CN103957086B - MU MIMO precoding implementation methods - Google Patents

Abstract

The invention discloses a kind of MU MIMO precoding implementation methods, especially by the combined channel matrix H to all users_SThe QR that are improved of extended matrix H decompose to obtain first pre-coding matrix to eliminate multi-user interference, and the result decomposed according to QR to determine the pre-coding matrix of each user, reduce the complexity of calculating；Then second more excellent pre-coding matrix of performance is obtained using lattice reduction method.The method of the present invention improves systematic function than traditional MU MIMO method for precoding while more low complex degree is obtained.

Description

MU-MIMO precoding implementation methods

Technical field

The invention belongs to mobile communication technology field, is related to multiple-input and multiple-output therein（Multiple Input Multiple Output, MIMO）Technology, and in particular to multiuser MIMO（Multiuser MIMO, MU-MIMO）In system Precoding algorithms.

Background technology

MIMO as a kind of technology that can greatly improve wireless communication spectrum efficiency, in the increasingly rare back of the body of frequency spectrum resource It is of increased attention under scape.With going deep into that multi-antenna technology is studied, MIMO technology is from point-to-point single user System extend to the multi-user system of point-to-multipoint.In MU-MIMO system, base station（Base Station, BS）Simultaneously to many Individual user's sending signal, due to the same running time-frequency resource of multiple users to share, will certainly cause inter-user interference（Multi-user Interference, MUI）, substantially reduce the efficiency of transmission of system.It is logical to high data rate in order to meet next generation communication system The requirement of letter, can effectively suppress the precoding technique of MUI to occur in a large number.

In descending MU-MIMO system, it is known that optimum precoding algorithms are dirty paper codes（Dirty Paper Coding, DPC）But, due to computational complexity it is too high, it is difficult to use in systems in practice.Therefore the low complexity of some suboptimums Degree precoding algorithms are suggested, wherein, block diagonalization（Block Diagonalization, BD）Precoding algorithms are current Widely used one kind in MU-MIMO, the main thought of the algorithm may be summarized to be at following 2 points：

Each user utilizes singular value decomposition（Singular Value Decomposition, SVD）Find other users The null space basis of combined channel matrix, constitute the pre-coding matrix of oneself with which, eliminate MUI with this, obtain equivalent SU- Mimo channel；Singular value decomposition is carried out to equivalent SU-MIMO channels, optimizes system energy using SVD precoding algorithms.

Therefore the pre-coding matrix W of user can be divided into two parts：W=W^aW^b, correspond at above-mentioned 2 points respectively.Traditional BD algorithms Although MUI can be completely eliminated, however it is necessary that using the singular value decomposition with higher computational complexity twice（SVD）To ask for The pre-coding matrix of each user, increased the complexity of algorithm itself, limit algorithm use in systems in practice, therefore A kind of GZI of low complex degree（Generalized ZF Channel Inversion）Precoding algorithms are suggested.

Separately below two kinds of method for precoding of BD and GZI are briefly described.

（One）, BD method for precoding

For convenience of description and analysis, it is assumed that in MU-MIMO system, the transmission antenna number of base station end is N_T, k-th use The reception antenna number at family is N_k, total number of users is K, and the K total reception antenna receipts number of user isBase station end Transmitting antenna number N_TMore than or equal to the total N of user's reception antenna_R。

To any user k, its channel matrix is H_k, interference channel matrix is Pre-coding matrix is W_k；The combined channel matrix of all K users isJoint pre-coding matrix is W=[W₁W₂…W_K]。

The method is comprised the following steps：

Step 1, base station obtain the down channel matrix H of each user_k(k=1,2,…,K).It is multiplexed in time division duplex（TDD） Under pattern, the channel information of user can be known in base station by channel reciprocity；It is multiplexed in FDD（FDD）Under pattern, Its channel information can be known by the feedback of user terminal in base station.

