CN110113084B - Channel prediction method of MIMO closed-loop transmission system - Google Patents

Abstract

The invention discloses a channel prediction method of a MIMO closed-loop transmission system, which belongs to the field of digital communication. The method predicts the channel state of the next moment according to the channel state of the previous two moments, and then feeds it back to the sender for precoding. Including: the MIMO system obtains the statistical information of the channel by measuring for a period of time, including the Doppler frequency offset, the correlation matrix of the transmitting end and the receiving end; Several columns of the matrix are extracted to construct two new matrices, which are modeled as two adjacent points of the Grassmannian manifold; based on the geodesic theory of the Grassmannian manifold, a geodesic line is constructed through a series of matrix transformations. The channel state is predicted and finally fed back to the sender. Compared with the traditional prediction method, the method of the present invention is closer to the real channel state at the next moment, and the performance of the chord distance error is better.

Description

Channel prediction method for MIMO closed-loop transmission system

technical field

The invention belongs to the technical field of wireless communication, and particularly relates to a channel prediction method of a MIMO closed-loop transmission system.

Background technique

Multi-antenna communication systems are equipped with multiple antennas at the transceiver end, which can make full use of space resources, have high communication rates and reliable communication quality, and have received extensive attention at home and abroad in recent years. Due to the outstanding advantages of this system, it has been adopted as a key technology in 4G and 5G communication systems.

Channel state information (CSI) is very important for communication systems, and can be used to decode received data, or fed back to the sender for preprocessing to improve system performance. CSI is usually obtained by channel estimation, which requires the transmitter to insert pilots at regular intervals for assistance. However, when the channel changes rapidly, in order to estimate the channel accurately, pilots have to be frequently inserted, which will undoubtedly increase the proportion of pilots and occupy more system resources. Therefore, the channel needs to be tracked and predicted. At present, most channel tracking algorithms are based on linear signal space, namely Euclidean space. On the other hand, as an important research achievement of modern geometry, differential manifolds promote the concepts of curves and surfaces in three-dimensional Euclidean space, and are an important space in topology and geometry. The research results of modern geometry based on differential manifolds have been applied in engineering fields such as pattern recognition and image processing. British "Bayesian and geometric subspace tracking" ("Bayesian and geometric subspace tracking", Advances in Applied Probability, 2004, 36(1):43-56) regards time-varying array signals as points of a Grassmannian manifold, based on the Tangent space and Bayesian theory propose a tracking method in time-varying signal space. But this method is very complex and requires some prior information about the data. The American "International Institute of Electrical and Electronics Engineers" ("Transmission subspacetracking for MIMO systems with low-rate feedback", IEEE Transactions on Communications, 2007, 55(8):1629-1639) proposed the Grassmannian channel subspace tracking method. The feedback link rate is very low, only 1 bit. The overall performance of the algorithm is good, but there is a problem of slow convergence. "Grassmannian subspace prediction for precoded spatial multiplexing MIMO with delayed feedback", IEEE Signal Processing Letters, 2011, 18(10): 555-558) proposed a Grassmannian subspace prediction technique, but its chord error performance is not ideal, and the prediction accuracy needs to be improve.

SUMMARY OF THE INVENTION

In view of the above problems existing in the prior art, the purpose of the present invention is to provide a geometric tracking method for the channel of a MIMO closed-loop transmission system, which can not only reduce the proportion of pilot signals, reduce the system burden, but also improve the prediction performance and accuracy.

In order to solve the above problems, the technical scheme adopted in the present invention is as follows:

A channel prediction method for a MIMO closed-loop transmission system, comprising the following steps:

(1) The statistical information of the channel is obtained by measurement, including the Doppler frequency offset, the correlation matrix θ _T and θ _R of the transmitting end and the receiving end;

(2) Perform singular value decomposition on the channel state matrices H(t) and H(t-1) of the current moment and the previous moment, respectively, to obtain the corresponding right singular value matrices V(t) and V(t-1), Extract the first D columns to create new matrices V _d (t) and V _d (t-1) respectively;

(3) Construct a special matrix E, perform singular value decomposition on E, and then select the column corresponding to the non-zero singular value in the left singular value matrix to establish a new matrix

(4) Perform singular value decomposition on the matrix [V _d (t-1)] ^H V _d (t) to construct matrices U ₂ (t-1) and B(t-1);

反馈给发送端。(5) Establish a geodesic equation based on Grassmannian manifold according to V _d (t) and V _d (t-1), search to find the optimal prediction step size, and then obtain the precoding matrix at the next moment

feedback to the sender.

