A method and system for channel estimation for a millimeter wave multiple-input multiple-output system

Abstract

The application provides a channel estimation method and system for a millimeter wave multiple-input multiple-output system, the method comprising: decomposing a channel measurement matrix determined based on a reference signal by using a singular value decomposition algorithm to obtain an initial first factor matrix and an initial second factor matrix; inputting an initial set comprising an initial first estimation matrix, the initial first factor matrix and the initial second factor matrix into a pre-trained iterative neural network to perform a plurality of rounds of update operations, so as to obtain an estimation matrix of the channel; wherein each round of update operation comprises: obtaining a first factor matrix and a second factor matrix of a current round output by using a projected gradient descent algorithm and a de-convolutional layer; and obtaining a first estimation matrix of a current round output based on a first estimation matrix of a current round input, the first factor matrix and the second factor matrix of the current round output. The application can improve the accuracy and efficiency of channel estimation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, and in particular to a channel estimation method and system for a millimeter wave multiple-input multiple-output system. BACKGROUND

[0002] In a millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) system, efficient beamforming relies on accurate channel state information (CSI). However, with the increase in the number of antennas, the pilot signals (i.e., reference signals) and the computational overhead of the traditional channel estimation algorithm also increase, affecting the efficiency of the MIMO system. Although the channel estimation algorithm based on compressed sensing can reduce the training cost by utilizing the sparsity of the mmWave channel, it often ignores the low-rank structure of the channel. In recent years, research has regarded channel estimation as a low-rank matrix completion problem in order to fully utilize the low-rank and sparse characteristics of the channel. However, the existing channel estimation methods based on low-rank matrix completion still have challenges in terms of computational complexity and estimation accuracy.

[0003] Therefore, there is an urgent need for a channel estimation method suitable for a mmWave MIMO system, which can estimate the channel matrix through low-rank matrix completion while reducing computational complexity and improving channel estimation accuracy. SUMMARY

[0004] In view of this, the embodiments of the present application provide a channel estimation method and system for a mmWave MIMO system, which can reduce computational complexity and improve channel estimation accuracy.

[0005] One aspect of the present application provides a channel estimation method for a mmWave MIMO system, the method comprising the following steps:

[0006] determining a channel measurement matrix based on a reference signal and a set of channel sensing positions, and decomposing the channel measurement matrix using a singular value decomposition algorithm to obtain an initial first factor matrix and an initial second factor matrix;

[0007] inputting an initial input set comprising the channel measurement matrix used as an initial first estimation matrix, the initial first factor matrix, and the initial second factor matrix into a pre-trained iterative neural network for a plurality of rounds of update operations to finally obtain an estimation matrix of the channel; wherein the iterative neural network takes the output of the current round of update operations as the input of the next round of update operations;

[0008] Each round of update operation comprises:

[0009] The first intermediate projection matrix and the second intermediate projection matrix of the current round are obtained based on the first factor matrix, the second factor matrix and the first estimation matrix of the input of the current round by using a projection gradient descent algorithm, and the first intermediate projection matrix and the second intermediate projection matrix of the current round are respectively converted into the first factor matrix and the second factor matrix of the output of the current round by the back projection convolution layer; and the first estimation matrix of the output of the current round is obtained based on the first estimation matrix of the input of the current round, the first factor matrix of the output of the current round and the second factor matrix of the output of the current round.

[0010] In some embodiments of the application, the initial input set further comprises a channel measurement matrix used as an initial second estimation matrix; and

[0011] In the case that the initial input set comprises the initial second estimation matrix, the each-round updating operation further comprises: inputting the first estimation matrix of the output of the current round into the denoising convolution layer to output the second estimation matrix of the output of the current round.

[0012] In some embodiments of the application, the first estimation matrix of the output of the current round is obtained based on the first estimation matrix of the input of the current round, the first factor matrix of the output of the current round and the second factor matrix of the output of the current round, comprising:

[0013] In the case that the first estimation matrix of the output of the final round is taken as the estimation matrix of the channel, the first estimation matrix of the output of the current round is obtained based on the first estimation matrix of the input of the current round, the first factor matrix and the second factor matrix of the output of the current round, the channel measurement matrix and the set first step size;

[0014] In the case that the second estimation matrix of the output of the final round is taken as the estimation matrix of the channel, the first estimation matrix of the output of the current round is obtained based on the first estimation matrix of the input of the current round, the first factor matrix and the second factor matrix of the output of the current round, the channel measurement matrix, the set first step size and the second estimation matrix of the input of the current round.

[0015] In some embodiments of the application, the first intermediate projection matrix and the second intermediate projection matrix of the current round are obtained based on the first factor matrix, the second factor matrix and the first estimation matrix of the input of the current round by using a projection gradient descent algorithm, comprising: for the first factor matrix, a gradient is calculated based on the first factor matrix, the second factor matrix, the first estimation matrix of the input of the current round and the set second step size, so as to obtain a gradient descent value; the gradient descent value is input into the projection convolution layer to output the first intermediate projection matrix;

[0016] For the second factor matrix, the gradient is calculated based on the first factor matrix output in the current round, the second factor matrix input in the current round and the first estimated matrix, and a third set step size, so as to obtain a gradient descent value, or the gradient is calculated based on the first factor matrix input in the current round, the second factor matrix and the first estimated matrix, and the third set step size, so as to obtain the gradient descent value; the gradient descent value is input into the projection convolution layer, and the second intermediate projection matrix is output.

[0017] In some embodiments of the present application, for the first factor matrix, the calculation process of the gradient descent value includes the following steps: calculating the product of the conjugate transpose of the first factor matrix input in the current round and the second factor matrix; calculating the difference between the product and the first estimated matrix input in the current round, multiplying the obtained difference, a set second step size and the second factor matrix input in the current round to obtain a gradient; subtracting the gradient from the first factor matrix input in the current round to obtain the gradient descent value.

[0018] For the second factor matrix, the calculation process of the gradient descent value includes the following steps: calculating the product of the conjugate transpose of the first factor matrix output in the current round and the second factor matrix input in the current round, or calculating the product of the conjugate transpose of the first factor matrix input in the current round and the second factor matrix input in the current round; calculating the difference between the product and the first estimated matrix input in the current round, multiplying the obtained difference, a set third step size and the first factor matrix output in the current round to obtain a gradient, and subtracting the gradient from the second factor matrix input in the current round to obtain the gradient descent value.