Step 2, the interference channel matrix to any user kCarry out SVD decompositionWherein,It isLeft singular matrix,It isSingular value diagonal matrix,WithIt is respectivelyRight singular matrix front r row and after（N_T-r）Row, r is matrixOrder.Can by matrix theory knowledge Know,It isKernel orthogonal basiss, i.e.,SoCan be used as first of user's k pre-coding matrixes PointInter-user interference is eliminated with this, independent equivalent channel matrix is obtained

For all K users, the Part I of its joint pre-coding matrix isWith this by The a plurality of independent parallel equivalent SU-MIMO channels of MU-MIMO channel decomposings：

Step 3, in order to obtain the maximum pre-coding gain of equivalent channel matrix, is carried out again to equivalent SU-MIMO channels SVD decomposesWherein, U_kIt isLeft singular matrix, Σ_kIt isIt is unusual Value diagonal matrix, V_kIt isRight singular matrix,It is V_kFront N_kRow.According to single user SVD precoding algorithms, chooseAs pre-coding matrix, it is possible to obtain the maximum pre-coding gain under Single User MIMO system.Therefore the precoding of user k The Part II of matrix isFor all K users, the Part II of its joint pre-coding matrix is

Step 4, obtains the pre-coding matrix of whole system：W=W^aW^b。

（Two）, GZI method for precoding

The method is comprised the following steps：

Step 1, calculates combined channel matrix H_SPseudoinverse：Its In,It isSubmatrix, dimension is N_T×N_k；

Step 2 is rightCarry out QR decomposition：Wherein,It is orthogonal matrix,It is upper triangular matrix.According to The property of pseudoinverse understandsI.e.BecauseIt is invertible matrix,SoCan conduct The Part I of user's k pre-coding matrixesSo as to obtain independent equivalent channel matrix

For all K users, the Part I of its joint pre-coding matrix is

Step 3, in order to obtain the maximum pre-coding gain of equivalent channel matrix, is carried out again to equivalent SU-MIMO channels SVD decomposesChoose right singular matrix V_kFront N_kRow prelisting as user k The Part II of code matrix, i.e.,For all K users, the Part II of its joint pre-coding matrix is

Step 4, obtains the pre-coding matrix W=W of whole system^aW^b。

Although GZI method for precoding is decomposed with solution pseudo-inverse operation and QR instead of in the BD method for precoding first steps SVD decomposes, and complexity decreases, but solution pseudoinverse remains a kind of higher computing of complexity, and both of which is needed The equivalent channel matrix that be directed to each user carries out SVD decomposition, therefore the complexity of GZI method for precoding is still higher.

The content of the invention

For the problems referred to above that prior art is present, the present invention devises a kind of decomposition based on improved QR and lattice reduction The MU-MIMO method for precoding of method, the method are improve while tradition MU-MIMO precoding algorithms complexities are reduced Algorithm performance.

The present invention concrete technical scheme be：A kind of MU-MIMO precodings implementation method, specifically includes following steps：

The combined channel matrix of all K users of step 1. isTo combining channel matrix H_S It is extended：Wherein, α=N_Rσ²/P_total, σ²Represent the variance of noise, P_totalRepresent that downlink is total Transmit power,Expression dimension is N_R×N_RUnit matrix；

Step 2. is to extended channel matricesConjugate transposeCarry out QR decomposition：Obtain Dimension is N_R×N_RUpper triangular matrixIt is (N with dimension_T+N_R)×N_RUnitary matriceIt is used in combinationRepresent unitary matrice's Front N_TOK,Represent unitary matriceRear N_ROK；

Step 3. byObtainAnd then obtain Wherein,It isSubmatrix, dimension is N_T×N_k, N_kFor k-th The reception antenna number of user；

Step 4. is obtainedOrthogonal basiss P_k, then the Part I of the arbitrarily pre-coding matrix of user k be Inter-user interference is eliminated with this, so as to obtain the equivalent channel matrix after first time precoding

For all K users, the Part I of its joint pre-coding matrix is W^a=[P₁P₂…P_k], with this by The a plurality of independent equivalent SU-MIMO channels of MU-MIMO channel decomposings, H_SW^a=diag{H₁P₁,H₂P₂,…,H_KP_K}；

The step 5. pair arbitrarily equivalent channel matrix of user kTranspositionCarry out lattice about to subtract（LR）Operation：Transformation matrix T_kFor unimodular matrix, i.e. T_kThe value of middle element is for complex integers and determinant meets det (T_k)=±1；

According to the property of LR, the more preferable equivalent channel matrix of orthogonality after about subtracting, is obtainedNoise can effectively be reduced to put Big problem.

