CN114665932B - Large-scale MIMO beam delay Doppler domain statistical channel information acquisition method - Google Patents

Abstract

The invention discloses a method for acquiring statistical channel information of a large-scale MIMO beam delay Doppler domain, wherein a beam delay Doppler domain channel model related in the method is based on a refined sampling steering vector matrix, and is closer to a physical channel model compared with the traditional beam domain channel model based on a DFT matrix. The invention provides a method for acquiring prior statistical channel information and posterior statistical channel information of a large-scale MIMO beam delay Doppler domain, wherein the method for acquiring the prior statistical channel information comprises a pilot signal-based method for acquiring the prior statistical channel information and a method for acquiring the prior statistical channel information under the condition of known instantaneous channel information, and the posterior statistical channel information comprises posterior channel mean and variance information. The method has lower complexity, can be applied to a practical large-scale MIMO system, provides support for a channel estimation and robust precoding transmission method, and has higher application value.

Description

Statistical Channel Information Acquisition Method in Massive MIMO Beam Delay-Doppler Domain

technical field

The invention belongs to the technical field of communication, and relates to a method and a system for acquiring statistical channel information in a massive MIMO beam delay Doppler domain.

Background technique

Massive Multiple-Input Multiple-Output (MIMO, Multiple-Input Multiple-Ouput) is one of the key technologies of the 5G wireless communication network. Massive MIMO greatly improves system capacity by using a large number of antennas in a base station (BS, Base Station), and makes full use of spatial dimension resources. In massive MIMO systems, multi-user MIMO (MU-MIMO) significantly enhances the transmission on the same time and frequency resources. As for the antenna array equipped on the base station side, a Uniform Plane Array (UPA, Uniform Plane Array) has been widely used in an actual massive MIMO system due to its compact size.

For massive MIMO systems, a commonly used channel statistical model in the literature is a traditional beam domain channel model based on a discrete Fourier transform (DFT, Discrete Fourier Transform) matrix. However, the traditional beam domain channel model will deviate from the actual physical channel model to a considerable extent. For this reason, a refined beam-domain statistical channel model based on an oversampled DFT matrix is proposed in the literature. By finely sampling the direction cosine, it is closer to the physical channel model when the antenna size is limited. In order to solve the problem of massive MIMO under the limited antenna size The universality problem of typical mobile scenarios provides the basis of the model. The model can also be extended to the beam-delay-Doppler domain, which also leads to performance gains for channel estimation. To obtain these performance gains in massive MIMO systems, the statistical parameters in the channel model need to be known in advance. Although the statistical parameters of the beam delay Doppler domain are very important, the problem of estimating these parameters is not addressed in the literature.

In the literature, statistical channel information is usually obtained based on estimated instantaneous channel information, or by an expectation-maximization algorithm that iteratively estimates instantaneous and statistical information. There are also literatures that directly obtain the covariance matrix without involving instantaneous channel state information. For the massive MIMO beam-delay-Doppler domain channel model, the statistical channel information acquisition problem becomes to obtain the channel power matrix in the beam-delay-Doppler domain, which has not been solved in the literature. In beam-delay-Doppler domain channel models, the angular delay domain or beam domain channel coefficients are sparse due to the limited number of resolvable multipaths. When noise is absent, the considered problem can also be viewed as a Multiple Measure Vectors (MMV) problem, which is a classic compressed sensing problem. The M-FOCUSS (MMV focal Underdefined system solver) algorithm can be used to solve this problem and obtain instantaneous channel information, which is then used to calculate statistical channel information.

However, noise is always present in wireless communication systems. In addition, the dimensionality of the MMV problem in the considered massive MIMO is too high, the computational complexity of the M-FOCUSS method is not satisfactory, and the M-FOCUSS method needs to acquire instantaneous channel information. Beam delay Doppler domain statistical channel information can also be used to improve the estimation performance of instantaneous channel information in practical massive MIMO systems. Therefore, before estimating the instantaneous channel information, it is better to obtain the statistical channel information of the problem under consideration. In conclusion, we need a new low-complexity approach to estimate beam delay Doppler-domain statistical channel information.

Contents of the invention

Technical problem: Aiming at the deficiencies of the existing technology, the purpose of the present invention is to provide a massive MIMO beam delay Doppler domain statistical channel information acquisition method, which can provide support for massive MIMO channel estimation and robust precoding transmission methods.

Technical solution: In order to achieve the above purpose, the present invention provides a massive MIMO beam delay Doppler domain statistical channel information acquisition method, including beam delay Doppler domain prior statistical channel information acquisition method and beam delay Doppler domain A method for obtaining a posteriori statistical channel information in the Le domain; the method for obtaining the channel information a priori statistics in the beam delay Doppler domain is divided into a method for obtaining a priori statistical information in the beam delay Doppler domain based on a pilot signal and a known instantaneous A method for obtaining prior statistical information in the beam delay Doppler domain in the case of channel information; the beam delay Doppler domain posterior statistical channel information includes the beam delay Doppler domain posterior mean value and the beam delay Doppler domain Le domain posterior variance.

Further, the method for obtaining prior statistical information of the beam delay Doppler domain based on the pilot signal includes the following steps:

Step A1, each mobile terminal transmits a pilot signal X _k on the same time-frequency resource, where k represents the user number; the transmission pilot signal X _k is the frequency domain transmission pilot signal X _{f, k} and the time domain transmission pilot Frequency signal X _{t, Kronecker product between k} ;

Step A2, the pilot signal Y _m received on the M time slots is multiplied by the space refined sampling steering vector matrix transposition matrix V ^T from the left and the pilot base time delay Doppler refined sampling steering vector matrix by right multiplication The yoke transpose matrix PH is converted to the beam delay Doppler domain V ^T Y _m P ^H , where m=1, 2,..., M, and the superscripts T and H represent transpose ^and conjugate transpose respectively;

与波束时延多普勒域总体参数函数T_rΩT_f+O_rNO_f之间的Kullback-Leibler(KL)散度获取多用户波束时延多普勒域先验统计信道信息Ω，其中上标*表示共轭；所述波束时延多普勒域总体参数函数中T_r，T_f，O_r，N，O_f均为已知矩阵；Step A3, by minimizing the beam delay Doppler domain sample statistics

The Kullback-Leibler (KL) divergence between T _r ΩT _f +O r NO _f and the global parameter function T r ΩT f +O _r NO f in the beam delay Doppler domain obtains the multi-user beam delay Doppler domain prior statistical channel information Ω, where the above The mark * indicates conjugation; T _r , T _f , O _r , N, and O _f in the overall parameter function in the beam delay Doppler domain are all known matrices;

Step A4, using the multi-user beam delay-Doppler domain prior statistical channel information Ω to recover the beam delay-Doppler domain prior statistical channel information Ω _k of each mobile terminal, where k represents the user number.

