A Simultaneous Channel Estimation and Localization Method for Massive MIMO Systems

Abstract

The present invention relates to a method for simultaneously estimating channels and positioning in a massive multiple-input multiple-output (MIMO) system. For a massive MIMO system, the construction of a high-order tensor model in the presence of a dual broadband effect is mainly realized, downlink channel estimation is performed, and user positioning and propagation environment mapping are realized. The implementation steps are: 1) considering the time-varying channel in a massive MIMO-OFDM system in the THz frequency band, the observed signal is reconstructed into a sixth-order PARAFAC decomposition model; 2) the real numberization of the constructed tensor model is realized; 3) the tensor model is fitted using a Bayesian inference algorithm and a factor matrix is ​​estimated; 4) the complex factor matrix is ​​restored and channel parameters are extracted; 5) the information of the extracted parameters is used to restore the channel and estimate the user position. The present invention can realize simultaneous communication and positioning in the absence of a line-of-sight path, has the advantages of high precision and strong stability, and can be used for both all-digital and analog-to-digital hybrid systems.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a simultaneous channel estimation and positioning method in a large-scale MIMO system. Background Art

[0002] In the future sixth generation mobile communication (6G) system, dense deployment of large-scale antenna arrays, use of high frequency bands (such as millimeter wave (mmWave) and terahertz (THz) bands) signals and increased bandwidth will enable the communication and positioning of wireless signals to be integrated into one system, thereby enhancing each other. Channel estimation can be used as a medium to achieve simultaneous communication and positioning, giving full play to the dual potential of wireless networks. Channel estimation is usually based on a sparse representation of the channel, where the parameters of the channel include angle, distance, gain, etc., which are also used for positioning at the receiving end.

[0003] Tensor decomposition has been widely used in channel estimation and symbol detection. At present, tensor-based positioning methods have attracted the attention of relevant scholars. Using the information contained in diffuse multipath, some scholars have proposed a method based on parallel factor (PARAFAC) decomposition for positioning and mapping of millimeter wave systems.

[0004] THz communication is the focus of 6G networks, which can provide greater bandwidth than the millimeter wave band. The short wavelength of THz signals allows large-scale antenna arrays to be packed into a small area, forming a massive multiple-input multiple-output (MIMO) architecture. However, for massive MIMO systems in the THz band, time delays and multipath delay spreads on the array aperture can cause spatial and frequency broadband (dual broadband) effects. In this case, the massive MIMO channel model that only considers the phase difference and ignores the delay difference between the received signals of different antennas is no longer applicable, and algorithms based on such models will suffer severe performance losses when estimating the channel and performing user positioning. Summary of the invention

[0005] Purpose of the invention: In view of the shortcomings of the prior art, the present invention proposes a method for simultaneous channel estimation and positioning in a large-scale MIMO system, the purpose of which is to use an algorithm based on Bayesian tensor decomposition to simultaneously perform channel estimation and positioning in a broadband THz large-scale MIMO system with dual broadband effect.

[0006] Technical solution: A method for simultaneous communication and positioning in a MIMO system according to the present invention comprises:

[0007] Considering the time-varying channel in THz-band massive MIMO-orthogonal frequency division multiplexing (OFDM) system, the observed signal is reconstructed into a sixth-order PARAFAC model.

[0008] Realize the constructed tensor model into real numbers;

[0009] Fit tensor models and estimate factor matrices using Bayesian inference algorithms;

[0010] Recover the complex factor matrix and extract channel parameters;

[0011] The information of the extracted parameters is used to recover the channel and estimate the user position.

[0012] Furthermore, considering the time-varying channel in the massive MIMO-OFDM system in the THz band, the observed signal is reconstructed into a sixth-order PARAFAC model, which includes:

[0013] The system includes a base station (BS) and a user (UE), whose locations are p T and p R Both the base station and the user end use uniform planar array (UPA), and the number of antennas is and Adopting analog-to-digital (AD) hybrid structure, and are the number of RF chains of BS and UE respectively. The total number of subcarriers is K of them are pilot subcarriers.

[0014] Assuming there are L propagation paths, the emission angle (AOD) corresponding to the lth path is The receiving angle (AOA) is l=1,...,L,φ l and θ l are azimuth and elevation respectively. We consider a time-varying channel, and the gain in the lth path and the tth time slot is α t,l , where t=1,...,N0. Based on the above parameters, the channel response of the kth subcarrier in the tth time slot is

[0015]

[0016] in represents the frequency shift of the kth subcarrier, k = 1, ..., K, f s is the bandwidth. The steering vectors of BS and UE are represented as a BS,k and a UE,k , which are in the form of where η 1,l =πsin(φ l )sin(θ l ), η 2,l =πcos(θ l ), due to the dual broadband effect, the steering matrix is ​​in the form of

[0017]

[0018] where f c is the carrier frequency, d∈{1,2}, is the number of antennas corresponding to the steering matrix. The steering matrix corresponding to the kth subcarrier is and in and All of them are Vandermonde structures, that is,

[0019]

[0020] Gain and delay information are integrated into the matrix Among them g l =[α 1,l ,...,α T,l ] T .

