CN114629533B - Information geometry method and system for large-scale MIMO channel estimation - Google Patents

Abstract

The invention discloses an information geometric method for large-scale MIMO channel estimation and a related system. The invention carries out channel estimation according to the information geometric theory, and obtains the posterior statistical information of each user terminal channel, including posterior mean and variance. The information geometry method defines a set of Gaussian distribution as an original manifold, constructs a target manifold and an auxiliary manifold according to the posterior distribution of a channel, iteratively calculates m-projections distributed on the target manifold on the auxiliary manifold, updates parameters distributed in the auxiliary manifold and the target manifold according to the m-projections, and finally takes the mean value and the variance distributed on the target manifold as the posterior mean value and the posterior variance of channel estimation. The information geometry method provided by the invention can obviously reduce the calculation complexity and pilot frequency overhead of channel estimation on the premise of ensuring the accuracy of the channel estimation, and effectively solve the problem of channel information acquisition of a large-scale MIMO system.

Description

Information geometry method and system for massive MIMO channel estimation

Technical Field

The present invention belongs to the field of communication technology and relates to an information geometry method and a related system for large-scale MIMO channel estimation.

Background Art

Massive Multiple-Input Multiple-Output (MIMO) technology is the core enabling technology of 5G cellular systems and their continued evolution. In a massive MIMO system, a base station (BS) equipped with a large number of antennas can provide services to dozens of users simultaneously on the same time and frequency resources, potentially providing huge capacity gains and significantly improving energy efficiency. Among all types of antenna arrays, the uniform plane array (UPA) is a good choice for practical applications due to its compact size and three-dimensional coverage capability. Orthogonal frequency division multiplexing (OFDM) technology is a multi-carrier modulation technology that can mitigate the impact of frequency selective fading in broadband wireless communications. Massive MIMO-OFDM plays an important role in 5G systems and has received widespread attention in future 6G systems.

In massive MIMO-OFDM systems, channel estimation plays a vital role because the system performance is highly dependent on the quality of the channel information obtained by the system. In practical systems, auxiliary pilot channel estimation, that is, the transmitter periodically sends a pilot signal, and the receiver obtains the channel state information (CSI) based on the received pilot signal, is a commonly used channel estimation method. Given the received pilot signal, the task of channel estimation is to obtain the posterior statistical information of the channel parameters. When the prior distribution of the channel parameters is Gaussian, its posterior distribution is also Gaussian, and its posterior information is given by the posterior mean and the posterior covariance matrix. However, due to the large dimension of the channel in massive MIMO-OFDM systems, the calculation of the posterior information is challenging. Traditional channel estimation algorithms, such as minimum mean squared error (MMSE) estimation, are difficult to be applied in massive MIMO-OFDM systems due to the large-dimensional matrix inversion in the calculation process. As the number of antenna units on the base station side and the number of supported user terminals further increase significantly, the computational complexity and pilot overhead of conventional channel information acquisition will increase significantly, becoming a bottleneck problem that needs to be solved.

The space defined by the posterior probability density function can be regarded as a differentiable manifold with a Riemann structure. Therefore, the definitions and tools in differential geometry can be well applied here, which is one of the themes of information geometry. Therefore, it is reasonable to apply information geometry to channel estimation. The main idea of information geometry is to study the intrinsic geometric structure of a specific set of probability density functions (PDFs) by considering the parameter space of the probability density function (PDF) as a differentiable manifold. In recent years, information geometry has been successfully applied to multi-sensor estimation fusion, false alarm rate detection, and generalized Bayesian prediction. There are several advantages of using information geometry theory to analyze estimation problems: first, information geometry can provide a unified framework for the theoretical analysis of existing algorithms; second, it provides an intuitive understanding of statistical models from a geometric perspective, which can promote the intrinsic study of existing problems; in addition, information geometry can also improve algorithms from a more general and intrinsic perspective.

Summary of the invention

Purpose of the invention: In view of the deficiencies in the prior art, the present invention discloses a large-scale MIMO channel estimation information geometry method and a related system, which can obtain the a posteriori information of each user terminal channel, while ensuring the estimation performance, and can further reduce the computational complexity compared with existing similar technical means.

Technical solution: In order to achieve the above-mentioned purpose, the present invention provides the following technical solution:

A massive MIMO channel estimation method comprises the following steps:

The base station side/user terminal obtains a priori statistical information of the channel through uplink/downlink detection;

The base station side/user terminal obtains the posterior statistical information of the channel by using the information geometry method through the received uplink/downlink pilot signal and the prior statistical information; the information geometry method defines the set of Gaussian distributions as the original manifold, and constructs the target manifold and the auxiliary manifold according to the posterior distribution of the channel, the target manifold and the auxiliary manifold are both submanifolds of the original manifold, iteratively calculates the m-projection of the distribution in the auxiliary manifold on the target manifold, and updates the distribution in the target manifold and the auxiliary manifold according to the m-projection, and finally uses the mean and variance of the distribution on the target manifold as the posterior mean and posterior variance of the channel estimation.

