CN117201235A - A robust multipath channel estimation method for antenna array systems - Google Patents
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Abstract
本发明涉及一种天线阵列系统稳健多径信道估计方法，属于信号处理领域。包括：建立存在阵列增益‑相位扰动下的大规模MIMO信号传播模型；设计的天线阵列移动方案，在接收端对获得的CSI矩阵进行数据重组得到多次观测的CSI统一表述；基于空域‑频域联合平滑方法对CSI协方差矩阵进行数据提取，获得秩恢复的CSI协方差矩阵；对秩恢复的CSI协方差矩阵进行特征分解，获得噪声子空间矩阵，进而在构造的一维角度谱、一维时延谱函数和阵列增益相位扰动的闭式解下实现角度、时延、增益相位扰动的联合估计。本发明对于阵列增益相位扰动具有稳健的参数估计性能，显著提高了参数估计精度和多径分辨能力。
The invention relates to a robust multipath channel estimation method for an antenna array system and belongs to the field of signal processing. Including: establishing a massive MIMO signal propagation model under the presence of array gain-phase disturbance; designing an antenna array moving scheme, and reorganizing the data of the obtained CSI matrix at the receiving end to obtain a unified expression of CSI for multiple observations; based on the spatial domain-frequency domain The joint smoothing method extracts data from the CSI covariance matrix to obtain the rank-restored CSI covariance matrix; performs eigendecomposition on the rank-restored CSI covariance matrix to obtain the noise subspace matrix, and then constructs one-dimensional angle spectrum, one-dimensional The joint estimation of angle, time delay and gain phase disturbance is realized under the closed-form solution of delay spectrum function and array gain phase disturbance. The present invention has robust parameter estimation performance for array gain phase disturbance, and significantly improves parameter estimation accuracy and multipath resolution capability.
Description
Technical Field
The invention belongs to the field of signal processing, relates to a channel estimation technology, and in particular relates to a parameterized multipath channel estimation method considering array channel inconsistency under a large-scale antenna array system.
Background
Large-scale multiple-input multiple-output (MIMO) is an emerging wireless communication technology, which greatly improves signal transmission efficiency and reliability by adding more antennas at the base station end. Because the number of the antennas is large, the channel state is complex, and the optimal resource allocation and power control can be realized only by accurately estimating and predicting the channel, so that the performance and the user experience of the system are improved. Therefore, channel estimation is an indispensable part of massive MIMO systems, and is one of the keys for achieving efficient communication.
Currently, channel estimation methods in massive MIMO systems can be broadly divided into two categories: 1) A non-parametric model-based method: such methods do not make any assumptions about the channel, and directly make channel estimates based on existing observations. 2) A parameterized model-based method: the characteristic parameters of the channel are assumed to be known or estimated, and the change rule of the channel is described by establishing a mathematical model. The non-parametric model method has the advantages of being adaptable to various channel models, and high in flexibility and adaptability, and strict priori assumptions do not need to be carried out on the channels. However, the defects are obvious, and firstly, a large number of training samples are needed to obtain an accurate estimation result, so that the calculation complexity is high; in addition, the performance of these algorithms may be significantly degraded in response to the channel state information (channel state information, CSI) matrix of practically large dimensions. For channel estimation under a parameterized model, the channel model is subjected to strict prior assumption, so that the complexity and the calculated amount of estimation are reduced, and meanwhile, a more accurate estimation result can be obtained.
In previous studies, both pure angle estimation and pure delay estimation techniques have matured. However, a single parameter dimension is obviously insufficient to describe the complete state information of the channel, so that the channel model under the multi-parameter dimension description is a main development trend of the current parameterized channel estimation. Currently, the channel estimation model in the multi-parameter dimension of the mainstream is joint angle and delay estimation (joint angle and delay estimation, jace), which enables a more complete and accurate estimation of the channel state through the joint of the angle domain and the delay domain.
It should be noted that the above-mentioned parametric channel estimation studies are all based on ideal antenna assumptions, i.e. the steering vectors of the antenna array are considered to be precisely known. However, in practice there are unknown array disturbances such as gain-phase disturbances, coupling, inaccurate array positions, etc., which can cause the preset array manifold to be inconsistent with the actual observations, thereby greatly affecting the parameter estimation performance. Although there are many studies on angle or delay estimation in the presence of array disturbance, there is still room for multi-parameter channel estimation study in which array disturbance conditions are considered in massive MIMO systems.