[0021] The precoding matrix at the BS end and the combined matrix at the UE end are and in n∈{T1,T2,R2,R2} is the central Hermitian matrix. The observation signals of K subcarriers are combined into a whole and written as a sixth-order parallel factor tensor model to obtain in is the noise tensor. The received signal of the kth subcarrier is The form is

[0022]

[0023] Furthermore, the constructed tensor model is converted to real numbers, including:

[0024] For the kth subcarrier, the received signal The modulo-5 expansion matrix is

[0025]

[0026] Using the properties of the Khatri-Rao product, the above equation can be rewritten as

[0027]

[0028] Among them are Loading Matrix Satisfaction

[0029]

[0030] Where Π represents the interchange matrix, is defined as Where x∈{T,R}. The matrix and are all central conjugate matrices, that is,

[0031]

[0032]

[0033] For the matrix Ω TR =Ω R Ω T ,have

[0034]

[0035] Then you can get

[0036]

[0037]

[0038] Central Hermitian matrix Z k can be constructed as

[0039]

[0040] in Z k Rearranged into a five-dimensional tensor have

[0041]

[0042] in express The five factor matrices of Each dimension and left-real matrix U n , n=1,...,5 modulo-n product, we can get the real-valued model for

[0043]

[0044] The left-real matrix U n satisfy express The five factor matrix of .

[0045] Furthermore, the Bayesian inference algorithm is used to fit the tensor model and estimate the factor matrix, including:

[0046] The signals of K subcarriers are processed in parallel. Since the processing flow of each subcarrier is the same, the subscript k is omitted in this section. Defined as The noise observation tensor is assumed to be Gaussian distributed, and the likelihood model is as follows

[0047]

[0048] Where ω is the noise accuracy, For B (n) The i n Assume that the factor matrix follows a zero-mean Gaussian prior distribution and has a covariance matrix λ l I, that is

[0049]

[0050] In addition, it is assumed that λ and noise accuracy ω obey the gamma distribution, that is,

[0051]

[0052]

[0053] Where Γ(·) is the gamma function. By combining the Bayesian hierarchical model, we can write the joint distribution of the model as

[0054]

[0055] Our goal is to calculate γ = {B (1) ,...,B (5) ,λ,ω} is as follows

[0056]

[0057] The exact posterior distribution in the above formula cannot be calculated directly, so variational Bayesian inference (VBI) is used to solve this problem, that is, to find a As an approximation to the exact posterior distribution, it can be achieved by minimizing the Kullback-Leibler (KL) divergence between q(γ) and the posterior distribution, that is,

[0058]

[0059] The lower bound of the model evidence is defined as because is a constant, since the KL minimization problem can be transformed into the problem of maximizing the lower bound of model evidence. Therefore, the update form of the factors in γ is

[0060]

[0061] in represents q(γ j) distribution for all j≠t corresponding variables. Based on the above formula, the specific update rule for each factor can be obtained. In each iteration, all factors are updated in turn, and the model evidence lower bound is calculated until convergence. The estimated five loading matrices and tensors will be output at the end of the loop.

[0062] Furthermore, the complex factor matrix is ​​restored and the channel parameters are extracted, specifically including:

[0063] The estimated real-valued factor matrix is ​​obtained by the real-valued Bayesian inference algorithm After that, the complex factor matrix corresponding to all subcarriers is restored. The complex factor matrix is express, Yes V n,k The complex factor matrix of the kth subcarrier can be used A correlation-based scheme can be applied to extract the spatial frequencies contained in the loading matrix The nth loading matrix contains the lth spatial frequency Given by the following formula

[0064]

[0065] in for The lth column of is the range of one-dimensional search, Yes V n,k The first column of Replace V n,k The real spatial frequency in . Then, we can get For the fifth factor matrix, we take The first N0 rows of and define The delay can be calculated from Q 2,k The formula is extracted from

[0066]

[0067] in corresponds to the kth i subcarriers The lth row, k i ,k j ∈{1,...,K}, the path gain can be estimated as

[0068]

[0069] Taking the average value of the recovery results on multiple subcarriers, we get and The estimated value of .

