CN110113084A - The channel prediction method of MIMO closed loop transmission system - Google Patents
The channel prediction method of MIMO closed loop transmission system Download PDFInfo
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- H04B17/373—Predicting channel quality or other radio frequency [RF] parameters
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- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
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- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/0413—MIMO systems
- H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
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Abstract
The invention discloses a kind of channel prediction methods of MIMO closed loop transmission system, belong to digital communicating field.Then this method feeds back to transmitting terminal and makees precoding according to the channel status of the channel state prediction subsequent time at the first two moment.Including: mimo system obtains the statistical information of channel by the measurement of a period of time, including Doppler shift, transmitting terminal and the correlation matrix of receiving end；The channel matrix of current time and previous moment is carried out singular value decomposition by receiver, and the several columns of right singular matrix are extracted two new matrixes of building, are modeled as two consecutive points of Grassmannian manifold；Based on the theory of geodesics of Grassmannian manifold, one geodesic curve of building is converted by series matrix, makes prediction to the channel status of subsequent time, finally feeds back to transmitting terminal.Compared with traditional prediction method, the method for the present invention is with the true channel status of subsequent time more closely, chordal distance error performance is more preferable.
Description
Technical field
The invention belongs to wireless communication technology fields, the in particular to channel prediction method of MIMO closed loop transmission system.
Background technique
Multiple antenna communication is equipped with more antennas in sending and receiving end, can make full use of space resources, with higher
Traffic rate and reliable communication quality receive extensive concern both at home and abroad in recent years.Since the system advantage is prominent, at present
It has been used as key technology to be used by 4G and 5G communication system.
Channel state information (channel state information, CSI) is particularly significant for communication system, can be with
It is pre-processed to transmitting terminal to improve system performance for decoded received data, or feedback.CSI generallys use channel estimation
It obtains, transmitting terminal is needed to assist per insertion pilot tone at regular intervals.But when channel variation is very fast, in order to accurate
Estimate channel, it has to frequently be inserted into pilot tone, this ratio that undoubtedly will cause pilot tone increases, and occupies compared with multi-system resource.
Therefore, it is necessary to be tracked and predicted to channel.Currently, most channel tracking algorithms are based on linear signal space, i.e. Europe
Space is obtained in several.On the other hand, important research achievement of the Differential Manifold as Modern Geometry, has been promoted in three-dimensional theorem in Euclid space
Curve and curved surface concept is a kind of important space in topology and geometry.Modern Geometry based on Differential Manifold is ground
Study carefully achievement and obtains some applications in the engineering fields such as pattern-recognition, image procossing.Britain's " applied optics progress "
(“Bayesian and geometric subspace tracking”,Advances in Applied Probability,
2004,36 (1): 43-56) point that time-varying array signal is regarded as to Grassmannian manifold, based on each point cut space and
Bayesian theory proposes a kind of tracking in time varying signal space.But this method is sufficiently complex, and needs data
Part prior information.The U.S. " International Electrical communicates journal with Electronic Engineering Association " (" Transmission subspace
Tracking for MIMO systems with low-rate feedback ", IEEE Transactions on
Communications, 2007,55 (8): 1629-1639) Grassmannian channel subspace tracking method is proposed, it feeds back
Link rate is very low, only 1 bit.The algorithm is generally speaking functional, but there is a problem of that convergence rate is slower.
“Grassmannian subspace prediction for precoded spatial multiplexing MIMO with
Delayed feedback ", IEEE Signal Processing Letters, 2011,18 (10): 555-558) it proposes
A kind of subspace Grassmannian Predicting Technique, but its string error performance is undesirable, and precision of prediction is to be improved.
Summary of the invention
In view of the above-mentioned problems existing in the prior art, it is an object of the invention to mention for the channel of MIMO closed loop transmission system
For a kind of trace geometry method, the accounting of pilot signal can be not only reduced, reduces system burden, and improve estimated performance and essence
Degree.