Further, the frequency-domain transmission pilot signal in step A1 is designed as multiple phase-shifted Zadoff-Chu (ZC) sequences, and the time-domain transmission pilot is designed as a repeated pilot.

Further, as described in step A3, the multi-user beam delay Doppler domain a priori statistical channel is obtained by minimizing the KL divergence between the beam delay Doppler domain sample statistics and the beam delay Doppler domain overall parameter function Information includes the following steps:

Step A3-1, initialize the number of iterations and multi-user beam delay Doppler domain a priori statistical channel information, and set an appropriate initial step size, minimum step size and correction factor;

Step A3-2, calculate the gradient function, and use the gradient descent method to update the multi-user beam delay Doppler domain prior statistical channel information;

Step A3-3, calculate the objective function value, if the objective function value becomes larger, reduce the step size according to the correction factor, and jump to step A3-2;

Step A3-4, update the number of iterations, and repeat steps A3-2 to A3-3 until the maximum number of iterations is reached or the step size is smaller than the minimum step size.

Further, fast Fourier transform is used in the process of calculating the gradient function described in step A3-2 to reduce complexity.

Further, the method for obtaining prior statistical information of beam delay Doppler domain in the case of known instantaneous channel information includes the following steps:

Step B1, obtaining the instantaneous channel information H _k,m of each user on M time slots, where m=1, 2,..., M, k is the user number;

Step B2, multiplying the instantaneous channel information H _{k and m} on the M time slots by left-multiplying the delay-Doppler refined sampling steering vector matrix conjugate transpose matrix U ^H and right-multiplying the space refined sampling steering vector matrix V is transformed into the beam delay Doppler domain U ^H H _k,m V, where the superscript H denotes the transpose;

与波束时延多普勒域总体参数函数T_krΩ_kT_kt之间的KL散度获取各移动终端波束时延多普勒域先验统计信道信息Ω_k，其中上标*表示共轭；所述波束时延多普勒域总体参数函数中T_kr，T_kt均为已知矩阵。Step B3, by minimizing the beam delay Doppler domain sample statistics

The KL divergence between the overall parameter function T _kr Ω _k T _kt and the beam delay Doppler domain obtains the prior statistical channel information Ω _k of the beam delay Doppler domain of each mobile terminal, where the superscript * represents the conjugate; Both T _kr and T _kt in the global parameter function in the beam delay Doppler domain are known matrices.

Further, in step B3, the beam delay Doppler domain prior statistics of each mobile terminal are obtained by minimizing the KL divergence between the beam delay Doppler domain sample statistics and the beam delay Doppler domain overall parameter function Channel information includes the following steps:

Step B3-1, initialize the number of iterations and the prior statistical channel information in the Doppler domain of the beam delay of each mobile terminal, and set the appropriate initial step size, minimum step size and correction factor;

Step B3-2, calculate the gradient function, and use the gradient descent method to update the prior statistical channel information of the beam delay Doppler domain of each mobile terminal;

Step B3-3, calculate the objective function value, if the objective function value becomes larger, reduce the step size according to the correction factor, and jump to step B3-2;

Step B3-4, update the number of iterations, and repeat steps B3-2 to B3-3 until the maximum number of iterations is reached or the step size is smaller than the minimum step size.

Further, fast Fourier transform is used in the process of calculating the gradient function described in step B3-2 to reduce complexity.

Further, the method for obtaining channel information in the beam delay Doppler domain a posteriori statistics includes the following steps:

Step C1, using the pilot-based acquisition method of beam delay Doppler domain a priori statistical channel information or the acquisition method of beam delay Doppler domain a priori statistical information in the case of known instantaneous channel information, to obtain The beam delay Doppler domain prior statistical channel information Ω _k of each user terminal before the current time slot, where k is the user number;

Step C2, obtaining the pilot signal sent by each user terminal in the current time slot;

Step C3, using the received pilot signal to estimate the beam delay Doppler domain channel matrix G _k,m-1,1 , combined with the beam delay Doppler domain prior statistical channel information and inter-channel correlation factor β _{k, m} acquires the beam delay Doppler domain posterior statistical channel information of each user terminal, where m represents the slot number; the beam delay Doppler domain posterior statistical channel information includes the posterior average β _{k, m} G _{k , m-1, 1} and the posterior variance

Description of drawings

Fig. 1 is a flowchart of a method for acquiring channel information based on massive MIMO beam delay Doppler domain a priori statistics based on pilot signals;

Fig. 2 is a flowchart of a method for obtaining prior statistical channel information in the massive MIMO beam delay Doppler domain under the condition of known instantaneous channel information;

3 is a flow chart of a method for obtaining a posteriori statistical channel information in the massive MIMO beam delay Doppler domain;

Fig. 4 is a comparison result diagram of the prior statistical information estimation accuracy between the patent scheme and the M-FOCUSS algorithm.

Fig. 5 is a performance comparison result graph when the patented solution and the prior statistical information estimated by the M-FOCUSS algorithm are applied to instantaneous channel parameter estimation.

Detailed ways

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

As shown in Fig. 1, the massive MIMO beam delay Doppler domain prior statistical channel information acquisition method based on the pilot signal disclosed in the embodiment of the present invention includes: each mobile terminal sends the pilot signal on the same time-frequency resource ;Convert the pilot signals received on multiple time slots to the beam delay Doppler domain; use the beam delay Doppler domain sample statistics to obtain the multi-user beam delay Doppler domain prior statistical channel Information: using the multi-user beam delay-Doppler domain prior statistical channel information to recover the beam delay-Doppler domain prior statistical channel information of each mobile terminal.

As shown in Figure 2, another embodiment of the present invention discloses a massive MIMO beam delay Doppler domain prior statistical channel information acquisition method under the condition of known instantaneous channel information, including: The instantaneous channel information on the network; the instantaneous channel information is converted into the beam delay Doppler domain; and the beam delay Doppler domain sample statistics are used to obtain the prior statistical channel information of each mobile terminal in the beam delay Doppler domain.

As shown in FIG. 3 , the massive MIMO beam domain a posteriori statistical channel information acquisition method disclosed in the embodiment of the present invention includes: obtaining the beam delay Doppler domain a priori statistical channel information of each user terminal before the current time slot; Obtain the pilot signal sent by each user terminal in the current time slot; use the received pilot signal to estimate the beam delay Doppler domain channel matrix, and combine the beam delay Doppler domain prior statistical channel information and inter-channel correlation factors to obtain The beam delay Doppler domain posterior statistics channel information of each user terminal.

The method of the invention is mainly applicable to a massive MIMO system in which a base station side is equipped with a large-scale antenna array to serve multiple users simultaneously. The specific implementation process of the present invention related to the beam delay Doppler domain statistical channel information acquisition method will be described in detail below in conjunction with specific communication system examples. The same applies to system models for other configurations.

