A single-cell massive MIMO beam completion channel estimation method

Abstract

The present invention discloses a single-cell massive MIMO beam-complemented channel estimation method, comprising the following steps: (1) a base station establishes a space-frequency domain received signal model for an angle-delay domain channel based on a received pilot signal and a beam-based channel characterization model; (2) each oversampled DFT matrix constituting a sensing matrix in the receiving model is completed into a DFT matrix, and received signal and noise completion are performed simultaneously to obtain a completed received signal model; (3) the completed signal and angle-delay domain channel are iteratively solved using an EM algorithm until convergence or a fixed number of iterations are reached, at which point the channel obtained is the estimated value of the angle-delay domain channel. The present invention can significantly resolve the complex matrix inversion problem in MMSE estimation, thereby reducing time complexity and space complexity, and can quickly converge to a better estimated value given a small number of iterations.

Description

Technical Field

[0001] The present invention relates to the field of communication technology and proposes a single-cell large-scale MIMO beam completion channel estimation method. Background Art

[0002] In massive MIMO-OFDM transmission, channel state information (CSI) is used in both uplink signal detection and downlink precoding design, and its accuracy directly impacts system performance. A common channel estimation method is pilot-assisted channel estimation, where the transmitter periodically transmits pilot signals, and the receiver estimates the CSI based on the received signals. Channel estimation involves estimating the a posteriori information of channel parameters given the received pilot signals. When the channel has Gaussian prior information, its posterior distribution is also Gaussian, determined solely by its mean and covariance matrix. Among pilot-assisted channel estimation methods, minimum mean square error (MMSE) estimation achieves optimal performance by minimizing the mean square error between the estimated and accurate channels. However, it requires complex matrix inversion and multiplication operations, making such complexity prohibitive in practical systems.

[0003] The space defined by probability distributions can be viewed as a differentiable manifold with a Riemannian structure. Therefore, it can be studied using information geometry. Information geometry analyzes information theory and statistical inference problems from an intrinsically geometric perspective and has been applied to massive MIMO channel estimation. Although information geometry channel estimation methods are less complex than MMSE estimation, their performance is insufficient for practical applications given a small number of iterations, and the damping factor required to ensure convergence is often difficult to obtain. However, tools from information geometry, such as the KL divergence and the EM algorithm, still play a significant role. Summary of the Invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a single-cell large-scale MIMO beam completion channel estimation method, which can obtain the a posteriori information of the spatial-frequency domain channel of each user in the cell. Under the same channel estimation performance, compared with existing algorithms, it can further reduce the time complexity and spatial complexity, and at the same time have better performance under the condition of fewer iterations.

[0005] Technical solution: The present invention provides a single-cell massive MIMO beam-completion channel estimation method, comprising the following steps:

[0006] (1) The base station establishes a spatial-frequency domain received signal model for the angle-delay domain channel based on the received pilot signal and the beam-based channel characterization model;

[0007] (2) Completing the oversampled DFT matrices that constitute the perception matrix in the received signal into a DFT matrix, and simultaneously completing the received signal and noise to obtain a completed received signal model;

[0008] (3) The EM algorithm is used to iteratively solve the completed signal and the angle delay domain channel until convergence or a fixed number of times is reached. The channel obtained at this time is the estimated value of the angle delay domain channel.

[0009] Furthermore, in step (1), the beam-based channel characterization model is: the space-frequency domain channel matrix can be obtained by weighting the angle delay domain channel matrix by sampling the rudder vector in the space domain and the frequency domain, wherein the angle delay domain channel is sparse and each non-zero element is statistically independent.

[0010] Furthermore, in step (1), the received pilot signal comes from an adjustable phase-shifted pilot signal with a specific phase shift factor sent by each user in the cell to the base station.

[0011] Furthermore, in step (2), the perception matrix is ​​obtained by performing Kronecker product on three oversampled DFT matrices in the frequency domain, vertical spatial domain, and horizontal spatial domain, and each of them is completed into a DFT matrix and then Kronecker product is performed to obtain a unitary matrix.

[0012] Furthermore, in step (3), the method for iteratively solving the completed signal and angle delay domain channel through the EM algorithm is as follows: based on the posterior distribution of the completed received signal and its joint distribution with the channel parameters, a data manifold and a model manifold are established respectively, and then e-projection and m-projection are alternately performed between the two manifolds, the posterior mean of the completed signal is updated through the e-projection, the posterior mean of the received signal and the completed signal are combined, and the channel parameters are updated through the m-projection until convergence.

