CN114665932B

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

Info

Publication number: CN114665932B
Application number: CN202210264919.6A
Authority: CN
Inventors: 卢安安; 高西奇; 陈衍; 章宇轩
Original assignee: Southeast University
Current assignee: Southeast University
Priority date: 2022-03-17
Filing date: 2022-03-17
Publication date: 2023-03-10
Anticipated expiration: 2042-03-17
Also published as: CN114665932A

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

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

Technical Field

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

Background

Large-scale Multiple-Input Multiple-output (MIMO) is one of the key technologies of 5G wireless communication networks. Large-scale MIMO greatly increases system capacity by using a large number of antennas at a Base Station (BS), making full use of space dimension resources. In massive MIMO systems, transmission of multi-user MIMO (MU-MIMO) on the same time and frequency resources is significantly enhanced. For an antenna Array provided on the base station side, a Uniform Planar Array (UPA) is widely used in a practical massive MIMO system due to its compact size.

For massive MIMO systems, one common channel statistical model in the literature is a traditional beam-domain channel model based on Discrete Fourier Transform (DFT) matrices. However, the conventional beam-domain channel model may deviate from the actual physical channel model to a considerable extent. A refined beam domain statistical channel model based on an oversampling DFT matrix is provided in the document, and is closer to a physical channel model when the antenna size is limited through the refined sampling direction cosine, so that a model basis is provided for solving the universality problem of large-scale MIMO to various typical mobile scenes under the condition that the antenna size is limited. The model can also be extended to the beam delay-doppler domain, which also brings performance gains to the channel estimation. To achieve 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 mentioned in the literature.

In the literature, statistical channel information is typically obtained based on estimated instantaneous channel information, or by an expectation-maximization algorithm that iteratively estimates instantaneous and statistical information. There is also literature to obtain the covariance matrix directly without reference to instantaneous channel state information. For a large-scale MIMO beam delay doppler domain channel model, the statistical channel information acquisition problem becomes the acquisition of a channel power matrix in the beam delay doppler domain, which has not been solved in the literature. In the beam delay Doppler domain channel model, the angle delay domain or beam domain channel coefficients are sparse due to the limited number of resolvable multipaths. When no noise is present, the problem under consideration can also be considered as a Multiple Measure Vector (MMV) problem, which is a classical compressed sensing problem. An M-focus (MMV focal undedredfied system solution) algorithm may be used to solve the 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 requires acquisition of instantaneous channel information. The beam delay Doppler domain statistical channel information can also be used for improving the estimation performance of instantaneous channel information in a practical large-scale MIMO system. Therefore, it is preferable to obtain statistical channel information for the problem under consideration before estimating instantaneous channel information. In summary, we need a new method with low complexity to estimate the statistical channel information in the beam delay-doppler domain.

Disclosure of Invention

The technical problem is as follows: aiming at the defects of the prior art, the invention aims to provide a large-scale MIMO beam delay Doppler domain statistical channel information acquisition method, which can provide support for large-scale MIMO channel estimation and a robust precoding transmission method.

The technical scheme is as follows: in order to achieve the above object, the present invention provides a method for obtaining statistical channel information in a large-scale MIMO beam delay doppler domain, comprising a method for obtaining prior statistical channel information in a beam delay doppler domain and a method for obtaining posterior statistical channel information in a beam delay doppler domain; 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.

Further, the method for obtaining 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 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 denotes transpose and conjugate transpose, respectively;

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 the prior statistical channel information omega of a multi-user beam delay Doppler domain by Kullback-Leibler (KL) divergence, wherein the upper mark 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 Where k represents a user number.

Further, the frequency domain transmission pilot signal in step A1 is designed to phase shift a plurality of Zadoff-Chu (ZC) sequences, and the time domain transmission pilot is designed to be a repeated pilot.

Further, the step A3 of obtaining the prior statistical channel information of the multi-user beam delay doppler domain by minimizing the KL divergence between the beam delay doppler domain sample statistics and the beam delay doppler domain global parameter function includes the following steps:

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 size according to a correction factor, and skipping to the step A3-2;

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

Further, the step A3-2 uses fast fourier transform to reduce complexity in the process of calculating the gradient function.

Further, the method for obtaining the prior statistical information of the 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.

Further, the step B3 of obtaining the priori statistical channel information of the beam delay doppler domain of each mobile terminal by minimizing the KL divergence between the beam delay doppler domain sample statistics and the beam delay doppler domain global parameter function includes the following steps:

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.