[0019] In some embodiments of the present application, after the gradient is calculated, the method further includes: taking the product of the scaling operator and the calculated gradient as the optimized gradient to calculate the gradient descent value; wherein, for the first factor matrix, the scaling operator is the inverse matrix of the product of the second factor matrix input in the current round and its conjugate transpose; for the second factor matrix, the scaling operator is the inverse matrix of the product of the first factor matrix output in the current round and its conjugate transpose, or the scaling operator is the inverse matrix of the product of the first factor matrix input in the current round and its conjugate transpose.

[0020] In some embodiments of the present application, before the first factor matrix and the second factor matrix output in the current round are obtained through the back projection convolution layer, the updating operation further includes: performing a soft threshold operation on each element in the first intermediate projection matrix and the second intermediate projection matrix obtained by using the projection gradient descent algorithm, to obtain an updated first intermediate projection matrix and an updated second intermediate projection matrix.

[0021] In some embodiments of the present application, in the case of taking the first estimated matrix output in the final round as the estimated matrix of the channel, the calculation formula of the first estimated matrix output in the current round is as follows:

[0022]

[0023] In the case of taking the second estimation matrix output by the final round as the estimation matrix of the channel, the calculation formula of the first estimation matrix output by the current round is as follows:

[0024]

[0025] Wherein, Z k+1 represents the first estimation matrix output by the current round, Z k represents the first estimation matrix input by the current round, represents a partial matrix composed of the element values of the channel sensing position set in Z k , η Z represents the first step length set, Y Ω represents the channel measurement matrix, M k represents the second estimation matrix input by the current round, L k+1 and R k+1 respectively represent the first factor matrix and the second factor matrix output by the current round, and β1 and β2 both represent weights.

[0026] In some embodiments of the present application, the loss function of the iterative neural network in the training stage is the mean square error between the channel real matrix and the channel estimation matrix output by the iterative neural network;

[0027] The projection convolution layer and the de-projection convolution layer are convolution layers symmetrical in structure and separated by a ReLU activation function.

[0028] Another aspect of the present application provides a channel estimation system of a millimeter wave multiple-input multiple-output system, comprising a processor and a memory, the memory storing computer instructions, and the processor being configured to execute the computer instructions stored in the memory, so that the system implements the steps of the method according to any one of the above embodiments.

[0029] The channel estimation method and system of the millimeter wave multiple-input multiple-output system according to the present application can realize low-rank matrix factorization through the projection gradient descent method and the de-projection convolution layer, so as to realize the iteration of the first factor matrix and the second factor matrix in each round of update operation, and to iteratively update the first estimation matrix by using the partial matrices input and output by the current round, thereby obtaining the channel estimation matrix. Compared with the prior art, the channel estimation method based on low-rank matrix completion according to the present application fully utilizes the low-rank and sparse characteristics of the channel, and can effectively reduce the calculation complexity in the estimation process and enhance the estimation accuracy.

[0030] Additional advantages, objects, and features of the application will be set forth in part in the description which follows, and in part will become apparent to those having ordinary skill in the art upon examination of the following or can be learned from practice of the application. The objects and other advantages of the application can be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.

[0031] It will be understood by those within the art that the objects and advantages of the application can be met by other embodiments not specifically described herein. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, nature's and combinations of the specific embodiments disclosed herein. It will be understood that many modifications and variations can be made by those skilled in the art in light of the before description or can be acquired from practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0032] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description, serve to explain the objects, advantages, and principles of the application. In the drawings:

[0033] Figure 1 Flow chart of the channel estimation method for the millimeter wave MIMO system in an embodiment of the present application.

[0034] Figure 2 Design diagram of the iterative neural network in an embodiment of the present application. DETAILED DESCRIPTION

[0035] In order to make the objects, technical solutions and advantages of the present application clearer, the following will further describe the present application with reference to the embodiments and drawings. Herein, the illustrative embodiments of the present application and their descriptions are used to explain the present application, but are not intended to limit the present application.

[0036] It should also be noted that, in order to avoid the present application being obscured by unnecessary details, only the structures and / or processing steps closely related to the solutions according to the present application are shown in the drawings, and other details not closely related to the present application are omitted.

[0037] It should be emphasized that the term "comprises / comprising" when used in this specification is taken to specify the presence of stated features, elements, steps or components but does not preclude the presence or addition of one or more other features, elements, steps, components, or groups thereof.

[0038] In the following, embodiments of the present application will be described with reference to the accompanying drawings. In the drawings, like reference numerals refer to same or similar functionalities, or same or similar steps.

[0039] The existing channel estimation methods still have challenges in terms of computational complexity and estimation accuracy. In view of this, the present application proposes to use an iterative neural network combining a low-rank factorization network and a deep unfolding network to realize channel estimation of a millimeter wave massive MIMO system. The channel estimation method proposed in the present application regards the channel estimation problem as a low-rank matrix completion problem to make full use of the sparsity and low-rank structure of the millimeter wave channel. Specifically, the present application can decompose the channel measurement matrix determined based on the reference signal into two low-rank factor matrices and optimize them through a projected gradient descent method. And the convolutional layer is used as a nonlinear sparse transformation module in the iterative neural network to realize the projection and deprojection of the matrix, so as to improve the channel estimation accuracy. Further, the iterative neural network of the present application can also contain a denoising module to reduce the influence of Gaussian noise in the signal transmission process and improve the channel estimation accuracy. The channel estimation method of the millimeter wave MIMO system proposed in the present application not only reduces the computational complexity, but also enhances the estimation accuracy, and can be applied to various wireless communication scenarios.

[0040] Since the present application mainly relies on an iterative neural network to realize channel estimation, the design idea of the iterative neural network is described as follows.

[0041] Suppose the downlink channel matrix to be estimated in the present application is kept static during the transmission of T training symbols , then the combined signal y(t) received by the receiving end located on the side of the channel to be estimated at each time t (i.e. when the tth training symbol is transmitted) can be represented as:

[0042] y(t)=w(t) H M real q(t)s(t)+w(t) H n(t); (1-1)

[0043] where q(t) and w(t) represent the beamforming vector and the combining vector randomly selected from the predetermined beamforming codebook and the combining codebook , w(t) H represents the conjugate transpose of w(t), and n(t) represents the additive white Gaussian noise (AWGN) with a mean of zero and a variance of σ 2 . And to simplify the operation process, s(t) can usually be set to 1.