Step 6. pair about subtract after equivalent channel matrixIt is extended：

Step 7. is to extended channel matricesConjugate transposeCarry out QR decomposition： It is N to dimension_k×N_kUpper triangular matrixIt is (N with dimension_k+N_k)×N_kUnitary matriceIt is used in combinationRepresent unitary matrice Front N_kOK,Represent unitary matriceRear N_kOK.

Step 8. byObtainSo

Step 9. pair arbitrarily user k, willAs the Part II of pre-coding matrix, i.e.,

For all K users, the Part II of its joint pre-coding matrix is

Step 10. obtains the pre-coding matrix W=W of whole system^aW^b。

Beneficial effects of the present invention：Combined channel matrix H of the method for the present invention first to all users_SExtended matrixThe QR that is improved decomposes to obtain first pre-coding matrix to eliminate multi-user interference, and the result decomposed according to QR come Determine the pre-coding matrix of each user, reduce the complexity of calculating；Then utilize lattice reduction（LR）Method obtains performance more Second excellent pre-coding matrix, the method for the present invention are obtaining the same of more low complex degree than traditional MU-MIMO method for precoding When, improve systematic function.

Description of the drawings

Fig. 1 is multi-user MIMO system schematic diagram in the embodiment of the present invention.

Fig. 2 is the complexity comparison schematic diagram of the inventive method and tradition BD and GZI methods.

Fig. 3 is the complexity comparison schematic diagram of the inventive method and tradition BD and GZI methods.

Fig. 4 is the power system capacity comparison schematic diagram of the inventive method and tradition BD and GZI methods.

Fig. 5 is the bit error rate comparison schematic diagram of the inventive method and tradition BD and GZI methods.

Specific embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described further.Parameter in embodiment not shadow Ring the generality of the present invention.

Method for precoding with the analysis present invention, does following setting to MU-MIMO system for convenience of description：Such as Fig. 1 institutes Show, sum of the transmitting antenna sum more than or equal to all user's reception antennas, i.e. N_T≥N_R；The data communicated by each user Fluxion is equal with its reception antenna number, and the distribution of base station end transmission power adopts average power allocation.

The signal that arbitrarily user k is received can be expressed as：

Formula（1）

Formula（1）In, H_kIt is the N of k-th user_k×N_TDimension channel matrix, H_kIn element it is separate and obey average For 0, variance is 1 multiple Gauss distribution；W_kIt is the N of k-th user_T×N_kDimension pre-coding matrix；s_kIt is the N of k-th user_kDimension is sent out Penetrate symbolic vector；n_kIt is N_kThe column vector of dimension, is the independent identically distributed additive white Gaussian noise of k-th user, and variance is σ_k ²。

The embodiment of the present invention simplifies combined channel matrix H_SThe process that pseudoinverse is solved, and consider noise to systematic function Impact, about subtract in combination with lattice（LR）Technology, improves systematic function, reduces the complexity of computing.Concrete steps are such as Under：

Step 1. pair combines channel matrix H_SIt is extended：Wherein, α=N_Rσ²/P_total, σ²Represent The variance of noise, P_totalThe total transmit power of downlink is represented,Expression dimension is N_R×N_RUnit matrix；

In this step, by combining channel matrix H_SIt is extended, based on extended matrixPseudoinverse solve computing Can be expressed as：

Formula（2）

From formula（2）As can be seen that the pseudoinverse of extended matrixUpper submatrix can be used as considering noise factor most Little mean square error（MMSE）Linear precoding matrix.

Step 2. is to extended channel matricesConjugate transposeCarry out QR decomposition：Obtain Dimension is N_R×N_RUpper triangular matrixIt is (N with dimension_T+N_R)×N_RUnitary matriceIt is used in combinationRepresent unitary matriceBefore N_TOK,Represent unitary matriceRear N_ROK.