Disclosure of Invention
The technical problems to be solved by the invention are as follows:
in order to solve the problem of parameterized multipath channel estimation under a large-scale antenna array system under the condition of inconsistent antenna array channels; the invention provides a robust multipath channel estimation method of an antenna array system, which mainly achieves the aim of improving parameter estimation precision and robustness through the improvement of the degree of freedom of an array and the aperture of a virtual array.
In order to solve the technical problems, the invention adopts the following technical scheme:
a method for robust multipath channel estimation for an antenna array system, comprising:
establishing a MIMO signal propagation model under array gain-phase disturbance;
designing an antenna array moving scheme, and receiving and recombining data of multiple observations by a base station to obtain a unified CSI expression of the multiple observations;
the obtained covariance matrix of the unified CSI is calculated, data extraction is carried out on the CSI covariance matrix based on a space domain-frequency domain joint smoothing method, and a CSI covariance matrix with recovered rank is obtained;
performing feature decomposition on the obtained CSI covariance matrix with the restored rank to obtain a corresponding noise subspace matrix; constructing a one-dimensional angle spectrum function based on the noise subspace matrix, and estimating an incident angle through spectrum peak searching; constructing a one-dimensional time delay spectrum function under the support of an estimated incidence angle, and searching and estimating path time delay through spectrum peaks; and estimating the array gain-phase disturbance by using a derived closed-form solution in combination with the incident angle and the path delay.
The invention further adopts the technical scheme that: the massive MIMO signal propagation model in the presence of array gain-phase disturbances is as follows:
assuming that the base station BS is equipped with a uniform linear array of M antenna elements, the user communicates with the BS in the far field; assuming that there are K propagation paths between the user's transmitted signal and the BS, including 1 line-of-sight path and K-1 non-line-of-sight paths; so that the BS received signal model in consideration of the presence of array gain-phase disturbances can be expressed as
Y＝ΓAPF T B+W
Wherein the method comprises the steps ofIs a diagonal matrix with diagonal elements gamma m M=1, 2, …, M-1 corresponds to the complex gain-phase perturbation of the m+1th array element;For array space response, +.>Is a steering vector corresponding to the kth path;is a diagonal matrix whose diagonal elements consist of the fading factors of K paths;the delay response of all N sub-carriers is defined,delay information of the nth subcarrier of all paths is contained;is a diagonal matrix of binary phase shift keying symbols, b n E { -1,1} defines the nth subcarrier BPSK symbol;Is an additive noise matrix;
so that the CSI matrix obtained at the BS side can be expressed as
Where z=wb may be considered as an estimation error for CSI matrix C, and performing column-straightening operation on CSI matrix C to obtain CSI vector
Wherein the method comprises the steps ofDefined as an array manifold with gain-phase perturbations,defined as path fading vector, ">Defined as a new additive noise vector that is assumed to conform to the variance σ 2 Is a zero-mean complex gaussian distribution.
The invention further adopts the technical scheme that: the antenna array moving scheme and the data recombination mode are as follows:
the total observation time of the BS is uniformly divided into L time slots, and the starting time is t respectively l L=1, 2, …, L; the antenna array of the BS remains stationary during each time slot, but at each time instant t l Moving a fixed distance Δd so that the BS can collect L observations, corresponding to L CSI vectors obtained, expressed as
Will beEvenly divided into N units, the nth unit is defined as +.>Represented as
Wherein F is n,: An nth row representing F; defining the recombined CSI vector in advance asIt is also divided into N units, the nth unit of which is denoted +.>Thereby having the following characteristics
Wherein the method comprises the steps ofRepresenting the expanded actual array manifold with L observations of gain-phase perturbations, +.>Thus, the recombined CSI vectorCan be expressed as
Wherein the method comprises the steps ofIndicating an equivalent channel response and,
the invention further adopts the technical scheme that: the method for carrying out data extraction on the CSI covariance matrix based on the space domain-frequency domain joint smoothing method, and obtaining the CSI covariance matrix with the recovered rank comprises the following specific steps:
recombinant CSI vectorsCovariance matrix>Can be expressed as
Wherein the method comprises the steps ofA covariance matrix representing ρ;
in the constructed selection matrixAnd->Down to CSI covarianceMatrix->Performing data extraction operations, i.e.