[0070] Further, the extracted parameter information is used to restore the channel and estimate the user position, specifically including:

[0071] After estimating the angle and delay information of all K subcarriers, these parameters are used to locate the UE and the scattering point. The direction vector of the lth AOD is defined as

[0072]

[0073] The direction vector f of the lth AOA R,p Assuming the BS position is known, applying the weighted least squares solution, the relationship between the estimated value of the UE position and the BS position is

[0074]

[0075] in c is the speed of light, is the weight of the lth path, which is related to the signal-to-noise ratio. T The location of is known, and the intersection of all paths determines the estimated value of The position of the target can be obtained by fitting, and the position of the scattering point can be further restored. Then the position of the scattering point used for mapping can be restored by the following method:

[0076]

[0077] in

[0078] Beneficial effects: Compared with the prior art, the main advantages of the present invention are: the present invention can estimate the user's position and perform environmental mapping in the absence of a line-of-sight (LOS) path; the use of the Bayesian inference algorithm can effectively improve the performance of positioning and parameter estimation; the constructed high-order tensor retains the internal structure information to ensure parameter estimation performance, and the present invention adopts an AD hybrid architecture to reduce RF overhead. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 is a flow chart of the parameter estimation method of the present invention;

[0080] Figure 2 A schematic diagram of a simultaneous channel estimation and positioning scenario of the present invention;

[0081] Figure 3 This is a performance diagram of angle estimation under different signal-to-noise ratios of the present invention;

[0082] Figure 4 It is a channel parameter estimation and positioning performance diagram of the present invention under different signal-to-noise ratios;

[0083] Figure 5 This is a schematic diagram of three-dimensional positioning of the present invention when the signal-to-noise ratio is fixed at 20dB; DETAILED DESCRIPTION

[0084] In order to make the features and advantages of the present invention more obvious and understandable, the present invention is described in detail below with reference to the accompanying drawings.

[0085] Figure 2 Schematic diagram of the simultaneous channel estimation and positioning scenario of the present invention, such as Figure 2 As shown, considering the THz band massive MIMO-OFDM system, the parameters are set as follows: the total number of subcarriers is K = 6 subcarriers are used for pilot training; the carrier frequency and bandwidth are 300 GHz and 15 GHz respectively, and the number of time slots is N0 = 10. The number of propagation paths is L = 3, and we assume that there is no LOS path. The UPA antenna array sizes of BS and UE are M T =16×16 and M R =12×12, the number of radio chains at both the transmitter and receiver is 8×8. The BS and UE are located at p T =[20,0,8] T and p R =[0,0,2] T .

[0086] Implementation Example 1

[0087] See also Figure 3 , Figure 3 This is a diagram of the angle estimation performance of the present invention under different signal-to-noise ratios. Figure 3 It shows that both algorithms with fully digital (FD) connection architectures provide higher parameter estimation accuracy because they utilize more RF resources. It can also be seen that the RMSE performance of all algorithms improves with the increase of SNR, and the proposed algorithm outperforms the existing ALS algorithm in both architectures, especially in the case of medium and high SNR.

[0088] Implementation Example 2

[0089] See also Figure 4 , Figure 4 This is a diagram of the channel parameter estimation and positioning performance of the present invention under different signal-to-noise ratios. Figure 4 It is shown that the algorithm provides higher channel estimation and positioning accuracy in both architectures of the transceiver.

[0090] Implementation Example 3

[0091] See also Figure 5 , Figure 5 It is a schematic diagram of three-dimensional positioning of the present invention when the signal-to-noise ratio is fixed at 20dB. Figure 5It shows that the scattered points estimated by the existing ALS algorithm of the AD hybrid architecture are the farthest from the true points, while the positions estimated by the proposed algorithm are more accurate.

[0092] In summary, the present invention considers the dual broadband effect in THz massive MIMO systems and proposes a robust PARAFAC-based method for simultaneous positioning and communication. Considering UPA and time-varying channels, a high-order observation tensor model is proposed. Then, the channel parameters are recovered with the help of the proposed real-valued Bayesian inference algorithm. The algorithm can estimate the channel and realize user positioning and propagation environment mapping without LOS path with high accuracy.

[0093] The above embodiments are only for helping to understand the method and main idea of ​​the present invention. The contents of this specification cannot be used to limit the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the attached claims.