[0013] Furthermore, the data manifold is a manifold composed of the completed probability distribution of the received signal, and the model manifold is a manifold composed of the joint probability distribution of the completed received signal and the channel parameters.

[0014] Furthermore, both e-projection and m-projection are based on minimizing the KL divergence between two manifolds.

[0015] Furthermore, e-projection obtains the posterior mean of the completed signal, and m-projection obtains the channel estimation value. In the t-th iteration, the posterior mean of the completed signal is the product of the completed perception matrix and the t-1-th channel estimation value, and the angle delay domain channel estimation value is the product of the diagonal matrix containing the prior term, the completed perception matrix and the combined signal.

[0016] Furthermore, in a specific implementation, the base station obtains the prior statistical information of each user terminal channel through uplink channel detection, and uses the prior information of the channel and the received pilot signal to calculate the posterior information of the angle delay domain channel of each user terminal through steps (1) to (3), and finally converts the obtained angle delay domain channel into the space-frequency domain through the beam-based channel characterization model.

[0017] The present invention also provides a computer program product, comprising a computer program / instruction, which, when executed by a processor, implements the steps of the single-cell massive MIMO beam-completion channel estimation method.

[0018] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: based on the pilot signal and the beam-based channel characterization model, a space-frequency domain receiving signal model for the angle delay domain channel is established, and then the oversampled DFT matrices that constitute the perception matrix are completed into DFT matrices, and the receiving signal and noise are completed at the same time to obtain a completed receiving signal model. The completed signal and the angle delay domain channel are iteratively solved by the EM algorithm until convergence or a fixed number of times is reached. The channel obtained at this time is the estimated value of the angle delay domain channel. The algorithm in the scheme of the present invention can converge to the MMSE channel estimation with lower time complexity and space complexity, and can achieve higher accuracy given a smaller number of iterations, providing a new way for channel estimation in actual systems. At the same time, the estimated angle delay domain channel can be converted to the space-frequency domain through the beam-based channel characterization model, so as to be used for uplink detection and downlink precoding, thereby improving the overall transmission rate of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 Schematic diagram of the uplink channel estimation method of the present invention;

[0020] Figure 2 Schematic diagram of alternating projection between two manifolds of the EM algorithm of the present invention;

[0021] Figure 3 Schematic diagram of the flow of the beam completion channel estimation method of the present invention;

[0022] Figure 4 Schematic diagram showing the comparison of channel estimation performance between the EM algorithm of the present invention and the existing method;

[0023] Figure 5 Schematic diagram showing the comparison of convergence curves of the EM algorithm of the present invention and the existing method at a signal-to-noise ratio of 20 dB;

[0024] Figure 6 The figure is a schematic diagram showing a comparison of the sum rate performance when the channels obtained at the 10th and 30th iterations respectively by the EM algorithm of the present invention and the existing method are used for downlink RZF precoding design. DETAILED DESCRIPTION

[0025] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0026] like Figure 1 As shown, an embodiment of the present invention provides a single-cell large-scale MIMO beam completion channel estimation method, including a base station establishing a space-frequency domain receiving signal model about the angle delay domain channel based on the received pilot signal and the beam-based channel characterization model; completing each oversampled DFT matrix that constitutes the perception matrix in the received signal into a DFT matrix, and simultaneously performing received signal and noise completion to obtain a completed received signal model; iteratively solving the completed signal and the angle delay domain channel through the EM algorithm until convergence or a fixed number of times, at which time the channel obtained is the estimated value of the angle delay domain channel. In specific implementation, the base station obtains the prior statistical information of each user terminal channel through uplink channel detection; the base station receives the pilot signal sent by each user terminal; and using the prior information of the channel and the received pilot signal, the a posteriori information of each user terminal channel is obtained through the beam completion channel estimation method. The beam completion channel estimation method is to update the posterior mean of the complement signal through e-projection, combine the posterior mean of the received signal and the complement signal, and update the channel parameters through m-projection until convergence; finally, the obtained angle delay domain channel is converted to the space-frequency domain through the beam-based channel characterization model.

[0027] Figure 2 A schematic diagram of the EM algorithm's alternating projections between the data manifold and the model manifold is presented. The data manifold consists of the probability distribution of the combined signal, and the model manifold consists of the joint probability distribution of the combined signal and the channel parameters. By alternating between e-projections and m-projections between the two manifolds, convergence to a stable point is achieved.