1. System configuration

Consider a 3D massive MIMO frequency selective fading system model, the downlink includes a base station (BS) and K users (UEs). The base station is equipped with large-scale uniform area array antennas, and each antenna is a dual-polarized antenna. The number of antennas in the vertical and horizontal directions is M _z and M _x respectively, and the total number of antennas on the base station side is M _t = M _z M _x . For simplicity, it is assumed that each user configures a single antenna. The system Doppler resource is divided into several time slots, each time slot includes M _b Doppler blocks, and each Doppler block includes M _d symbol intervals. The massive MIMO system considered in this embodiment works in Time Division Duplexing (TDD, Time Division Duplexing) mode. For simplicity, it is assumed that there are only uplink channel training and downlink transmission phases, and the downlink transmission includes precoding field pilot and data signal transmission. In each time slot, the base station only receives user uplink pilot signals in the first Doppler block. The 2nd to M _b Doppler blocks are used by the base station to transmit pilot and data signals in the downlink precoding domain. The length of the uplink training sequence is the length of the block, that is, T symbol intervals. For the Frequency Division Duplexing (FDD, Frequency Division Duplexing) mode, the uplink channel training phase can be replaced by the downlink channel feedback phase, and the downlink transmission phase remains unchanged. Specifically, the downlink omnidirectional pilot signal is transmitted in the first block, and the feedback from the mobile terminal is received.

2. Refined Beam Delay Doppler Domain Prior Statistical Channel Model

The following is a detailed description of the refined beam delay Doppler domain prior statistical model based on the refined sampling steering vector matrix. In the traditional beam domain channel model, the number of spatial steering vectors is the same as the number of antennas. The refined beam delay Doppler domain statistical model introduced in the channel model is more spatial steering vectors than the number of antennas. Delay domain and Doppler domain are refined to better describe channel statistics. Firstly, the definitions related to OFDM are given. T _c represents the Doppler interval of OFDM symbols, Δf=1/T _c represents the subcarrier spacing, and the number of subcarriers is M _c , where M _p subcarriers are used to transmit pilots, and the length of the cyclic prefix is is M _g .

First, the refined beam domain channel model under a single subcarrier is considered, and then extended to the refined beam delay Doppler domain channel model. Consider a stationary uncorrelated scattering channel model. The carrier frequency is f _c , the speed of light is c, and d represents the antenna spacing of the receiving end linear array (ULA). Suppose there are P _u resolvable paths between BS and user u. Let τu _,p,m denote the propagation delay on the mth antenna of BS and the pth path of user u, expressed as follows

τ _{u, p, m} = τ _{u, p} + (m-1)ΔτΩ _{u, p} (1)

Where Δτ=d/c, τ _u,p represent the propagation delay of user u and the first antenna of ULA on the p-th path. Ω _u,p = cos θ _u,p is the direction cosine with respect to the uplink angle of arrival (AoA) or downlink angle of departure (AoD). The impulse response of the uplink time-varying channel user u to the mth antenna of the BS is expressed as follows

where αu _,p is a complex-valued random gain. Assuming that the p-th path contains Q _p sub-paths with the same propagation delay, then α _{u, p} is expressed as follows

where β _{u, p, q} , φ _{u, p, q} , v _{u, p, q} denote the gain, initial phase and Doppler frequency shift of sub-path q, respectively. Assume that φ _{u, p, q} are uniformly distributed on [0, 2π). When Q _p tends to infinity, α _u,p (t) can be regarded as a zero-mean complex Gaussian random process. Then the uplink channel from user u to base station BS can be obtained as

in

g _{u, p} (t, τ) = α _{u, p} (t) δ(τ--τ _{u, p} ) (5)

g(Ω, τ) = [g ₁ (Ω, τ), ..., g _M (Ω, τ)] ^T (6)

是h_u(t，τ)的傅立叶变换。用户u到基站在第k个子载波第l个符号上的上行信道频率响应表示为make

is the Fourier transform of h _u (t, τ). The uplink channel frequency response from user u to the base station on the lth symbol of the kth subcarrier is expressed as

Further, get the frequency response of the uplink channel

in

表示采样数。集合

其中

的取值范围为

令

表示用户u的方向余弦集。因此h_u，l，k表示为represents the steering vector for the kth subcarrier. Next, Ω is uniformly sampled. make

Indicates the number of samples. gather

in

The range of values is

make

Represents the set of direction cosines of user u. Hence h _u,l,k is expressed as

则h_u，l，k可以近似表示为make

Then h _{u, l, k} can be approximately expressed as

in

定义第k个子载波处的采样导向矢量矩阵为The beam domain channel from user u to the base station on the kth subcarrier of the lth symbol can be expressed as

Define the sample steering vector matrix at the kth subcarrier as

Finally (12) can be written as

The above is deduced when the ULA line array is configured on the base station side. The following will be extended to the uniform area array (UPA), and the delay Doppler domain will be introduced at the same time. In UPA, d _z and d _x represent the antenna spacing in the vertical and horizontal directions of the receiving end area array respectively. The sampling matrix V is obtained by replacing the original DFT matrix with the oversampled DFT matrix. Let M′ _z , M′ _x , M′ _c , and M′ _d be vertical antenna direction, horizontal antenna direction, time delay, and Doppler refinement factors, respectively. Then N _z ＝M _z M′ _z , N _x ＝M _x M′ _x , N _p ＝M _p M′ _p , N _d ＝M _d M′ _d are the vertical antenna direction cosine v=cosθ and the horizontal antenna direction cosine respectively u=sinθcosφ, normalized delay τ, normalized Doppler f sampling number, where θ and φ are the polar angle and azimuth angle of the downlink departure angle or uplink arrival angle on the BS side respectively. According to formula (10), the vertical antenna direction cosine, horizontal antenna direction cosine, (normalized) time delay, and (normalized) Doppler refined sampling steering vector can be obtained as

Where v _n =2(n-1)/N _x , u _m =2(m-1)/N _z , τ _q =(q-1)/N _p , fl=(l-1)/N _d . According to the stacking method of (14), the vertical and horizontal antenna direction cosine refined sampling steering vector matrices, and the delay and Doppler refined sampling steering vector matrices are as follows

就足够描述信道特性，其中

令N_t＝N_zN_x则

为空间精细化采样导向矢量矩阵。得到信道模型Since the normalized delay range is τ∈[0, N _g /N _c ), then

is sufficient to describe the channel characteristics, where

Let N _t ＝N _z N _x then

Sampling steering vector matrix for spatial refinement. get channel model

为第k个用户空间频率时间空间域信道，

为第k个用户波束频率时间域信道。假设

为波束时延多普勒域信道，W为独立同分布复高斯随机变量组成的随机矩阵，M_k为第k个用户的波束时延多普勒域信道的幅度矩阵。并定义第k个用户的波束时延多普勒域信道的能量矩阵为Ω_k＝M_k⊙M_k，Ω_k即为所述波束时延多普勒域先验统计信道信息。波束时延多普勒域信道与波束频率时间域信道可以通过如下式子进行转化in

is the kth user space frequency time space domain channel,

is the frequency-time domain channel of the kth user beam. suppose

is the beam delay Doppler domain channel, W is a random matrix composed of independent and identically distributed complex Gaussian random variables, and M _k is the amplitude matrix of the beam delay Doppler domain channel of the kth user. The energy matrix of the channel in the beam delay Doppler domain of the kth user is defined as Ω _k =M _k ⊙M _k , and Ω _k is the prior statistical channel information in the beam delay Doppler domain. Beam delay Doppler domain channel and beam frequency time domain channel can be converted by the following formula

将(25)式代入(24)式得到完整信道模型Delay-Doppler refined sampling steering vector matrix

Substitute (25) into (24) to get the complete channel model

Compared with the traditional beam-domain prior statistical channel model based on DFT matrix, the refined statistical model has more statistical feature directions, so it can more accurately represent the actual physical channel model.