Preferably, the target manifold is a set of Gaussian distributions whose elements are independent of each other, and the auxiliary manifold is a set of Gaussian distributions whose covariance matrix is the inverse matrix of the sum of a diagonal matrix and a rank-1 matrix; the m-projection is obtained by minimizing the KL divergence between the distribution in the auxiliary manifold and the target manifold.

Preferably, the mean and covariance matrix of the distribution in the target manifold and the auxiliary manifold are represented by the parameter vector and parameter real diagonal matrix of the respective auxiliary calculations; wherein the covariance of the distribution in the target manifold is represented as the inverse matrix of the difference between the inverse of the prior variance and the parameter real diagonal matrix, and the mean is represented by the product of the covariance matrix and the parameter vector; the covariance matrix of the distribution in the auxiliary manifold is represented as the inverse matrix of the difference between the inverse of the prior variance and the parameter real diagonal matrix and the sum of the rank-1 matrices, wherein the rank-1 matrix is represented by the corresponding rows in the perception matrix and the noise variance, and the mean is represented by the product of the covariance and the parameter vector combined with the corresponding rows in the perception matrix, the corresponding elements of the received pilot signal vector, and the vector consisting of the noise variance.

Preferably, the covariance matrix of the auxiliary manifold is expanded using the Sherman-Morrison formula.

Preferably, the step of obtaining the posterior mean and posterior variance of the channel estimation by using the information geometry method comprises:

(1) Establishing the original manifold, target manifold, and auxiliary manifold of the massive MIMO channel;

(2) Initialize the parameters distributed on the auxiliary manifold and the target manifold;

(3) calculating the m-projection of the distribution in the auxiliary manifold on the target manifold based on the parameters distributed on the auxiliary manifold, the received pilot signal, and the prior channel statistical information;

(4) updating the parameters distributed on the auxiliary manifold and the target manifold according to the m-projection; repeating steps (3)-(4) until a preset number of iterations is reached or the parameters distributed on the target manifold converge.

Preferably, the prior statistical information and the posterior statistical information of the space-frequency beam domain channel are calculated based on the space-frequency beam based channel statistical characterization model. In the space-frequency beam based channel statistical characterization model, the space-frequency domain channel matrix is obtained by multiplying the space-frequency beam domain channel matrix by the sampling space steering vector matrix on the left and by the transposed matrix of the sampling frequency steering vector matrix on the right, and each element of the space-frequency beam domain channel is statistically independent; for the base station side, the posterior mean and posterior variance of the space-frequency beam domain channel are converted into the posterior mean and posterior variance of the space-frequency domain channel by using the sampling space steering vector matrix and the sampling frequency steering vector matrix; for the user terminal side, the posterior statistical information of each space-frequency beam domain channel is fed back to the base station, and the base station side converts the obtained posterior mean and posterior variance of the space-frequency beam domain channel into the posterior mean and posterior variance of the space-frequency domain channel by using the sampling space steering vector matrix and the sampling frequency steering vector matrix.

A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the computer program implements the large-scale MIMO channel estimation method when loaded into the processor.

A large-scale MIMO communication system comprises a base station and a plurality of user terminals, wherein the base station is used to: obtain a priori statistical information of a channel of each user terminal through uplink detection; obtain a posteriori statistical information of each user terminal by using an information geometry method through a received uplink pilot signal and the a priori statistical information; the information geometry method defines a set of Gaussian distributions as an original manifold, and constructs a target manifold and an auxiliary manifold according to the posterior distribution of the channel, wherein both the target manifold and the auxiliary manifold are submanifolds of the original manifold, iteratively calculates the m-projection of the distribution in the auxiliary manifold on the target manifold, and updates the distribution in the target manifold and the auxiliary manifold according to the m-projection, and finally uses the mean and variance of the distribution on the target manifold as the posterior mean and posterior variance of the channel estimation.

A large-scale MIMO communication system comprises a base station and a plurality of user terminals, wherein the user terminals are used to: obtain a priori statistical information of respective channels through downlink channel detection; obtain a posteriori statistical information of respective channels through received downlink pilot signals and a priori statistical information by using an information geometry method and a channel prediction method and feed the information back to the base station; the information geometry method defines a set of Gaussian distributions as an original manifold, and constructs a target manifold and an auxiliary manifold according to the posterior distribution of the channel, wherein both the target manifold and the auxiliary manifold are submanifolds of the original manifold, iteratively calculates the m-projection of the distribution in the auxiliary manifold on the target manifold, and updates the distribution in the target manifold and the auxiliary manifold according to the m-projection, and finally uses the mean and variance of the distribution on the target manifold as the posterior mean and posterior variance of the channel estimation.

A massive MIMO communication system comprises a base station and a plurality of user terminals, wherein the base station or the user terminal comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the computer program implements the massive MIMO channel estimation method when loaded into the processor.

Beneficial effects: Compared with the prior art, the information geometry method for massive MIMO channel estimation proposed in the present invention can obtain the a posteriori mean and a posteriori variance of the channel with lower computational complexity and pilot overhead while ensuring the accuracy of channel estimation. The obtained a posteriori mean and a posteriori variance can be further applied to robust precoding and robust detection to improve system performance, thereby further improving the overall transmission efficiency of the system.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a channel estimation method according to an embodiment of the present invention;

FIG2 is a flow chart of a channel estimation method according to another embodiment of the present invention;

FIG3 is a flow chart of an information geometry method for channel estimation according to an embodiment of the present invention;

FIG4 is a schematic diagram showing a comparison of channel estimation performance between an information geometry method according to an embodiment of the present invention and an existing method;

FIG5 is a schematic diagram showing a comparison of convergence curves of the information geometry method and the existing method when the signal-to-noise ratio is 20 dB in an embodiment of the present invention.

