in step 3, the rank-recovered CSI covariance matrix R... CSI Its equivalent channel response is Ψ1=F1⊙E1, which can be expressed as

[0135]

[0136]

[0137] in Indicates the first The second observation has a steering vector with gain-phase perturbation. Additionally,

[0138]

[0139] in

[0140]

[0141]

[0142]

[0143] For R CSI By performing eigenvalue decomposition, its noise subspace (matrix) can be obtained. It is due to the smallest The eigenvectors corresponding to each eigenvalue are used. With the incident angle θ as the variable, the following function is constructed.

[0144]

[0145] Where θ∈[-90°, 90°]. Therefore, the following one-dimensional angular spectrum function can be given:

[0146]

[0147] Where det{·} denotes the determinant of the matrix. Theoretically, χ θ (θ kFor each k = 1, 2, ..., K, there exists a local maximum in the angle spectrum. Therefore, the angle value corresponding to the local maximum in the angle spectrum is the estimated incident angle, expressed as:

[0148] Similarly, using the time delay τ as a variable, we construct the following function corresponding to the k-th path.

[0149]

[0150] in Given the estimated incident angle, the following one-dimensional time delay spectrum function corresponding to the k-th path is constructed:

[0151]

[0152] Obviously, χ τ,k (τ k The path should have a maximum value in the k-th delay spectrum. Therefore, the delay value corresponding to the maximum value in the k-th delay spectrum is the estimated delay value of the k-th path, expressed as:

[0153] definition Therefore, Ωγ=0, where Define ω as the first column of Ω. Composed of the columns of Ω except for ω, The array gain-phase perturbation vector can be estimated using the following formula.

[0154]

[0155] in This indicates the Moore-Penrose inverse operation.

[0156] Example:

[0157] Step 1: Preprocess and reassemble the data from multiple observations to obtain a unified CSI representation of the observations.

[0158] In such Figure 2 Under the antenna array movement scheme shown, the base station obtains L sets of CSI vectors through L observations, which are represented as follows:

[0159]

[0160] Will Divide the unit into N uniform units, and define the nth unit as... Represented as

[0161]

[0162] Where Fn,: Let F represent the nth row. Therefore, the recombined CSI vector is predefined as... Similarly, it is divided into N units, and the nth unit is represented as... Therefore,

[0163]

[0164] in This represents the actual array manifold with an L-order observation expansion having gain-phase perturbations. Thus, the reconstructed CSI vector It can be represented as

[0165]

[0166] in Represents the equivalent channel response.

[0167] Step 2: Perform rank recovery operation on the CSI covariance matrix using the designed spatial-frequency joint smoothing method.

[0168] Reconstructed CSI vector covariance matrix It can be represented as

[0169]

[0170] in Let represent the covariance matrix of ρ. In the constructed selection matrix... and Below, the CSI covariance matrix Perform data extraction operations, i.e.

[0171]

[0172] Where p = 1, 2, ..., P and q = 1, 2, ..., Q. Thus, the rank-recovered CSI covariance matrix R is obtained. CSI , represented as

[0173]

[0174] Step 3: Construct a one-dimensional angular spectrum function and estimate the incident angle through spectral peak search.

[0175] Construct a function with the incident angle θ as the variable. Where θ∈[-90°, 90°]. Therefore, the following one-dimensional angular spectrum function can be given:

[0176]

[0177] Where det{·} denotes the determinant of the matrix. Theoretically, χ θ (θ k For each k = 1, 2, ..., K, there exists a local maximum in the angle spectrum. Therefore, the angle value corresponding to the local maximum in the angle spectrum is the estimated incident angle, expressed as:

[0178] Step 4: Construct a one-dimensional time delay spectrum function supported by the estimated incident angle, and complete the path delay estimation through spectral peak search.

[0179] Using the time delay τ as a variable, construct the following function corresponding to the k-th path.

[0180]

[0181] in Given the estimated incident angle, the following one-dimensional time delay spectrum function corresponding to the k-th path is constructed:

[0182]

[0183] Obviously, χ τ,k (τ k The path should have a maximum value in the k-th delay spectrum. Therefore, the delay value corresponding to the maximum value in the k-th delay spectrum is the estimated delay value of the k-th path, expressed as:

[0184] Step 5: Using the derived closed-form solution, and supported by the estimated incident angle and path delay, estimate the array gain-phase perturbation:

[0185] definition Therefore, Ωγ=0, where Define ω as the first column of Ω. Composed of the columns of Ω except for ω, The array gain-phase perturbation vector can be estimated using the following formula.

[0186]

[0187] in This indicates the Moore-Penrose inverse operation.

[0188] The effectiveness of this invention will be verified through simulation experiments.

[0189] Figure 3 This is a scatter plot of the angle and time delay values ​​estimated by the method proposed in this invention under 500 Monte Carlo tests. The simulation assumes the base station uses a 5-element uniform linear array, and the gain-phase of each element is not pre-calibrated. Figure 3It can be seen that, when receiving signals from 5 paths simultaneously, the proposed method effectively maintains stable and highly accurate angle and time delay estimation results even with array gain phase perturbations.

[0190] Figure 4 , 5 Figures 6 and 7 respectively demonstrate the relationship between the root mean square error (RMSE) of the angle, delay, and gain-phase perturbation estimated by the proposed methods (labeled Proposed and Proposed-known) and the signal-to-noise ratio (SNR). The simulation assumes a 5-element uniform linear array at the base station, with the gain-phase of each element not pre-calibrated. It can be seen that, when simultaneously receiving signals from two paths, the estimation accuracy of each parameter by the proposed method consistently maintains a significant advantage over existing algorithms (labeled JADE-SCS and JADE-SCS-known). Furthermore, the RMSE curves estimated by the proposed method converge and closely adhere to their respective Cramer-Rao lowerbound (CRLB) limits.