3. Acquisition method of beam delay Doppler domain prior statistics channel information based on pilot signal

1. Reception model based on pilot signal

For the considered massive MIMO system working in TDD mode, due to the reciprocity of uplink and downlink channels, the obtained uplink channel statistics can be directly used as downlink channel statistics. For FDD system channel instantaneous reciprocity does not exist, the downlink statistical channel information can be acquired by the user side and fed back to the base station. A method for acquiring channel information based on pilot signal-based refined beam delay Doppler domain a priori statistics is given below.

In this embodiment, each mobile terminal transmits a pilot signal X _k on the same time-frequency resource, where k represents the user number; the transmission pilot signal X _k is the frequency domain transmission pilot signal X _{f, k} and the time domain Send pilot signal X _{t, the Kronecker product between k} . The frequency domain transmission pilot sequence is designed as a phase-shifted multiple Zadoff-Chu (ZC) sequence, and its pilot allocation idea is to divide K users into Q groups, each group has P users, and users in different groups use ZC sequences with different roots, different users in the same group use different phase shift sequences, replace the user’s table below k with q, p without causing confusion, where q, p represent the root coefficient and cyclic shift coefficient respectively , so the frequency domain transmission pilot sequence of the kth user (or the pth user under the qth root) can be specifically expressed as

in

其中diag表示对角化函数。发送导频矩阵可以表示为Among them, N _l is the smallest prime number larger than M _p . The pilots sent in the time domain are designed as repeated pilots, that is, the pilots sent at different times on the same subcarrier are the same. Then the frequency domain transmission pilot matrix and the time domain transmission pilot matrix are respectively X _{f, k} = diag(x _{q, p} ) and

where diag represents the diagonalization function. The transmit pilot matrix can be expressed as

I_M表示M维单位阵。基于以上发送导频，接收导频信号矩阵可以表示为in

I _M represents an M-dimensional unit matrix. Based on the above transmitted pilots, the received pilot signal matrix can be expressed as

的复高斯白噪声矩阵，其中各元素假设独立同分布。由于Among them, I _{M, N} = [I _M , 0] is an M×N-dimensional matrix, 0 is a matrix of all 0s, and Z is a power of

The complex white Gaussian noise matrix of , where the elements are assumed to be independent and identically distributed. because

表示位移长度为n的N维循环位移矩阵。于是接收导频信号矩阵的表达式可以整理为in

Represents an N-dimensional cyclic displacement matrix with displacement length n. Then the expression of the received pilot signal matrix can be organized as

以及

根据循环移位矩阵的性质，如果不同下标p下

的元素在G_q中的分布是不重叠的，则需要满足P≤N_p/N_f。接着，记G＝[G₁，...，G_Q]以及

G，P分别称为多用户波束时延多普勒域信道以及导频基时延多普勒精细化采样导向矢量矩阵。并记M＝[M₁，...，M_Q]。则接收导频信号模型可以写为remember

as well as

According to the nature of the cyclic shift matrix, if the subscript p is different

The distribution of the elements in G _q is non-overlapping, and P≤N _p /N _f needs to be satisfied. Next, record G=[G ₁ , . . . , G _Q ] and

G and P are respectively called the multi-user beam delay-Doppler domain channel and the pilot base delay-Doppler refined sampling steering vector matrix. And record M=[M ₁ , . . . , M _Q ]. Then the received pilot signal model can be written as

Y＝V ^* GP+Z (33)

于是，基于导频信号的波束时延多普勒域先验统计信道信息获取问题即为根据多个时隙的接收导频信号估计能量矩阵Ω。Define the multi-user beam delay-Doppler domain channel energy matrix Ω=M⊙M, Ω is also called the multi-user beam delay-Doppler domain prior statistical channel information. When P≤N _p /N _f , if Ω is obtained accurately, the beam delay Doppler domain channel energy matrix of each user can be recovered losslessly

Therefore, the problem of acquiring channel information based on the beam delay-Doppler domain a priori statistics of pilot signals is to estimate the energy matrix Ω according to the received pilot signals of multiple time slots.

2. Acquisition method of beam delay Doppler domain prior statistics channel information

Next, the channel energy matrix is obtained by using the minimum Kullback-Leibler (KL) divergence criterion through receiving pilot signals of multiple time slots. Define the overall parameter function Φ in the beam delay Doppler domain as

After substituting the specific expression of Y, we can get

Φ＝T _r ΩT _f +O _r NO _f (35)

in,

T _r ＝(V ^T V ^* )⊙(V ^T V ^* ) ^* (36)

T _f ＝(PP ^H )⊙(PP ^H ) ^* (37)

where 1 represents an all-ones matrix. In order to estimate the channel energy matrix Ω from Φ, first define the objective function f(M) as the KL divergence between Φ and T _r ΩT _f +O _r NO _f

Transform this problem into an optimization problem

M ^★ ＝argmin _M f(M) (40)

It can be found that several items in f(M _k ) have nothing to do with M _k , so the above problem is simplified as

M ^★ ＝argmin _M g(M) (41)

where g(M) is expressed as

In order to solve this optimization problem, the derivative of g(M) with respect to M needs to be calculated. The derivatives of the two terms in g(M) with respect to M are given below,

Among them, Q is

Then the gradient of g(M) can be expressed as

Using the gradient method to solve the objective function, the following iterative equation is obtained

Where δ is the step size of the gradient method, and the step size of each iteration can be determined by line search. The idea of line search is: calculate the size of the objective function in each iteration, and reduce the step size if the value of the objective function increases in this iteration. long, and repeat the above steps until the value of the objective function decreases. M can be finally obtained through multiple iterations. It is worth emphasizing that when calculating Φ, the sample statistics of (V ^T YP ^H )⊙(V ^T YP ^H ) ^* on multiple time slots are used instead.