[0028] Figure 3 The specific steps of the beam completion channel estimation method are illustrated, including: (1) setting the initial value of the number of iterations to 0 to initialize the angle delay domain channel parameters; (2) updating the posterior mean of the completed signal through e-projection; (3) combining the original received signal and the posterior mean of the completed signal; (4) updating the angle delay domain channel parameters through m-projection; (5) repeating steps (2) to (4) until the preset number of iterations is reached or the result converges, at which time the channel obtained is the estimated value of the angle delay domain channel.

[0029] The present invention's solution is primarily targeted at MIMO-OFDM systems where a large-scale antenna array is deployed at a single-cell base station to simultaneously serve multiple user devices. The beam-completion channel estimation method proposed in this invention is described in detail below using a specific communication system example. It should be noted that the present invention is applicable not only to the system model described in the following example but also to system models with other antenna configurations.

[0030] (1) System model

[0031] Consider a single-cell massive MIMO-OFDM system operating in time division duplexing (TDD) mode. The base station is equipped with N r =N rv ×N rh A uniform planar array of antennas can simultaneously serve K single-antenna users, where N rv and N rh The total number of OFDM subcarriers is recorded as N c , where the cyclic prefix length is N g , the number of training subcarriers is N p The base station estimates the CSI based on the received pilot signal.

[0032] Assume that the number of sampled direction cosines is M r =F rv F rh N r , the sampling delay number is M f =F p N f , where F rv ,F rh ,F p is the refinement factor, and Define the number of spatial beams in the vertical and horizontal directions as M rv =F rv N rv ,

[0033] M rh =F rh N rh , the number of frequency beams is M p =F p N p Use F N Represents an N-dimensional DFT matrix, I M represents the M-dimensional identity matrix, 0 M,N Represents an M-row, N-column all-zero matrix, I M,N Indicates [I M ,0 M,N-M ](when M<N) or

[0034] [I N ,0 N,M-N ] T (When M>N). Matrix and Defined as the oversampled DFT matrix.

[0035] is a matrix composed of sampled space rudder vectors, where the symbol denotes the Kronecker product. Similarly, It is also defined as the oversampled DFT matrix, which consists of the sampling frequency rudder vector:

[0036] u(τ l )=[1 exp{-j2πΔfτ l} … exp{-j2π(N p -1)Δfτ l}] T , (1)

[0037] where τ l is the sampling delay, l is the phase shift factor, and Δf is the subcarrier spacing. The former can be defined as:

[0038]

[0039] Using the beam-based channel characterization model, the spatial-frequency domain channel matrix G k Can be modeled as

[0040] G k =VH k U T ,(3)Among them is the angle delay domain channel matrix, M k is the channel amplitude matrix in the delay domain from user k to the base station, W k Each element is independently and identically distributed in The random matrix, symbol ⊙ represents the Hadamard product. Define the angle delay domain channel power matrix Ω k =M k ⊙M k Since the beam domain channel is sparse, Ω k contains a large number of zero elements, so the base station has sufficient resources to estimate Ω k The base station can obtain the angle delay domain channel power matrix of each user in advance through uplink detection.

[0041] Those skilled in the art will understand that the sampling rudder vector representation in the above-mentioned beam-based statistical channel model only takes the uniform planar array as an example. For systems using different antenna arrays such as uniform linear arrays and uniform circular arrays, the above-mentioned model is still applicable, and it is only necessary to replace V with the matrix composed of the corresponding sampling space rudder vectors.

[0042] (2) Problem Statement

[0043] The purpose of beam-domain channel estimation is to obtain the a posteriori information of beam-domain channel parameters. is the frequency domain pilot signal sent by the kth user, and the corresponding P k=diag(p k ) is the pilot matrix, where diag(p) ​​represents a diagonal matrix with p on the main diagonal. The pilot signal is received in the space-frequency domain It can be expressed as

[0044]

[0045] in is the spatial frequency domain channel from user k to the base station, and Z is the Gaussian noise matrix.