The result that QR decomposes in this step can be to pseudoinverseSolution procedure simplified：

Formula（3）

By formula（3）Understand,It is the least mean-square error for considering noise factor（MMSE）Linear predictive coding Matrix, wherein,It isSubmatrix, dimension is N_T×N_k。

Step 3. is to upper triangular matrixConjugate transpose carry out inversion operation, obtain Wherein,It isSubmatrix, dimension is N_T×N_k。

In this step, can be directly to matrixCarry out inversion operation, it is also possible to decompose using extended channel matrices QR As a result obtainingFurther to reduce the complexity of algorithm computing.

According to the formula that extended matrix QR decomposes：It can be seen that： It is hereby achieved that upper triangular matrixIt is inverse：Then upper triangular matrixThe inverse matrix of conjugate transpose can be with ByThe conjugate transpose of inverse matrix obtain, i.e.,

Step 4. is according to upper triangular matrixConjugate transpose inverse matrixAnd extension Channel matrix QR decomposes what is obtainedMatrix, obtains the Part I of pre-coding matrix.

In this step, according to upper triangular matrixConjugate transpose inverse matrixAnd Extended channel matrices QR decompose what is obtainedMatrix, obtainsBut Due to wherein each submatrixRow between and it is non-orthogonal, in addition it is also necessary to alignment be orthogonalized, such as Using Schimidt orthogonalization（GSO）Algorithm, obtainsOrthogonal basiss P_k, that is, obtained correspondence user k after consideration noise factor The Part I of pre-coding matrix be：

For all K users, the Part I of its joint pre-coding matrix is W^a=[P₁P₂…P_k]。

Equivalent channel matrix of the step 5. in order to obtain the maximum pre-coding gain of equivalent channel matrix, to any user kTranspositionCarry out lattice about to subtract（LR）Operation：Transformation matrix T_kFor unimodular matrix, i.e. T_kMiddle unit The value of element is for complex integers and determinant meets det (T_k)=±1.According to the property of LR, orthogonality is obtained after about subtracting preferably etc. Effect channel matrixNoise scale-up problem can effectively be reduced.

Step 6. pair about subtract after equivalent channel matrixIt is extended：

Step 7. is to extended channel matricesConjugate transposeCarry out QR decomposition： It is N to dimension_k×N_kUpper triangular matrixIt is (N with dimension_k+N_k)×N_kUnitary matriceIt is used in combinationRepresent unitary matriceFront N_kOK,Represent unitary matriceRear N_kOK.

Step 8. byObtainSo

Step 9. pair arbitrarily user k, willAs the Part II of pre-coding matrix, i.e.,

For all K users, the Part II of its joint pre-coding matrix is

Step 10. obtains the pre-coding matrix W=W of whole system^aW^b。

After step 10, according to lattice reduction（LR）Method understands that receiving terminal only needs docking collection of letters y to carry out simply Linear transformation, can just recover sending signal s.

Computational complexity to traditional BD methods with the inventive method is analyzed below, concrete such as table 1（Traditional BD methods Analysis of complexity）, table 2（The analysis of complexity of GZI methods）, table 3（The analysis of complexity of the inventive method）It is shown：

Table 1

Table 2

Table 3

Method for precoding of the present invention is answered with tradition BD and GZI method for precoding with reference to Fig. 2, Fig. 3, Fig. 4, Fig. 5 Miscellaneous degree, volumetric properties and the bit error rate（BER）Carry out emulation comparison.

Fig. 2 compares tradition BD method for precoding, GZI method for precoding and Ben Fa in the case of different user number K The complexity of bright method.System emulation condition is：The reception antenna number N of each user_k=2 (k=1,2 ..., K), Base Transmitter day Line number N_T=KN_k, the domain of variation K=2 of number of users:10.

Fig. 3 compares the reception antenna number N in user_kTradition BD method for precoding, GZI precoding sides in the case of difference The complexity of method and the inventive method.System emulation condition is：Number of users K=3, Base Transmitter antenna number N_T=KN_k, each user Reception antenna number domain of variation N_k=2:8.As can be seen that traditional BD method for precoding is due to having used complexity higher SVD decomposes, and causes this algorithm complex very high, and constantly increases with the increase of number of users.Based on pseudoinverse solve with The GZI method for precoding that QR decomposes reduces the complexity of algorithm to a certain extent.And inventive algorithm is in above two side On the basis of method, decompose with reference to extended matrix QR and lattice reduction（LR）Technology, effectively reduces the complexity of algorithm.