Further, the step B3-2 uses fast fourier transform to reduce complexity in the process of calculating the gradient function.

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

step C1, obtaining the wave beam delay Doppler domain prior statistical channel information omega of each user terminal before the current time slot by using the wave beam delay Doppler domain prior statistical channel information obtaining method based on pilot frequency or the wave beam 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 frequency 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 posterior statistical channel information of the wave beam time delay Doppler domain comprises a posterior mean value beta _k，m G _k，m-1，1 And posterior variance

Drawings

FIG. 1 is a flow chart of a method for obtaining large-scale MIMO beam delay Doppler domain prior statistical channel information based on pilot signals;

FIG. 2 is a flowchart of a large-scale MIMO beam delay Doppler domain prior statistical channel information acquisition method under the condition of known instantaneous channel information;

FIG. 3 is a flowchart of a method for obtaining posterior statistical channel information in a large-scale MIMO beam delay Doppler domain;

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

Fig. 5 is a diagram showing the comparison result of the performance when the prior statistical information estimated by the scheme and the M-FOCUSS algorithm is applied to the instantaneous channel parameter estimation.

Detailed Description

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

As shown in fig. 1, the method for obtaining the prior statistical channel information in the large-scale MIMO beam delay doppler domain based on the pilot signal disclosed in the embodiment of the present invention includes: each mobile terminal sends pilot signals on the same time-frequency resource; converting pilot signals received on a plurality of time slots into a beam delay Doppler domain; obtaining multi-user wave beam delay Doppler domain prior statistical channel information by utilizing the wave beam delay Doppler domain sample statistic; and recovering the priori statistical channel information of the beam delay Doppler domain of each mobile terminal by using the priori statistical channel information of the multi-user beam delay Doppler domain.

As shown in fig. 2, another embodiment of the present invention discloses a method for obtaining a priori statistical channel information in a large-scale MIMO beam delay-doppler domain under a known situation of instantaneous channel information, including: acquiring instantaneous channel information of each user on a plurality of time slots; converting the instantaneous channel information into a beam delay Doppler domain; and obtaining the prior statistical channel information of the beam delay Doppler domain of each mobile terminal by using the beam delay Doppler domain sample statistics.

As shown in fig. 3, the method for obtaining posterior statistical channel information in a large-scale MIMO beam domain disclosed in the embodiment of the present invention includes: acquiring wave beam delay Doppler domain prior statistical channel information of each user terminal before the current time slot; acquiring pilot signals sent by each user terminal in the current time slot; and estimating a wave beam delay Doppler domain channel matrix by using the received pilot signal, and acquiring wave beam delay Doppler domain posterior statistical channel information of each user terminal by combining the wave beam delay Doppler domain prior statistical channel information and the inter-channel correlation factor.

The method of the invention is mainly suitable for a large-scale MIMO system which is provided with a large-scale antenna array at the base station side to serve a plurality of users simultaneously. The following describes in detail a specific implementation process of the method for acquiring statistical channel information in a beam delay-doppler domain according to the present invention with reference to a specific communication system example, and it should be noted that the method of the present invention is not only applicable to the specific system model described in the following example, but also applicable to system models with other configurations.

1. System configuration

Consider a 3D massive MIMO frequency selective fading system model, with the downlink comprising a Base Station (BS) and K Users (UEs). The base station is provided with large-scale uniform area array antennas, each antenna is a dual-polarized antenna, and the number of the antennas in the vertical direction and the number of the antennas in the horizontal direction are respectively M _z And M _x The total number of antennas at the base station side is M _t ＝M _z M _x . For simplicity, it is assumed that each user configures a single antenna. Dividing the Doppler resource of the system into a plurality of time slots, wherein each time slot comprises M _b A Doppler block, each Doppler block containing M _d One symbol interval. The massive MIMO system considered in this embodiment operates in a Time Division Duplex (TDD) mode. For simplicity, it is assumed that only uplink channel training and downlink transmission phases exist, and downlink transmission includes pre-coded field pilot and data signaling. In each time slot, the base station receives the uplink pilot signal of the user only in the first Doppler block. 2 nd to M _b The Doppler block is used for the base station to transmit the downlink pre-coding domain pilot frequency and the data signal. The length of the uplink training sequence is the length of a block, i.e., T symbol intervals. For a Frequency Division Duplex (FDD) mode, the uplink channel training phase may be replaced with the downlink channel feedback phase, and the downlink transmission phase remains the same. Specifically, a downlink omni-directional pilot signal is transmitted in a first block, and mobile terminal feedback is received.