[0044] Suppose represents has N T elements, (Indicates N R elements), and the beamforming matrix and the combining matrix are full-rank matrices constructed by using all the vectors in the set and At this time, if formula (1-1) is expressed in the form of a matrix, the signal γ received by the receiving end when the reference signal with the training length T mentioned above is received can be defined as:

[0045]

[0046] wherein W H denotes the matrix of additive white Gaussian noise, W H M real Q represents a low-rank matrix obtained by combining the beamforming matrix, the combining matrix, and the real matrix of the channel.

[0047] Further, since the number of signals T input into the channel is usually less than the number N R ×N T of elements in the real matrix of the channel M real , the signals transmitted in the channel can not pass through all positions in the channel, and considering that there can be attenuation, phase shift, or noise in the transmission process of the signals, a sampling operator can be used to define a partial observation matrix (i.e., a channel measurement matrix) Y Ω based on the reference signals transmitted in the channel to be estimated. The sampling operator can be defined as:

[0048]

[0049] wherein Ω represents a set of positions of the channel to be estimated through which the reference signals pass, i.e., a set of channel sensing positions (Ω is an invariant set), and Ω contains T elements (denoted as |Ω| = T). y i，j represents the element value at position (i, j) in matrix Y (determined based on the reference signals input and output by the channel to be estimated). That is, the element values at each position in Ω are known values determined based on the reference signals.

[0050] By introducing the sampling operator, the channel estimation problem can be converted into a low-rank matrix completion problem. Moreover, considering that the subsequent matrix completion involves obtaining a signal estimation matrix Y from the channel measurement matrix Y Ω , in order to distinguish the channel measurement matrix from the matrix Y on which the sampling is performed (since the channel sensing position Ω is pre-set, the result of sampling the matrix Y is also YΩ ), where Y Ω represents the channel measurement matrix obtained from the signal, and represents sampling of the completed matrix Y.

[0051] After introducing the sampling operator in formula (1-2), it can be expressed as Meanwhile, for the convenience of implementing low-rank matrix completion, the following simplification can be made: it is assumed that Q and W can be unit matrices, i.e. and At this time

[0052] It can be known from formula that the channel estimation process based on low-rank matrix completion can be to fill the channel measurement matrix Y Ω to obtain a signal estimation matrix Y, and then to construct a channel estimation matrix M recon by removing the influence of additive white Gaussian noise, so that the obtained M recon is regarded as M real . Therefore, in the low-rank matrix completion process, the channel can be reconstructed by solving the following constrained optimization problem (which can be regarded as the loss function of the channel estimation process):

[0053]

[0054] where r is an estimated value of the rank of the channel real matrix M real . In actual applications, the estimated rank r can be determined by channel tracking technology or based on existing channel statistical data, and the present application does not specifically limit the determination method of the estimated rank r. Since F-norm is commonly used to evaluate the error, stability and convergence of a matrix, the present application uses F-norm to evaluate the convergence of low-rank matrix completion, represents the square of the F-norm of .

[0055] As an example, to meet the above operation conditions, the estimated rank r mentioned in the present application is less than N R , N T and T, and the size between N R , N T and T is not specifically limited. In addition, the ranks of Y Ω , Y, M recon and M real and the matrix size (N R × N T ) are consistent.

[0056] The difficulty of solving formula (1-3) lies in reconstructing the channel matrix M reconLow-Rank Decomposition is a technique to decompose a high-dimensional matrix into multiple low-rank matrices, which is often used to reduce the number of parameters and computation in low-rank matrix completion, thereby reducing the complexity of the model. Singular Value Decomposition (SVD) algorithm is a commonly used matrix completion method, which can represent any complex matrix as the multiplication of three smaller and simpler sub-matrices. Therefore, according to the channel real matrix M real and the channel estimation matrix M recon , M recon (or M real ) can be decomposed into a left singular vector matrix U , a singular value diagonal matrix ∑, and the transpose of a right singular vector matrix V , which can be expressed as: M recon = U∑V H (or M ). Since ∑ is a diagonal matrix, it can be simplified as M recon = LR H , where L = U∑ 1 / 2 and R = V∑ 1 / 2 , and and On the contrary, the channel estimation matrix M recon can be constructed using the low-rank factor matrices L and R.

[0057] However, in the process of applying the singular value decomposition algorithm, the following constraint condition is defined to evaluate the feasibility of low-rank matrix completion: if formula (1-4) is met, it is considered that the matrices U and V satisfy the μ-uncorrelated condition.

[0058] where ||U|| 2,∞ represents the maximum value of the l2-norm of each row of matrix U, ||U|| F represents the F-norm of matrix U, and μ represents the measurement parameter of the uncorrelated condition.

[0059] Generally, the Projected Gradient Descent (PGD) algorithm can be used to ensure that the matrices U and V satisfy the μ-uncorrelated condition in the matrix completion process, so L and R can be searched on the following constraint set:

[0060]

[0061] where the projection operators and can be designed using the channel sparsity in the angular domain, L ＊and R ＊ respectively represent the channel real matrix M real The first factor matrix and the second factor matrix obtained by performing SVD are L ＊ = U ＊ ∑ 1 / 2 , R ＊ = V ＊ ∑ 1 / 2 , and respectively represent sparse matrices with a L and a R number of non-zero elements, represents the maximum value of the l1-norm of each row, represents the maximum value of the l1-norm of each row.

[0062] Further, considering the constraint conditions on L and R in formula (1-5), the constraint optimization problem can be re-expressed according to formula (1-3) and formula (1-5) in the following form:

[0063]

[0064] Solving formula (1-6) can obtain the low-rank factor matrices L and R that meet the above constraint optimization problem, thereby obtaining the channel estimation matrix M recon . In order to facilitate the solving operation, formula (1-6) can be divided into a projection gradient descent process and a projection recovery (back projection) process

[0065] ① The projection matrix corresponding to the optimized matrices L' and R' is obtained by using the projection gradient descent algorithm. By using the known L and R that do not necessarily satisfy the small μ incoherence condition, the optimized L' and R' that satisfy the small μ incoherence condition can be obtained through the projection gradient descent algorithm (the gradient descent is used for optimizing L and R, and the projection is used to ensure that L is searched on the constraint set during the optimization process). The formula for solving by using the projection gradient descent can be expressed as:

[0066]

[0067] Wherein, A' is the projection of L' on the convex set , B' is the projection of R' on the convex set , and thus and are intermediate variables in the gradient descent process, and η L and η R are the gradient steps corresponding to the matrices L and R, respectively.

