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

Abstract

The application discloses a millimeter wave uplink channel estimation method based on time correlation and block sparsity, which realizes sparse representation of a rectangular surface array channel under multiple observation times by utilizing strong sparsity of a channel in a millimeter wave massive MIMO system and redefining the angle of a received signal. On this basis, a channel prior structure is proposed by simultaneously considering time correlation of the channel and correlation within each scattering cluster, the sparse characteristics of the channel and noise variance are represented by hyperparameters, and iterative estimation of each hyperparameter is completed based on an SBL framework and an EM algorithm. Compared with a traditional channel estimation method, the proposed method does not require prior information such as noise variance and channel covariance. Compared with a classical compressive sensing method, the proposed method can effectively simulate and estimate time variation and scattering characteristics of the channel, and improve the accuracy of channel estimation.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of communication technology, more particularly, to a millimeter wave uplink channel estimation method based on time correlation and block sparsity. BACKGROUND

[0002] Massive MIMO (mMIMO) technology is one of the key technologies of the 5th Generation (5G) mobile communication, and is also considered to play an important role in beyond 5G (B5G) and 6th Generation (6G) mobile communication. In the massive MIMO system of millimeter wave, the transmission signal will face a larger fading, and different users communicating with the same base station will face the problem of mutual interference. Fortunately, precoding and beamforming technology 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 a high-performance channel estimation algorithm in the massive MIMO system of millimeter wave.

[0003] Due to the high propagation and reflection loss of the millimeter wave channel, the channel will exhibit strong sparsity, that is, the signal will only produce a few scattering clusters through the channel, and each cluster contains a few multipaths. Based on this characteristic, many scholars have used compressed sensing (CS) technology to solve the problem of sparse channel estimation. The most classic methods include orthogonal matching pursuit (OMP) and sparse Bayesian learning (SBL). Among them, OMP is based on the least square idea, and selects the strongest base from the dictionary matrix each time, and after several selections, the actual channel can be approximately fitted. However, OMP requires prior information of sparse signals, and in channel estimation, it requires accurate multipath number, which is difficult to guarantee in practice. SBL is a method based on automatic decision theory, which also has good performance in dealing with signals with unknown sparsity. On this basis, there are many improved algorithms based on OMP and SBL, including considering the block sparsity of sparse signals, or considering the change of sparse signals between multiple observation times, but there is still a lack of estimation methods that discuss both the block sparsity of signals and the time-varying nature of signals.

[0004] For a practical millimeter wave massive MIMO channel, its fading size changes slowly in multiple consecutive times and presents correlation. There is a certain angular spread in each scattering cluster of the channel, which makes the channel present block sparsity in the angle domain, that is, the angles of the actual coming paths appear in blocks. The application fully considers the above two characteristics, and proposes an uplink channel estimation method suitable for millimeter wave massive MIMO based on the SBL framework. The method can simultaneously characterize and estimate the time correlation and block sparsity of the channel, so as to more closely match the actual channel characteristics and obtain more accurate estimation results. On the structure of the array, we will discuss the case of a rectangular surface array, because the rectangular surface array has a more efficient and compact structure than the uniform linear array. SUMMARY

[0005] The application provides a millimeter wave uplink channel estimation method based on time correlation and block sparsity. The method eliminates the coupling of two angle latitudes in the UPA channel steering vector through angle redefinition, and realizes the full characterization of the channel characteristics by constructing a prior model containing time correlation and block correlation. Based on the SBL framework, the position parameters required to characterize the channel are regarded as superparameters to be estimated, and the superparameters are iteratively updated based on the expectation maximization (EM) method until convergence to complete channel estimation. Compared with the traditional channel estimation method, the proposed method does not require prior information such as channel noise parameters and channel sparsity, and achieves more accurate estimation results.

[0006] To achieve the above object, the technical scheme of the application is as follows:

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

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

[0009] S2: The base station distinguishes the signals from different users through the characteristics of the orthogonal pilot, and performs sparse representation on the received signals at multiple observation times;

[0010] S3: The first-order autoregressive (AR) process is used to characterize the time correlation and block correlation, so as to construct a sparse prior, and the noise variance, channel block sparse prior, time correlation coefficient and block correlation coefficient are regarded as unknown superparameters, and the distribution of each parameter is obtained based on the SBL framework;

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

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

[0013] S6: Calculate the actual channel using the estimation results of the sparse representation of the channel.