To sum up, the acquisition method of beam delay Doppler domain prior statistics channel information based on pilot signal is as follows:

Step 1: Each mobile terminal transmits a pilot signal X _k on the same time-frequency resource, where k represents the user number; the transmitted pilot signal X _k is the frequency domain transmission pilot signal X _{f, k} and the time domain transmission pilot Signal X _{t, Kronecker product between k} ;

Step 2: The pilot signal Y _m received on the M time slots is multiplied by the space refined sampling steering vector matrix transposition matrix V ^T on the left and the pilot base delay Doppler refined sampling steering vector matrix by right multiplication Yoke transpose matrix ^PH transforms to beam delay Doppler domain V ^T Y _m P ^H , where m=1, 2, ..., M;

与波束时延多普勒域总体参数函数T_rΩT_f+O_rNO_f之间的KL散度获取多用户波束时延多普勒域先验统计信道信息Ω；所述波束时延多普勒域总体参数函数中T_r，T_f，O_r，N，O_f均为已知矩阵；Step 3: By minimizing the beam delay Doppler domain sample statistics

The KL divergence between T _r ΩT _f +O r NO _f and the overall parameter function T r ΩT f +O _r NO f of the beam delay Doppler domain obtains the prior statistical channel information Ω of the beam delay Doppler domain; the beam delay Doppler T _r , T _f , O _r , N, O _f in the general parameter function of Le domain are all known matrices;

Step 4: Using the multi-user beam delay-Doppler domain prior statistical channel information Ω to recover the beam delay-Doppler domain prior statistical channel information Ω _k of each mobile terminal.

The above step 3 obtains the multi-user beam delay Doppler domain a priori statistical channel information by minimizing the KL divergence between the beam delay Doppler domain sample statistics and the beam delay Doppler domain overall parameter function Can be further refined into:

Step 1: Initialize the number of iterations as t=0, initialize M ^t , set the appropriate initial step size δ ⁰ , minimum step size δ _min and correction factor 0<α<1;

Step 2: Calculate Gradients

Among them, [Q] _ij needs to be updated as follows with M ^t :

update using gradient descent

Step 3: Calculate the size of the objective function f(M ^t+1 ), f(M ^t ), if f(M ^t+1 )≥f(M ^t ), update the step size δ ^t = αδ ^t , and jump to Step 2;

Step 4: Update the number of iterations t=t+1, repeat steps 2 to 3 until the maximum number of iterations or step size δ ^t <δ _min is reached, and calculate Ω ^t =M ^t ⊙M ^t .

3. Quick implementation method

其中N＝N_xN_zN_cN_d；而其他运算的计算复杂度均不高于

因此降低算法复杂度的关键在于简化T_rΩT_f以及T_rQT_f的计算。下面利用循环阵性质对其进行计算上的简化。其中循环阵为Computational complexity is measured by a complex multiplier. Among the above-mentioned beam delay Doppler domain prior statistical channel information acquisition methods based on pilot signals, the most complex one is the calculation of T _r ΩT _f and T _r QT _f in the gradient function , the computational complexity of directly using matrix multiplication is

Among them, N＝N _x N _z N _c N _d ; while the computational complexity of other operations is not higher than

Therefore, the key to reducing the complexity of the algorithm is to simplify the calculation of T _r ΩT _f and T _r QT _f . In the following, it is simplified in calculation by using the property of cyclic matrix. where the cyclic matrix is

First, a lemma about cyclic matrices is given:

E=I _{M, N} F _N is an oversampled DFT matrix, where I _{M, N} = [I _M , 0 _{M, NM} ], M≤N, I _M , OM _{, NM} represent the M-dimensional unit matrix and M× (NM) dimensional zero matrix, F _N is an N-dimensional DFT array; D=diag(d) is an M-dimensional diagonal matrix, and d is an M-dimensional real vector. Then the matrix (E ^H DE)⊙(E ^H DE) is a cyclic matrix, which can be specifically expressed as

where the matrix function A(d) with respect to the vector d is

It can be proved that when the refinement factors M′ _z , M′ _x , M′ _c , and M′ _d are integers, and the distance between the base station antennas is half a wavelength, V _x , V _z , U _c , U _d are oversampled DFT Array. According to the above lemma, it can be obtained that T _r and T _f both have the following structure

Where 1 _{M, 1} represents the M-dimensional column vector, ∑ is the block diagonal matrix

其中N＝N_xN_zN_pN_d，T为迭代次数。Therefore, the calculation of T _r ΩT _f and T _r QT _f can be realized by fast Fourier transform. The computational complexity is measured by the complex multiplier, and the computational complexity of the algorithm implemented by fast Fourier transform is

Where N=N _x N _z N _p N _d , T is the number of iterations.

4. Acquisition method of beam delay Doppler domain a priori statistical channel information under known instantaneous channel information

The method of obtaining the prior statistical channel information in the beam delay Doppler domain by using the pilot signal is described above. In an actual system, the instantaneous channel information can also be obtained first, and then the instantaneous channel information can be used to estimate the beam delay Doppler domain a priori statistical channel information. A method for acquiring the prior statistical channel information Ω _k in the beam delay Doppler domain is given below when the instantaneous channel information is known. Multiply H _k to the left by U ^H and right to V to get

U ^H H _k V＝U ^H U(M _k ⊙W)V ^H V (54)

Further, there are

At this time, the overall parameter function Φ _k in the beam delay Doppler domain becomes

or expressed element-wise as

Further, one can get

Φ _k ＝ T _kr Ω _k T _kt (58)

At this time, T _kr =(U ^H U)⊙(U ^H U) ^* , T _kt =(V ^H V)⊙(V ^H V) ^* . The KL divergence function of Φ _k and channel energy matrix function matrix T _kr Ω _k T _kt simplifies to

g(M _k )＝-∑ _ij [Φ _k ] _ij log[T _kr Ω _k T _kt ] _ij +∑ _ij [T _kr Ω _k T _kt ] _ij +c ₀ (59)

In the above formula, c ₀ is a constant irrelevant to M _k . Similarly, in order to obtain M _k with the smallest KL divergence for optimization, the objective function is derived first,

最后得到g(M_k)的梯度为where J is a matrix of all 1s,

Finally, the gradient of g(M _k ) is obtained as

Using the gradient method to solve the objective function, the following iterative equation is obtained

Where δ _k is the step size of the gradient method of the kth user, and the step size of each iteration can be determined by line search. Multiple iterations can finally obtain Mk.