[0068] As an example, to accelerate the convergence process of the intermediate variables A' and B', a scaling operator in Scaled Gradient Descent can also be introduced in the gradient descent process. The design (R H R) -1 and (L H L) -1 are the scaling operators corresponding to the matrices L and R respectively, so the process of solving by using the projected gradient descent method can be expressed by the following formula:

[0069]

[0070] After obtaining A' and R' on the convex set by using the projected gradient descent method, the inverse projection operation can be used to convert A' to L' in the original space and B' to R' in the original space, that is, the inverse projection operation is used to convert A' and B' from the convex set to L' and R' in the original space, which can be expressed by the following formula:

[0071]

[0072] Further, before performing the inverse projection operation, the soft threshold operation can also be used to optimize A' and B', that is, the soft threshold operation is applied to each element value A' i，j and B' i，j in the matrix A' and B' element by element. Wherein A' i，j represents the element value at position (i, j) in the matrix A', B' i，j represents the element value at position (i, j) in the matrix B', i∈{1, 2,..., N R}, j∈{1, 2,..., N T}. Therefore, the conversion formula of L and R' can be expressed as:

[0073]

[0074] Wherein θ L and θ R are the corresponding soft thresholds of L' and R' respectively, soft(A', θ L ) =∑soft(A' i，j , θ L ), and soft(B', θ R ) =∑soft(B' i，j , θ R ).

[0075] and

[0076]

[0077] That is, the above formula (1-6) can realize the channel estimation algorithm by using low-rank matrix factorization (LRMF). However, in practical applications, it is challenging to obtain the sparsity of the real factor matrix, which limits the potential application of LRMF; and the sparse transformation using the discrete Fourier transform (DFT) matrix cannot obtain the accurate transformation matrix of the channel, which may cause energy leakage, especially when the actual channel parameters are not on the discrete grid.

[0078] Further, since the multiplication operation of the factor matrices L and R to be solved is included in formula (1-6), the calculation amount in the solving operation process is large. Therefore, in order to reduce the calculation amount and the complexity of calculation during optimization, the present application introduces an auxiliary matrix Z, which is used to replace the product of the conjugate transpose of L and R in formula (1-6), that is, to add the constraint condition Z = LR H . And since the obtained channel estimation matrix M recon can be decomposed to obtain L and R by using its low-rank property, further adding the constraint condition Z = M recon , if the influence of additive white Gaussian noise is ignored, the obtained Z can be regarded as the channel estimation matrix; if the channel estimation matrix can be obtained only after removing the Gaussian noise contained in Z.

[0079] In the case of not considering the influence of noise N, formula (1-6) can be expressed as:

[0080]

[0081] In the case of considering the influence of noise N, formula (1-6) can be expressed as:

[0082]

[0083] wherein, represents a constraint term that ensures that the input signal is consistent with the received signal, represents a prior constraint term for M k , represents a constraint condition and the penalty term of Z k = M k , represents a channel prior sparse constraint term.

[0084] Inspired by the concept of deep unfolding, formula (1-6) can be solved by using an iterative updating method. Moreover, in order to optimize the iteration performance, the present application uses a learnable nonlinear transformation function and to replace the use of D R and D LThe implemented projection process, and utilize a learnable threshold θ * (θ L and θ R ) to implement soft threshold iteration to optimize A' and B'. Thus, formula (1-7) can be expressed as:

[0085] Formula (1-8) can be expressed as:

[0086]

[0087] wherein, represents a projection optimization operation on L, represents a projection optimization operation on R, represents a sparse transformation operation on M by a nonlinear transformation function

[0088] As an example, and may be a learnable nonlinear transformation function implemented by a convolutional neural network (CNN), which can adaptively learn the optimal nonlinear sparse transformation from data. The present application does not specifically limit the parameters of the convolutional neural network (such as the number of convolution kernels, the size of the convolution kernel, and the number of layers, etc.), as long as it can implement nonlinear sparse transformation.

[0089] From the above reasoning process, it can be seen that the iteration process of each parameter using the neural network structure designed by the present application is as follows:

[0090] ① Iterative update of L k+1 and R k+1

[0091] According to formula (1-9) and formula (1-10), after removing the terms in the loss function (constraint optimization problem) that are irrelevant to the update of the low-rank factor matrices L and R, the process of solving L and R by iterative update can be obtained by solving the following formula (2-1) subproblem:

[0092]

[0093] wherein, k represents the iteration number, k = 0, 1, 2,..., k max , L k and R k represent the factor matrices output by the kth iteration, and formula (2-1) can represent the L and R to be minimized in each iteration update process.

[0094] As an example, the two formulas in formula (2-1) are solved simultaneously L k+1 and R k+1 , if L is updated first​k+1 Further updates yield R k+1 If the subproblems of L and R are solved in the order of iteration, then the solution of the subproblems of L and R through iteration can be expressed as follows:

[0095]

[0096] Using L k or L k+1 The solution obtained R k+1 Since the values ​​are relatively close, this application can simultaneously solve for L. k+1 and R k+1 L can also be updated in a certain order. k+1 and R k+1 .

[0097] Furthermore, when designing iterative neural networks, the projective gradient descent method and back-projection operation can be used to solve for L. k+1 and R k+1 This application employs nonlinear transformation. Function representation L k A is obtained by projecting the corresponding gradient descent value. k+1 (or Function representation of R k B is obtained by projecting the corresponding gradient descent value. k+1 ), and those employing nonlinear transformations The function represents A k+1 Perform a back projection operation to obtain L k+1 (or The function represents B k+1 Perform a back projection operation to obtain R k+1 ), that is, utilizing functions and The functions replace D respectively R and D L Perform projection optimization operations, using functions and Functions replace projection operators and Perform a back projection operation.

[0098] Taking the solution order of formula (2-1) as an example, after introducing the depth unfolding network, the projection gradient descent and back projection operations also exhibit iterative processes. The iterative process of the k-th projection gradient descent algorithm can be expressed by the following formula (2-2):

[0099]

[0100] Among them, A k+1 It is L k+1 In convex sets The projection on Bk+1 is R k+1 In the convex set on the projection, therefore and are intermediate variables in the gradient update process. η L and η R are the gradient update steps of L k and R k respectively.

[0101] As an example, the scaling operators and of L k and R k respectively can also be designed, then according to formula (2-2), the iterative process of the kth projection gradient descent algorithm can be represented by formula (2-3) as follows:

[0102]

[0103] After obtaining A k+1 and B k+1 on the convex set by using the projection gradient descent method, the inverse projection operation and the soft threshold iteration algorithm can be used to convert A k+1 to L k+1 in the original space and B k+1 to R k+1 in the original space, which can be represented by formula (2-4) as follows:

[0104]

[0105] As an example, considering the transpose relationship between D R and D L and , as shown in Figure 2 , the network structure is symmetrically designed function and function.