The singular value decomposition in step 2 is expressed as:

H(t)=U(t)Λ(t)V ^H (t)

H(t-1)=U(t-1)Λ(t-1)V ^H (t-1)

where the superscript ^H represents the Hermitian operation of the matrix.

In the step 4, the singular value decomposition of the matrix [V _d (t-1)] ^H V _d (t) can be expressed as:

[V _d (t-1)] ^H V _d (t)=U ₁ (t-1)C(t-1)[V ₁ (t-1)] ^H

The matrices U ₂ (t-1) and B(t-1) constructed in the step 4 are as follows:

in,

Among them, A(t-1)=U ₂ (t-1)Φ(t-1)[U ₁ (t-1)] ^H , Φ(t-1)=sin ^-1 (S(t-1) ), the function sin ^-1 (.) means to find the arc sine of the matrix point by point.

The geodesic equation based on the Grassmannian manifold established in the step 5 is as follows:

是从N_T×N_T的单位矩阵中选择前D列组成，函数EXP(.)代表矩阵的指数运算；

s表示预测步长。Among them, the matrix of N _T × D

It is composed of the first D columns selected from the N _T ×N _T identity matrix, and the function EXP(.) represents the exponential operation of the matrix;

s represents the prediction step size.

The step 5 finds the optimal prediction step size according to the following formula:

where the function f(.) is the chord distance between two points of the Grassmannian manifold, expressed as follows:

||.|| _F represents the Frobenius norm of the matrix, D is the number of transmitted data substreams, and E(.) represents the expectation.

Compared with the prior art, the beneficial effects of the present invention are:

The invention applies the geodesic theory of Grassmannia manifold to channel tracking and prediction, predicts the channel state of the next moment according to the channel state of the previous two moments, and then feeds it back to the transmitting end for precoding. Compared with the traditional prediction method, the method of the present invention is closer to the real channel state at the next moment, and the performance of the chord distance error is better.

Description of drawings

Fig. 1 is the flow chart of the channel prediction method of the MIMO closed-loop transmission system of the present invention;

FIG. 2 is a performance comparison diagram between the method in FIG. 1 and the traditional method in a 4-transmit and 4-receive system.

Detailed ways

The technical solutions of the present invention will be further described below with reference to the accompanying drawings. It should be understood that the embodiments provided below are only to disclose the present invention in detail and completely, and to fully convey the technical idea of the present invention to those skilled in the art, and the present invention can also be implemented in many different forms, and does not Limited to the embodiments described here. The terms used in the exemplary embodiments shown in the drawings are not intended to limit the invention.

The present invention is applicable to a point-to-point MIMO closed-loop transmission system, wherein the transmitting end and the receiving end are equipped with multiple antennas, and the system has a feedback link to feed back the channel information of the next moment (time period). The input-output relationship of the MIMO system can be expressed as:

y(t)=H(t)W(t)x(t)+n(t) (1)

where H(t) is an N _R ×N _T dimensional matrix at time (time slice) t, and W(t) is an N _T ×D precoding matrix with Frobenius norm 1 for each column of the matrix and different columns It is orthogonal; n(t) is Gaussian white noise, x(t) is the transmitted data, and its autocorrelation matrix satisfies E[x(t) ^xH (t)]=I _d , I _d is the d-order identity matrix , the symbol E(.) represents the expectation operation, and the superscript ^H represents the Hermitian transpose.

The MIMO channel is modeled as:

Among them, the N _T ×N _T -dimensional matrix θ _T and the N _R ×N _R -dimensional matrix θ _R represent the channel correlation matrices of the transmitter and receiver, respectively; H _ω (t) is the N _R ×N at time (time segment) t _T -dimensional random matrix, each element of the matrix obeys a Gaussian distribution with mean zero and variance 1, and the elements are independent of each other. Let matrix H _ω (t)=(h _ij (t)), the time correlation between each element can be described by Jake's model:

E[h _ij (t ₁ )(h _ij (t ₂ )) ^* ]=J ₀ (2πf _d (t ₂ -t ₁ )) (3)

where f _d is the Doppler frequency offset and the function J ₀ (.) is a zero-order Bessel function of the first kind.