Wherein p=1, 2, …, P and q=1, 2, …, Q; thus, a CSI covariance matrix R of rank recovery is obtained CSI ：
Wherein the method comprises the steps of
The invention further adopts the technical scheme that: the characteristic decomposition is carried out on the obtained CSI covariance matrix with the rank recovery, and the corresponding noise subspace matrix is obtained specifically as follows:
CSI covariance matrix R for rank recovery CSI Its equivalent channel response is ψ 1 ＝F 1 ⊙E 1 Can be expressed as
Wherein the method comprises the steps ofIndicate->Sub-observing a steering vector with gain-phase perturbations; in addition, in the case of the optical fiber,
wherein the method comprises the steps of
For R CSI Performing characteristic decomposition operation to obtain noise subspace matrix
The invention further adopts the technical scheme that: the method for estimating the incident angle by the spectral peak search comprises the following steps of:
constructing a function by taking the incident angle theta as a variableWherein θ ε [ -90 °,90 °]The method comprises the steps of carrying out a first treatment on the surface of the Giving the following one-dimensional angular spectrum function as
Where det {.cndot } represents the determinant of the matrix, in theory χ θ (θ k ) K=1, 2, …, K has a local maximum in the angular spectrum; therefore, the angle value corresponding to the local maximum in the angle spectrum is the estimated incident angle, expressed as
The invention further adopts the technical scheme that: constructing a one-dimensional time delay spectrum function under the support of an estimated incidence angle, and searching an estimated path time delay through a spectrum peak specifically comprises the following steps:
with the time delay τ as a variable, construct the following function corresponding to the kth path
Wherein the method comprises the steps ofIs the estimated angle of incidence, thereby constructing a one-dimensional delay profile function corresponding to the kth path as follows
Obviously, χ τ,k (τ k ) Should have a maximum value on the kth delay profile, whereby the delay value corresponding to the maximum value in the kth delay profile is the delay estimate of the kth path, expressed as
The invention further adopts the technical scheme that: the method for estimating the array gain-phase disturbance by utilizing the derived closed solution specifically comprises the following steps of:
definition of the definitionThus there is Ω=0, whereFirst column defining ω as Ω, +.>Consisting of columns of omega other than omegaTo->Representing an array gain-phase disturbance vector, which can be estimated from the following equation
Wherein the method comprises the steps ofRepresents the Moore-Penrose reverse operation.
A computer system, comprising: one or more processors, a computer-readable storage medium storing one or more programs, wherein the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the methods described above.
A computer readable storage medium, characterized by storing computer executable instructions that when executed are configured to implement the method described above.
The invention has the beneficial effects that:
the invention provides a robust parameterized multipath channel estimation method under a large-scale antenna array system, and provides a brand-new airspace-frequency domain joint smoothing method which can effectively recover the rank of a coherent signal covariance matrix so as to realize the resolution of multipath signals.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, like reference numerals being used to refer to like parts throughout the several views.
FIG. 1 is a flow chart of the algorithm of the present invention.
Fig. 2 is a schematic diagram of an antenna array moving scheme according to the present invention.
Fig. 3 is a plot of the estimated angle and time delay values for 500 monte carlo trials of the present invention.
FIG. 4 is a graph showing the relation between the root mean square error and the signal to noise ratio of the angle estimation according to the present invention.
Fig. 5 is a diagram showing the relation between the root mean square error and the signal to noise ratio of the delay estimation according to the present invention.
FIG. 6 is a graph showing the relation between the root mean square error and the signal to noise ratio of the gain-phase disturbance estimation according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
In order to solve the problem that the traditional parameterized channel estimation algorithm cannot effectively perform parameter estimation under the condition that antenna array channels are inconsistent. The invention provides a parameterized channel estimation method for joint angles and time delays by using a designed airspace-frequency domain joint smoothing method under array gain phase disturbance under a large-scale antenna array system. The method has robust parameter estimation performance for array gain phase disturbance, and compared with the existing algorithm, the method has the advantage that the parameter estimation precision and the multipath resolution capability are remarkably improved.