DETAILED DESCRIPTION

The technical solution provided by the present invention will be described in detail below in conjunction with specific embodiments. It should be understood that the following specific implementation methods are only used to illustrate the present invention and are not used to limit the scope of the present invention.

As shown in FIG1 , a large-scale MIMO channel estimation method disclosed in an embodiment of the present invention is applicable to a base station side, including obtaining a priori statistical information of a channel of each user terminal by uplink detection on the base station side; obtaining a posteriori statistical information of a channel of each user terminal by using an information geometry method through a received uplink pilot signal and a priori statistical information; wherein the information geometry method defines a set of Gaussian distributions as an original manifold, and constructs a target manifold and an auxiliary manifold according to the posterior distribution of the channel, iteratively calculates the m-projection of the distribution in the auxiliary manifold on the target manifold, and updates the distribution in the target manifold and the auxiliary manifold according to the m-projection, and finally uses the mean and variance of the distribution on the target manifold as the posterior mean and posterior variance of the channel estimation.

As shown in FIG2 , another embodiment of the present invention discloses a large-scale MIMO channel estimation method, which is applicable to the user terminal side, including the user terminal obtaining the prior statistical information of each channel through downlink channel detection; the user terminal obtains the a posteriori statistical information of each channel by using the information geometry method through the received downlink pilot signal and the a priori statistical information, and the a posteriori information includes the a posteriori mean and the a posteriori variance; wherein the information geometry method is consistent with the base station side method, except that the multi-user is degraded to a single user. The user terminal can be a mobile terminal or a fixed terminal such as a mobile phone, a vehicle-mounted device, or a smart device.

FIG3 illustrates the specific steps of obtaining a posteriori statistical information using the information geometry method, including: (1) establishing the original manifold, auxiliary manifold and target manifold of the massive MIMO channel; (2) initializing the parameters distributed on the auxiliary manifold and the target manifold; (3) calculating the m-projection of the auxiliary manifold on the target manifold based on the parameters distributed on the auxiliary manifold, the received pilot signal and the prior channel statistical information; (4) updating the parameters distributed on the auxiliary manifold and the target manifold based on the m-projection; repeating steps (3)-(4) until a preset number of iterations or the parameters distributed on the target manifold converge, the mean and variance distributed on the target manifold are the a posteriori mean and a posteriori variance of the channel, respectively.

The method of the present invention is mainly applicable to a large-scale MIMO system in which a large-scale antenna array is equipped at the base station side to simultaneously serve multiple users. The specific implementation process of the channel estimation information geometry method involved in the present invention is described in detail below in conjunction with a specific communication system example. It should be noted that the method of the present invention is not only applicable to the specific system model given in the following example, but also to system models with other configurations.

1. System Configuration

其中用于上行训练额的子载波集记为

其大小为

在TDD模式下，由于信道互易性，上行训练获取的CSI可以用于上行信号检测和下行预编码传输，因此实施例中考虑上行大规模MIMO-OFDM信道估计。Consider a massive MIMO-OFDM system operating in time division multiplexing (TDD) mode. The base station is equipped with a UPA antenna array, where the number of antennas is N _r =N _r,v ×N _r,h , N _r,v and N _r,h are the number of antennas in each column and row, respectively, and the antenna spacing in the horizontal and vertical directions is denoted by Δ _v and Δ _{h ,} respectively. The base station simultaneously serves K users equipped with single antennas in the same cell. In OFDM modulation, the number of subcarriers is N _c , and the system sampling interval and cyclic prefix length are denoted by T _s and N _{g ,} respectively. The subcarrier set is denoted by

The subcarrier set used for uplink training is denoted as

Its size is

In TDD mode, due to channel reciprocity, the CSI obtained through uplink training can be used for uplink signal detection and downlink precoding transmission, so uplink massive MIMO-OFDM channel estimation is considered in the embodiment.

2. Space-frequency beam-based channel statistical characterization model and channel estimation problem statement

The system model, space-frequency beam-based channel statistical characterization model and channel estimation problem are explained in detail below.