In summary, the beam delay Doppler domain a priori statistical channel information acquisition method in the case of known instantaneous channel information:

Step 1: Obtain the instantaneous channel information H _k,m of each user on M time slots, where m=1, 2,..., M, k is the user number;

Step 2: Multiply the instantaneous channel information H _{k and m} on the M time slots by the delay-Doppler refined sampling steering vector matrix conjugate transpose matrix U ^H and the space refined sampling steering vector matrix V converted to the beam delay Doppler domain U ^H H _k,m V;

与波束时延多普勒域总体参数函数T_krΩ_kT_kt之间的KL散度获取各移动终端波束时延多普勒域先验统计信道信息Ω_k，其中上标*表示共轭；所述波束时延多普勒域总体参数函数中T_kr，T_kt均为已知矩阵。Step 3: By minimizing the beam delay Doppler domain sample statistics

The KL divergence between the overall parameter function T _kr Ω _k T _kt and the beam delay Doppler domain obtains the prior statistical channel information Ω _k of the beam delay Doppler domain of each mobile terminal, where the superscript * represents the conjugate; Both T _kr and T _kt in the global parameter function in the beam delay Doppler domain are known matrices.

In the above step 3, the prior statistical channel in the beam delay Doppler domain of each mobile terminal is obtained by minimizing the KL divergence between the sample statistics in the beam delay Doppler domain and the overall parameter function in the beam delay Doppler domain Information can be further refined into:

设置合适的初始步长

最小步长δ_k，min以及修正因子0＜α＜1；Step 1: The number of iterations is initially t=0, initialize

Set an appropriate initial step size

Minimum step size δ _{k, min} and correction factor 0<α<1;

Step 2: Calculate Gradients

做如下更新：where [Q] _ij is to follow

Do the following updates:

update using gradient descent

如果

则更新步长

并跳转到步骤2；Step 3: Calculate the objective function size

if

Then update the step size

and jump to step 2;

计算

Step 4: Update the number of iterations t=t+1, repeat steps 2 to 3 until the maximum number of iterations or step size is reached

calculate

Similar to the previous section, it can be proved that when the refinement factors M′ _z , M′ _x , M′ _c , and M′ _d are integers, and the distance between the base station antennas is half a wavelength, V _x , V _z , U _c , U _d is the oversampled DFT array, so T _kr , T _kt can be expressed as

其中N＝N_xN_zN_pN_d，T为迭代次数。where 1 _{M, 1} represents an M-dimensional column vector. Therefore, the calculation of T _kr ΩT _kt and T _kt Q ^T T _kr in the calculation of the gradient function in the above step can be realized by fast Fourier transform. The computational complexity is measured by the complex multiplier, and the computational complexity of the algorithm implemented by fast Fourier transform is

Where N=N _x N _z N _p N _d , T is the number of iterations.

5. Posteriori statistical channel model in beam delay Doppler domain and acquisition method of posterior statistical channel information

It is assumed that the channel information obtained by the 1st Doppler block on the time slot m-1 is used for the transmission of the mth time slot. In order to describe the Doppler correlation characteristics of massive MIMO, a first-order Gaussian Markov model is used to describe the Doppler correlation model. Under this model, the beam delay Doppler domain channel on the nth Doppler block of the mth slot can be expressed as

和

的相关因子函数，为和用户移动速度有关的多普勒相关因子。相关因子α_k，m的获得方法有多种，这里假设相关因子已知。实际中，可以采用信道样本的经验相关因子，也可以采用文献中常用的基于Jakes自相关模型的相关因子α_k，m的计算方法，即α_k，m(n)＝J₀(2πv_kf_cnTτ/c)，其中J₀(·)表示第一类零阶Bessel函数，τ表示一个时间间隔对应的时间，v_k表示第k用户速度，f_c表示载波频率，c为光速。式(67)中模型用来进行信道预测。本实施例中，为考虑系统实现复杂度，在整个时隙m上进行预编码。简便起见，不考虑信道估计误差，假设可以获得精细化波束时延多普勒域信道矩阵

的准确信道信息，可以得到时隙m上精细化波束时延多普勒信道的后验统计信息为where α _{k, m} (N _b +n-1) is the channel

and

The correlation factor function of is the Doppler correlation factor related to the user's moving speed. There are many ways to obtain the correlation factor α _k,m , and here it is assumed that the correlation factor is known. In practice, the empirical correlation factor of channel samples can be used, or the calculation method of correlation factor α _k,m based on the Jakes autocorrelation model commonly used in literature can be used, that is, α _k,m (n)=J ₀ (2πv _k f _c nTτ/c), where J ₀ (·) represents the zero-order Bessel function of the first kind, τ represents the time corresponding to a time interval, v _k represents the velocity of the kth user, f _c represents the carrier frequency, and c is the speed of light. The model in (67) is used for channel prediction. In this embodiment, in order to consider the complexity of system implementation, precoding is performed on the entire time slot m. For the sake of simplicity, without considering the channel estimation error, it is assumed that the refined beam delay Doppler domain channel matrix can be obtained

The accurate channel information of , the posterior statistical information of the refined beam delay Doppler channel on time slot m can be obtained as

Where β _k,m and the channel on the entire time slot m are related to H _k,m-1,1 correlation factor α _k,m , a feasible way is to take the root mean square of all correlation factors α _k,m on the time slot. Further, the beam delay Doppler domain posterior statistical channel model on time slot m can be obtained as

则后验统计模型可进一步表示为When considering the channel estimation error, the channel posterior statistical model in formula (67) needs to be further derived from the channel estimation error model, Doppler correlation model and prior statistical model. In order to facilitate the calculation in the beam delay Doppler domain, H _{k, m-1, 1} is expressed as

Then the posterior statistical model can be further expressed as

为波束时延多普勒域后验均值，

的方差为波束时延多普勒域后验方差。上述波束时延多普勒域后验均值和波束时延多普勒域后验方差构成了波束时延多普勒域后验统计信道信息。对于TDD系统，

可以通过反馈获得，在此基础上结合波束时延多普勒域先验统计信息可以获得波束时延多普勒域后验统计信息。波束时延多普勒域后验统计信息获取方法总结为in

is the posterior mean of the beam delay Doppler domain,

The variance of is the beam delay Doppler domain posterior variance. The beam delay-Doppler domain posterior mean value and the beam delay-Doppler domain posterior variance constitute the beam delay-Doppler domain posterior statistical channel information. For TDD systems,

It can be obtained through feedback, and on this basis, combined with the prior statistical information of the beam delay Doppler domain, the posterior statistical information of the beam delay Doppler domain can be obtained. The method of obtaining the posterior statistical information in the beam delay Doppler domain is summarized as

Step 1: Use any one of the massive MIMO beam delay-Doppler domain prior statistical channel information acquisition methods in the first two chapters to obtain the beam delay-Doppler domain prior statistical channel information Ω of each user terminal before the current time slot _k , where k is the user number;

Step 2: Obtain the pilot signal sent by each user terminal in the current time slot;

Step 3: Estimate the beam delay-Doppler domain channel matrix G _{k, m-1, 1} by using the received pilot signal, and combine the beam delay-Doppler domain prior statistical channel information and the inter-channel correlation factor β _{k, m} acquires the beam delay Doppler domain posterior statistical channel information of each user terminal, where m represents the slot number; the beam delay Doppler domain posterior statistical channel information includes the posterior average β _{k, m} G _{k , m-1, 1} and the posterior variance

6. Implementation effect

In order to enable those skilled in the art to better understand the solution of the present invention, the implementation effect of acquiring channel information based on beam delay domain a priori statistics in the pilot signal in this embodiment under specific system configurations is given below, which is omitted for brevity. Doppler domain.