To solve the above-mentioned problems, the technical solution adopted in the present invention is as follows:
A kind of channel prediction method of MIMO closed loop transmission system, comprising the following steps:
(1) statistical information of channel is obtained by measurement, including Doppler shift, transmitting terminal and the correlation matrix of receiving end
θTAnd θR；
(2) singular value decomposition is done to the channel state matrix H (t) and H (t-1) at current time and previous moment respectively, obtains
To corresponding right singular value matrix V (t) and V (t-1), D column create new matrix V before extracting respectivelyd(t) and Vd(t-1)；
(3) a Special matrix E is constructed, singular value decomposition is made to E, then selects non-zero singular value in left singular value matrix
Corresponding column establish a new matrix
(4) to matrix [Vd(t-1)]HVd(t) singular value decomposition is done, matrix U is constructed2(t-1) and B (t-1)；
(5) according to Vd(t) and Vd(t-1) geodesic equation based on Grassmannian manifold is established, search is found optimal
Prediction step, and then obtain the pre-coding matrix of subsequent timeFeed back to transmitting terminal.
Singular value decomposition in the step 2 indicates are as follows:
H (t)=U (t) Λ (t) VH(t)
H (t-1)=U (t-1) Λ (t-1) VH(t-1)
Wherein subscriptHThe Hermitian of representing matrix is operated.
The step 4 is to matrix [Vd(t-1)]HVd(t) doing singular value decomposition can state are as follows:
[Vd(t-1)]HVd(t)=U1(t-1)C(t-1)[V1(t-1)]H
The matrix U that the step 4 constructs2(t-1) and B (t-1) is as follows:
Wherein,
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
() indicates sine value of negating point by point to matrix.
The geodesic equation based on Grassmannian manifold that the step 5 is established is as follows:
Wherein, NTThe matrix of × DIt is from NT×NTUnit matrix in select before D column composition, function EXP () represent
The exponent arithmetic of matrix；S indicates prediction step.
The step 5 finds optimum prediction step-length according to the following formula:
Wherein, function f () is the chordal distance of two points of Grassmannian manifold, is expressed as follows:
||.||FThe Frobenius norm of matrix is represented, D is to send substream of data number, and expectation is asked in E () representative.
Compared with the prior art, the invention has the benefit that
The present invention uses the theory of geodesics of Grassmannia manifold in channel tracking and prediction, when according to the first two
Then the channel status of the channel state prediction subsequent time at quarter feeds back to transmitting terminal and makees precoding.With traditional prediction technique
It compares, the method for the present invention is closer to the true channel status of subsequent time, and chordal distance error performance is more preferable.
Detailed description of the invention
Fig. 1 is the channel prediction method flow chart of MIMO closed loop transmission system of the invention；
Fig. 2 is performance comparison figure of the method in 44 receipts systems of hair with conventional method in Fig. 1.
Specific embodiment
Technical solution of the present invention is described further with reference to the accompanying drawing.It is to be appreciated that examples provided below
Merely at large and fully disclose the present invention, and sufficiently convey to person of ordinary skill in the field of the invention
Technical concept, the present invention can also be implemented with many different forms, and be not limited to the embodiment described herein.For
The term in illustrative embodiments being illustrated in the accompanying drawings not is limitation of the invention.
The present invention is suitable for point-to-point MIMO closed loop transmission system, and wherein transmitting terminal and receiving end are equipped with more days
Line, system have the channel information of feedback link feedback subsequent time (period).The input/output relation of mimo system can
To indicate are as follows:
Y (t)=H (t) W (t) x (t)+n (t) (1)
Wherein, H (t) is the N in moment (time slice) tR×NTMatrix is tieed up, W (t) is NTThe pre-coding matrix of × D, should
The Frobenius norm of matrix each column be 1 and different lines be orthogonal；N (t) is white Gaussian noise, and x (t) is to send data,
Its autocorrelation matrix meets E [x (t) xH(t)]=Id, IdIt is d rank unit matrix, symbol E () represents expectation computing, subscriptHGeneration
Table Hermitian transposition.