1. System Model

为第k个用户在单个OFDM符号内的频域发送序列。在上行训练中，第n个子载波上的频域接收信号矢量可以表示为remember

The frequency domain received signal vector on the nth subcarrier in the uplink training can be expressed as

为第k个用户在第n个子载波上的空域信道，

为循环对称高斯噪声，噪声功率为

进一步，定义第k个用户的空间频率域信道矩阵为in

is the spatial channel of the kth user on the nth subcarrier,

is a cyclically symmetric Gaussian noise, and the noise power is

Furthermore, the spatial frequency domain channel matrix of the kth user is defined as

其中x_k＝[x_k[N₁]…x_k[N₂]]^T，以及令

上标T表示矩阵或向量的转置。进一步，空间频率域接收信号模型可以写为make

where x _k =[x _k [N ₁ ]…x _k [N ₂ ]] ^T , and let

The superscript T represents the transpose of a matrix or vector. Furthermore, the spatial frequency domain received signal model can be written as

2. Space-frequency beam-based channel statistical characterization model

Define the direction cosine u = sinθ, v = cosθsinφ, where θ, φ∈[-π/2,π/2] are the polar angle and azimuth angle respectively. Further, define the spatial rudder vector v(u,v) as

表示Kronecker积，λ_c为波长。定义频率舵矢量u(τ)为in

represents the Kronecker product, λ _c is the wavelength. The frequency rudder vector u(τ) is defined as

其中

并且有

N_v,N_h,N_τ为采样倍数。则采样空间舵矢量矩阵和采样频率舵矢量矩阵可以分别表示为Where τ is the delay, Δ _f =1/N _c T _s is the subcarrier spacing. Further, the direction cosine u,v∈[-1,1] and the delay τ∈[0,N _g T _s ) are sampled and quantized as

in

And there are

N _v , N _h , N _τ are sampling multiples. Then the sampling space rudder vector matrix and the sampling frequency rudder vector matrix can be expressed as

The considered spatial-frequency beam-based channel statistical characterization model is: the spatial-frequency domain channel matrix is obtained by multiplying the spatial-frequency beam-domain channel by the sampling spatial rudder vector matrix on the left and the transposed matrix of the sampling frequency rudder vector matrix on the right, where each element of the spatial-frequency beam-domain channel is statistically independent. The specific expression is:

G _k = VH _k ^FT (12)

定义为空频波束域信道矩阵。假设采样倍数N_v≥N_r,v,N_h≥N_r,h,N_τ≥N_f，并定义精细化因子

当精细化因子为整数时，可以验证采样舵矢量矩阵有DFT结构。in

Defined as the space-frequency beam domain channel matrix. Assume that the sampling multiples _Nv ≥Nr _,v , _Nh ≥Nr _,h , _{Nτ ≥Nf} , and define the refinement factor

When the refinement factor is an integer, it can be verified that the sampled rudder vector matrix has a DFT structure.

Those skilled in the art will understand that the specific vector representation in the above model only takes a uniform planar array as an example. For systems using different antenna arrays such as uniform linear arrays, uniform circular arrays, etc., the above-mentioned space-frequency beam-based channel statistical characterization model is still applicable, and it is only necessary to change V to the corresponding spatial sampling rudder vector matrix.

3. Problem Statement

Combining the spatial frequency domain received signal model (3) and the spatial frequency beam-based channel statistical characterization model (12), we can obtain

Y＝VH _a M+Z (13)

进一步，对等式两边矢量化并去除空频波束域中的零元可以得到in

Furthermore, vectorizing both sides of the equation and removing the zeros in the space-frequency beam domain yields

y＝Ah+z (14)

为根据H_a非零元位置从

抽取相关列得到的矩阵,N＝N_rN_p,M为H_a中的非零元个数；y,z分别为对Y,Z矢量化后的矢量；h为H_a矢量化并抽取非零元得到的矢量。信道估计问题为利用接收导频信号y，获取各用户终端的空频波束域信道h的后验统计信息。空频波束域信道的后验统计信道信息为空频波束域信道的后验均值和后验方差；信道后验均值和后验方差包括：基站侧在给定接收到的上行导频信号条件下的空频波束域信道的条件均值和条件方差。假设

其中D为正定实对角矩阵，为各用户的先验方差，I为单位阵，

为噪声方差，

表示均值为μ、协方差矩阵为Σ的循环对称高斯分布。于是，空频波束域信道后验分布p(h|y)也属于高斯分布，其均值和协方差分别为in

According to the non-zero position _{of Ha,}

The matrix obtained by extracting the relevant columns, N = N _r N _p , M is the number of non-zero elements in _Ha ; y, z are the vectors after vectorizing Y and Z respectively; h is the vector obtained by vectorizing _Ha and extracting non-zero elements. The channel estimation problem is to use the received pilot signal y to obtain the a posteriori statistical information of the space-frequency beam domain channel h of each user terminal. The a posteriori statistical channel information of the space-frequency beam domain channel is the a posteriori mean and a posteriori variance of the space-frequency beam domain channel; the channel a posteriori mean and a posteriori variance include: the conditional mean and conditional variance of the space-frequency beam domain channel under the given received uplink pilot signal condition at the base station side. Assume

Where D is a positive definite real diagonal matrix, is the prior variance of each user, I is the unit matrix,

is the noise variance,

represents a cyclic symmetric Gaussian distribution with mean μ and covariance matrix Σ. Therefore, the channel posterior distribution p(h|y) in the space-frequency beam domain also belongs to a Gaussian distribution, and its mean and covariance are respectively

以下将基于信息几何方法，设计低复杂度的空频波束域信道估计方法。Where the superscript H is the conjugate transpose of the matrix or vector. It can be verified that the posterior mean (15) and the minimum mean square error (MMSE) estimation results are equivalent. The computational complexity of the posterior information of the space-frequency beam domain channel, including the posterior mean (15) and the posterior covariance (16), is

In the following, a low-complexity space-frequency beam domain channel estimation method will be designed based on the information geometry method.