[0014] Preferably, the flowchart of the method of the present invention is as follows: Figure 1 As shown in the diagram, the redefinition of the angle of arrival is illustrated below. Figure 2 As shown.

[0015] Preferably, in step S1, the system includes U users, and the signal received by the base station at time q can be expressed as follows: in For the channel between the u-th user and the base station, satisfying Here θ and for Figure 2 The redefined angle and the directional vector d is the distance between adjacent antennas at the base station, and λ is the wavelength of the transmitted signal. Let T be the pilot sequence for the u-th user, and the length of the pilot sequence T is greater than the number of users U.

[0016] Preferably, in step S2, the base station receives a specific user signal through orthogonal pilot signal processing. The received signals at Q observation times can be represented as After vectorization, y = vec(Y T This signal can be sparsely represented as in for The dictionary matrix of the angular field can be denoted as: The dictionary matrix of the θ-angle field can be denoted as: remember This represents the sparse representation of the channel at Q observation times.

[0017] Preferably, in step S3, the distribution of each parameter is defined as follows:

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

[0019] p(z) = CN(0,∑0),

[0020] in Here, we exploit the block sparsity of the channel to divide z into blocks, a block sparsity prior for the channel, which indicates whether a non-zero block appears at that position in z, a block structure formed by the angular spread of each scattering cluster in the channel, satisfying G θ = Vxd, a temporal correlation of the channel over Q observation times, with additive complex Gaussian noise b satisfying p(n|a) = CN(0, a -1 ), where a = σ -2 is the noise resolution, then the received signal y also satisfies a Gaussian distribution:

[0021] p(y|z; a) = CN(Φz, a -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; a, G, X, Y) = CN(m(a, G, X, Y), S(a, G, X, Y)), satisfying:

[0023]

[0024] Preferably, the superparameters to be estimated in step S4 are denoted as Θ = (a, G, X, Y), and the solution process of each parameter based on the EM algorithm is as follows:

[0025] Based on the maximum posterior criterion, the cost function for updating the superparameters is:

[0026]

[0027] where (·) (i) denotes the result of the i-th iteration, then the superparameters a, G, X, Y satisfy:

[0028]

[0029]

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

[0031] Preferably, the step S5 is used to judge the convergence of the channel estimation by the convergence of Γ, set the iteration error threshold as σ tol , and the maximum iteration number as i max When or the iteration number i≥i max , output the converged channel expectation value μ as the actual value of z.

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

[0033] Figure 1 FIG. 1 is a flowchart of the method of the present application.

[0034] Figure 2 FIG. 3 is a schematic diagram of the redefinition of the angle of arrival.

[0035] Figure 3 FIG. 5 is a schematic diagram of the comparison of the normalized mean square error of the channel estimation under different signal-to-noise ratios provided by the embodiment.

[0036] Figure 4 FIG. 6 is a schematic diagram of the comparison of the normalized mean square error of the channel estimation under different time observations provided by the embodiment. DETAILED DESCRIPTION

[0037] The drawings are only used for illustrative purposes, and cannot be understood as a limitation on the patent;

[0038] In order to better illustrate the embodiment, some components in the drawings may be omitted, enlarged or reduced, and do not represent the actual product size;

[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 application will be further described below in combination with the drawings and embodiments.

[0041] Embodiment 1

[0042] The present example provides a millimeter wave uplink channel estimation method based on time correlation and block sparsity, which comprises the following steps:

[0043] S1: The base station end is equipped with a uniform surface array with M=M x ×M y single antenna, the user end transmits mutually orthogonal pilot sequences, and the base station end obtains the received signal after passing through the complex Gaussian channel.

[0044] S2: The base station distinguishes signals from different users by the characteristics of the orthogonal pilot and performs sparse representation on the received signals at multiple observation instants;

[0045] S3: A first-order auto regressive (AR) process is used to characterize the time correlation and block correlation, thereby constructing a sparse prior, and the noise variance, channel block sparse prior, time correlation coefficient and block correlation coefficient are used as unknown hyperparameters, and parameter distributions are obtained based on the SBL framework;

[0046] S4: The maximum a posteriori probability of the unknown hyperparameters is solved by using an EM algorithm for iteration;

[0047] S5: A threshold and the number of iterations are set, and when the channel block sparse prior converges or the number of iterations reaches a set value, the iteration is ended, and an estimation result of the channel sparse representation is obtained;

[0048] S6: The actual channel is calculated by the estimation result of the channel sparse representation.