The invention provides a parameterized channel estimation method for joint angles and time delays by using a designed airspace-frequency domain joint smoothing method under array gain phase disturbance, which specifically comprises the following steps:
step 1: establishing a large-scale MIMO signal propagation model under array gain-phase disturbance;
step 2: under the designed antenna array moving scheme, carrying out data recombination on the obtained CSI matrix at a receiving end, thereby realizing the uniform expression of the CSI for multiple observations;
step 3: calculating a covariance matrix of the unified CSI obtained in the step 2, and extracting data of the CSI covariance matrix under a designed airspace-frequency domain joint smoothing method to obtain a CSI covariance matrix with recovered rank;
step 4: and (3) performing feature decomposition on the CSI covariance matrix obtained in the step (3) for rank recovery to obtain a corresponding noise subspace matrix, and further realizing joint estimation of angle, time delay and gain phase disturbance under the constructed one-dimensional angle spectrum, one-dimensional time delay spectrum function and closed-form solution of array gain phase disturbance.
The steps are as follows:
the massive MIMO signal propagation model in the presence of array gain-phase disturbances described in step 1 is as follows:
suppose that a Base Station (BS) is equipped with a uniform linear array of M antenna elements, with which a user communicates in the far field. It is assumed that there are K propagation paths between the user's transmitted signal and the BS, including 1 line-of-sight (LOS) path and K-1 non-line-of-sight (NLOS) paths. So that the BS received signal model in consideration of the presence of array gain-phase disturbances can be expressed as
Y＝ΓAPF T B+W
Wherein the method comprises the steps ofIs a diagonal matrix with diagonal elements gamma m M=1, 2, …, M-1 corresponds to the complex gain-phase perturbation of the (m+1) th array element (referenced to the first array element);for array space response, +.>Is a steering vector corresponding to the kth path;Is a diagonal matrix, its diagonalThe elements consist of fading factors of K paths;Defining the delay response of all N sub-carriers, < >>Delay information of the nth subcarrier of all paths is contained;is a diagonal matrix of binary phase shift keying (binary phase shift keying, BPSK) symbols, b n E { -1,1} defines the nth subcarrier BPSK symbol;is an additive noise matrix.
Without loss of generality, it can be considered that the BPSK symbol sequence b= [ b 1 ,b 2 ,...,b N ] T Is known in advance to the BS as a training or pilot signal, so that the CSI matrix obtained at the BS side can be expressed as
Where z=wb may be regarded as an estimation error for CSI matrix C. The column straightening operation is carried out on the CSI matrix C, so that the CSI vector is obtained
Wherein the method comprises the steps ofDefined as an array manifold with gain-phase perturbations,defined as path fading vector, ">Defined as a new additive noise vector that is assumed to conform to a variance v 2 Is a zero-mean complex gaussian distribution.
The antenna array moving scheme and the data reorganizing mode described in the step 2 are as follows:
the total observation time of the BS is uniformly divided into L time slots, and the starting time is t respectively l L=1, 2, …, L. The antenna array of the BS remains stationary during each time slot, but at each time instant t l Moving a fixed distance Δd so that the BS can collect L observations, corresponding to L CSI vectors obtained, expressed as
Considering the small motion scale of the antenna array, all observed path attenuation factors, time delays and angles of incidence can be considered unchanged, i.e. ρ l ＝ρ，F l =f, sum of
Wherein the method comprises the steps ofThe spatially invariant matrix is represented, which is a diagonal matrix.
Will beEvenly divided into N units, the nth unit is defined as +.>Represented as
Wherein F is n,: Represents the nth row of F. Thus, the recombined CSI vector is defined in advance asIt is also divided into N units, the nth unit of which is denoted +.>Thereby having the following characteristics
Wherein the method comprises the steps ofRepresenting the expanded actual array manifold with L observations of gain-phase perturbations, +.>Thus, the recombined CSI vectorCan be expressed as
Wherein the method comprises the steps ofRepresenting equivalent channel response, +.>
The spatial domain-frequency domain joint smoothing method and the method for obtaining the CSI covariance matrix of rank recovery in the step 3 are as follows:
recombinant CSI vectorsCovariance matrix>Can be expressed as
Wherein the method comprises the steps ofRepresenting the covariance matrix of ρ, notably R ρ Is equal to 1.
Manifold disturbance array corresponding to first observationAs a minimum unit, Q parts are extracted therefrom, where the Q-th part is expressed as
Wherein the method comprises the steps ofDefining a selection matrixWhich is expressed as
Obviously, there are
Note that F also has rotation invariant properties, P parts are extracted from F, eachAll are in charge of>With associated subcarriers, i.e
Wherein the method comprises the steps ofAnd have->Representing a frequency rotation invariant matrix. F (F) 1 From F->Line composition, denoted as
F 1 ＝[f(τ 1 ),f(τ 2 ),...,f(τ K )]
Wherein the method comprises the steps ofSimilarly, a selection matrix is definedRepresented as
Obviously, there is F p ＝G F,p F。
Selection matrix G constructed as described above E,q And G F,p For CSI covariance matrix as followsPerforming data extraction operations, i.e.