It is understood by those skilled in the art that the perception matrix A in the received signal model (14) may have different forms in other channel statistical representation models, and any statistical inference problem that satisfies the received signal model (14) and the same Gaussian prior may be solved using information geometry methods, rather than being limited to beam domain channel estimation problems. Removing zeros from the received signal model (14) is intended to reduce the amount of computation, and is a preferred solution but not a necessity.

3. Information Geometry Method for Space-Frequency Beam Domain Channel Estimation

1. Establishment of original manifold, target manifold and auxiliary manifold

First, the set of Gaussian distributions is defined as the original manifold, specifically:

M _or :p(h)＝p _G (h；μ,Σ)＝exp{-(h-μ)Σ ^-1 (h-μ) ^H } (17)

的基础上，后验分布p(h|y)可以表示为where μ, Σ are the mean and covariance of the distribution p _G (h; μ, Σ) on the original manifold, respectively. Further, under the Gaussian assumption

Based on , the posterior distribution p(h|y) can be expressed as

为A的第n行；d_h＝f(0,-D^-1)，t_h＝f(h,I⊙(hh^T))，其中⊙为Hadamard积，函数f(a,A)＝[a^T,vec(A)^T]^T；符号

表示同维度矢量的操作符号，

C,ψ_q为归一化因子；c_n(h)为where _hi is the i-th element of h, _yn is the n-th element of y,

is the nth row of A; d _h = f(0, -D ^-1 ), t _h = f(h, I⊙(hh ^T )), where ⊙ is the Hadamard product, and the function f(a, A) = [a ^T , vec(A) ^T ] ^T ; the symbol

Represents the operation symbol of vectors of the same dimension,

C, _ψq is the normalization factor; c _n (h) is

Furthermore, the target manifold is defined as a set of Gaussian distributions whose elements are independent of each other, specifically:

分别为辅以计算的参数矢量和参数实对角矩阵，

为M维实对角矩阵的集合。上述目标流形为原始流形的子流形，目标流形上分布

的均值μ₀及方差Σ₀和θ₀,Θ₀的关系为in

are the parameter vector and parameter real diagonal matrix assisted by calculation,

is a set of M-dimensional real diagonal matrices. The above target manifold is a submanifold of the original manifold.

The relationship between the mean μ ₀ and variance Σ ₀ and θ ₀ , Θ ₀ is

Σ ₀ =(D ^-1 -Θ ₀ ) ^-1 (22)

Furthermore, we define N auxiliary manifolds, which are a set of Gaussian distributions whose covariance matrix is the inverse matrix of the sum of a diagonal matrix and a rank-1 matrix. The nth auxiliary manifold contains c _n (h), specifically:

上述辅助流形为原始流形的子流形，辅助流形上分布

的均值μ_n及协方差Σ_n和θ_n,Θ_n的关系为in

The auxiliary manifold is a submanifold of the original manifold.

The relationship between the mean μ _n and covariance Σ _n and θ _n , Θ _n is

Since the covariance matrix _Σn distributed on the auxiliary manifold is the inverse matrix of the sum of a diagonal matrix and a matrix of rank 1, it can be expanded using the Sherman-Morrison formula, so _Σn can be written as

2. Channel Estimation Method

The information geometry method for channel estimation is divided into four steps, namely, establishing the original manifold, auxiliary manifold and target manifold of the massive MIMO space-frequency beam domain channel, initializing the parameters distributed on the auxiliary manifold and the target manifold, calculating the m-projection distributed on the target manifold in the auxiliary manifold according to the parameters distributed on the auxiliary manifold, the received pilot signal and the space-frequency beam domain prior channel information, and updating the parameters distributed on the auxiliary manifold and the target manifold according to the m-projection. The step of establishing the original manifold, auxiliary manifold and target manifold of the massive MIMO space-frequency beam domain channel is shown in the previous section, and the subsequent steps are described in detail below.

(1) Initialize the parameters distributed on the auxiliary manifold and the target manifold

以及辅助流形参数

Set the initial value of the number of iterations t = 0 and initialize the target manifold parameters

And auxiliary manifold parameters

(2) Calculate the m-projection of the distribution in the auxiliary manifold on the target manifold

向目标流形m-投影，得到的分布记为

所述m-投影为在目标流形上寻找一个分布

使

和辅助流形上分布

之间的KL散度最小，即The m-projection of the distribution in the auxiliary manifold on the target manifold is calculated based on the parameters of the distribution on the auxiliary manifold, the received pilot signal, and the prior channel information in the space-frequency beam domain.

Projecting onto the target manifold m-, the resulting distribution is recorded as

The m-projection is to find a distribution on the target manifold

make

and the auxiliary manifold distribution

The KL divergence between is the smallest, that is

The KL divergence is defined as

表示关于概率分布p(x)的期望。给定辅助流形参数

KL散度可以表示为

其中c_p为常数。

可以表示为in

Represents the expectation about the probability distribution p(x). Given the auxiliary manifold parameters

The KL divergence can be expressed as

Where c _p is a constant.

