Millimeter wave uplink channel estimation method based on time correlation and block sparsity

Abstract

The invention discloses a millimeter wave uplink channel estimation method based on time correlation and block sparsity, which realizes sparse representation of a rectangular area array channel under a plurality of observation times by utilizing relatively strong sparsity of a channel in a millimeter wave large-scale MIMO (Multiple Input Multiple Output) system and redefining a received signal angle. On the basis, time correlation existing in the channel and correlation in each scattering cluster are considered at the same time, a channel prior structure is provided, sparse characteristics and noise variance of the channel are represented through hyper-parameters, and iterative estimation of each hyper-parameter is completed based on an SBL frame and an EM algorithm. Compared with a traditional channel estimation method, the method does not need prior information such as noise variance and channel covariance. Compared with a classical compressed sensing method, the method provided by the invention can effectively simulate and estimate the time change and scattering characteristics of the channel and improve the accuracy of channel estimation.

Description

Technical Field

[0001] The present invention relates to the field of communication technologies, and more specifically, to a millimeter-wave uplink channel estimation method based on time correlation and block sparsity. Background Art

[0002] Massive Multiple-Input Multiple-Output (mMIMO) technology is one of the key technologies for the fifth-generation mobile communication (5G), and is also considered to play an important role in beyond 5G (B5G) and sixth-generation mobile communication (6G). In a millimeter-wave massive MIMO system, the transmitted signal will face significant fading, and at the same time, different users communicating with the same base station will face the problem of mutual interference. Fortunately, precoding and beamforming technologies can effectively improve the above problems, and accurate Channel State Information (CSI) is an important prerequisite for precoding and beamforming. Therefore, it is important and urgent to develop high-performance channel estimation algorithms in millimeter-wave massive MIMO systems.

[0003] Due to the high propagation and reflection losses in millimeter-wave channels, the channels will exhibit strong sparsity, that is, the signal will only generate a few scattering clusters through the channel, and each cluster contains a few multipaths. Based on this characteristic, many scholars have currently used Compressed Sensing (CS) technology to solve the sparse channel estimation problem. The most classic methods include Orthogonal Matching Pursuit (OMP) and Sparse Bayesian Learning (SBL), etc. Among them, OMP is based on the idea of least squares. Each time, the basis with the strongest correlation with the received signal is selected from the dictionary matrix. After several selections, the actual channel can be approximately fitted. However, OMP requires prior information of sparse signals, that is, the accurate number of multipaths is required in channel estimation, which is difficult to guarantee in practice. SBL is a method based on automatic decision theory, and it also has good performance in dealing with signals with unknown sparsity. On this basis, there have been many improved algorithms based on OMP and SBL, including considering the block sparsity of sparse signals or the change of sparse signals between multiple observation times, but currently, there is a lack of estimation methods that simultaneously discuss the block sparsity and time-variability of signals.

[0004] For an actual millimeter-wave massive MIMO channel, the fading magnitude slowly varies and shows correlation over multiple consecutive time instants. There is a certain angular spread in each scattering cluster of the channel, which makes the channel exhibit block sparsity in the angular domain, that is, the angles of the actual incoming paths appear in blocks. The present invention fully considers the above two characteristics and proposes an uplink channel estimation method for millimeter-wave massive MIMO based on the SBL framework. This method can simultaneously characterize and estimate the temporal correlation and block sparsity of the channel, thus better conforming to the actual channel characteristics and obtaining more accurate estimation results. In terms of the array structure, we will discuss the case of a rectangular planar array because the rectangular planar array has a more efficient and compact structure compared to the uniform linear array. Summary of the Invention

[0005] The present invention provides a millimeter-wave uplink channel estimation method based on temporal correlation and block sparsity. This method eliminates the coupling of the two angular dimensions in the UPA channel steering vector through angle redefinition, and realizes the full characterization of the channel characteristics by constructing a prior model containing temporal correlation and block correlation. Based on the SBL framework, the position parameters required to characterize the channel are regarded as hyperparameters to be estimated, and the hyperparameters are iteratively updated until convergence based on the Expectation Maximization (EM) method to complete the channel estimation. Compared with traditional channel estimation methods, the proposed method does not require prior information such as channel noise parameters and channel sparsity, and obtains more accurate estimation results.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A millimeter-wave uplink channel estimation method based on temporal correlation and block sparsity, comprising the following steps:

[0008] S1: The base station is equipped with a uniform planar array with M = M x ×M y antennas at the root, the user terminal is equipped with a single antenna, and the user terminal transmits mutually orthogonal pilot sequences. After passing through the complex Gaussian channel, the base station obtains the received signal;

[0009] S2: The base station distinguishes the signals from different users through the characteristics of orthogonal pilots and sparsely represents the received signals at multiple observation instants;

[0010] S3: Use the first-order Auto Regressive (AR) process to characterize the temporal correlation and block correlation, thereby constructing a sparse prior, and regard the noise variance, channel block sparse prior, temporal correlation coefficient, and block correlation coefficient as unknown hyperparameters, and obtain the parameter distributions based on the SBL framework;

[0011] S4: Use the EM algorithm to iteratively solve the maximum a posteriori probability of the unknown hyperparameters;

[0012] S5: Set the threshold and the number of iterations. When the channel block sparse prior converges or the number of iterations reaches the set value, the iteration ends, and the estimated result of the channel sparse representation is obtained;

[0013] S6: Calculate the actual channel through the estimated result of the channel sparse representation.

[0014] Preferably, the schematic flow diagram of the method of the present invention is as Figure 1 shown, and the schematic diagram of the redefinition of the arrival angle is as Figure 2 shown.

[0015] Preferably, in step S1, the system includes a total of U users. The signal received by the base station at the qth moment can be expressed as where is the channel between the u-th user and the base station, satisfying Here, θ and are the redefined angles in Figure 2 The steering vector d is the spacing between adjacent antennas at the base station end, λ is the wavelength of the transmitted signal, is the pilot sequence of the u-th user, and the length T of the pilot sequence is greater than the number of users U.

[0016] Preferably, in step S2, the base station receives the signal by separating the specific user signals through orthogonal pilots The received signals at Q observation times can be expressed as After vectorization, y = vec(Y T ), and this signal can be sparsely represented as where is the dictionary matrix in the angular domain, which can be denoted as is the dictionary matrix in the θ angular domain, which can be denoted as Denote as the sparse representation result of the channel at Q observation times.

[0017] Preferably, in step S3, the definitions of the respective parameter distributions are as follows:

[0018] According to the SBL framework, set the sparse representation z to have a Gaussian prior distribution:

[0019] p(z) = CN(0, ∑ 0 ),

[0020] where Here, we utilize the block-sparse property of the channel and divide z into blocks, which is the channel block-sparse prior and is used to indicate whether a non-zero block appears at this position in z. is the block structure formed by each scattering cluster in the channel due to angular spread, satisfying G θ = V × d, is the temporal correlation of the Q observation times of the channel. Denote the additive complex Gaussian noise b as satisfying p(n|α) = CN(0, α -1 ), where α = σ -2 is the noise resolution. Then the received signal y also satisfies a Gaussian distribution:

[0021] p(y|z; α) = CN(Φz, α -1 I),

[0022] According to the derivation of the second likelihood function, the posterior distribution of z also satisfies a Gaussian distribution, with p(z|y; Γ, Ξ, Υ) = CN(μ(α, Γ, Ξ, γ), ∑(α, Γ, Ξ, Υ)), satisfying:

[0023]

[0024] Preferably, the hyperparameters to be estimated in step S4 are denoted as Θ = (α, Γ, Ξ, γ). The solution process of each parameter based on the EM algorithm is as follows:

[0025] Based on the maximum a posteriori criterion, the cost function for updating the hyperparameters is:

[0026]

[0027] where (·) (i) represents the result of the i-th iteration. Then the hyperparameters α, Γ, Ξ, γ satisfy respectively:

[0028]

[0029]