2. Refined wave beam time delay Doppler domain prior statistical channel model

The detailed description of the refined beam delay doppler domain prior statistical model based on the refined sampling steering vector matrix is described below. The number of the space guide vectors in the traditional wave beam domain channel model is the same as that of the antennas, and the refined wave beam delay Doppler domain statistical model provided by the invention refines the time delay domain and the Doppler domain while introducing more space guide vectors than the number of the antennas in the channel model, thereby better describing the channel statistical characteristics. First, given the definition of OFDM correlation, T _c Denotes the OFDM symbol Doppler interval, Δ f =1/T _c Representing the subcarrier spacing, the number of subcarriers being M _c Wherein M is _p The sub-carrier is used for sending pilot frequency, and the length of the cyclic prefix is M _g 。

Firstly, a refined beam domain channel model under a single subcarrier is considered, and then the refined beam domain channel model is popularized to the refined beam delay Doppler domain channel model. Consider a model of a stationary uncorrelated scattering channel. Carrier frequency of f _c The light speed is c, and d represents the antenna spacing of the receiving end linear array (ULA). Suppose there is a P between the BS and user u _u The bars may resolve the path. Let τ be _u，p，m The propagation delay on the p path representing the m antenna of the BS and the user u is expressed as follows

τ _u，p，m ＝τ _u，p +(m-1)ΔτΩ _u，p (1)

Where Δ τ = d/c, τ _u，p Representing the propagation delay of the first antennas of user u and ULA in the p-th path. Omega _u，p ＝cosθ _u，p Is the direction cosine of the angle of arrival upstream (AoA) or the angle of departure downstream (AoD). The impulse response of the m-th antenna from the uplink time-varying channel user u to the BS is expressed as follows

Wherein alpha is _u，p Is a complex-valued random gain. Suppose that the p-th path contains Q _p Sub-paths with the same propagation delay, then a _u，p Is expressed as follows

Wherein beta is _u，p，q ，φ _u，p，q ，v _u，p，q Respectively, the gain, initial phase and doppler shift of the sub-path q. Suppose phi _u，p，q Evenly distributed over [0,2 pi ]. When Q is _p Towards infinity, α _u，p (t) can be viewed as a zero-mean complex Gaussian random process. Thus, the uplink channel from the user u to the base station BS can be obtained as

Wherein

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)

Order to

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

Further, the frequency response of the uplink channel is obtained

Wherein

Indicating the steering vector for the k-th subcarrier. Below, Ω is uniformly sampled. Order to

Representing the number of samples. Collection of

Wherein

Has a value range of

Order to

Representing the set of directional cosines for user u. Thus h _u，l，k Is shown as

Order to

Then h is _u，l，k Can be approximately expressed as

Wherein

The beam domain channel from user u to the base station on the kth subcarrier of the ith symbol can be represented as

Defining a matrix of sample steering vectors at the kth subcarrier as

Finally, the formula (12) can be written as

The above is derived under the condition that the ULA linear array is configured at the base station side, and the following is expanded to a uniform area array (UPA) and a delay-doppler domain is introduced at the same time. In UPA, d _z And d _x And the antenna spacing in the vertical and horizontal directions of the receiving end area array is respectively represented. And replacing the original DFT matrix with the oversampled DFT matrix to obtain a sampling matrix V. M's' _z ，M′ _x ，M′ _c ，M′ _d Vertical antenna direction, horizontal antenna direction, time delay, doppler refinement factors, respectively. Then N is _z ＝M _z M′ _z ，N _x ＝M _x M′ _x ，N _p ＝M _p M′ _p ，N _d ＝M _d M′ _d The cosine v = cos theta in the vertical antenna direction, the cosine u = sin theta cos phi in the horizontal antenna direction, the normalized time delay tau, and the normalized Doppler f sampling number,wherein theta and phi are the polar angle and the azimuth angle of the BS side downlink departure angle or uplink arrival angle, respectively. According to the formula (10), the cosine in the vertical antenna direction, the cosine in the horizontal antenna direction, (normalized) time delay, and (normalized) Doppler refined sampling guide vectors can be obtained as