It can be expressed as

Θ_on求偏导Further separate

Θ _on partial derivative

The upper horizontal line indicates taking the conjugate. Setting the partial derivative equal to 0 gives

Since the original manifold is an e-flat submanifold, the distribution on the auxiliary manifold belongs to the original manifold, and the target manifold is a submanifold of the original manifold, the m-projection of the distribution on the auxiliary manifold to the target manifold is unique. Therefore, the parameters obtained by the above first-order sufficient conditions are the parameters of the m-projection point. Combining equations (32) (33) and equations (24) (26), the m-projection result can be further sorted out as

(3) Update the parameters distributed on the auxiliary manifold and the target manifold

是对

的近似，辅助流形上分布的

是对

的近似。

在目标流形上的投影结果为The goal of information geometry methods is to find the probability distribution of the approximate posterior distribution on the auxiliary manifold and the target manifold respectively.

Yes

Approximation of, the distribution on the auxiliary manifold

Yes

Approximation of .

The projection result on the target manifold is

并根据辅助流形和目标流形的定义可以得到

是对c_n(h)的近似。进一步可以得到辅助流形和目标流形上分布的参数更新方式in

According to the definition of auxiliary manifold and target manifold, we can get

It is an approximation of c _n (h). We can further obtain the parameter update method distributed on the auxiliary manifold and the target manifold:

In order to make the algorithm more stable, the above iteration is relaxed, and the update of the parameters distributed on the auxiliary manifold and the target manifold can be further expressed as

Where 0≤α≤1.

远低于MMSE估计

的复杂度，从而支持同时估计大量用户的信道，有效地降低了导频开销。目标流形上分布的均值和方差即分别为空频波束域信道的后验均值和后验方差，具体为The number of iterations t=t+1 is further updated, and equations (34)(35)(39)(40)(41) are iterated until the preset number of iterations or the parameters distributed on the target manifold converge. In the above iterative process, the multiplication operation only involves the multiplication of an N-dimensional diagonal matrix and an N-dimensional vector, the multiplication of an N-dimensional diagonal matrix and an N-dimensional diagonal matrix, and the multiplication of a scalar and an N-dimensional vector. The number of multiplications of the above operations is M, so the computational complexity of each iteration is

Much lower than MMSE estimates

The complexity of , thus supporting the simultaneous estimation of channels for a large number of users, effectively reducing the pilot overhead. The mean and variance of the distribution on the target manifold are the a posteriori mean and a posteriori variance of the space-frequency beam domain channel, respectively, and are specifically

和后验方差

进一步通过采样空间舵矢量矩阵和采样频率舵矢量矩阵将各用户空频波束域信道的后验均值和后验方差转换为空间频率域信道的后验均值

和后验方差

具体为Furthermore, the posterior mean of each user's space-frequency beam domain channel is obtained through the non-zero element position of each user's space-frequency beam domain channel

and the posterior variance

The posterior mean and posterior variance of each user's space-frequency beam domain channel are further converted into the posterior mean of the space-frequency domain channel by sampling the space steering vector matrix and the sampling frequency steering vector matrix.

and the posterior variance

Specifically

It can be understood by those skilled in the art that when the information geometry method is applied to downlink channel estimation, its calculation process is basically the same as that of the uplink estimation. At this time, the received signal model (3) degenerates to contain only a single user, that is, the subscript k is only 1. Then, the application of the channel standard model, signal processing process and information geometry method is completely consistent with the uplink channel estimation. After obtaining the posterior statistical information of the channel, combined with channel prediction and other methods, each user terminal sends the obtained channel posterior statistical information to the base station. The base station side uses the sampling space steering vector matrix and the sampling frequency steering vector matrix to convert the obtained space-frequency beam domain channel posterior mean and posterior variance into the space-frequency domain channel posterior mean and posterior variance.

IV. Implementation Effect

In order to enable those skilled in the art to better understand the solution of the present invention, a comparison of the channel estimation performance results of the information geometry method in this embodiment and the existing method under two specific system configurations is given below.

First, the estimation performance results of the information geometry method in this embodiment are compared with the existing methods. The compared methods include MMSE estimation, the GAMP method proposed in the document "Generalized approximate message passing for estimation with random linear mixing, in IEEE ISIT, St. Petersburg, Russia, July 31-August 5, 2011, pp. 2168–2172.", and Algorithm 2 (hereinafter referred to as VEP) in the document "Unifying message passing algorithms under the framework of constrained bethe free energy minimization, IEEE Trans. Wireless Commun., vol. 20, no. 7, pp. 4144–4158, Jul. 2021.". Consider a massive MIMO system configured with N _r = 128, K = 48 and N _t = 1, where the base station antennas are configured with N _r,v = 8 and N _r,h = 16. Figure 4 shows a comparison of the channel estimation performance of the information geometry method in this embodiment with the GAMP and VEP methods at different signal-to-noise ratios in the uplink of the considered massive MIMO system. The maximum number of iterations of the information geometry method, GAMP and VEP are all set to 100 times. From Figure 4, it can be seen that under all signal-to-noise ratios, the information geometry method (IGA) can obtain channel estimation performance that is almost the same as MMSE estimation. When the channel estimation performance is -29dB, the signal-to-noise ratio gain of the information geometry method compared to GAMP and VEP is approximately 5dB. This shows that compared with the GAMP and VEP methods, the information geometry method in this embodiment can obtain more accurate channel estimation performance.