[0030] where (·) ij represents the element in the i-th row and j-th column of the matrix, and E ij represents a matrix with all elements being 0 except the element in the i-th row and j-th column being 1. (expressed in MATLAB language), (expressed in MATLAB language), and ∑ y = α-1 I + Φ∑ 0 Φ H 。

[0031] Preferably, the function of step S5 is to judge the convergence of channel estimation through the convergence of Γ, and the iterative error threshold is set to σ tol , and the maximum number of iterations is i max , when or the number of iterations i ≥ i max , the converged channel expected value μ is output as the actual value of z

[0032] Preferably, the function of step S6 is to estimate the actual channel through the sparse distribution z of the channel, and the specific expression is BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is a schematic flow chart of the method of the present invention

[0034] Figure 2 is a schematic diagram of the redefinition of the incoming angle

[0035] Figure 3 is a schematic diagram of the comparison of the normalized mean square error of channel estimation at different signal-to-noise ratios provided by the embodiment

[0036] Figure 4 is a schematic diagram of the comparison of the normalized mean square error of channel estimation at different numbers of time observations provided by the embodiment DETAILED DESCRIPTION OF THE EMBODIMENTS

[0037] The drawings are only for illustrative purposes and should not be construed as limitations of this patent

[0038] To better illustrate this embodiment, some components in the drawings are omitted, enlarged or reduced, and do not represent the size of the actual product

[0039] For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted

[0040] The technical solutions of the present invention will be further described below with reference to the drawings and embodiments

[0041] Embodiment 1

[0042] This example provides a millimeter-wave uplink channel estimation method based on time correlation and block sparsity, including the following steps

[0043] S1: The base station is equipped with M = M x ×M yA uniform planar array of root antennas, with a single antenna equipped at the user end. The user end transmits mutually orthogonal pilot sequences. After passing through a complex Gaussian channel, the base station end obtains the received signal;

[0044] S2: The base station distinguishes the signals from different users through the characteristics of orthogonal pilots, and sparsely represents the received signals at multiple observation times;

[0045] S3: Use a first-order autoregressive (AR) process to characterize the temporal correlation and block correlation, thereby constructing a sparse prior, and taking the noise variance, channel block sparse prior, temporal correlation coefficient, and block correlation coefficient as unknown hyperparameters, and obtaining the parameter distributions based on the SBL framework;

[0046] S4: Use the EM algorithm to iteratively solve the maximum a posteriori probability of the unknown hyperparameters;

[0047] S5: Set the threshold and the number of iterations. When the channel block sparse prior converges or the number of iterations reaches the set value, the iteration ends, and the estimated result of the channel sparse representation is obtained;

[0048] S6: Calculate the actual channel through the estimated result of the channel sparse representation.

[0049] Embodiment 2

[0050] On the basis of Embodiment 1, the following content is further disclosed in this embodiment:

[0051] In step S1, the system includes a total of U users. The received signal at the base station at the q-th moment can be expressed as

[0052] Where is the channel between the u-th user and the base station, satisfying Here, θ and are Figure 2 the redefined angles in d is the spacing between adjacent antennas at the base station end, λ is the wavelength of the transmitted signal, is the pilot sequence of the u-th user, and the length T of the pilot sequence is greater than the number of users U.

[0053] In step S2, the base station separates the specific user signals through orthogonal pilots to receive the signals The received signals at Q observation times can be expressed as After vectorization, y = vec(Y T ), and this signal can be sparsely represented as Where is The dictionary matrix of the angular domain can be denoted as For the dictionary matrix of the θ angular domain, it can be denoted as Denote as the sparse representation result of the channel at Q observation times.