[0049] Embodiment 2

[0050] Based on Embodiment 1, the following contents are further disclosed in this embodiment:

[0051] In step S1, the system contains U users in total, and the received signal of the base station at the qth instant can be expressed as wherein is the channel between the uth user and the base station, satisfying Herein, θ and are the angles after redefinition in Figure 2 is the angle domain dictionary matrix, which can be denoted as d is the distance between adjacent antennas at the base station end, λ is the wavelength of the transmission signal, is the pilot sequence of the uth user, and the pilot sequence length T is greater than the number of users U.

[0052] In step S2, the base station distinguishes the received signal by the specific user signal through the orthogonal pilot The received signal at Q observation instants can be expressed as After vectorization, y = vec(Y T ), the signal can be sparsely represented as wherein is the angle domain dictionary matrix, which can be denoted as is the angle domain dictionary matrix, which can be denoted as is the angle domain dictionary matrix, which can be denoted as Let The sparse representation results of the channel at Q observation time instants.

[0053] In step S3, each parameter distribution is defined as follows:

[0054] According to the SBL framework, the sparse representation z is set to have a Gaussian prior distribution:

[0055] p(z) = CN(0,∑0),

[0056] where Here, we divide z into K blocks according to the block sparse property of the channel: K blocks, is the channel block sparse prior, which indicates whether a non-zero block appears at the position of z, is the block structure formed by the angle spread of each scattering cluster in the channel, satisfying G θ = Bxd, is the time correlation of the channel at Q observation time instants, and the additive complex Gaussian noise n satisfies p(n|a) = CN(0, a -1 ), where a = σ -2 is the noise resolution, and the received signal y also satisfies a Gaussian distribution:

[0057] p(y|z; a) = CN(Φz, a -1 U),

[0058] According to the derivation of the second likelihood function, the posterior distribution of z also satisfies a Gaussian distribution, and p(z|y; a, G, X, Y) = CN(μ(a, G, X, Y),∑(a, G, X, Y)), which satisfies:

[0059]

[0060] In step S4, the super parameters to be estimated are denoted as Θ = (a, G, X, Y), and the solving process of each parameter based on the EM algorithm is as follows:

[0061] Based on the maximum posterior criterion, the cost function for updating the super parameters is:

[0062]

[0063] where (·) (i) represents the result of the i-th iteration, and the super parameters a, G, X, and Y satisfy:

[0064]

[0065] where (·) ij represents the element in the i-th row and j-th column of the matrix, and E ijdenotes a matrix in which the element in the i-th row and the j-th column is 1 and other elements are 0, (in MATLAB language), (in MATLAB language), ∑ y = α -1 I + Φ∑0Φ H .

[0066] The step S5 is used for judging the convergence of the channel estimation through the convergence of Γ, setting the iteration error threshold as σ tol , and the maximum iteration number as i max When the iteration error is less than σ or the iteration number i is greater than or equal to i max , the converged channel expectation value μ is output as the actual value of z.

[0067] The step S6 is used for estimating the actual channel through the sparse distribution of the channel z, and the specific expression is

[0068] Embodiment 3

[0069] Based on the embodiments 1 and 2, the following specific embodiments are provided in the embodiment.

[0070] The simulation parameters are set as follows: it is assumed that the base station end is equipped with a 15x12 uniform planar array, the multipath channel contains 3 clusters, each cluster contains 3 paths, the angle spread in each cluster is set as 15°, the pilot sequence adopts the column of the discrete Fourier transform matrix to ensure mutual orthogonality, the angle of arrival is generated randomly according to the normal distribution, and the channel observation number Q is 3 in the Figure 3 , the signal-to-noise ratio SNR is 10 dB in the Figure 4 , the iteration error threshold σ tol = 10 -4 , the maximum iteration number i max = 30, and 100 Monte Carlo experiments are performed.

[0071] Based on the embodiment, the new method proposed in the application is compared with the orthogonal matching pursuit algorithm and the sparse Bayesian learning algorithm in performance, and the specific comparison is as follows: according to Figure 3 , Figure 4As shown, the proposed method can improve the estimation accuracy of the channel regardless of the signal-to-noise ratio and the number of channel observations. 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 fully utilizes the correlation between multiple channel observations, and further improves the accuracy of channel estimation by simulating and estimating the correlation. In addition, compared with the matching pursuit algorithm, the proposed algorithm is based on the SBL framework and does not require prior information of the channel sparse structure, and has better environmental adaptability.