[0046] Using adjustable phase shift pilot, different users are distinguished by different cyclic shift coefficients. The phase shift factor is (k-1)M f +1,k=1,…,K. On this basis, the pilot sequence p sent by the kth user k for

[0047]

[0048] in is a ZC sequence, whose nth element is

[0049]

[0050] where N l is less than N p Substituting the channel model (3) and pilot sequence (5) into the received signal (4), we can get

[0051]

[0052] in satisfy definition So It can be further simplified to

[0053]

[0054] The equal sign here utilizes the cyclic shift property of the phase shift sequence, namely: is a cyclic shift matrix, defined as

[0055]

[0056] Left-multiplying (right-multiplying) a matrix is ​​equivalent to circularly shifting the matrix up by n rows (right by n columns), so the received signal (7) can be further rewritten as

[0057]

[0058] in The corresponding beam domain signal power matrix is The number of users K satisfies

[0059] Multiply both sides of the above equation After that you can get

[0060]

[0061] in After vectorizing both sides, we have

[0062] y=Ah+z,(12)where For convenience, we define N=N r N p , M=M r M p ;and because is a unitary matrix. Assume that the non-zero elements in h are independent of each other and h is independent of z, and that in is the known channel prior variance.

[0063] Due to the sparsity of the beam domain channel, the matrix D contains a large number of zero elements. Define E d To extract the matrix, the non-zero elements in h can be expressed as in is the number of non-zero elements, and the corresponding extracted perception matrix is ​​expressed as Based on this, the new received signal model can be written as:

[0064]

[0065] in is the positive definite diagonal matrix after decimation of D. The channel estimation problem can be expressed as estimating the received signal y from The posterior mean of MMSE is estimated as

[0066]

[0067] The computational complexity of MMSE estimation is When the number of base station antennas and users is large, such complexity is usually unbearable.

[0068] (3) Beam Completion Channel Estimation Method

[0069] The basic idea of ​​beam completion is to complete the oversampled DFT matrix in the sensing matrix into a unitary matrix, thereby avoiding the problem of large-dimensional matrix inversion in MMSE estimation. For the received signal (12), the sensing matrix is ​​the Kronecker product of three oversampled DFT matrices. The received signal model after completion is rewritten as

[0070]

[0071] After exchanging the positions of some rows of y′, we can get

[0072]

[0073] in and Is the completion signal, and

[0074]

[0075] This can be shortened to

[0076]

[0077] The perception matrix is the DFT matrix The unitary matrix obtained after partial row exchange. The noise vector after completion Still assuming obedience

[0078] (A1) Alternating projections in a noiseless channel

[0079] First, consider the beam completion in a high signal-to-noise ratio scenario, i.e., a noiseless channel. The results of this special case help us understand the subsequent EM algorithm. In a noiseless channel, Equations (16) and (18) degenerate into

[0080]

[0081] and

[0082]

[0083] Order set Represents the set of non-zero element indices in D, and then defines the constraint set for The optimization problem for solving h is

[0084]

[0085] Construct two sets and make h l-1 is the result of the (l-1)th iteration, then yes A point in the. Towards The projection process can be expressed as the following optimization problem

[0086]

[0087] This is a The unconstrained convex optimization problem is solved as Can get yes A point on it Projection is equivalent to the following optimization problem

[0088]

[0089] This is a quadratic problem with convex constraints, and element-wise optimization is considered. The objective function is Derivative

[0090]

[0091] By calculating the zero point of the derivative, the optimal solution can be obtained as Written in vector form is

[0092]

[0093] Therefore, we can get and

[0094]

[0095] because That is, the function is a non-monotonic increasing function greater than 0, so it can converge to the local optimal solution of the original problem.

[0096] (A2) EM algorithm

[0097] Based on the received signal (18), a model manifold is established where h can be considered as a function parameter. Random vector Depend on It consists of two parts, where y is the observation signal, The purpose of beam-domain channel estimation is to estimate the parameter h from the observation y, that is, to find the probability density function p that makes y Y (y; h) The largest parameter h. The traditional method is to eliminate it through marginalization operation Right now

[0098]

[0099] However, the core operation of beam completion is to introduce the completion signal To solve the problem of inverting large-dimensional matrices, the integral operation is not applicable. Assuming that the observed signal is y0, then The empirical distribution of can be expressed as follows:

[0100]

[0101] The δ(y-y0) function represents an impulse function with a probability of 1 at y0 and a probability of 0 at other points. Therefore, the completed observation point Can be split into original observation points and an arbitrary conditional distribution Right now

[0102]

[0103] The set consisting of this distribution is called the data manifold, that is, It is derived from the observed signal y0 and is m-flat because the distribution is is linear. Substituting (28) into (29) we get:

[0104]

[0105] Assume there is a point and The KL divergence between these two points is

[0106]

[0107] The optimization problem in (21) can now be generalized to

[0108]

[0109] This is equivalent to respectively and h minimize the KL divergence. Rewriting (31) and simplifying it to:

[0110]

[0111] in is a known independent and h are constants.