Next, a schematic diagram comparing the convergence curves of the information geometry method and the existing methods in this embodiment is given. Keeping the large-scale parameters under consideration unchanged, the signal-to-noise ratio is set to 20dB, and taking MMSE estimation as the performance baseline for reference, the convergence curves of the information geometry method, GAMP and VEP methods are drawn. From Figure 5, it can be found that the information geometry method (IGA) requires about 200 iterations to converge, and after convergence, its estimation performance is almost completely consistent with the MMSE estimation. The GAMP and VEP methods require more than 550 iterations to converge. This shows that compared with the existing algorithms, the information geometry method converges faster.

Based on the same inventive concept, an embodiment of the present invention discloses a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the computer device implements the above-mentioned large-scale MIMO channel estimation method applicable to a base station or a user terminal.

In a specific implementation, the device includes a processor, a communication bus, a memory, and a communication interface. The processor may be a general-purpose central processing unit (CPU), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits for controlling the execution of the program of the present invention. The communication bus may include a path to transmit information between the above components. The communication interface uses any transceiver-like device for communicating with other devices or communication networks. The memory may be a read-only memory (ROM) or other types of static storage devices that can store static information and instructions, a random access memory (RAM) or other types of dynamic storage devices that can store information and instructions, or an electrically erasable programmable read-only memory (EEPROM), a read-only compact disk (CD-ROM) or other optical disk storage, a disk storage medium or other magnetic storage device, or any other medium that can be used to carry or store the desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited thereto. The memory may be independent and connected to the processor via a bus. The memory may also be integrated with the processor.

The memory is used to store the application code for executing the scheme of the present invention, and the execution is controlled by the processor. The processor is used to execute the application code stored in the memory, thereby realizing the channel estimation method provided by the above embodiment. The processor may include one or more CPUs, or may include multiple processors, each of which may be a single-core processor or a multi-core processor. The processor here may refer to one or more devices, circuits, and/or processing cores for processing data (e.g., computer program instructions).

Based on the same inventive concept, an embodiment of the present invention discloses a massive MIMO communication system, including a base station and multiple user terminals, wherein the base station obtains a priori statistical information of the channel of each user terminal through uplink detection, and obtains a posteriori statistical information of each user terminal through the received uplink pilot signal and the a priori statistical information using an information geometry method. The specific channel estimation information geometry method is referred to the aforementioned embodiment and will not be described here.

Based on the same inventive concept, a large-scale MIMO communication system disclosed in an embodiment of the present invention includes a base station and multiple user terminals, wherein the user terminals obtain a priori statistical information of their respective channels through downlink channel detection, and obtain a posteriori statistical information of their respective channels through the received downlink pilot signal and the a priori statistical information using an information geometry method and a channel prediction method and feed it back to the base station. The specific channel estimation information geometry method is referred to the aforementioned embodiment and will not be described in detail here.

Based on the same inventive concept, an embodiment of the present invention discloses a large-scale MIMO communication system, including a base station and multiple user terminals, wherein the base station or the user terminal includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the computer program is loaded into the processor to implement the aforementioned large-scale MIMO channel estimation method. In the embodiments provided in the present application, it should be understood that the disclosed method can be implemented in other ways without exceeding the spirit and scope of the present application. The current embodiment is only an illustrative example and should not be used as a limitation, and the specific content given should not limit the purpose of the present application. For example, some features can be ignored or not performed.

The technical means disclosed in the scheme of the present invention are not limited to the technical means disclosed in the above-mentioned implementation mode, but also include technical schemes composed of any combination of the above-mentioned technical features. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications are also regarded as the protection scope of the present invention.

Claims (10)