Wherein p=1, 2, …, P and q=1, 2, …, Q, and
thus, the CSI covariance matrix R of rank recovery CSI Can be expressed as
Wherein the method comprises the steps of
The constructed one-dimensional angle spectrum, one-dimensional delay spectrum function and array gain phase disturbance closed solution in the step 4 are as follows:
after the spatial domain-frequency domain joint smoothing operation in the step 3, for the CSI covariance matrix R of rank recovery CSI Its equivalent channel response is ψ 1 ＝F 1 ⊙E 1 Can be expressed as
Wherein the method comprises the steps ofIndicate->The secondary observations have steering vectors with gain-phase perturbations. In addition, in the case of the optical fiber,
wherein the method comprises the steps of
For R CSI The characteristic decomposition operation is carried out to obtain the noise subspace (matrix)It consists of +.>And the feature vectors corresponding to the feature values are formed. The incident angle theta is used as a variable to construct the following function
Wherein θ ε [ -90 °,90 ° ]. Thus, one-dimensional angular spectrum functions as follows can be given
Where det {.cndot } represents the determinant of the matrix. Theoretically, χ θ (θ k ) K=1, 2, …, K has a local maximum in the angular spectrum. Therefore, the angle value corresponding to the local maximum in the angle spectrum is the estimated incident angle, expressed as
Similarly, with the delay τ as a variable, the following function corresponding to the kth path is constructed
Wherein the method comprises the steps ofIs the estimated incident angle, thereby constructing a one-dimensional time delay spectrum function corresponding to the kth path as follows
Obviously, χ τ,k (τ k ) Should have a maximum value on the kth delay profile, whereby the delay value corresponding to the maximum value in the kth delay profile is the delay estimate of the kth path, expressed as
Definition of the definitionThus there is Ω=0, whereFirst column defining ω as Ω, +.>Consists of omega columns other than omega, in order +.>Representing an array gain-phase disturbance vector, which can be estimated from the following equation
Wherein the method comprises the steps ofRepresents the Moore-Penrose reverse operation.
Examples:
step 1, preprocessing and data recombination are carried out on multi-observation data, and unified CSI expression of multi-observation is obtained:
under the antenna array moving scheme shown in fig. 2, the base station side obtains L sets of CSI vectors through L observations, which are respectively expressed as
Will beEvenly divided into N units, the nth unit is defined as +.>Represented as
Wherein F is n,: Represents the nth row of F. Thus, the recombined CSI vector is defined in advance asIt is also appliedDivided into N units, the nth unit of which is denoted +.>Thereby having the following characteristics
Wherein the method comprises the steps ofRepresenting the expanded actual array manifold with L observations of gain-phase perturbations, +.>Thus, the recombined CSI vectorCan be expressed as
Wherein the method comprises the steps ofIndicating an equivalent channel response and,
step 2, performing rank recovery operation on the CSI covariance matrix under a designed airspace-frequency domain joint smoothing method:
recombinant CSI vectorsCovariance matrix>Can be expressed as
Wherein the method comprises the steps ofRepresenting the covariance matrix of p. In the constructed selection matrixAnd->Under, the CSI covariance matrix is->Performing data extraction operations, i.e.
Where p=1, 2, …, P and q=1, 2, …, Q. Thus, a CSI covariance matrix R of rank recovery is obtained CSI Expressed as
Step 3, constructing a one-dimensional angle spectrum function, and completing estimation of an incident angle through spectrum peak search:
constructing a function by taking the incident angle theta as a variableWherein θ ε [ -90 °,90 °]. Thus, one-dimensional angular spectrum functions as follows can be given
Where det {.cndot } represents the determinant of the matrix. Theoretically, χ θ (θ k ) K=1, 2, …, K has a local maximum in the angular spectrum. Therefore, the angle value corresponding to the local maximum in the angle spectrum is the estimated incident angle, expressed as
Step 4, constructing a one-dimensional time delay spectrum function under the support of the estimated incidence angle, and completing the estimation of path time delay through spectrum peak search:
with the time delay τ as a variable, construct the following function corresponding to the kth path
Wherein the method comprises the steps ofIs the estimated incident angle, thereby constructing a one-dimensional time delay spectrum function corresponding to the kth path as follows
Obviously, χ τ,k (τ k ) Should have a maximum value on the kth delay profile, whereby the delay value corresponding to the maximum value in the kth delay profile is the delay estimate of the kth path, expressed as
Step 5, under the support of the estimated incidence angle and path delay, estimating the array gain-phase disturbance by using a derived closed solution:
definition of the definitionThus there is Ω=0, whereFirst column defining ω as Ω, +.>Consists of omega columns other than omega, in order +.>Representing an array gain-phase disturbance vector, which can be estimated from the following equation
Wherein the method comprises the steps ofRepresents the Moore-Penrose reverse operation.