[0112] Let P t-1 , that is, the channel parameter h t-1 is the optimal point obtained by minimizing the KL divergence about P in the (t-1)th iteration, and the observation point Given. P t-1 Towards The projection result is the optimal distribution obtained by minimizing (31) Right now

[0113]

[0114] In information geometry, the projection of a distribution onto an m-flat submanifold is called an e-projection. It is an m-flat manifold. This projection process is similar to the e-projection. When there is no ambiguity, it is still called the e-projection.

[0115] Substituting the constraint that the integral of the probability density function is 1, the Lagrangian function is constructed as

[0116]

[0117] Lagrangian function about Derivative

[0118]

[0119] After substituting the constraints, we get

[0120]

[0121] The Lagrange multiplier derived from this formula is λ=logp(y;h t-1 )-1. Substituting (37) into (36), we can get that the optimal point of the t-th e-projection is

[0122]

[0123] Then get The posterior mean is

[0124]

[0125] Afterwards, in the given Under the condition of h minimizing (31), that is,

[0126]

[0127] When there is no prior information, the manifold becomes This is an e-flat manifold. The projection of a distribution onto an e-flat submanifold is called an m-projection. Similarly, the projection derived from (40) is still called an m-projection when there is no ambiguity.

[0128] This formula can be further transformed into maximizing the second term of formula (33), namely

[0129]

[0130] About h * Derivative

[0131]

[0132] Let the value of this derivative be 0, and we can get the maximum value of h in formula (41) as

[0133]

[0134] make Substituting the result in (39) into

[0135]

[0136] Alternating e-projection and m-projection can make the value of KL divergence monotonically decrease, so the iterative formula can converge to a stable point, let it be h ★ , then at the stable point we have

[0137]

[0138] Ride on both sides Further

[0139]

[0140] because is a unitary matrix, so we have Then, the above formula can be further simplified to

[0141]

[0142] This is equivalent to the MMSE estimate.

[0143] The above e-projection and m-projection processes are collectively referred to as the EM algorithm. Definition The EM algorithm can be expressed as iteratively executing the following steps (taking the tth iteration as an example):

[0144] Update the posterior mean of the completion signal by e-projection: in is the extraction matrix, representing the Extraction and completion signal The corresponding partial perception matrix

[0145] Combine the original signal and the complement signal posterior mean:

[0146] Update the values ​​of the angle delay domain channel parameters through m projection:

[0147] After the EM algorithm converges, the posterior mean of the angle-delay domain channel can be obtained. The angle-delay domain channel is then transformed into the space-frequency domain using the beam-based channel representation model.

[0148] The time complexity and space complexity of the beam completion channel estimation method are given below. The computational complexity of each iteration of the EM algorithm is mainly on the special matrix multiplication vector, that is, and In the form of. Taking Ab as an example for analysis, define the matrix Satisfy b=vec(B), then we have

[0149]

[0150] This can be achieved by FFT and double FFT. Therefore, the computational complexity of Ab is

[0151]

[0152] Similarly, A H The computational complexity of s is and The computational complexity is equivalent to Ab and A respectively. H s. Therefore, the time complexity of this algorithm is

[0153]

[0154] where T is the number of iterations. This is much lower than the MMSE estimate The time complexity of .

[0155] Then analyze the space complexity of the EM algorithm. The maximum dimension of the intermediate matrix generated in the process of calculating Ab is M r M p , so the space complexity is This is also much lower than the MMSE estimate. The space complexity of .

[0156] (4) Implementation effect

[0157] In order to make people in this technical field better understand the scheme of the present invention, the performance comparison of the scheme of the present invention and the existing methods under a specific system configuration is given below. The methods used for comparison are MMSE estimation (as the optimal performance) and the information geometry channel estimation method (hereinafter referred to as IGA) proposed in the document [Channel estimation for massive MIMO: an information geometry approach [J]. IEEE Transactions on Signal Processing, 2022, 70: 4820–4834.]. Consider a parameter N r =N rv ×N rh =8×16,N c =2048,N p =120,N g =144, K = 12, the refinement factor is set to 2, the user transmit power and the space-frequency domain channel energy are normalized to 1, and the normalized mean square error of the space-frequency domain channel is used as the measurement indicator.