Wherein v is _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 mode of the formula (14), the cosine fine sampling guide vector matrix of the vertical and horizontal antenna directions and the time delay and Doppler fine sampling guide vector matrix are as follows

Due to the fact that the normalized time delay range is tau epsilon [0,N _g /N _c ) Is thus

It is sufficient to describe the channel characteristics, among them

Let N _t ＝N _z N _x Then

The steering vector matrix is sampled for spatial refinement. Obtaining a channel model

Wherein

For the k-th user space-frequency-time-space-domain channel,

the frequency-time domain channel is the k user beam. Suppose that

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

Refined sampling guide vector matrix for delay-doppler

Substituting the equation (25) into the equation (24) to obtain a complete channel model

Compared with the traditional wave beam domain prior statistical channel model based on the DFT matrix, the refined statistical model has more statistical characteristic directions, so that the actual physical channel model can be more accurately characterized.

3. Method for acquiring priori statistical channel information of wave beam delay Doppler domain based on pilot signal

1. Pilot signal based reception model

For a large-scale MIMO system considered to work in a TDD mode, the obtained uplink channel statistical information can be directly used as the downlink channel statistical information due to the reciprocity of the uplink channel and the downlink channel. For the condition that the instantaneous reciprocity of the FDD system channel does not exist, the user side can acquire and feed back the downlink statistical channel information to the base station. A method for obtaining channel information of a prior statistic in a refined beam delay Doppler domain based on a pilot signal is provided below.

In this embodiment, each mobile terminal transmits pilot 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 Kronecker product between. The frequency domain transmitting pilot frequency sequence is designed to be a plurality of Zadoff-Chu (ZC) sequences with phase shift, the pilot frequency distribution thought is to divide K users into Q groups, each group comprises P users, the users in different groups use the ZC sequences with different roots, the users in the same group use the phase shift sequences with different phase shifts, the table K below the users is replaced by Q and P under the condition of not causing confusion, wherein Q and P respectively represent root systemsThe number and cyclic shift coefficient, so that the frequency domain transmission pilot sequence of the kth user (or the p-th user under the qth root) can be specifically expressed as

Wherein

Wherein N is _l Is a ratio of M _p The largest minimum prime number. The time domain transmission pilot is designed as a repeated pilot, i.e. the pilots transmitted at different times on the same subcarrier are the same. Then the frequency domain transmit pilot matrix and the time domain transmit pilot matrix are X, respectively _f，k ＝diag(x _q，p ) And

where diag denotes a diagonalization function. The transmit pilot matrix may be represented as

Wherein

I _M An M-dimensional unit matrix is represented. Based on the above transmit pilots, the receive pilot signal matrix may be represented as

Wherein I _M，N ＝[I _M ，0]Is an M × N dimensional matrix, 0 is an all 0 matrix, and Z is a power of

Wherein each element is assumed to be uniqueAre distributed in a vertical mode. Due to the fact that

Wherein

Representing an N-dimensional cyclic shift matrix of shift length N. The expression of the received pilot signal matrix can then be collated as

Note the book

And

according to the nature of the cyclic shift matrix, if under different subscripts p

At the element of G _q If the distributions are non-overlapping, P.ltoreq.N needs to be satisfied _p /N _f . Then, note G = [ G = [ G ] ₁ ，...，G _Q ]And

g and P are respectively called a multi-user beam delay Doppler domain channel and a pilot frequency base delay Doppler refined sampling guide vector matrix. And note M = [ M = ₁ ，...，M _Q ]. The received pilot signal pattern can be written as

Y＝V ^* GP+Z (33)

Defining a multi-user beam delay Doppler domain channel energy matrix omega = M ∑ M, wherein omega is also called multi-user beam delay Doppler domain prior statistical channel information. When P is less than or equal to N _p /N _f If the omega is accurately obtained, each user can be recovered without lossThe beam delay Doppler domain channel energy matrix

Therefore, the problem of obtaining the channel information through the prior statistics of the beam delay doppler domain based on the pilot signal is to estimate an energy matrix Ω according to the received pilot signals of a plurality of time slots.