[0072] The above examples show that the method of the present application simultaneously considers the time correlation and block sparsity of the channel, and by fully simulating the two characteristics, the performance is obviously improved, and under different signal-to-noise ratios and channel observation numbers, the proposed method has an advantage over the classical compressed sensing method.

[0073] The same or similar reference signs correspond to the same or similar components;

[0074] The position relationship described in the drawings is only for illustrative purposes and should not be construed as a limitation on the patent;

[0075] Obviously, the above examples of the present application are only examples for clearly illustrating the present application, and are not limitations on the embodiments of the present application. Based on the above description, those skilled in the art can make other different forms of changes or variations. Here, it is not necessary and impossible to exhaust all embodiments. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application should be included in the protection scope of the claims of the present application.

Claims

1. A method for millimeter wave uplink channel estimation based on time correlation and block sparsity, characterized in that, The method comprises the following steps: S1: the base station is equipped with M x ×M y = M uniform planar arrays of antennas, the user terminal is equipped with a single antenna, the user terminal transmits mutually orthogonal pilot sequences, and the base station obtains the received signal after passing through a complex Gaussian channel; S2: the base station distinguishes signals from different users by the characteristics of the orthogonal pilot and performs sparse representation on the received signals at multiple observation instants; S3: a first-order auto regressive (AR) process is used to represent the time correlation and block correlation, thereby constructing a sparse prior, and noise variance, channel block sparse prior, time correlation coefficient and block correlation coefficient are used as unknown hyperparameters, and each parameter distribution is obtained based on the SBL framework, and each parameter distribution is defined as follows: According to the SBL framework, the sparse representation z has a Gaussian prior distribution: p(z) = CN(0,∑0), where Here, we exploit the block sparsity of the channel to divide z into blocks, is the channel block sparsity prior, which indicates whether a non-zero block appears at is the block structure of each scattering cluster in the channel due to angular spread, satisfying G θ = B × d, is the time correlation of the channel over Q observation times, and let the additive complex Gaussian noise n satisfy 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: p(y | z; a) = CN(Φz, a -1 I), According to the derivation of the second likelihood function, the posterior distribution of z also satisfies the Gaussian distribution, and p(z|y;Γ,Θ,γ) = CN(μ(α,Γ,Ξ,γ),∑(α,Γ,Ξ,γ)), which satisfies: S4: the maximum a posteriori probability of the unknown hyperparameters is solved by using the EM algorithm for iteration; S5: a threshold and an iteration number are set, when the channel block sparse prior converges or the iteration number reaches a set value, the iteration is ended, and an estimation result of the channel sparse representation is obtained; S6: the actual channel is calculated through the estimation result of the channel sparse representation. 2.The method of claim 1, wherein, The system contains U users in step S1, and the signal received by the base station at the qth moment can be expressed as wherein is the channel between the u th user and the base station, satisfying Here θ and is the angle after redefinition, and the steering vector d is the distance 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 pilot sequence length T is greater than the number of users U. 3.The method of claim 2, wherein, In step S2, the base station separates the specific user signal from the received signal through the orthogonal pilot The received signal at Q observation instants can be represented as After vectorization, y = vec(Y T ), the signal can be sparsely represented as where is the dictionary matrix in the angle domain, which can be denoted as is the dictionary matrix in the angle domain, which can be denoted as is the dictionary matrix in the angle domain, which can be denoted as Let be the sparse representation result of the channel at Q observation instants.

4. The method of claim 3, wherein, In step S4, the to-be-estimated hyperparameters are denoted as Θ=(α,Γ,Ξ,Υ), and the solving process of each parameter based on the EM algorithm is as follows: Based on the maximum a posteriori criterion, the cost function for updating the hyperparameters is: where (·) (i) denotes the result of the i-th iteration, then the hyperparameters a, G, X, Y satisfy: wherein (·) ij denotes the element in the i-th row and j-th column of matrix E ij denotes the matrix with 1 in the i-th row and j-th column and 0 elsewhere, 5. The method of claim 4, wherein, The step S5 is to judge the convergence of the channel estimation by the convergence of Γ, set the iteration error threshold as σ tol , and the maximum iteration number as i max . When or the iteration number i≥i max , output the converged channel expectation value μ as the actual value of z.

6. The method of claim 5, wherein, The role of step S6 is to estimate the actual channel through the sparse distribution of the channel, and the specific expression is

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