[0054] In step S3, the definitions of the parameters are as follows:

[0055] According to the SBL framework, set the sparse representation z to have a Gaussian prior distribution:

[0056] p(z) = CN(0, ∑ 0 ),

[0057] where Here, we utilize the block-sparse characteristic of the channel and divide z into blocks, is the channel block-sparse prior, used to indicate whether a non-zero block appears at this position in z, is the block structure formed by the angular expansion of each scattering cluster in the channel, satisfying G θ = B × d, is the time correlation of the channel at Q observation times. Denote the additive complex Gaussian noise n as satisfying p(n|α) = CN(0, α -1 ), where α = σ -2 is the noise resolution, then the received signal y also satisfies a Gaussian distribution:

[0058] p(y|z; α) = CN(Φz, α -1 U),

[0059] According to the derivation of the second likelihood function, the posterior distribution of z also satisfies a Gaussian distribution, with p(z|y; Γ, Ξ, Υ) = CN(μ(α, Γ, Ξ, Υ), ∑(α, Γ, Ξ, Υ)), satisfying:

[0060]

[0061] In step S4, the hyperparameters to be estimated are denoted as Θ = (α, Γ, Ξ, Υ). The solution process of each parameter based on the EM algorithm is as follows:

[0062] Based on the maximum a posteriori criterion, the cost function for updating the hyperparameters is:

[0063]

[0064] where (·) (i) represents the result of the i-th iteration. Then the hyperparameters α, Γ, Ξ, γ respectively satisfy:

[0065]

[0066] wherein (·) ij represents the element at the i-th row and j-th column of the matrix, and E ij represents a matrix in which all elements are 0 except that the element at the i-th row and j-th column is 1, (expressed in MATLAB language), (expressed in MATLAB language), ∑ y = α -1 I + Φ∑ 0 Φ H .

[0067] The function of step S5 is to judge the convergence of channel estimation through the convergence of Γ, and the iterative error threshold is set to σ tol , and the maximum number of iterations is i max , when or the number of iterations i ≥ i max , the converged channel expected value μ is output as the actual value of z.

[0068] The function of step S6 is to estimate the actual channel through the sparse distribution situation z of the channel, and the specific expression is

[0069] Embodiment 3

[0070] Based on Embodiment 1 and Embodiment 2, the following specific embodiments are provided:

[0071] Set the simulation parameters as follows: Assume that the base station is equipped with a 15×12 uniform planar array, the multipath channel contains 3 clusters, each cluster contains 3 paths, the angular spread within each cluster is set to 15°, the pilot sequence uses the columns of the discrete Fourier transform matrix to ensure orthogonality, the arrival angle is randomly generated using a normal distribution, in Figure 3 the number of channel observations Q = 3, in Figure 4 the signal-to-noise ratio SNR = 10 dB, the iterative error threshold σ tol = 10 -4 , the maximum number of iterations i max = 30, 100 Monte Carlo experiments.

[0072] Based on this embodiment, the new method proposed by the present invention is compared with the orthogonal matching pursuit algorithm and the sparse Bayesian learning algorithm in terms of performance, as follows: According to Figure 3 、 Figure 4As shown, regardless of how the signal-to-noise ratio and the number of channel observations are set, the proposed method can improve the accuracy of channel estimation. Specifically, as the number of channel observations increases, the performance of the orthogonal matching pursuit algorithm and the sparse Bayesian learning algorithm cannot be improved, while the proposed method makes full use of the correlation existing between multiple channel observations. By simulating and estimating this correlation, the accuracy of channel estimation is further improved. In addition, compared with the matching pursuit algorithm, the proposed algorithm is based on the SBL framework and does not require prior information on the channel sparse structure, thus having better environmental adaptability.

[0073] The above examples show that the method described in the present invention simultaneously considers the temporal correlation and block sparsity existing in the channel. By fully simulating these two characteristics, obvious performance improvement has been achieved. Under different signal-to-noise ratios and numbers of channel observations, the proposed method has advantages over the classical compressive sensing methods.