[0106] ②Although the constraint Z = LR H is considered in the present application, there may be errors such as residual errors in the solving process, therefore the present application considers solving Z k+1 based on the above formula (1-7) or (1-8) in the iterative update process.

[0107] In the case of not considering noise, the update formula of Z k+1 can be obtained by solving the following subproblem:

[0108]

[0109] In the case of considering noise, Z k+1The update formula of L

[0110]

[0111] From the above formula, the update of L k+1 and R k+1 can be obtained. k+1 The update of Z k+1 can be further obtained. Applying the first-order Taylor expansion to the above formula, assuming that it satisfies the l1-Lipschitz continuity, then

[0112]

[0113] After sorting, the update formula of Z k+1 can be obtained as follows:

[0114]

[0115] or

[0116]

[0117] where C1 is a constant, β1 is the weight of the update of L k+1 and R k+1 , and β2 is the weight of M k obtained by denoising Z k . ξ and γ are the coefficients of the penalty term, η Z is the step size of the gradient descent corresponding to Z k , and l1 is a constant.

[0118] (3) According to formula (1-9) and formula (1-10), after removing irrelevant terms, the iterative update process of M can be obtained by solving the following subproblem:

[0119]

[0120] The solving process is similar to the LASSO problem, which can be solved by a convolutional neural network. Therefore, the update formula of M k+1 can be expressed as:

[0121] M k+1 = D Θ (Z k+1 ); (2-10)

[0122] That is, the convolutional neural network constructed by inputting Z k+1 into the D Θ function can output the denoised estimation matrix M k+1 .

[0123] The application provides a channel estimation method for a millimeter wave MIMO system Ω to obtain an estimated matrix Z of the channel kmax or Mk max . As shown in the figure, the method provided by the application can specifically include steps S110-S120. Figure 1

[0124] Step S110: determining a channel measurement matrix based on a reference signal and a set channel sensing position, and decomposing the channel measurement matrix by using a singular value decomposition algorithm to obtain an initial first factor matrix and an initial second factor matrix.

[0125] The channel real matrix of the channel to be estimated is a blank matrix with a known matrix size; since the set channel sensing position in the channel can sense the input signal and transmit the signal to the receiving end, the values of part of the elements in the channel matrix can be determined through the transmission and reception of the signal, and a channel measurement matrix Y Ω is obtained. Specifically, the signal sending end on one side of the channel to be estimated can input a reference signal into the channel to be estimated, and the signal receiving end on the other side of the channel to be estimated can receive the corresponding signal, and the reference signal can be transmitted through the set channel sensing position Ω in the channel to be estimated. The element values of the set channel sensing position in the channel matrix of the channel to be estimated can be determined based on the transmitted reference signal and the received reference signal, and a channel measurement matrix Y Ω is obtained (that is, the channel measurement matrix is a partial estimation matrix of the channel determined based on the reference signal). The way of determining the channel measurement matrix in the application can adopt the prior art, and the application does not make a specific limitation thereto.

[0126] Further, although the channel matrix itself has low rank and sparse characteristics, the channel measurement matrix Y Ω is a matrix of partial observation values, and may not have the low rank characteristic, so that a low rank matrix with a rank r can be cut out from Y Ω for singular value decomposition, that is, Y Ω is approximately decomposed into low rank factor matrices L and R Therefore, Y Ω can be decomposed by using the SVD algorithm to obtain an initial first factor matrix L0 and an initial second factor matrix R0 (or an initial first factor matrix R0 and an initial second factor matrix L0). For convenience of description, the first factor matrix is L k and the second factor matrix is R k in the following description.

[0127] ​Step S120: inputting the initial input set including the initial first estimation matrix Z0, the initial first factor matrix L0 and the initial second factor matrix R0 into the pre-trained iterative neural network to perform a multi-round updating operation to obtain the estimation matrix M of the channel recon .

[0128] As an example, if the Gaussian noise in the signal transmission process is considered, i.e., the second estimation matrix M kmax as the estimation matrix M of the channel recon , the initial input set includes the initial first estimation matrix Z0, the initial first factor matrix L0, the initial second factor matrix R0 and the initial second estimation matrix M0; if the Gaussian noise in the signal transmission process is not considered, i.e., the first estimation matrix Z kmax as the estimation matrix M of the channel recon , the initial input set includes the initial first estimation matrix Z0, the initial first factor matrix L0 and the initial second factor matrix R0. In addition, in order to make full use of the information carried in the transmission signal, the channel measurement matrix Y Ω is used as the initial value of the first estimation matrix and the second estimation matrix, i.e., the channel measurement matrix is used as the initial first estimation matrix Z0 and the initial second estimation matrix M0.

[0129] As shown in Figure 2 , the initial input set is input into the pre-trained iterative neural network to perform a multi-round updating operation, and the estimation matrix of the channel can be obtained. Moreover, the iterative neural network uses the output of the current round updating operation as the input of the next round updating operation, i.e., the input parameter matrix (L, R and Z) and the output parameter (also a matrix L, R and Z) of each round updating operation are the same.

[0130] In some embodiments of the present application, each round updating operation in the iterative neural network includes:

[0131] Step S210: using the projection gradient descent algorithm to obtain the first intermediate projection matrix A k and the second intermediate projection matrix B k based on the first factor matrix L k , the second factor matrix R k+1 and the first estimation matrix Z k+1 of the current round input, and converting the first intermediate projection matrix A k+1 and the second intermediate projection matrix B k+1 of the current round output into the first factor matrix L k+1 and the second factor matrix R k+1 respectively through the de-projection convolution layer.

[0132] More specifically, the first factor matrix L k , the second factor matrix R k+1 and the first estimation matrix Z k+1 of the current round input are used in step S210 to obtain the first intermediate projection matrix A k+1 and the second intermediate projection matrix B k+1 , and the first intermediate projection matrix A k+1 and the second intermediate projection matrix B k+1 are converted into the first factor matrix L k+1 and the second factor matrix R k+1 respectively through the de-projection convolution layer.k a second factor matrix R k and a first estimation matrix Z k , to obtain a first factor matrix L k+1 and a second factor matrix R k+1 However, the projection gradient update steps for the first factor matrix and the second factor matrix can be the same or different. This is because, as can be seen from the above formula (2-1), the update order of the first factor matrix L k and the second factor matrix R k is not necessarily synchronized, and the first factor matrix can be updated first, and then the second factor matrix is updated using the updated first factor matrix (or, the second factor matrix is updated first, and then the first factor matrix is updated); or the first factor matrix L k and the second factor matrix R k can be updated synchronously. The present application does not specifically limit the update order of the first factor matrix and the second factor matrix. Hereinafter, the first factor matrix L k is updated first to obtain L k+1 , and then the second factor matrix R k+1 is updated based on L k to obtain R k+1 is described as an example.