Firstly, the specific system configuration of this embodiment is introduced. Consider a MIMO system equipped with a large-scale uniform array, the number of antennas on the base station side is M _t =128, the number of antennas in the horizontal direction and vertical direction is M _x =16, M _z =8, and the antenna spacing is set to half a wavelength, The user side is equipped with a single antenna. The system adopts OFDM modulation, where the carrier frequency f _c =4.8GHz, the subcarrier spacing Δf=30kHz, the cyclic prefix length is M _g =144, the number of subcarriers is M _c =2048, and the number of sending subcarriers is M _p =120 . The refinement factor is set to M' _z =M' _x =M' _c =2. In this embodiment, two scenarios with different numbers of users are considered, and the numbers of users are K=Q×P=1×12 and K=Q×P=2×12 respectively.

与实际能量矩阵Ω的归一化均方误差(NMSE)。从图4中可以看出在两种场景下，本专利方案估计的波束时延域先验统计信息准确度都要高于M-FOCUSS，尤其在低信噪比下；除此之外本专利方案也显现出强大的抗噪性能，在低信噪比下也能估计出较准确的先验统计信息。Figure 4 shows the comparison of the estimation accuracy of prior statistical information between this patent scheme and the M-FOCUSS algorithm. where the evaluation metric is the estimated energy matrix

The normalized mean square error (NMSE) from the actual energy matrix Ω. It can be seen from Figure 4 that in both scenarios, the accuracy of the prior statistical information in the beam delay domain estimated by this patent solution is higher than that of M-FOCUSS, especially at low signal-to-noise ratios; The scheme also shows strong anti-noise performance, and can estimate more accurate prior statistical information under low signal-to-noise ratio.

与实际的空间频率域信道H_k之间的均方误差(MSE)作为性能评估指标，其中空间频率域信道H_k已经做了归一化处理

从图中可以看出当信噪比SNR＜10dB时，本专利方案相对M-FOCUSS算法可以带来大量信道估计性能增益；即使在SNR＞10dB时，本专利方案下的信道估计性能也能和MFOCUSS算法的性能基本持平。Figure 5 shows the performance comparison between the patented solution and the prior statistical information estimated by the M-FOCUSS algorithm when applied to instantaneous channel parameter estimation. Among them, the instantaneous channel parameter estimation adopts the minimum mean share error (MMSE) estimation algorithm, and the estimated spatial frequency domain channel

The mean square error (MSE) between the channel H _k in the spatial frequency domain and the actual channel H k is used as a performance evaluation index, where the channel H _k in the spatial frequency domain has been normalized

It can be seen from the figure that when the signal-to-noise ratio SNR<10dB, the patented solution can bring a large amount of channel estimation performance gain compared to the M-FOCUSS algorithm; even when the SNR>10dB, the channel estimation performance under the patented solution can also be compared with The performance of the MFOCUSS algorithm is basically the same.

其中N＝N_xN_zN_p，T为迭代次数，这要远远低于M-FOCUSS算法

的复杂度。Finally, it is worth noting that this patented solution can be implemented using fast Fourier transform, and the computational complexity is

Where N=N _x N _z N _p , T is the number of iterations, which is much lower than the M-FOCUSS algorithm

of complexity.

Based on the same inventive concept, the embodiment of the present invention also discloses a computing device, including a memory, a processor, and a computer program stored in the memory and operable on the processor. When the computer program is loaded into the processor, the The aforementioned massive MIMO beam delay-Doppler domain priori statistical channel information acquisition method, or massive MIMO beam delay Doppler domain posterior statistical channel information acquisition method.

In a specific implementation, the device includes a processor, a communication bus, a memory, and a communication interface. The processor can be a general-purpose central processing unit (CPU), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits used to control the execution of programs of the present invention. A communication bus may include a path for transferring information between the aforementioned components. A communication interface, using any device, such as a transceiver, used to communicate with other devices or a communication network. The memory may be a read-only memory (ROM) or other type of static storage device that can store static information and instructions, a random access memory (RAM) or other type of dynamic storage device that can store information and instructions, or an electronically Erasable programmable read-only memory (EEPROM), compact disk-read-only (CD-ROM) or other optical disk storage, disk storage medium or other magnetic storage device, or capable of carrying or storing desired program code in the form of instructions or data structures and any other medium that can be accessed by a computer, but is not limited to. The memory can exist independently and be connected to the processor through the bus. Memory can also be integrated with the processor.

Wherein, the memory is used to store the application program code for executing the solution of the present invention, and the execution is controlled by the processor. The processor is configured to execute the application program code stored in the memory, so as to realize the information acquisition method provided in the foregoing embodiments. The processor may include one or more CPUs, or multiple processors, and each of these processors may be a single-core processor or a multi-core processor. A processor herein may refer to one or more devices, circuits, and/or processing cores for processing data (eg, computer program instructions).

Based on the same inventive concept, the embodiment of the present invention also discloses a massive MIMO communication system, including a base station and multiple user terminals, the base station is used to: receive pilot signals sent by each mobile terminal; Convert the received pilot signal to the beam delay Doppler domain; use the beam delay Doppler domain sample statistics to obtain multi-user beam delay Doppler domain prior statistical channel information; use the multiple The user beam delay-Doppler domain prior statistical channel information restores the beam delay-Doppler domain prior statistical channel information of each mobile terminal.

Based on the same inventive concept, the embodiment of the present invention also discloses a massive MIMO communication system, which includes a base station and multiple user terminals, and the base station is used to: acquire the instantaneous channel information of each user on multiple time slots; The instantaneous channel information is converted to the beam delay Doppler domain; the beam delay Doppler domain prior statistical channel information of each mobile terminal is obtained by using the beam delay Doppler domain sample statistics.

Based on the same inventive concept, the embodiment of the present invention also discloses a massive MIMO communication system, including a base station and a plurality of user terminals, and the base station is used for: using the massive MIMO beam delay Doppler domain prior The statistical channel information acquisition method obtains the beam delay Doppler domain prior statistical channel information of each user terminal before the current time slot; obtains the pilot signal sent by each user terminal in the current time slot; uses the received pilot signal to estimate the beam The channel matrix in the delay-Doppler domain combines the prior statistical channel information in the beam delay-Doppler domain and the inter-channel correlation factors to obtain the posterior statistical channel information in the beam delay-Doppler domain for each user terminal.

Based on the same inventive concept, the embodiment of the present invention also discloses a massive MIMO communication system, which includes a base station and multiple user terminals, and the base station is provided with the above-mentioned computing device.