1. A massive MIMO channel estimation method, comprising the following steps: The base station side/user terminal obtains a priori statistical information of the channel through uplink/downlink detection; The base station side/user terminal obtains the posterior statistical information of the channel by using the information geometry method through the received uplink/downlink pilot signal and prior statistical information; the information geometry method defines the set of probability density functions of Gaussian distribution as the original manifold, and constructs the target manifold and the auxiliary manifold according to the posterior distribution of the channel, the target manifold and the auxiliary manifold are both submanifolds of the original manifold, iteratively calculates the m-projection of the distribution in the auxiliary manifold on the target manifold, and updates the distribution in the target manifold and the auxiliary manifold according to the m-projection, and finally uses the mean and variance of the distribution on the target manifold as the posterior mean and posterior variance of the channel estimation; the target manifold is a set of probability density functions of a class of Gaussian distributions whose elements are independent of each other, and the auxiliary manifold is a set of probability density functions of a class of Gaussian distributions whose covariance matrix is the inverse matrix of the sum of a diagonal matrix and a matrix with a rank of 1. 2. The massive MIMO channel estimation method according to claim 1, wherein the m-projection is obtained by minimizing the KL divergence between the distribution in the auxiliary manifold and the target manifold. 3. The large-scale MIMO channel estimation method according to claim 1 is characterized in that the mean and covariance matrix of the distribution in the target manifold and the auxiliary manifold are represented by the parameter vector and parameter real diagonal matrix of the respective auxiliary calculations; wherein the covariance matrix of the distribution in the target manifold is represented as the inverse matrix of the difference between the inverse of the prior variance and the parameter real diagonal matrix, and the mean is represented by the product of the covariance and the parameter vector; the covariance of the distribution in the auxiliary manifold is represented as the inverse matrix of the difference between the inverse of the prior variance and the parameter real diagonal matrix and the sum of the rank-1 matrices, wherein the rank-1 matrix is represented by the corresponding rows in the perception matrix and the noise variance, and the mean is represented by the product of the covariance matrix and the parameter vector combined with the corresponding rows in the perception matrix, the corresponding elements of the received pilot signal vector, and the vector consisting of the noise variance. 4. The large-scale MIMO channel estimation method according to claim 2, wherein the covariance matrix of the auxiliary manifold is expanded using the Sherman-Morrison formula. 5. The method for massive MIMO channel estimation according to claim 1, wherein the step of obtaining the a posteriori mean and a posteriori variance of the channel by using information geometry method comprises: (1) Establishing the original manifold, target manifold, and auxiliary manifold of the massive MIMO channel; (2) Initialize the parameters distributed on the auxiliary manifold and the target manifold; (3) Calculate the m-projection of the distribution in the auxiliary manifold on the target manifold based on the parameters distributed on the auxiliary manifold, the received pilot signal, and the prior statistical information of the channel; (4) updating the parameters distributed on the auxiliary manifold and the target manifold according to the m-projection; repeating steps (3)-(4) until a preset number of iterations is reached or the parameters distributed on the target manifold converge. 6. The large-scale MIMO channel estimation method according to claim 1 is characterized in that the prior statistical information and the posterior statistical information of the space-frequency beam domain channel are calculated based on the space-frequency beam basis channel statistical characterization model, in which the space-frequency beam basis channel statistical characterization model is a space-frequency domain channel matrix obtained by multiplying the space-frequency beam domain channel matrix by the sampling space rudder vector matrix on the left and by the transposed matrix of the sampling frequency rudder vector matrix on the right, and each element of the space-frequency beam domain channel is statistically independent; for the base station side, the posterior mean and posterior variance of the space-frequency beam domain channel are converted into the posterior mean and posterior variance of the space-frequency domain channel by using the sampling space rudder vector matrix and the sampling frequency rudder vector matrix; for the user terminal side, the posterior statistical information of each space-frequency beam domain channel is fed back to the base station, and the base station side uses the sampling space rudder vector matrix and the sampling frequency rudder vector matrix to convert the obtained posterior mean and posterior variance of the space-frequency beam domain channel into the posterior mean and posterior variance of the space-frequency domain channel. 7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is loaded into the processor, the method for massive MIMO channel estimation according to any one of claims 1 to 6 is implemented. 8. A large-scale MIMO communication system, comprising a base station and multiple user terminals, characterized in that the base station is used to: obtain the prior statistical information of the channel of each user terminal through uplink detection; obtain the posterior statistical information of each user terminal by using the information geometry method through the received uplink pilot signal and the prior statistical information; the information geometry method defines a set of probability density functions of Gaussian distribution as the original manifold, and constructs a target manifold and an auxiliary manifold according to the posterior distribution of the channel, the target manifold and the auxiliary manifold are both submanifolds of the original manifold, iteratively calculates the m-projection of the distribution in the auxiliary manifold on the target manifold, and updates the distribution in the target manifold and the auxiliary manifold according to the m-projection, and finally uses the mean and variance of the distribution on the target manifold as the posterior mean and posterior variance of the channel estimation; the target manifold is a set of probability density functions of a class of Gaussian distributions whose elements are independent of each other, and the auxiliary manifold is a set of probability density functions of a class of Gaussian distributions whose covariance matrix is the inverse matrix of the sum of a diagonal matrix and a rank-1 matrix. 9. A large-scale MIMO communication system, comprising a base station and multiple user terminals, characterized in that the user terminals are used to: obtain a priori statistical information of each channel through downlink channel detection; obtain a posteriori statistical information of each channel through the received downlink pilot signal and the priori statistical information using information geometry methods and channel prediction methods and feed it back to the base station; the information geometry method defines a set of probability density functions of Gaussian distribution as the original manifold, and constructs a target manifold and an auxiliary manifold according to the posterior distribution of the channel, the target manifold and the auxiliary manifold are both submanifolds of the original manifold, iteratively calculate the m-projection of the distribution in the auxiliary manifold on the target manifold, and update the distribution in the target manifold and the auxiliary manifold according to the m-projection, and finally use the mean and variance of the distribution on the target manifold as the posterior mean and posterior variance of the channel estimation; the target manifold is a set of probability density functions of a class of Gaussian distributions whose elements are independent of each other, and the auxiliary manifold is a set of probability density functions of a class of Gaussian distributions whose covariance matrix is the inverse matrix of the sum of a diagonal matrix and a rank-1 matrix. 10. A large-scale MIMO communication system, comprising a base station and multiple user terminals, characterized in that the base station or the user terminal comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when loaded into the processor, implements the large-scale MIMO channel estimation method according to any one of claims 1 to 6.

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