2. Method for acquiring prior statistical channel information of beam delay Doppler domain

Next, a channel energy matrix is obtained by minimizing a Kullback-Leibler (KL) divergence criterion through the received pilot signals of a plurality of slots. Defining the total parameter function phi of the wave beam delay Doppler domain as

Substituting into specific expression of Y to obtain

Φ＝T _r ΩT _f +O _r NO _f (35)

Wherein,

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

T _f ＝(PP ^H )⊙(PP ^H ) ^* (37)

where 1 represents the all 1 matrix. To estimate the channel energy matrix Ω from Φ, an objective function f (M) is first defined as Φ and T _r ΩT _f +O _r NO _f KL divergence between

Converting the problem into an optimization problem

M ^★ ＝argmin _M f(M) (40)

F (M) can be found _k ) Several items in and M _k Irrelevant, so the above problems are simplified to

M ^★ ＝argmin _M g(M) (41)

Wherein g (M) is represented by

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

wherein Q is

The gradient of g (M) can then be expressed as

Solving the objective function using a gradient method yields the following iterative equation

Wherein δ is the step length of the gradient method, the step length of each iteration can be determined by a line search mode, and the line search idea is as follows: computing object functions in each iterationNumber size, decrease step size if the objective function value increases in that iteration, and repeat the above steps until the objective function value decreases. M can be finally obtained through multiple iterations. It is worth emphasizing that in calculating Φ, a plurality of time slots (V) are utilized ^T YP ^H )⊙(V ^T YP ^H ) ^* Instead of the sample statistics.

In summary, the method for acquiring the channel information of the beam delay doppler domain prior statistics based on the pilot signal comprises the following steps:

step 1: each mobile terminal sends pilot 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 2: pilot signal Y received in 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 Wherein M =1,2, ·, M;

and step 3: doppler domain sample statistics by minimizing beam delay

And beam delay Doppler domain overall parameter function T _r ΩT _f +O _r NO _f Obtaining the prior statistical channel information omega of a multi-user wave beam delay Doppler domain by the KL divergence between the two wave beam delay Doppler domains; t in the beam delay Doppler domain overall parameter function _r ，T _f ，O _r ，N，O _f Are all known matrices;

and 4, step 4: 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 。

The obtaining of the prior statistical channel information of the multi-user beam delay doppler domain by minimizing the KL divergence between the beam delay doppler domain sample statistics and the beam delay doppler domain overall parameter function in the step 3 may be further refined as follows:

step 1: the number of initialization iterations is t =0, and M is initialized ^t Setting a suitable initial step size delta ⁰ Minimum step delta _min And a correction factor 0 < alpha < 1;

step 2: calculating gradients

Wherein [ Q ]] _ij To follow M ^t The following updates are made:

updating using gradient descent method

And step 3: calculating the size f (M) of the objective function ^t+1 )，f(M ^t ) If f (M) ^t+1 )≥f(M ^t ) Then update the step δ ^t ＝αδ ^t And jumping to the step 2;

and 4, step 4: updating the iteration times t = t +1, and repeating the steps 2 to 3 until the maximum iteration times or the step delta is reached ^t ＜δ _min Calculate Ω ^t ＝M ^t ⊙M ^t 。

3. Quick implementation method

The complex multiplication number is used for measuring the calculation complexity, and the highest complexity in the method for acquiring the prior statistical channel information of the wave beam delay Doppler domain based on the pilot signal is T in the gradient function _r ΩT _f And T _r QT _f The calculation complexity of directly adopting matrix multiplication is

Wherein N = N _x N _z N _c N _d (ii) a The computational complexity of other operations is not higher than

Therefore, the key to reducing the complexity of the algorithm is to simplify T _r ΩT _f And T _r QT _f And (4) calculating. The following is a computational simplification of the cyclic array property. Wherein the cyclic array is

First, a lemma is given for the cyclic array:

E＝I _M，N F _N is an oversampled DFT array, where I _M，N ＝[I _M ，0 _M，N-M ]，M≤N，I _M ，O _M，N-M Respectively represent an M-dimensional unit matrix and an M x (N-M) -dimensional zero matrix, F _N Is an N-dimensional DFT array; d = diag (D) is an M-dimensional diagonal matrix, D is an M-dimensional real vector. Then matrix (E) ^H DE)⊙(E ^H DE) is a cyclic array, which can be expressed in particular as

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

It can be proved that when refinement factor M' _z ，M′ _x ，M′ _c ，M′ _d Is an integer, and the base station side antenna pitch is half wavelength, V _x ，V _z ，U _c ，U _d Is an oversampled DFT matrix. According to the above theory, T can be obtained _r ，T _f All have the following structures

Wherein 1 _M，1 Representing M-dimensional column vectors, sigma being a block diagonal matrix

Thus T _r ΩT _f And T _r QT _f The calculation of (c) may be implemented using a fast fourier transform. The complex multiplication number is used for measuring the calculation complexity, and the calculation complexity of the algorithm after the fast Fourier transform is adopted is

Wherein N = N _x N _z N _p N _d And T is the iteration number.

