CN106789781A - The interference elimination method of block diagonalization precoding is converted based on Givens - Google Patents

Abstract

The invention discloses an interference elimination method based on Givens transform block diagonalization precoding, and the specific steps include: (1) estimating the channel matrix participating in the precoding; (2) performing QR on the joint user channel matrix after conjugate transposition Decomposition; (3) finding the pseudo-inverse of the joint user channel matrix; (4) constructing the first half of the precoding matrix; (5) constructing the second half of the precoding matrix; (6) obtaining the final joint precoding matrix. The present invention uses an interference elimination method based on Givens transform block diagonalization precoding to obtain an orthogonal matrix with better orthogonality, thereby obtaining a more accurate orthonormal basis of the null space of the user channel matrix, and finally obtaining the required The joint precoding matrix of . The invention can be used in a multi-user communication system to eliminate inter-user interference and improve the quality of signals received by users and the stability of the system.

Description

Interference Elimination Method Based on Givens Transform Block Diagonalization Precoding

technical field

The invention belongs to the technical field of communication, and further relates to an interference elimination method based on Givens transform block diagonal precoding in the technical field of wireless communication precoding. The invention can be used in a multi-user communication system to eliminate inter-user interference and improve the quality of signals received by users and the stability of the system.

Background technique

Precoding technology refers to preprocessing the mixed signal before the downlink base station broadcasts the signal to multiple users, so that the user receiving end can easily separate the useful signal from the mixed receiving signal, reducing or eliminating the interference between users . Since the processing capability of the base station is much larger than that of the user end, the precoding technology also releases the processing pressure of the user end.

Precoding technologies are generally classified into linear precoding and nonlinear precoding. Although nonlinear precoding can achieve ideal channel capacity, its high complexity makes it difficult to apply in practice. In the linear precoding method, the block diagonalization method is the most commonly used. It is based on the zero-forcing idea. By performing block diagonalization processing on the channel matrix, the MIMO channel is equivalent to multiple parallel independent spatial sub-channels. to eliminate multi-user interference. However, the traditional block diagonalization method requires two singular value decompositions for each user, and the overall complexity of the method is too high due to the high complexity of the singular value decomposition. At the same time, excessive complexity does not bring better BER performance benefits. Therefore, reducing complexity or BER becomes the key to research in precoding technology.

Keke Zu et al. proposed a QR decomposition and Block Diagonalization Algorithm for Maximum Likelihood Detection. This method calculates the pseudo-inverse of each user's equivalent channel matrix, and performs QR decomposition on it to obtain the zero-space orthogonal basis of each user's interference channel matrix. According to the zero-space orthogonal basis of the interference channel matrix of each user, the linear precoding matrix of each user is constructed. However, the disadvantage of this method is that the calculation complexity is still high when calculating the pseudo inverse of the null space of the user channel matrix.

The University of Electronic Science and Technology of China discloses a Gram-Schmidt orthogonalization-based block Diagonalized precoding method. The method determines the total user channel matrix according to the downlink channel matrix of each user in the system, and performs QR decomposition on the conjugate transpose matrix to obtain the product of the orthogonal matrix and the upper triangular matrix. Then, the total user channel matrix is expressed as the product of the lower triangular matrix and the orthogonal conjugate transpose matrix, and the inverse calculation is performed on the lower triangular matrix to obtain the zero-space orthogonal basis of the interference channel matrix of each user. According to the zero-space orthogonal basis of the interference channel matrix of each user, the linear precoding matrix of each user is constructed based on Gram-Schmidt orthogonalization, and the transmitted signal of each user is linearly precoded by using the constructed linear precoding matrix . Since only the total channel matrix is decomposed, the method further reduces the complexity of precoding and improves the coding efficiency. However, the disadvantage of this method is that the bit error rate of the user signal in the system is still high, especially when the signal reception quality is poor in a low signal-to-noise ratio scenario.

Contents of the invention

The purpose of the present invention is to overcome the above-mentioned deficiencies in the prior art, provide a kind of interference elimination method based on Givens transform block diagonalization precoding, eliminate the interference between users in the multi-user communication system, and reduce bit error rate, improve user receiving signal Quality, enhance the stability of the system.