[0074] The same or similar reference numerals correspond to the same or similar components;

[0075] The descriptions of the positional relationships in the drawings are only for illustrative purposes and should not be construed as limitations on this patent;

[0076] Obviously, the above examples of the present invention are only examples for clearly illustrating the present invention and are not limitations on the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to enumerate all implementation manners here. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A millimeter wave uplink channel estimation method based on time correlation and block sparsity, characterized in that: The following steps are involved: S1: The base station is equipped with N x ×N y =N uniform array of antennas, the user end is equipped with a single antenna, the base station sends a pilot sequence, and after passing through the complex Gaussian channel, the user end receives the received signal; S2: Based on the 2D-DFT matrix, the UPA channel is sparsely represented by angle redefinition, and the received signal is sparsely represented; S3: Introduce the grid offset, take the noise variance, sparse angle distribution probability, and grid offset as unknown hyperparameters, and obtain the distribution of each parameter based on the SBL framework. S4: Use the SBL framework and block MM algorithm to iteratively solve the maximum posterior probability of unknown hyperparameters. S5: Set the threshold and the number of iterations. When the sparse distribution hyperparameters converge or the number of iterations reaches the set value, the iteration ends and the channel sparse representation estimation result is obtained. S6: Calculate the actual channel through the channel sparse representation estimation result.

2. The millimeter wave uplink channel estimation method based on time correlation and block sparsity according to claim 1, characterized in that: In step S1, the system includes U users in total. At the qth time, the base station receives the signal which can be expressed as in is the channel between the u-th user and the base station, satisfying Here θ and is the angle after redefinition in Figure 2, and the steering vector d is the distance between adjacent antennas at the base station, λ is the wavelength of the transmission signal, is the pilot sequence of the u-th user, and the pilot sequence length T is greater than the number of users U.

3. The millimeter wave uplink channel estimation method based on time correlation and block sparsity according to claim 2, characterized in that: In step S2, the base station receives a signal by processing a specific user signal through orthogonal pilot signals. The received signal at Q observation times can be expressed as After vectorization, y=vec(Y T ), the signal can be sparsely represented as in for The dictionary matrix of the angular domain can be written as is the dictionary matrix of the θ angle domain, which can be written as remember is the sparse representation result of the channel at Q observation moments.

4. The millimeter wave uplink channel estimation method based on time correlation and block sparsity according to claim 3, characterized in that: In step S3, the distribution of each parameter is defined as follows: According to the SBL framework, the sparse representation z is set to have a Gaussian prior distribution: p(z)=CN(0,∑0), in Here, we use the block sparseness of the channel to divide z into Blocks, is the channel block sparse prior, which is used to indicate whether there is a non-zero block at this location in z. is the block structure formed by the angle expansion of each scattering cluster in the channel, satisfying G θ =V×d, is the time correlation of the channel Q observation times, and the additive complex Gaussian noise n satisfies p(n|α)=CN(0,α -1 ), where α = σ -2 is the noise resolution, then the received signal y also satisfies the Gaussian distribution: p(y|z;α)=CN(Φz,α -1 1), According to the derivation of the second-like probability function, the posterior distribution of z also satisfies the Gaussian distribution, and p(z|y; Γ,Ξ,Υ)=CN(μ(α,Γ,Ξ,Υ),∑(α,Γ,Ξ,Υ)), which satisfies:

5. The millimeter wave uplink channel estimation method based on time correlation and block sparsity according to claim 4, characterized in that: The hyperparameters to be estimated in step S4 are denoted as Θ = (α, Γ, Ξ, Υ). The process of solving the parameters based on the EM algorithm is as follows: Based on the maximum a posteriori criterion, the cost function for updating the hyperparameters is: in(·) (i) represents the result of the i-th iteration, then the hyperparameters α, Γ, Ξ, and Υ satisfy: in (·) ij represents the element in the i-th row and j-th column of the matrix, E ij It represents a matrix in which all elements are 0 except the element in the i-th row and j-th column, which is 1. (expressed in MATLAB language), (expressed in MATLAB language), ∑ y =α -1 I+Φ∑0Φ H .

6. The millimeter wave uplink channel estimation method based on time correlation and block sparsity according to claim 5, characterized in that: The function of step S5 is to judge the convergence of channel estimation by the convergence of Γ, and set the iterative error threshold to σ tol , the maximum number of iterations is i max ,when Or the number of iterations i ≥ i max When , the converged channel expected value μ is output as the actual value of z.

7. The millimeter wave uplink channel estimation method based on time correlation and block sparsity according to claim 6, characterized in that: The function of step S6 is to estimate the actual channel through the sparse distribution of the channel z. The specific expression is:

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