4. Method for acquiring wave beam delay Doppler domain prior statistical channel information under known instantaneous channel information

The foregoing describes a method for acquiring channel information by beam delay-doppler domain prior statistics using pilot signals. In an actual system, instantaneous channel information can be obtained first, and then the instantaneous channel information is used for estimating the wave beam delay Doppler domain prior statistical channel information. The following is to give a kind of prior statistics of channel information omega in the beam delay-doppler domain under the condition that the instantaneous channel information is known _k And (4) an acquisition method. H is to be _k Left-hand multiplying U ^H And right-handed by V

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

Further, there are

At this time, the beam delay Doppler domain overall parameter function phi _k Become into

Or expressed as an element

Further, can obtain

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) ^* 。Φ _k And channel energy matrix function matrix T _kr Ω _k T _kt Reduced to KL divergence function

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 sum of M _k Independent constants. Also, to optimize for M with the minimum KL divergence _k Firstly, the derivation is carried out on the objective function,

wherein J is a matrix of all 1 s,

finally, g (M) is obtained _k ) Has a gradient of

Wherein delta _k For the kth user gradient step size, the step size of each iteration can be determined by a line search method. And finally, mk can be obtained through multiple iterations.

In summary, the method for acquiring the prior statistical channel information in the beam delay doppler domain under the condition of the known instantaneous channel information comprises the following steps:

step 1: 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 2: the instantaneous channel information H on the M time slots _k，m Conjugate transpose matrix U of sampling steering vector matrix refined through left-multiplication delay Doppler ^H Converting the sum right multiplication space refined sampling steering vector matrix V into a beam delay Doppler domain U ^H H _k，m V；

And step 3: by minimizing beam delay Doppler domain sample statistics

The obtaining of the prior statistical channel information of the beam delay doppler domain of each mobile terminal by minimizing the KL divergence between the beam delay doppler domain sample statistics and the beam delay doppler domain overall parameter function in the step 3 may be further refined as follows:

step 1: the iteration number is initially t =0, and initialization is carried out

Setting proper initial step length

Minimum step size delta _k，min And a correction factor 0 < alpha < 1;

step 2: calculating gradients

Wherein [ Q ]] _ij To follow

The following updates are made:

updating using gradient descent method

And step 3: calculating the size of the objective function

If it is not

The step size is updated

And skipping to the step 2;

and 4, step 4: updating the iteration times t = t +1, and repeating the steps 2 to 3 until the maximum iteration times or step size is reached

Calculating out

Similar to the previous section, it can be proved that when the refinement factor M' _z ，M′ _x ，M′ _c ，M′ _d Is an integer, and the base station side antenna pitch is half wavelength, V _x ，V _z ，U _c ，U _d For over-sampling DFT arrays, then T _kr ，T _kt Can be expressed as

Wherein 1 is _M，1 Representing an M-dimensional column vector. Then T in the gradient function calculation of the above step _kr ΩT _kt And T _kt Q ^T T _kr The calculation of (c) may be implemented using a fast fourier transform. The complex multiplication number is used for measuring the calculation complexity, and the calculation complexity of the algorithm after the fast Fourier transform is adopted is

Wherein N = N _x N _z N _p N _d And T is the iteration number.

5. Wave beam time delay Doppler domain posterior statistical channel model and posterior statistical channel information obtaining method

Suppose that the channel information obtained by the 1 st doppler block on slot m-1 is used for the transmission of the mth slot. To describe the large-scale MIMO Doppler correlation characteristics, a first-order Gaussian Markov model is adopted to describe the Doppler correlation model. Under the model, the beam delay Doppler domain channel on the nth Doppler block of the mth time slot can be expressed as

Wherein alpha is _k，m (N _b + n-1) is the channel

And

is a doppler correlation factor related to the velocity of the user's movement. Correlation factor alpha _k，m There are several methods of obtaining, here assuming that the correlation factor is known. In practice, empirical correlation factors of channel samples may be used, and correlation factors α based on Jakes autocorrelation model commonly used in literature may also be used _k，m Is calculated by a method of _k，m (n)＝J ₀ (2πv _k f _c nT τ/c), wherein J ₀ (. Cndot.) denotes a first class of zero-order Bessel function, τ denotes the time corresponding to a time interval, v _k Representing the kth user speed, f _c Representing the carrier frequency and c the speed of light. The model in equation (67) is used for channel prediction. In this embodiment, in order to consider the complexity of system implementation, precoding is performed on the entire slot m. For simplicity, it is assumed that a refined beam delay-doppler domain channel matrix can be obtained without considering channel estimation errors