Mimo channel modeling are as follows:
Wherein, NT×NTTie up matrix θTAnd NR×NRTie up matrix θRRespectively represent the channel Correlation Moment of transmitting terminal and receiving end
Battle array；Hω(t) it is N in moment (time slice) tR×NTRandom matrix is tieed up, matrix each element obeys equal value zero, variance 1
Gaussian Profile, and it is mutually indepedent between element.Order matrix Hω(t)=(hij(t)), the temporal correlation between each element can
To be described with Jake ' s model:
E[hij(t1)(hij(t2))*]=J0(2πfd(t2-t1)) (3)
Wherein fdIt is Doppler shift, function J0() is first kind zero Bessel function.
As shown in Figure 1, channel prediction method to MIMO closed loop transmission system system the following steps are included:
Step 1, system obtains the statistical information of channel, including Doppler shift f by the measurement of a period of timed, send
The correlation matrix θ at end and receiving endTAnd θR。
In one embodiment, the sending and receiving end of mimo system is equipped with 4 antennas, sends substream of data number D=2.Letter
The correlation matrix θ in roadTAnd θRIt is all made of correlation of indices model, coefficient is respectively set to 0.2 and 0.3；Normalized Doppler shift
fdTsIt is set as 0.05, wherein TsIt is the interval of adjacent moment (time slice).
The channel model that statistical information is substituted into formula (2)-(3) description, pays attention to (the t of formula (3)2-t1) should change into it is adjacent
Time at intervals Ts, obtain channel matrix sample.
Step 2, singular value point is done to 4 × 4 dimensions channel matrix H (t) and H (t-1) of current time and previous moment respectively
Solution, obtains corresponding right singular value matrix V (t) and V (t-1), extracts preceding 2 column, two 4 × 2 matrix Vs of creation respectivelyd(t) and Vd
(t-1), t=1,2 ... Ns, wherein NsIt is number of samples.
Here, the singular value decomposition of H (t) and H (t-1) respectively indicate are as follows:
H (t)=U (t) Λ (t) VH(t) (4)
H (t-1)=U (t-1) Λ (t-1) VH(t-1) (5)
Wherein subscriptHThe Hermitian of representing matrix is operated.
Previous moment and the channel information Vd at current time (t-1) and Vd (t) are extracted by step 2, is modeled as
Two points of Grassmannian manifold, to construct the geodesic equation of the two points.
Step 3, a Special matrix E=I is constructed4-Vd(t-1)[Vd(t-1)]H, wherein I4It is 4 × 4 unit matrix；It is right
E makees singular value decomposition, then selects the corresponding column of non-zero singular value in left singular value matrix, establishes 4 × 2 new matrixesConstructing E is to find out vd(t-1) orthogonal complement matrixIt is easily verified that E and vd(t-1) orthogonal, but E
It is not also orthogonal matrix, so singular value decomposition need to be made to E.
Step 4, to matrix [Vd(t-1)]HVd(t) singular value decomposition is done, matrix U is constructed2(t-1) and B (t-1).Here,
[Vd(t-1)]HVd(t)=U1(t-1)C(t-1)[V1(t-1)]H (6)
Wherein, 2 × 2 matrix4 × 4 matrix Bs (t-1) indicate are as follows:
Wherein, 2 × 2 matrix As (t-1)=U2(t-1)Φ(t-1)[U1(t-1)]H, 2 × 2 matrix Φ (t-1)=sin-1(S
(t-1)), function sin-1() indicates sine value of negating point by point to matrix.
Step 3 and 4 geodesic equations being provided to find out in step 5 that are done.There is geodesic equation, it could basis
The first two point gives a forecast to following precoding.
Step 5, according to Vd(t) and Vd(t-1) geodesic equation based on Grassmannian manifold is established, search is found
Optimum prediction step-length obtains the pre-coding matrix of subsequent timeFeed back to transmitting terminal.Include the following steps:
5-1) according to Vd(t) and Vd(t-1) geodesic equation is established:
Wherein, 4 × 2 matrix I4,2It is that preceding 2 column composition is selected from 4 × 4 unit matrix, function EXP () represents square
The exponent arithmetic of battle array；4 × 4 matrix
5-2) find optimum prediction step-length SOPT。
Wherein, function f () represents the chordal distance of two points of Grassmannian manifold, is expressed as follows:
||.||FThe Frobenius norm of matrix is represented, expectation is asked in E () representative.Formula (11) indicates given prediction step s,
Chordal distance error between the channel information of prediction and true channel information.