[0191] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A robust multipath channel estimation method for an antenna array system, characterized in that... include: A MIMO signal propagation model with array gain-phase perturbation is established; the large-scale MIMO signal propagation model with array gain-phase perturbation is as follows: Assume that the base station BS is equipped with a A uniform linear array of antenna elements is used for communication between the user and the BS in the far field; assuming there is a signal between the user's transmitted signal and the BS. One transmission path, including one line-of-sight path and The non-line-of-sight path; therefore, the BS received signal model considering the presence of array gain-phase perturbations can be expressed as: in It is a diagonal matrix whose diagonal elements Corresponding to the Complex gain-phase perturbation of each array element; For array space response, For the corresponding to the first The guide vector of the path; It is a diagonal matrix whose diagonal elements are composed of The fading factor of each path; Defined all The time delay response of each subcarrier, The first one containing all paths Delay information for each subcarrier; It is a diagonal matrix composed of binary phase shift keying symbols. Defined the first One subcarrier BPSK symbol; It is an additive noise matrix; Therefore, the CSI matrix obtained from the BS end can be represented as in This can be considered as for the CSI matrix. The estimation error of the CSI matrix Perform column straightening to obtain the CSI vector. in Defined as an array manifold with gain-phase perturbation. Defined as path fading vector, Defined as a new additive noise vector, which is assumed to conform to the variance of... The zero-mean complex Gaussian distribution; Design an antenna array movement scheme where the base station receives multiple observation data and reassembles the data to obtain a unified CSI representation of the multiple observations; the antenna array movement scheme and data reassembly method are as follows: The total observation time of BS is evenly divided into Each time slot has a starting time of [number] times. The BS antenna array remains stationary within each time slot, but at each moment... Move a fixed distance Thus, BS can collect The observed signal, corresponding to the obtained The second CSI vector is represented as Will Evenly divided into The unit is defined as the first... Each unit is , represented as in express The Okay; define the recombined CSI vector in advance as follows: Similarly, it is divided into The unit, its first Each unit is represented as Therefore, in Indicates a condition with gain-phase perturbation The actual array manifold of the expansion observed in the second observation. Therefore, the reconstructed CSI vector It can be represented as in Represents the equivalent channel response. ; The covariance matrix of the unified CSI is calculated, and the CSI covariance matrix is ​​extracted using a spatial-frequency domain joint smoothing method to obtain the rank-recovered CSI covariance matrix; specifically, the extraction of the CSI covariance matrix using the spatial-frequency domain joint smoothing method to obtain the rank-recovered CSI covariance matrix is ​​as follows: Reconstructed CSI vector covariance matrix It can be represented as in express The covariance matrix; In the constructed selection matrix and Below, the CSI covariance matrix Perform data extraction operations, i.e. in and Thus, the rank-recovered CSI covariance matrix is ​​obtained. : in ; The eigenvalues ​​of the obtained rank-recovered CSI covariance matrix are decomposed to obtain its corresponding noise subspace matrix. A one-dimensional angle spectrum function is constructed based on the noise subspace matrix, and the incident angle is estimated by searching for spectral peaks. A one-dimensional time delay spectrum function is constructed with the estimated incident angle, and the path delay is estimated by searching for spectral peaks. Combining the incident angle and the path delay, the array gain-phase perturbation is estimated using the derived closed-form solution.

2. The robust multipath channel estimation method for an antenna array system according to claim 1, characterized in that, The specific steps for performing eigenvalue decomposition on the obtained rank-recovered CSI covariance matrix to obtain its corresponding noise subspace matrix are as follows: For the rank-restored CSI covariance matrix Its equivalent channel response is , can be represented as in Indicates the first The second observation has a steering vector with gain-phase perturbation; additionally, in right By performing eigenvalue decomposition, its noise subspace matrix can be obtained. .

3. The robust multipath channel estimation method for an antenna array system according to claim 2, characterized in that, The specific steps for constructing a one-dimensional angle spectrum function based on the noise subspace matrix and estimating the incident angle through spectral peak search are as follows: At the angle of incidence For variables, constructor ,in Therefore, the following one-dimensional angular spectrum function is given: in The determinant of a matrix, theoretically, The angle spectrum has local maxima; therefore, the angle value corresponding to the local maxima in the angle spectrum is the estimated incident angle, expressed as: .

4. The robust multipath channel estimation method for an antenna array system according to claim 3, characterized in that, The construction of a one-dimensional time delay spectrum function supported by the estimated incident angle, and the estimation of path delay through spectral peak search, specifically involves: With delay As a variable, construct the following corresponding to the first... Functions for a path in The estimated incident angle is used to construct the following corresponding to the first... The one-dimensional time delay spectrum function of the path is Obviously, It should be in the It has a maximum value on the time delay spectrum, therefore, it is related to the th time delay spectrum. The time delay value corresponding to the maximum value in the time delay spectrum is the th time delay value. The estimated delay for each path is expressed as follows: .

5. The robust multipath channel estimation method for an antenna array system according to claim 4, characterized in that, The method of estimating array gain-phase perturbation using the derived closed-form solution, combining incident angle and path delay, specifically involves: definition Therefore, ,in ;definition for The first column, Depend on The Exclusion Other columns besides, to The array gain-phase perturbation vector can be estimated using the following formula. in This indicates the Moore-Penrose inverse operation.

6. A computer system, characterized in that... include: One or more processors, a computer-readable storage medium for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to perform the method of any one of claims 1-5.

7. A computer-readable storage medium, characterized in that... The device stores computer-executable instructions, which, when executed, are used to implement the method described in any one of claims 1-5.

Images