[0133] In some embodiments of the present application, the update process for the first factor matrix is as follows: using the projection gradient descent algorithm, based on the first factor matrix L k , the second factor matrix R k and the first estimation matrix Z k , a first intermediate projection matrix A k+1 of the current round is obtained, and the first intermediate projection matrix A k+1 of the current round is converted into the first factor matrix L k+1 of the current round output through the de-projection convolution layer. The update process for the second factor matrix is as follows: based on the first factor matrix L k+1 of the current round output, the second factor matrix R k of the current round input and the first estimation matrix Z k , a second intermediate projection matrix B k+1 of the current round is obtained, and the second intermediate projection matrix B k+1 of the current round is converted into the second factor matrix R k+1 of the current round output through the de-projection convolution layer.

[0134] For the first factor matrix, the step of obtaining the first intermediate projection matrix A k+1 using the projection gradient descent algorithm includes: based on the first factor matrix L k of the current round input, the second factor matrix R kFirst estimation matrix Z k and the set second step size η L Calculate the gradient to obtain the gradient descent value; input the calculated gradient descent value into the projection convolutional layer, and output the first intermediate projection matrix A. k+1 For the second factor matrix, the second intermediate projection matrix B is obtained using the projection gradient descent algorithm. k+1 The steps include: based on the first factor matrix L of the current round output k+1 The second factor matrix R of the current round input k and the first estimated matrix Z k And the third set step size η R Calculate the gradient to obtain the gradient descent value (if L is updated synchronously). k+1 and R k+1 Then, for the second factor matrix, the second intermediate projection matrix B is obtained using the projection gradient descent algorithm. k+1 The steps include: based on the first factor matrix L of the current round input k The second factor matrix R of the current round input k and the first estimated matrix Z k And the third set step size η R Calculate the gradient (to obtain the gradient descent value); input the obtained gradient descent value into the projection convolutional layer, and output the second intermediate projection matrix B. k+1 .

[0135] In some embodiments of the present invention, as shown in formula (2-2), the calculation process of the gradient descent value for the first factor matrix includes the following steps: calculating the first factor matrix L of the current round input. k With the second factor matrix R k conjugate transpose The product of; calculate the product. The difference Z between the first estimated matrix of the current round input and the difference Z. k The difference obtained The set second step size η L And the second factor matrix R of the current round input k Multiply to obtain the gradient; use the first factor matrix L of the current round input. k Subtracting the gradient yields the gradient descent value. For the second factor matrix, the gradient descent calculation process includes the following steps: Calculate the first factor matrix L of the current round's output. k+1 The second factor matrix R of the current round input k conjugate transpose The product (if L is updated synchronously) k+1 and R k+1 Then, for the second factor matrix, calculate the first factor matrix L of the current round input. kThe second factor matrix R of the current round input k conjugate transpose (product); calculate the product. Subtract the first estimated matrix Z from the current round input k The difference, the obtained difference The set third step length η R and the first factor matrix L of the current round output k+1 Multiplying yields the gradient, which is then used to calculate the second factor matrix R of the current round's input. k Subtracting the gradient gives the gradient descent value.

[0136] As an example, as shown in formula (2-3), after calculating the gradient using formula (2-2), the method further includes: using the product of the scaling operator and the calculated gradient as the optimized gradient to calculate the gradient descent value, thereby accelerating convergence; wherein, for the first factor matrix, the scaling operator is the second factor matrix R input in the current round. k and its conjugate transpose The inverse matrix of the product; for the second factor matrix, the scaling operator is the first factor matrix L output in the current round. k+1 and its conjugate transpose The inverse matrix of the product (if L is updated synchronously) k+1 and R k+1 For the second factor matrix, the scaling operator is the first factor matrix L output in the current round. k and its conjugate transpose (the inverse matrix of the product).

[0137] Furthermore, as shown in Equation (2-4), the first factor matrix L of the current round output is obtained through the back-projection convolution layer. k+1 Second factor matrix R k+1 Previously, each update operation also included: processing the first intermediate projection matrix A obtained using the projection gradient descent algorithm. k+1 Second intermediate projection matrix B k+1 Perform a soft thresholding operation on each element in the matrix to obtain the updated first intermediate projection matrix soft(A). k+1 ,θ L ) and the second intermediate projection matrix soft(B k+1 ,θ R That is, during the iteration process, the first intermediate projection matrix A is optimized using a soft thresholding iterative algorithm. k+1 Second intermediate projection matrix B k+1 .

[0138] As an example, the projective convolutional layer in this application can be used as a projection operator in the projective gradient descent algorithm, and the first intermediate projection matrix A can be obtained from the matrix of the current round input through the projection optimization operation.k+1 and the second intermediate projection matrix B k+1 , and since A k+1 and B k+1 are the first factor matrix L k+1 and the second factor matrix R k+1 output by the current round, the first intermediate projection matrix A k+1 and the second intermediate projection matrix B k+1 can be mapped to the original space by performing the de-projection operation through the de-projection convolution layer, to obtain the first factor matrix L k+1 and the second factor matrix R k+1 output by the current round, so the projection convolution layer and the de-projection convolution layer are convolution layers that are structurally symmetrical and separated by a ReLU activation function.

[0139] In some embodiments of the present application, after updating L k+1 and R k+1 in step S210, step S220 can be performed: based on the first estimation matrix Z k input by the current round, the first factor matrix L k+1 output by the current round, and the second factor matrix R k+1 output by the current round, the first estimation matrix Z k+1 output by the current round is obtained. Specifically, in the case where the first estimation matrix Z kmax output by the final round is taken as the estimation matrix M recon of the channel, based on the first estimation matrix Z k input by the current round, the first factor matrix L k+1 and the second factor matrix R k+1 output by the current round, the channel measurement matrix Y Ω , and the set first step size η Z , the first estimation matrix Z k+1 output by the current round is obtained. In the case where the second estimation matrix Mk max output by the final round is taken as the estimation matrix M recon of the channel, based on the first estimation matrix Z k input by the current round, the first factor matrix L k+1 and the second factor matrix R k+1 output by the current round, the channel measurement matrix Y Ω , the set first step size η Z , and the second estimation matrix M k input by the current round, the first estimation matrix Z k+1 output by the current round is obtained.