[0158] First, a performance comparison between the beam completion channel estimation method and existing methods in general scenarios is given. Figure 4 The user average normalized mean square error performance curves of the three methods at 30 and 300 iterations are given. This figure shows that the proposed scheme can approach the performance of MMSE estimation at a higher number of iterations, and the performance gap does not exceed 1dB at a 30dB signal-to-noise ratio. Figure 5 The convergence curves of the user-averaged normalized mean square error (NMSE) for the three methods at a 20dB signal-to-noise ratio (SNR) are shown. The figure shows that the proposed solution achieves better estimation performance when the number of iterations is small. The estimated channels obtained after 10 and 30 iterations were used in downlink precoding design to verify the reliability of the channel estimation. Figure 6 The sum rate performance of the RZF precoder in this case is demonstrated. This result shows that the sum rate performance of the channel estimated by the proposed scheme for precoding reaches 89.8% and 93.7% of the MMSE estimation at a 20dB signal-to-noise ratio after 10 and 30 iterations, respectively. In addition, the sum rate performance of the proposed algorithm is significantly better than that of the IGA at the 10th iteration.

[0159] An embodiment of the present invention further discloses a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the above-mentioned single-cell massive MIMO beam-completion channel estimation method.

[0160] The technical means disclosed in the solutions of the present invention are not limited to those disclosed in the above-mentioned embodiments, but also include technical solutions composed of any combination of the above-mentioned technical features. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A single-cell massive MIMO beam completion channel estimation method, characterized in that: The steps include: (1) The base station establishes a space-frequency domain received signal model for the angle delay domain channel based on the received pilot signal and the beam-based channel characterization model; the beam-based channel characterization model is as follows: the space-frequency domain channel matrix is ​​obtained by weighting the angle delay domain channel matrix with the spatial domain and frequency domain sampling rudder vectors, wherein the angle delay domain channel is sparse and each non-zero element is statistically independent; (2) Completing the oversampled DFT matrices constituting the perception matrix in the received signal into DFT matrices, and simultaneously performing the received signal and noise completion to obtain a completed received signal model; the perception matrix is ​​obtained by performing the Kronecker product of three oversampled DFT matrices in the frequency domain, vertical spatial domain, and horizontal spatial domain, and completing each of them into DFT matrices and then performing the Kronecker product to obtain a unitary matrix; (3) The EM algorithm is used to iteratively solve the completed signal and the angle delay domain channel until convergence or a fixed number of times is reached. The channel obtained at this time is the estimated value of the angle delay domain channel.

2. The single-cell massive MIMO beam completion channel estimation method according to claim 1, characterized in that: In step (1), the received pilot signal comes from the adjustable phase-shifted pilot signal sent by each user in the cell to the base station.

3. The single-cell massive MIMO beam completion channel estimation method according to claim 1, characterized in that: In step (3), the method for iteratively solving the completed signal and angle delay domain channel by the EM algorithm is as follows: based on the posterior distribution of the completed received signal and its joint distribution with the channel parameters, a data manifold and a model manifold are established respectively, e-projection and m-projection are alternately performed between the two manifolds, the posterior mean of the completed signal is updated by the e-projection, the posterior mean of the received signal and the completed signal are combined, and the channel parameters are updated by the m-projection until convergence.

4. The single-cell massive MIMO beam completion channel estimation method according to claim 3, characterized in that: The data manifold is a manifold composed of the probability distribution of the completed received signal, and the model manifold is a manifold composed of the joint probability distribution of the completed received signal and the channel parameters.

5. The single-cell massive MIMO beam completion channel estimation method according to claim 3, characterized in that: Both e-projection and m-projection are based on minimizing the KL divergence between two manifolds.

6. The single-cell massive MIMO beam completion channel estimation method according to claim 3, characterized in that: The posterior mean of the completed signal is obtained by e-projection, and the channel estimation value is obtained by m-projection. In the t-th iteration, the posterior mean of the completed signal is the product of the completed perception matrix and the t-1-th channel estimation value, and the angle delay domain channel estimation value is the product of the diagonal matrix containing the prior term, the completed perception matrix, and the combined signal.

7. The single-cell massive MIMO beam completion channel estimation method according to claim 1, characterized in that: The base station obtains the prior statistical information of each user terminal channel through uplink channel detection, and uses the channel prior information and the received pilot signal to calculate the posterior information of the angle delay domain channel of each user terminal through steps (1) to (3). Finally, the obtained angle delay domain channel is converted into the space-frequency domain through the beam-based channel characterization model.

8. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of a single-cell massive MIMO beam-completion channel estimation method according to any one of claims 1 to 7 are implemented.

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