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

Wherein beta is _k，m And channels and H on the whole time slot m _k，m-1，1 Correlation factor alpha _k，m In this regard, one possibility is to take all the correlation factors α over the time slot _k，m Root mean square (rms). Further, a posterior statistical channel model of the wave beam delay Doppler domain on the time slot m can be obtained as

When considering the channel estimation error, the channel posterior statistical model in equation (67) needs to be further derived according to the channel estimation error model, the doppler correlation model and the prior statistical model. To facilitate the computation in the beam delay Doppler domain, H is _k，m-1，1 Is shown as

The posterior statistical model can be further expressed as

Wherein

Is the posterior mean of the beam delay-doppler domain,

the variance of (1) is the posterior variance of the beam delay Doppler domain. The posterior mean value of the wave beam delay Doppler domain and the posterior variance of the wave beam delay Doppler domain form posterior statistical channel information of the wave beam delay Doppler domain. For a TDD system, the number of active terminals is,

the method can be obtained through feedback, and the posterior statistical information of the beam delay Doppler domain can be obtained on the basis by combining the prior statistical information of the beam delay Doppler domain. The method for acquiring posterior statistical information of beam delay Doppler domain is summarized as

Step 1: obtaining the prior statistical channel information omega of the wave beam delay Doppler domain of each user terminal before the current time slot by using the prior statistical channel information obtaining method of any one large-scale MIMO wave beam delay Doppler domain of the first two sections _k Wherein k is a user number;

step 2: acquiring pilot signals sent by each user terminal in the current time slot;

and step 3: estimating a beam delay Doppler domain channel matrix G using received pilot signals _k，m-1，1 Combining the beam delay Doppler domain prior statistical channel information and the correlation factor beta between channels _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 posterior statistical channel information of the wave beam time delay Doppler domain comprises a posterior mean value beta _k，m G _k，m-1，1 And posterior variance

6. Effects of the implementation

In order to make those skilled in the art better understand the solution of the present invention, the following provides the implementation effect of the prior statistical channel information acquisition based on the beam delay domain of the pilot signal in this embodiment under a specific system configuration, where the doppler domain is omitted for simplicity.

First, a specific system configuration of the present embodiment is described. Considering a MIMO system equipped with large-scale uniform area array, the number of base station side antennas is M _t =128, where the number of antennas in horizontal and vertical directions is M, respectively _x ＝16，M _z And =8, the antenna pitch is set to a half wavelength, and the user side is provided with a single antenna. The system employs OFDM modulation in which the carrier frequency f _c =4.8GHz, subcarrier spacing Δ f =30kHz, cyclic prefix length M _g =144, number of subcarriers M _c =2048, number of transmission subcarriers M _p =120. Refinement factor is set to M' _z ＝M′ _x ＝M′ _c And (2). In this embodiment, a scenario in which two users are different is considered, and the users are K = Q × P =1 × 12 and K = Q × P =2 × 12, respectively.

FIG. 4 shows the comparison of the prior statistical information estimation accuracy of the scheme of the patent and the M-FOCUSS algorithm. Wherein the evaluation index is an estimated energy matrix

Normalized Mean Square Error (NMSE) with the actual energy matrix omega. As can be seen from fig. 4, in both scenarios, the accuracy of the prior statistical information of the beam delay domain estimated by the scheme of the present invention is higher than that of M-FOCUSS, especially in low signal-to-noise ratio; besides, the patent scheme also shows strong anti-noise performance, and can estimate more accurate prior statistical information under low signal-to-noise ratio.

Fig. 5 shows a comparison of the performance of the scheme of the present patent with that of the prior statistical information estimated by the M-FOCUSS algorithm when applied to the estimation of instantaneous channel parameters. Wherein the instantaneous channel parameter estimation adopts Minimum Mean Square Error (MMSE) estimation algorithm to estimate the spatial frequency domain channel

With the actual space-frequency domain channel H _k Mean Square Error (MSE) between as performance evaluation index, where space-frequency domain channel H _k Has been subjected to normalization processing

It can be seen from the figure that when the SNR is less than 10dB, the scheme of the present invention can bring a large amount of channel estimation performance gains compared with the M-FOCUSS algorithm; even when SNR is more than 10dB, the channel estimation performance under the patent scheme can be basically equal to the performance of the MFOCUSS algorithm.