[0140] More specifically, in the case where the first estimation matrix Z kmax output by the final round is taken as the estimation matrix Mrecon the first estimation matrix Z k+1 of the current round is calculated as follows:

[0141]

[0142] the second estimation matrix M max of the final round is taken as the estimation matrix M recon of the channel, the first estimation matrix Z k+1 of the current round is calculated as follows:

[0143]

[0144] wherein Z k+1 denotes the first estimation matrix of the current round, Z k denotes the first estimation matrix of the current round input, denotes a partial matrix composed of the element values of the channel sensing position set in Z k , η Z denotes the first step set, Y Ω denotes the channel measurement matrix, M k denotes the second estimation matrix of the current round input, L k+1 and R k+1 denote the first factor matrix and the second factor matrix of the current round output respectively, β1 denotes the weight of L k+1 and R k+1 , and β2 denotes the weight of M k .

[0145] In some embodiments of the present application, in the case that the initial input set comprises an initial second estimation matrix, each round of update operation further comprises step S230: inputting the first estimation matrix Z k+1 of the current round output into the denoising convolution layer to obtain the second estimation matrix M k+1 of the current round output, so as to take the second estimation matrix of the final round output as the estimation matrix of the channel.

[0146] As an example, since the input of the projection convolution layer, the back-projection convolution layer and the denoising convolution layer is a two-dimensional matrix, and the output of the convolution layer is also a two-dimensional matrix, a dimension transformation is required before inputting the convolution layer and after outputting the convolution layer. For example, the matrix dimension of L R is N k ×r, and the matrix dimension of R T is r×N k , which can be reshaped to 1×N R ×r and 1×N Ta tensor of x r. Moreover, the projection convolution layer, the de-projection convolution layer and the denoising convolution layer mentioned in the present application can all be composed of a multi-layer CNN structure, because different layers of the convolutional neural network can remove different types and levels of noise interference, and therefore the hierarchical feature learning mechanism of the CNN helps to more accurately recover the signal.

[0147] According to the above steps S210-S230, the iterative neural network can be divided into three parts, an LRMF module, an estimated matrix updating module and an estimated matrix denoising module. In the LRMF module, a high-dimensional feature representation of the input data can be obtained through the projection convolution layer and the de-projection convolution layer, and the sparsity of the matrix can be constrained through the soft threshold operation; in the estimated matrix denoising module, different types and levels of noise interference are removed by using the denoising convolution layer to achieve accurate signal recovery; in the estimated matrix updating module, based on the matrix output by the LRMF module, the weight β1 of the LRMF module and the weight β2 of the estimated matrix denoising module, the Z H that meets the constraint condition Z = LR k+1 can be obtained. In each round of update operation in the iterative neural network, the learnable parameters to be used include the gradient update step (the first step η Z , the second step η L and the third step η R ), the soft threshold parameters θ L and θ R , the update parameters β1 and β2 of the first estimated matrix, and the neural network weights (Θ M , Θ L and Θ R are the weights of D Θ , and and and .

[0148] As an example, the multiple rounds of update operations can be performed by means of the multi-layer neural network in the iterative neural network, each layer of the neural network can perform one round of update operation, and the values of the learnable parameters of each layer of the neural network can be different, and at this time all the learnable parameters of the iterative neural network can be represented as

[0149] In some embodiments of the present application, in the training phase of the iterative neural network, the signal sensing positions Ω of each batch (E = 1, 2,..., E max ) are randomly generated. Moreover, the loss function of the iterative neural network in the training phase is the mean square error (used to evaluate the computational complexity and accuracy) between the channel real matrix and the channel estimated matrix output by the iterative neural network, which can be expressed by the following formula:

[0150]

[0151] wherein f(*) represents an iterative neural network, represents a loss function.

[0152] The channel estimation method of the millimeter wave multi-MIMO system provided in the application has the following advantages:

[0153] ① The millimeter wave channel has low rank and sparse characteristics, and the channel estimation can be regarded as low rank matrix completion, thereby improving the accuracy and efficiency of channel estimation.

[0154] ② The iterative neural network designed by using the convolutional neural network can adaptively learn the optimal nonlinear sparse transformation, avoiding the inaccuracy caused by the discrete Fourier transform matrix.

[0155] ③ The projection and deprojection operations ensure that the factor matrix is searched on the constraint set during the channel estimation optimization process, thereby improving the estimation accuracy.

[0156] ④ The denoising module can effectively remove different types and levels of noise interference, which helps to more accurately restore the signal.

[0157] Corresponding to the above method, the application also provides a channel estimation system of a millimeter wave multi-input multi-output system, which comprises a computer device, the computer device comprises a processor and a memory, the memory stores computer programs / instructions, and the processor is used to execute the computer programs / instructions stored in the memory, and when the computer programs / instructions are executed by the processor, the system realizes the steps of the method as described above.

[0158] Those skilled in the art should understand that the exemplary components, systems and methods described in conjunction with the embodiments disclosed herein can be realized in hardware, software or a combination of both. Whether to be realized in hardware or software depends on the specific application and design constraints of the technical solution. The skilled person can use different methods to realize the described functions for each specific application, but such implementation should not be considered beyond the scope of the application. When realized in hardware, it can be, for example, an electronic circuit, an application specific integrated circuit (ASIC), appropriate firmware, a plug-in, a functional card, etc. When realized in software, the elements of the application are program or code segment used to perform the required tasks. The program or code segment can be stored in a machine-readable medium or transmitted through a data signal carried in a carrier wave on a transmission medium or communication link.

[0159] It is to be expressly understood that the invention is not limited to the specific configurations and process described above and illustrated in the accompanying drawings. For the sake of clarity, detailed descriptions of known methods are omitted. In the above-described embodiments, several specific steps are described and illustrated as examples. However, the method processes of the present invention are not limited to the specific steps described and illustrated, and various changes, modifications and additions can be made thereto by one of ordinary skill in the art without departing from the spirit of the present invention, and the order of the steps can be changed.

[0160] In the present invention, features described and / or illustrated with respect to one embodiment can be used in the same or a similar way in one or more other embodiments, and / or in combination with or instead of features of other embodiments.