The effectiveness of the present invention is verified by simulation experiments as follows.
Fig. 3 is a graph of the angular and time delay values estimated under 500 monte carlo tests for the proposed method, in which the simulation sets the base station to adopt a uniform linear array of 5 array elements, and the gain-phase of each array element is not calibrated in advance. As can be seen from fig. 3, in the case of receiving 5 path signals simultaneously, the proposed method effectively maintains stable and highly accurate angle and delay estimation results in the presence of array gain phase disturbance.
Fig. 4, 5 and 6 show the root mean square error (root mean square error, RMSE) of the angle, delay, gain-phase perturbations and signal-to-noise ratio (SNR) estimated by the Proposed methods (labeled as Proposed and Proposed-known), respectively. The simulation setting base station adopts a uniform linear array of 5 array elements, and the gain-phase of each array element is not calibrated in advance. It can be seen that in the case of simultaneous reception of 2 path signals, the estimation accuracy of the individual parameters of the proposed method always remains a significant advantage for the existing algorithms (labeled JADE-SCS and JADE-SCS-known). In addition, the RMSE curves estimated by the proposed method all converge and fit closely to the respective lower Crimet (CRLB).
While the invention has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions of equivalents may be made without departing from the spirit and scope of the invention.
Claims (10)
1. A method for robust multipath channel estimation for an antenna array system, comprising:
establishing a MIMO signal propagation model under array gain-phase disturbance;
designing an antenna array moving scheme, and receiving and recombining data of multiple observations by a base station to obtain a unified CSI expression of the multiple observations;
the obtained covariance matrix of the unified CSI is calculated, data extraction is carried out on the CSI covariance matrix based on a space domain-frequency domain joint smoothing method, and a CSI covariance matrix with recovered rank is obtained;
performing feature decomposition on the obtained CSI covariance matrix with the restored rank to obtain a corresponding noise subspace matrix; constructing a one-dimensional angle spectrum function based on the noise subspace matrix, and estimating an incident angle through spectrum peak searching; constructing a one-dimensional time delay spectrum function under the support of an estimated incidence angle, and searching and estimating path time delay through spectrum peaks; and estimating the array gain-phase disturbance by using a derived closed-form solution in combination with the incident angle and the path delay.
2. The method for estimating a robust multipath channel of an antenna array system as claimed in claim 1, wherein the massive MIMO signal propagation model in the presence of array gain-phase disturbances is as follows:
assuming that the base station BS is equipped with a uniform linear array of M antenna elements, the user communicates with the BS in the far field; assuming that there are K propagation paths between the user's transmitted signal and the BS, including 1 line-of-sight path and K-1 non-line-of-sight paths; so that the BS received signal model in consideration of the presence of array gain-phase disturbances can be expressed as
Y＝ΓAPF T B+W
Wherein the method comprises the steps ofIs a diagonal matrix with diagonal elements gamma m M=1, 2, …, M-1 corresponds to the complex gain-phase perturbation of the m+1th array element;For array space response, +.>Is a steering vector corresponding to the kth path;is a diagonal matrix whose diagonal elements consist of the fading factors of K paths;the delay response of all N sub-carriers is defined,delay information of the nth subcarrier of all paths is contained;is a diagonal matrix of binary phase shift keying symbols, b n E { -1,1} defines the nth subcarrier BPSK symbol;Is an additive noise matrix;
so that the CSI matrix obtained at the BS side can be expressed as
Where z=wb may be considered as an estimation error for CSI matrix C, and performing column-straightening operation on CSI matrix C to obtain CSI vector
Wherein the method comprises the steps ofDefined as an array manifold with gain-phase perturbations,defined as path fading vector, ">Defined as a new additive noise vector that is assumed to conform to the variance σ 2 Is a zero-mean complex gaussian distribution.