As shown in Figure 1, the channel prediction method for the MIMO closed-loop transmission system includes the following steps:

Step 1, the system obtains the statistical information of the channel by measuring for a period of time, including the Doppler frequency offset f _d , the correlation matrices θ _T and θ _R of the transmitting end and the receiving end.

In one embodiment, the transceiver ends of the MIMO system are equipped with four antennas, and the number of transmitted data sub-streams is D=2. The correlation matrices θ _T and θ _R of the channel both adopt the exponential correlation model, and the coefficients are set to 0.2 and 0.3 respectively; the normalized Doppler frequency offset f _d T _s is set to 0.05, where T _s is the adjacent moment (time segment). ) interval.

Substitute the statistical information into the channel model described by formulas (2)-(3). Note that (t ₂ -t ₁ ) in formula (3) should be replaced by the adjacent time interval T _s to obtain channel matrix samples.

Step 2: Perform singular value decomposition on the 4 × 4-dimensional channel matrices H(t) and H(t-1) at the current moment and the previous moment, respectively, to obtain the corresponding right singular value matrices V(t) and V(t- 1), extract the first 2 columns to create two 4×2 matrices V _d (t) and V _d (t-1), t=1,2...N _s , where N _s is the number of samples.

Here, the singular value decompositions of H(t) and H(t-1) are expressed as:

H(t)=U(t)Λ(t)V ^H (t) (4)

H(t-1)=U(t-1)Λ(t-1)V ^H (t-1) (5)

where the superscript ^H represents the Hermitian operation of the matrix.

Through step 2, the channel information Vd(t-1) and Vd(t) of the previous moment and the current moment are extracted and modeled as two points of the Grassmannian manifold, so as to construct the geodesic equation of these two points.

构造E是为了求出v_d(t-1)的正交补矩阵

容易验证E与v_d(t-1)正交，但是E还不是正交矩阵，所以需对E作奇异值分解。Step 3, construct a special matrix E=I ₄ -V _d (t-1)[V _d (t-1)] ^H , where I ₄ is a 4×4 identity matrix; perform singular value decomposition on E, and then select Create a new 4×2 matrix for the columns corresponding to non-zero singular values in the left singular value matrix

E is constructed to find the orthogonal complement of v _d (t-1)

It is easy to verify that E is orthogonal to v _d (t-1), but E is not an orthogonal matrix, so it is necessary to perform singular value decomposition on E.

Step 4: Perform singular value decomposition on the matrix [V _d (t-1)] ^H V _d (t) to construct matrices U ₂ (t-1) and B(t-1). here,

[V _d (t-1)] ^H V _d (t)=U ₁ (t-1)C(t-1)[V ₁ (t-1)] ^H (6)

4×4矩阵B(t-1)表示为：Among them, 2 × 2 matrix

The 4×4 matrix B(t-1) is expressed as:

Among them, 2×2 matrix A(t-1)=U ₂ (t-1)Φ(t-1)[U ₁ (t-1)] ^H , 2×2 matrix Φ(t-1)=sin ^{− 1} (S(t-1)), the function sin ^-1 (.) means to find the arc sine of the matrix point by point.

All steps 3 and 4 do is to solve the geodesic equation in step 5. With the geodesic equation, we can make predictions about future precoding based on the first two points.

反馈给发送端。包括如下步骤：Step 5: Establish a geodesic equation based on Grassmannian manifold according to V _d (t) and V _d (t-1), search to find the optimal prediction step size, and obtain the precoding matrix at the next moment

feedback to the sender. It includes the following steps:

5-1) Establish the geodesic equation according to V _d (t) and V _d (t-1):

Among them, the 4×2 matrix I _4,2 is composed of the first 2 columns selected from the 4×4 identity matrix, and the function EXP(.) represents the exponential operation of the matrix; the 4×4 matrix

5-2) Find the optimal prediction step size S _OPT .

Among them, the function f(.) represents the chord distance between two points of the Grassmannian manifold, which is expressed as follows:

||.|| _F represents the Frobenius norm of the matrix, and E(.) represents the expectation. Equation (11) represents the chord distance error between the predicted channel information and the real channel information given the prediction step size s.