[0161] The above description is only preferred embodiments of the present invention, and is not intended to limit the present invention. The embodiments of the present invention can be variously changed and modified by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the scope of the present invention.

Claims

1. A method of channel estimation for a millimeter wave multiple-input multiple-output system, the method comprising: The method comprises the following steps: determining a channel measurement matrix based on a reference signal and a set channel sensing position, and decomposing the channel measurement matrix by using a singular value decomposition algorithm to obtain an initial first factor matrix and an initial second factor matrix; inputting an initial input set comprising the channel measurement matrix used as an initial first estimation matrix, the initial first factor matrix and the initial second factor matrix into a pre-trained iterative neural network to perform a plurality of rounds of update operations, and finally obtaining an estimation matrix of the channel; wherein the iterative neural network takes the output of the current round of update operations as the input of the next round of update operations; each round of update operation comprises: obtaining a first intermediate projection matrix and a second intermediate projection matrix of the current round of update operations based on the first factor matrix, the second factor matrix and the first estimation matrix input in the current round by using a projection gradient descent algorithm, and converting the first intermediate projection matrix and the second intermediate projection matrix of the current round of update operations into the first factor matrix and the second factor matrix output in the current round of update operations respectively through an inverse projection convolution layer; and obtaining the first estimation matrix output in the current round of update operations based on the first estimation matrix input in the current round, the first factor matrix output in the current round and the second factor matrix output in the current round; the obtaining of the first intermediate projection matrix and the second intermediate projection matrix of the current round of update operations based on the first factor matrix, the second factor matrix and the first estimation matrix input in the current round by using the projection gradient descent algorithm comprises: for the first factor matrix, calculating a gradient based on the first factor matrix, the second factor matrix, the first estimation matrix input in the current round and a second set step length, thereby obtaining a gradient descent value; inputting the gradient descent value into a projection convolution layer to output the first intermediate projection matrix; for the second factor matrix, calculating a gradient based on the first factor matrix output in the current round, the second factor matrix input in the current round and the first estimation matrix, and a third set step length, thereby obtaining a gradient descent value, or calculating a gradient based on the first factor matrix, the second factor matrix and the first estimation matrix input in the current round, and the third set step length, thereby obtaining a gradient descent value; inputting the gradient descent value into a projection convolution layer to output the second intermediate projection matrix; for the first factor matrix, the calculation process of the gradient descent value comprises the following steps: calculating the product of the first factor matrix input in the current round and the conjugate transpose of the second factor matrix; calculating the difference between the product and the first estimation matrix input in the current round, multiplying the obtained difference, the second set step length and the second factor matrix input in the current round to obtain a gradient; subtracting the gradient from the first factor matrix input in the current round to obtain the gradient descent value; The calculation process of the gradient descent value for the second factor matrix comprises the following steps: calculating the product of the first factor matrix of the current round output and the conjugate transpose of the second factor matrix of the current round input, or calculating the product of the first factor matrix of the current round input and the conjugate transpose of the second factor matrix of the current round input; calculating the difference between the product and the first estimation matrix of the current round input, multiplying the obtained difference, a set third step length and the first factor matrix of the current round output to obtain a gradient, and subtracting the gradient from the second factor matrix of the current round input to obtain the gradient descent value.

2. The method of claim 1, wherein, The initial input set further comprises a channel measurement matrix used as an initial second estimation matrix; and In the case where the initial input set comprises the initial second estimation matrix, the each-round updating operation further comprises: inputting the first estimation matrix of the current round output into the denoising convolution layer to output the second estimation matrix of the current round output.

3. The method of claim 2, wherein, The calculation of the first estimation matrix of the current round output based on the first estimation matrix of the current round input, the first factor matrix of the current round output and the second factor matrix of the current round output comprises: In the case where the first estimation matrix of the final round output is taken as the estimation matrix of the channel, the first estimation matrix of the current round output is calculated based on the first estimation matrix of the current round input, the first factor matrix and the second factor matrix of the current round output, the channel measurement matrix and a set first step length; In the case where the second estimation matrix of the final round output is taken as the estimation matrix of the channel, the first estimation matrix of the current round output is calculated based on the first estimation matrix of the current round input, the first factor matrix and the second factor matrix of the current round output, the channel measurement matrix, a set first step length and the second estimation matrix of the current round input.

4. The method of claim 1, wherein, After the gradient is calculated, the method further comprises: calculating the product of a scaling operator and the calculated gradient as an optimized gradient to obtain the gradient descent value; wherein, for the first factor matrix, the scaling operator is the inverse matrix of the product of the second factor matrix of the current round input and the conjugate transpose thereof; for the second factor matrix, the scaling operator is the inverse matrix of the product of the first factor matrix of the current round output and the conjugate transpose thereof, or the scaling operator is the inverse matrix of the product of the first factor matrix of the current round input and the conjugate transpose thereof.

5. The method of claim 1, wherein, Before the first factor matrix and the second factor matrix of the current round output are obtained through the back-projection convolution layer, the updating operation further comprises: performing a soft threshold operation on each element in the first intermediate projection matrix and the second intermediate projection matrix obtained by using the projection gradient descent algorithm to obtain an updated first intermediate projection matrix and an updated second intermediate projection matrix.

6. The method of claim 3, wherein, In the case where the first estimation matrix of the final round output is taken as the estimation matrix of the channel, the calculation formula of the first estimation matrix of the current round output is as follows: ； In the case where the second estimation matrix of the final round output is taken as the estimation matrix of the channel, the calculation formula of the first estimation matrix of the current round output is as follows: ； wherein denotes a first estimate matrix of the current round output, denotes a first estimate matrix of the current round input, denotes a part matrix consisting of the element values of the channel aware position set in denotes a first step size set, denotes a channel measurement matrix, denotes a second estimate matrix of the current round input, and denote a first factor matrix and a second factor matrix of the current round output, respectively, and both denote a weight.​ 7. The method of claim 1, wherein, The loss function of the iterative neural network in the training stage is the mean square error between a channel real matrix and a channel estimation matrix output by the iterative neural network; The projection convolution layer and the back-projection convolution layer are convolution layers that are structurally symmetrical and separated by a ReLU activation function.

8. A channel estimation system for a millimeter wave multiple-input multiple- output system, comprising a processor and a memory, wherein, The memory stores computer instructions, and the processor is configured to execute the computer instructions stored in the memory, and the system implements the steps of the method in any one of claims 1 to 7 when the computer instructions are executed by the processor.

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