In the embodiments provided in the present application, it should be understood that the disclosed methods can be implemented in other ways without exceeding the spirit and scope of the present application. The present embodiment is only an exemplary example and should not be taken as a limitation, and the specific content given should not limit the purpose of the present application. For example, some features may be ignored, or not implemented. The content not described in detail in this application is all prior art.

The technical means disclosed in the solutions of the present invention are not limited to the technical means disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features. It should be pointed out that for those skilled in the art, some 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 (6)

1. A large-scale MIMO wave beam delay Doppler domain statistical channel information acquisition method is characterized in that the wave beam delay Doppler domain statistical channel information acquisition method comprises a wave beam delay Doppler domain prior statistical channel information acquisition method and a wave beam delay Doppler domain posterior statistical channel information acquisition method; the method for acquiring the prior statistical channel information of the beam delay Doppler domain comprises a method for acquiring the prior statistical information of the beam delay Doppler domain based on a pilot signal and a method for acquiring the prior statistical information of the beam delay Doppler domain under the condition of known instantaneous channel information; the wave beam delay Doppler domain posterior statistical channel information comprises a wave beam delay Doppler domain posterior mean value and a wave beam delay Doppler domain posterior variance;

the method for acquiring the prior statistical information of the wave beam delay Doppler domain based on the pilot signal comprises the following steps:

step A1, each mobile terminal sends pilot frequency signal X on the same time frequency resource _k Wherein k represents a user number; the transmission pilot signal X _k Transmitting a pilot signal X for the frequency domain _f,k And time domain transmission pilot signal X _t,k (iii) the Kronecker product of;

step A2, pilot signals Y received on M time slots _m Guide vector matrix transposition matrix V for refined sampling through left multiplication space ^T And right-multiplying pilot frequency base delay Doppler refined sampling guide vector matrix conjugate transpose matrix P ^H Transition to Beam delay Doppler Domain V ^T Y _m P ^H Where M =1,2,.., M, superscript T, H represents transpose and sum, respectivelyConjugate transpose;

step A3, through minimizing wave beam delay Doppler domain sample statistic

And beam delay Doppler domain overall parameter function T _r ΩT _f +O _r NO _f Obtaining multi-user beam delay Doppler domain prior statistical channel information omega by the Kullback-Leibler divergence, wherein the superscript represents conjugation; t in the beam delay Doppler domain overall parameter function _r ,T _f ,O _r ,N,O _f Are all known matrices;

step A4, recovering the prior statistical channel information omega of the beam delay Doppler domain of each mobile terminal by utilizing the prior statistical channel information omega of the multi-user beam delay Doppler domain _k Wherein k represents a user number;

the method for acquiring the prior statistical information of the wave beam delay Doppler domain under the condition of the known instantaneous channel information comprises the following steps:

step B1, obtaining instantaneous channel information H of each user on M time slots _k,m Wherein M =1,2., M, k is the user number;

step B2, the instantaneous channel information H on the M time slots is processed _k,m Steering vector matrix conjugate transpose matrix U for refined sampling by left-multiplying delay Doppler ^H Converting a sum-right space refined sampling steering vector matrix V into a beam delay Doppler domain U ^H H _k,m V, where superscript H denotes transpose;

step B3, through minimizing beam delay Doppler domain sample statistic

And beam delay Doppler domain overall parameter function T _kr Ω _k T _kt KL divergence between the two obtains prior statistical channel information omega of wave beam delay Doppler domain of each mobile terminal _k Wherein superscript denotes conjugation; t in the beam delay Doppler domain overall parameter function _kr ,T _kt Are all known matrices；

The method for acquiring the posterior statistical channel information of the beam delay Doppler domain comprises the following steps:

step C1, obtaining wave beam time delay Doppler domain prior statistical channel information omega of each user terminal before the current time slot by utilizing the wave beam time delay Doppler domain prior statistical channel information obtaining method based on pilot frequency or the wave beam time delay Doppler domain prior statistical information obtaining method under the condition of known instantaneous channel information _k Wherein k is a user number;

step C2, acquiring pilot signals sent by each user terminal in the current time slot;

step C3, estimating a wave beam delay Doppler domain channel matrix G by utilizing the received pilot signal _k,m-1,1 Combining the beam delay Doppler domain prior statistics channel information and the inter-channel correlation factor beta _k,m Obtaining posterior statistical channel information of a wave beam delay Doppler domain of each user terminal, wherein m represents a time slot number; the wave beam time delay Doppler domain posterior statistical channel information comprises posterior mean value beta _k,m G _k,m-1,1 And posterior variance

2. The method for obtaining statistical channel information in the large-scale MIMO beam delay-Doppler domain according to claim 1, wherein the frequency-domain transmit pilot signals in step A1 are designed as phase-shifted Zadoff-Chu sequences, and the time-domain transmit pilot signals are designed as repeated pilots.

3. The method for obtaining large-scale MIMO beam delay-doppler domain statistical channel information according to claim 1, wherein the step A3 of obtaining the prior statistical channel information of the multi-user beam delay-doppler domain by minimizing KL divergence between the beam delay-doppler domain sample statistics and the beam delay-doppler domain global parameter function includes the steps of:

step A3-1, initializing iteration times and multi-user beam delay Doppler domain prior statistical channel information, and setting appropriate initial step length, minimum step length and correction factors;

step A3-2, calculating a gradient function, and updating the prior statistical channel information of the multi-user beam delay Doppler domain by using a gradient descent method;

step A3-3, calculating an objective function value, if the objective function value is increased, reducing the step length according to the correction factor, and skipping to the step A3-2;

and step A3-4, updating the iteration times, and repeating the step A3-2 to the step A3-3 until the maximum iteration times is reached or the step size is smaller than the minimum step size.

4. The method according to claim 3, wherein the step A3-2 of calculating the gradient function uses fast Fourier transform to reduce complexity.

5. The method for obtaining large-scale MIMO beam delay-doppler domain statistical channel information according to claim 1, wherein the step B3 of obtaining the priori statistical channel information of the beam delay-doppler domain of each mobile terminal by minimizing KL divergence between the beam delay-doppler domain sample statistics and the beam delay-doppler domain global parameter function includes the steps of:

step B3-1, initializing iteration times and priori channel information of each mobile terminal beam delay Doppler domain, and setting appropriate initial step length, minimum step length and correction factors;

step B3-2, calculating a gradient function, and updating the priori statistical channel information of the wave beam delay Doppler domain of each mobile terminal by using a gradient descent method;

step B3-3, calculating an objective function value, if the objective function value is increased, reducing the step length according to the correction factor, and skipping to the step B3-2;

and step B3-4, updating the iteration times, and repeating the steps B3-2 to B3-3 until the maximum iteration times is reached or the step size is smaller than the minimum step size.

6. The method of claim 5, wherein the step B3-2 of calculating the gradient function uses fast Fourier transform to reduce complexity.

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