Claims

1. A simultaneous channel estimation and positioning method in a massive MIMO system, characterized in that The method includes: Considering the time-varying channel in the massive MIMO-OFDM system in the THz band, the observed signal is reconstructed into a sixth-order PARAFAC model, which specifically includes: the system includes a base station (BS) and a user (UE), whose positions are p T and p R , both the base station and the user end use uniform planar array (UPA), and the number of antennas is and Adopting analog-to-digital (AD) hybrid structure, and are the number of RF chains of BS and UE respectively, and the total number of subcarriers is Among them, K are pilot subcarriers. Assuming there are L propagation paths, the emission angle (AOD) corresponding to the lth path is The receiving angle (AOA) is φ l and θ l are azimuth and elevation respectively, we consider a time-varying channel, and the gain in the lth path and the tth time slot is α t,l , where t = 1, ..., N0, based on the above parameters, the channel response of the kth subcarrier in the tth time slot is in represents the frequency shift of the kth subcarrier, k = 1, ..., K, f s is the bandwidth, and the steering vectors of BS and UE are represented as a BS,k and a UE,k , which are in the form of where η 1,l =πsin(φ l )sin(θ l ), η 2,l =πcos(θ l ), due to the dual broadband effect, the steering matrix is ​​in the form of where f c is the carrier frequency, d∈{1,2}, is the number of antennas corresponding to the steering matrix, and the steering matrix corresponding to the kth subcarrier is and in and All of them are Vandermonde structures, that is, Gain and delay information are integrated into the matrix Among them g l =[α 1,l ,…,α T,l ] T , the BS-side precoding matrix and the UE-side combined matrix are and in As the central Hermitian matrix, the observation signals of K subcarriers are constructed as a sixth-order parallel factor tensor model, and we get in is the noise tensor, and the received signal of the kth subcarrier is The form is The tensor model constructed is converted to real numbers, including: for the kth subcarrier, the received signal The modulo-5 expansion matrix is Using the properties of the Khatri-Rao product, the above equation can be rewritten as Among them are Loading Matrix Satisfaction Where Π represents the interchange matrix, is defined as where x∈{T,R}, the matrix and are all central conjugate matrices, that is, For the matrix Ω TR =Ω R Ω T ,have Therefore, we can get Central Hermitian matrix Z k can be constructed as in Z k Rearranged into a five-dimensional tensor have in express The five factor matrices of Each dimension and left-real matrix U n , n=1,...,5 modulo-n product, we can get the real-valued model for The left-real matrix U n satisfy express The five factor matrix of The Bayesian inference algorithm is used to fit the tensor model and estimate the factor matrix, which includes: the signals of K subcarriers are processed in parallel. Since the processing flow of each subcarrier is the same, the subscript k is omitted. Defined as The noise observation tensor is assumed to be Gaussian distributed, and the likelihood model is as follows Where ω is the noise accuracy, For B (n) The i n row, assuming that the factor matrix follows a zero-mean Gaussian prior distribution with a covariance matrix λ l I, that is In addition, it is assumed that λ and noise accuracy ω obey the gamma distribution, that is, Where Γ(·) is the gamma function. By combining the Bayesian hierarchical model, we can write the joint distribution of the model as Our goal is to calculate Υ = {B (1) ,...,B (5) ,λ,ω} is as follows The exact posterior distribution in the above formula cannot be calculated directly, so variational Bayesian inference (VBI) is used to solve this problem, that is, to find a As an approximation of the exact posterior distribution, it can be achieved by minimizing the Kullback-Leibler (KL) divergence between q(Υ) and the posterior distribution, that is, The lower bound of the model evidence is defined as because is a constant, the KL minimization problem can be transformed into the problem of maximizing the lower bound of model evidence, so the update form of the factors in Υ is in represents q(Υ j ) distribution for all j≠t corresponding variables. Based on the above formula, the specific update rule of each factor can be obtained. In each iteration, all factors are updated in turn, and the evidence lower bound is calculated until convergence. The estimated five loading matrices and tensors will be output at the end of the loop. Restore the complex factor matrix and extract the channel parameters, including: express, Yes V n,k The complex factor matrix of the kth subcarrier can be used Calculation, a correlation-based scheme can be applied to extract the spatial frequencies contained in the loading matrix contains the angle information, and the nth loading matrix contains the lth spatial frequency Given by the following formula in for The lth column of is the range of one-dimensional search, so, Yes V n,k The first column of Replace V n,k The real spatial frequency in To extract AODs and AoAs, for the fifth factor matrix, we take The first N0 rows of and define The delay can be calculated from Q 2,k The formula is extracted from in corresponds to the kth i subcarriers The lth row, k i ,k j ∈{1,...,K}, the path gain can be estimated as Taking the average value of the recovery results on multiple subcarriers, we get and An estimated value of The extracted parameter information is used to restore the channel and estimate the user position, specifically including: after estimating the angle and delay information of all K subcarriers, these parameters are used to locate the UE and the scattering point, and the direction vector of the lth AOD is defined as The direction vector f of the lth AOA R,p Similarly, assuming that the BS position is known, the relationship between the estimated value of the UE position and the BS position is calculated by applying the weighted least squares solution. in c is the speed of light, is the weight of the lth path, which is related to the signal-to-noise ratio. T The location of is known, and the intersection of all paths determines the estimated value of The position of the target can be obtained by fitting, and the position of the scattering point can be further restored. Then, the position of the scattering point used for mapping can be restored by the following method: in

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