Finally, it is worth noting that the scheme of the patent can be implemented by using fast Fourier transform, and the computational complexity is

Wherein N = N _x N _z N _p T is iteration number which is far lower than that of the M-FOCUSS algorithm

Of the system.

Based on the same inventive concept, the embodiment of the present invention further discloses a computing device, which includes a memory, a processor, and a computer program stored in the memory and operable on the processor, where the computer program is loaded into the processor to implement the method for obtaining the foregoing large-scale MIMO beam delay doppler domain prior statistical channel information, or the method for obtaining the large-scale MIMO beam delay doppler domain posterior statistical channel information.

In a particular 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), microprocessor, application Specific Integrated Circuit (ASIC), or one or more integrated circuits for controlling the execution of programs in accordance with the inventive arrangements. The communication bus may include a path that transfers information between the aforementioned components. A communications interface, using any transceiver or the like, for communicating with other devices or communications networks. The memory may be, but is not limited to, a read-only memory (ROM) or other type of static storage device that may store static information and instructions, a random-access memory (RAM) or other type of dynamic storage device that may store information and instructions, an electrically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (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 desired program code in the form of instructions or data structures and that can be accessed by a computer. The memory may be self-contained and coupled to the processor via a bus. The memory may also be integral to the processor.

Wherein, the memory is used for storing application program codes for executing the scheme of the invention and is controlled by the processor to execute. The processor is used for executing the application program codes stored in the memory, so as to realize the information acquisition method provided by the embodiment. The processor may include one or more CPUs, or may include a plurality of processors, and each of the 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 (e.g., computer program instructions).

Based on the same inventive concept, the embodiment of the invention also discloses a large-scale MIMO communication system, which comprises a base station and a plurality of user terminals, wherein the base station is used for: receiving pilot signals sent by each mobile terminal; converting pilot signals received on a plurality of time slots into a beam delay Doppler domain; obtaining multi-user beam delay Doppler domain prior statistical channel information by using the beam delay Doppler domain sample statistics; and recovering the priori statistical channel information of the beam delay Doppler domain of each mobile terminal by using the priori statistical channel information of the multi-user beam delay Doppler domain.

Based on the same inventive concept, the embodiment of the invention also discloses a large-scale MIMO communication system, which comprises a base station and a plurality of user terminals, wherein the base station is used for: acquiring instantaneous channel information of each user on a plurality of time slots; converting the instantaneous channel information into a beam delay Doppler domain; and obtaining the prior statistical channel information of the beam delay Doppler domain of each mobile terminal by using the beam delay Doppler domain sample statistics.

Based on the same inventive concept, the embodiment of the invention also discloses a large-scale MIMO communication system, which comprises a base station and a plurality of user terminals, wherein the base station is used for: obtaining the prior statistical channel information of the beam delay Doppler domain of each user terminal before the current time slot by using the acquisition method of the prior statistical channel information of the large-scale MIMO beam delay Doppler domain; acquiring pilot signals sent by each user terminal in the current time slot; and estimating a wave beam delay Doppler domain channel matrix by using the received pilot signal, and acquiring wave beam delay Doppler domain posterior statistical channel information of each user terminal by combining the wave beam delay Doppler domain prior statistical channel information and the inter-channel correlation factor.

Based on the same inventive concept, the embodiment of the invention also discloses a large-scale MIMO communication system, which comprises a base station and a plurality of user terminals, wherein the base station is provided with the computing equipment.

In the examples provided herein, it is to be understood that the disclosed methods may be practiced otherwise than as specifically described without departing from the spirit and scope of the present application. The present embodiment is an exemplary example only, and should not be taken as limiting, and the specific disclosure should not be taken as limiting the purpose of the application. For example, some features may be omitted, or not performed. All matters not described in detail in this application are prior art.

The technical means disclosed in the invention scheme are not limited to the technical means disclosed in the above embodiments, but also include the technical scheme formed by any combination of the above technical features. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and such improvements and modifications are also considered to be within the scope of the present invention.

Claims

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 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 A3-3, 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:

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