When the channel statistics do not change, the optimal step size also does not change, so this step only needs to be calculated once.

5-3) Obtain the precoding matrix at the next moment. That is, substituting the optimal prediction step size s _OPT into the geodesic equation, we get

给发送端。5-4) Feedback

to the sender.

计算得到。可以看到，在预测步长s的整个变化范围内(0～1)，提出方法的弦距离误差均比传统方法小。传统方法的弦距离误差在s_OPT＝0.7时达到最小值-8.80dB；提出方法的弦距离误差在s_OPT＝0.8时达到最小值-9.96dB，优于传统方法1.16dB。Figure 2 is a comparison of the chord distance error performance between the method of the present invention and the traditional method under the system of 4 transmitters and 4 receivers. For the traditional method, see "Grassmannian subspace prediction forprecoded spatial multiplexing MIMO with delayed feedback", IEEE Signal Processing Letters, 2011, 18(10): 555-558), where the chord distance error is given by the formula

Calculated. It can be seen that the chord distance error of the proposed method is smaller than that of the traditional method in the entire variation range of the prediction step s (0-1). The chord distance error of the traditional method reaches the minimum value of -8.80dB when s _OPT =0.7; the chord distance error of the proposed method reaches the minimum value of -9.96dB when s _OPT =0.8, which is 1.16dB better than the traditional method.

Claims (2)

1. A method for channel prediction in a MIMO closed-loop transmission system, the method comprising the steps of:

(1) obtaining statistical information of the channel by measurement, including Doppler frequency offset, correlation matrix theta of the transmitting end and the receiving end_TAnd theta_RObtaining a channel state matrix according to the channel model;

(2) respectively carrying out singular value decomposition on the channel state matrixes H (t) and H (t-1) at the current moment and the previous moment to obtain corresponding right singular value matrixes V (t) and V (t-1), respectively extracting the front D columns of the channel state matrixes H (t) and H (t-1) to create new matrixes V_d(t) and V_d(t-1), D is the number of transmitted data substreams;

(3) constructing a special matrix E, E ═ I_NT-V_d(t-1)[V_d(t-1)]^HIn which I_NTIs N_T×N_TIdentity matrix of N_TThe number of antennas at the transmitting end is determined, singular value decomposition is carried out on E, a column corresponding to a non-zero singular value in a left singular value matrix is selected, and a new matrix is established

(4) Pair matrix [ V ]_d(t-1)]^HV_d(t) performing singular value decomposition to construct a matrix U₂(t-1) andb (t-1), wherein the matrix [ V ] is aligned_d(t-1)]^HV_d(t) singular value decomposition is performed as: [ V ]_d(t-1)]^HV_d(t)＝U₁(t-1)C(t-1)[V₁(t-1)]^H(ii) a Matrix U₂(t-1) and B (t-1) are respectively:

wherein,

A(t-1)＝U₂(t-1)Φ(t-1)[U₁(t-1)]^H，Φ(t-1)＝sin^-1(S (t-1)), function sin^-1(.) represents the inverse sine value point by point of the matrix;

(5) according to V_d(t) and V_d(t-1) establishing a geodesic equation based on Grassmannian manifold, searching and finding the optimal prediction step length, and further obtaining the precoding matrix at the next moment

And feeding back to the sending end, wherein a geodesic equation based on Grassmannian manifold is as follows:

wherein,

is from N_T×N_TSelecting N composed of the first D columns in the unit matrix_TA x D matrix, function EXP (.) representing the exponential operation of the matrix;

s represents a prediction step size;

finding the optimal predicted step length S according to the following formula_OPT：

Where E (.) represents the expectation, and the function f (.) is the chordal distance of two points of the Grassmannian manifold, expressed in the form:

||.||_Fthe Frobenius norm of the representative matrix, D is the number of transmitted data substreams;

obtaining a precoding matrix of a next time

The method comprises the following steps: substituting the optimal predicted step length s_OPTTo the geodesic equation to obtain

2. The channel prediction method of the MIMO closed-loop transmission system according to claim 1, wherein the singular value decomposition of H (t) and H (t-1) in step (2) is represented as:

H(t)＝U(t)Λ(t)V^H(t)

H(t-1)＝U(t-1)Λ(t-1)V^H(t-1)

wherein the superscript is^HThe Hermitian operation of the matrix is represented.

Images