When channel statistical information is constant, optimal step size is also constant, and therefore, this step only needs to calculate once.
5-3) obtain the pre-coding matrix of subsequent time.Substitute into optimum prediction step-length sOPTTo geodesic equation, obtain
5-4) feed backTo transmitting terminal.
Fig. 2 is that the chordal distance error performance of the method for the present invention and conventional method compares under 44 receipts systems of hair, conventional method
See " International Electrical communicates flash report with Electronic Engineering Association " (" Grassmannian subspace prediction for
Precoded spatial multiplexing MIMO with delayed feedback ", IEEE Signal
Processing Letters, 2011,18 (10): 555-558), chordal distance error is by formula hereIt is calculated.It can be seen that being proposed in the entire variation range of prediction step s (0~1)
The chordal distance error of method is smaller than conventional method.The chordal distance error of conventional method is in sOPTReach minimum value-when=0.7
8.80dB；The chordal distance error of proposition method is in sOPTReach minimum value -9.96dB when=0.8, is better than conventional method 1.16dB.
Claims (7)
1. a kind of channel prediction method of MIMO closed loop transmission system, which is characterized in that the described method comprises the following steps:
(1) statistical information of channel is obtained by measurement, including Doppler shift, transmitting terminal and the correlation matrix of receiving end θTWith
θR, according to channel model, obtain channel state matrix；
(2) singular value decomposition is done to the channel state matrix H (t) and H (t-1) at current time and previous moment respectively, obtains phase
The right singular value matrix V (t) answered and V (t-1), D column create new matrix V before extracting respectivelyd(t) and Vd(t-1), D is to send number
According to subflow number；
(3) a Special matrix E is constructed,WhereinIt is NT×NTUnit matrix, NTIt is hair
The antenna number of sending end makees singular value decomposition to E, selects the corresponding column of non-zero singular value in left singular value matrix, establishes one newly
Matrix
(4) to matrix [Vd(t-1)]HVd(t) singular value decomposition is done, matrix U is constructed2(t-1) and B (t-1)；
(5) according to Vd(t) and Vd(t-1) geodesic equation based on Grassmannian manifold is established, optimum prediction is found in search
Step-length, and then obtain the pre-coding matrix of subsequent timeFeed back to transmitting terminal.
2. the channel prediction method of MIMO closed loop transmission system according to claim 1, which is characterized in that the step 1
The singular value decomposition of middle H (t) and H (t-1) respectively indicate are as follows:
H (t)=U (t) Λ (t) VH(t)
H (t-1)=U (t-1) Λ (t-1) VH(t-1)
Wherein subscriptHThe Hermitian of representing matrix is operated.
3. the channel prediction method of MIMO closed loop transmission system according to claim 1, which is characterized in that the step 4
In to matrix [Vd(t-1)]HVd(t) singular value decomposition expression is done are as follows:
[Vd(t-1)]HVd(t)=U1(t-1)C(t-1)[V1(t-1)]H。
4. the channel prediction method of MIMO closed loop transmission system according to claim 3, which is characterized in that the step 4
Construct matrix U2(t-1) it is respectively as follows: with B (t-1)
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() is indicated to square
The point-by-point sine value of negating of battle array.
5. the channel prediction method of MIMO closed loop transmission system according to claim 4, which is characterized in that the step 5
The geodesic equation based on Grassmannian manifold established are as follows:
Wherein,It is from NT×NTUnit matrix in select before D column composition NT× D matrix, function EXP () represent matrix
Exponent arithmetic；S indicates prediction step.
6. the channel prediction method of MIMO closed loop transmission system according to claim 5, which is characterized in that the step 5
Optimum prediction step-length S is found according to the following formulaOPT:
Wherein, expectation is asked in E () representative, and function f () is the chordal distance of two points of Grassmannian manifold, representation are as follows:
||.||FThe Frobenius norm of matrix is represented, D is to send substream of data number.
7. the channel prediction method of MIMO closed loop transmission system according to claim 6, which is characterized in that the step 5
Obtain the pre-coding matrix of subsequent timeMethod is as follows: substituting into optimum prediction step-length sOPTTo geodesic equation, obtain
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