3. The method for estimating robust multipath channel of antenna array system as claimed in claim 2, wherein said antenna array moving scheme and data reorganization mode are as follows:
the total observation time of the BS is uniformly divided into L time slots, and the starting time is t respectively l L=1, 2, …, L; the antenna array of the BS remains stationary during each time slot, but at each time instant t l Moving a fixed distance Δd so that the BS can collect L observations, corresponding to L CSI vectors obtained, expressed as
Will beEvenly divided into N units, the nth unit is defined as +.>Represented as
Wherein F is n,: An nth row representing F; defining the recombined CSI vector in advance asIt is also divided into N units, the nth unit of which is denoted +.>Thereby having the following characteristics
Wherein the method comprises the steps ofRepresenting the expanded actual array manifold with L observations of gain-phase perturbations, +.>Thus, the recombined CSI vectorCan be expressed as
Wherein the method comprises the steps ofRepresenting equivalentChannel response->
4. The method for estimating robust multipath channels of antenna array system according to claim 3, wherein the data extraction of CSI covariance matrix based on spatial domain-frequency domain joint smoothing method is specifically:
recombinant CSI vectorsCovariance matrix>Can be expressed as
Wherein the method comprises the steps ofA covariance matrix representing ρ;
in the constructed selection matrixAnd->Under, the CSI covariance matrix is->Performing data extraction operations, i.e.
Wherein p=1, 2, …, P and q=1, 2, …, Q; thus, a CSI covariance matrix R of rank recovery is obtained CSI ：
Wherein the method comprises the steps of
5. The method for estimating robust multipath channels of antenna array system according to claim 1, wherein said performing feature decomposition on CSI covariance matrix of rank recovery obtained is specifically:
CSI covariance matrix R for rank recovery CSI Its equivalent channel response is ψ 1 ＝F 1 ⊙E 1 Can be expressed as
Wherein the method comprises the steps ofIndicate->Sub-observing a steering vector with gain-phase perturbations; in addition, in the case of the optical fiber,
wherein the method comprises the steps of
For R CSI Performing characteristic decomposition operation to obtain noise subspace matrix
6. The method for estimating robust multipath channels of an antenna array system as claimed in claim 5, wherein said constructing a one-dimensional angular spectrum function based on a noise subspace matrix, estimating the incident angle by spectral peak search is specifically:
constructing a function by taking the incident angle theta as a variableWherein θ ε [ -90 °,90 °]The method comprises the steps of carrying out a first treatment on the surface of the Giving the following one-dimensional angular spectrum function as
Where det {.cndot } represents the determinant of the matrix, in theory χ θ (θ k ) K=1, 2, …, K has a local maximum in the angular spectrum; therefore, the angle value corresponding to the local maximum in the angle spectrum is the estimated incident angle, expressed as
7. The method for estimating a robust multipath channel of an antenna array system as claimed in claim 6, wherein said constructing a one-dimensional delay profile function under the support of the estimated angle of incidence, estimating the path delay by the spectral peak search is specifically:
with the time delay τ as a variable, construct the following function corresponding to the kth path
Wherein the method comprises the steps ofIs the estimated angle of incidence, thereby constructing a one-dimensional delay profile function corresponding to the kth path as follows
Obviously, χ τ,k (τ k ) Should have a maximum value on the kth delay profile, whereby the delay value corresponding to the maximum value in the kth delay profile is the delay estimate of the kth path, expressed as
8. The method for estimating a robust multipath channel of an antenna array system as claimed in claim 7, wherein said estimating the gain-phase disturbance of the array using a derived closed-form solution by combining the angle of incidence and the path delay is specifically:
definition of the definitionThereby having omega γ =0, whereinFirst column defining ω as Ω, +.>Consists of omega columns other than omega, in order +.>Representing an array gain-phase disturbance vector, which can be estimated from the following equation
Wherein the method comprises the steps ofRepresents the Moore-Penrose reverse operation.
9. A computer system, comprising: one or more processors, a computer-readable storage medium storing one or more programs, wherein the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method of any of claims 1-8.
10. A computer readable storage medium, characterized in that computer executable instructions are stored, which instructions, when executed, are for implementing the method of any of claims 1-8.
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