Fig. 4 is traditional BD method for precoding, GZI method for precoding and the inventive method under conditions of different signal to noise ratios Volumetric properties comparison diagram.Simulated conditions are set as：Base Transmitter antenna number N_T=4, the reception antenna number of each user is 2, is used Amount K=2, it can be seen that the inventive method is with than traditional BD and the higher power system capacity of GZI method for precoding.

Fig. 5 is traditional BD method for precoding, GZI method for precoding and the inventive method under conditions of different signal to noise ratios The bit error rate（BER）Comparison diagram.Simulated conditions are set as：Base Transmitter antenna number N_T=4, the reception antenna number of each user is 2, number of users K=2.As can be seen that the inventive method is with than traditional BD and the more excellent bit error rate performance of GZI method for precoding, Further confirmed the inventive method reduce computational complexity while, can be with lift system performance.

Claims (2)

1. a kind of MU-MIMO precodings implementation method, specifically includes following steps：

The combined channel matrix of all K users of step 1. isTo combining channel matrix H_SCarry out Extension：Wherein, α=N_Rσ²/P_total, σ²Represent the variance of noise, P_totalRepresent that downlink is total Transmit power,Expression dimension is N_R×N_RUnit matrix, N_RRepresent that the K total reception antenna of user receives number；

Step 2. is to extended channel matricesConjugate transposeCarry out QR decomposition：Obtain dimension For N_R×N_RUpper triangular matrixIt is (N with dimension_T+N_R)×N_RUnitary matriceIt is used in combinationRepresent unitary matriceFront N_T OK, N_TThe transmitting antenna number of base station end is represented,Represent unitary matriceRear N_ROK；

Step 3. byObtainAnd then obtain Wherein,It isSubmatrix, dimension is N_T×N_k, N_kFor k-th The reception antenna number of user；

Step 4. is obtainedOrthogonal basiss P_k, then the Part I of the arbitrarily pre-coding matrix of user k beSo as to Obtain the equivalent channel matrix after first time precoding

For all K users, the Part I of its joint pre-coding matrix is W^a=[P₁ P₂ … P_k], MU-MIMO is believed Road is decomposed into a plurality of independent equivalent SU-MIMO channels, H_SW^a=diag { H₁P₁,H₂P₂,…,H_KP_K}；

The step 5. pair arbitrarily equivalent channel matrix of user kTranspositionCarry out lattice and about subtract (LR) operation：Wherein transformation matrix T_kFor unimodular matrix, i.e. T_kThe value of middle element is for complex integers and determinant meets det (T_k) =± 1；

Step 6. pair about subtract after equivalent channel matrixIt is extended：

Step 7. is to extended channel matricesConjugate transposeCarry out QR decomposition：Obtain dimension For N_k×N_kUpper triangular matrixIt is (N with dimension_k+N_k)×N_kUnitary matriceIt is used in combinationRepresent unitary matriceFront N_k OK,Represent unitary matriceRear N_kOK；

Step 8. byObtainSo

Step 9. pair arbitrarily user k, willAs the Part II of pre-coding matrix, i.e.,：

$W_k^b=Q_k^1{\left({\stackrel{\‾}{R}}_k^H\right)}^{-1}=\frac{1}{\sqrt{\mathrm{\α}}}{Q}_k^1{\left(Q_k^2\right)}^H;$

For all K users, the Part II of its joint pre-coding matrix is：

$W^b=diag\{\frac{1}{\sqrt{\mathrm{\α}}}{Q}_1^1{\left(Q_1^2\right)}^H,\frac{1}{\sqrt{\mathrm{\α}}}{Q}_2^1{\left(Q_2^2\right)}^H,...,\frac{1}{\sqrt{\mathrm{\α}}}{Q}_K^1{\left(Q_K^2\right)}^H\};$

Step 10. obtains the pre-coding matrix W=W of whole system^aW^b。

2. a kind of MU-MIMO precodings implementation method according to described in claim 1, it is characterised in that step 4 is especially by applying Close special orthogonalization (GSO) method is obtainedOrthogonal basiss P_k。