The idea of realizing the present invention is: use the QR decomposition based on Givens transform to replace the high-complexity singular value decomposition operation in the traditional block diagonalization method, or replace the Grams in the block diagonalization method based on Gram-Schmidt orthogonalization Schmidt orthogonalization operation, so as to obtain an orthogonal matrix with better orthogonality, and then obtain a more accurate orthonormal basis of the null space of the user interference channel matrix, obtain the final precoding matrix, eliminate inter-user interference, and at the same time It also reduces the bit error rate in multi-user MIMO systems.

The concrete steps that realize the object of the present invention are as follows:

(1) Estimate the channel matrix involved in precoding:

(1a) Using a channel estimation method, estimate the downlink channel matrix of all users participating in precoding to form a joint user channel matrix;

(1b) Conjugate transpose the joint user channel matrix to obtain the joint user channel matrix after the conjugate transpose;

(2) Carry out QR decomposition to the joint user-channel matrix after conjugate transposition:

QR decomposition is performed on the joint user channel matrix after the conjugate transposition, and an orthogonal matrix and an upper triangular matrix for representing the joint user channel matrix are obtained;

(3) Find the pseudo-inverse of the joint user channel matrix:

(3a) inverse the upper triangular matrix after the conjugate transposition, and obtain the lower triangular matrix after the inversion;

(3b) multiplying the lower triangular matrix and the orthogonal matrix after the inversion to obtain the pseudo-inverse of the joint user channel matrix;

(4) Construct the first half of the precoding matrix:

(4a) divide the upper triangular matrix of the joint user channel matrix into several sub-matrices equal to the number of users, and use the obtained sub-matrix as the upper triangular matrix of each user;

(4b) Select an unprocessed user among all users participating in precoding, and obtain the inverse of the conjugate transpose of the upper triangular matrix of the selected user, and obtain the lower triangular matrix after the inversion of the selected user;

(4c) multiplying the lower triangular matrix after the inversion of the selected user with the orthogonal matrix of the joint user channel matrix to obtain the pseudo-inverse of the null space of the selected user channel matrix;

(4d) Utilizing the QR decomposition based on Givens transform, decomposing the pseudo-inverse of the null space of the selected user channel matrix to obtain the orthogonal matrix and upper triangular matrix of the selected user decomposition;

(4e) judge whether all users have traversed, if so, then perform step (4f), otherwise, perform step (4b);

(4f) Extract the orthogonal matrix decomposed by each user to form a block diagonalization matrix, and use the block diagonalization matrix as the first half of the joint precoding matrix;

(5) Construct the second half of the precoding matrix:

(5a) Choose an unprocessed user among all users participating in precoding, multiply the orthogonal matrix decomposed by the selected user with the downlink channel matrix of the selected user, and obtain the equivalent single-user channel matrix of the selected user ;

(5b) Singular value decomposition is performed on the equivalent single-user channel matrix of the selected user to obtain the left unitary matrix of the selected user and the right unitary matrix of the selected user;

(5c) The first x right singular vectors of the right unitary matrix of the selected user are used as the second half of the precoding matrix of the selected user, and the conjugate transpose of the left unitary matrix of the selected user is used as the receiving matrix of the selected user , x represents the rank of the equivalent single-user channel matrix of the selected user;

(5d) judge whether all users have been traversed, if so, then perform step (5e), otherwise, perform step (5a);

(5e) forming the second half of each user precoding matrix into the second half of the joint precoding matrix;

(6) Obtain the final joint precoding matrix:

The first half of the joint precoding matrix is multiplied by the second half of the joint precoding matrix to obtain the final joint precoding matrix.

Compared with the prior art, the present invention has the following advantages:

First, since the present invention utilizes the QR decomposition based on Givens transform to obtain an orthogonal matrix with better orthogonality, it overcomes the disadvantage of high bit error rate of user signals in the prior art, so that the present invention eliminates many Inter-user interference in the user communication system reduces the bit error rate at the same time.

Second, since the present invention utilizes the inverse of the conjugate transpose of the upper triangular matrix of the user, the pseudo-inverse of the null space of the user channel matrix is obtained, which overcomes the complexity of calculation in the prior art when seeking the pseudo-inverse of the null space of the user channel matrix Due to the disadvantage of relatively high degree, the present invention can reduce the computational complexity of interference cancellation in the multi-user communication system, and improve the coding efficiency of interference cancellation in the multi-user communication system.

Description of drawings

Fig. 1 is a flow chart of the present invention;

Fig. 2 is a simulation diagram of the present invention.

detailed description

The present invention will be described in further detail below in conjunction with the accompanying drawings.

With reference to accompanying drawing 1, the specific steps of the present invention are described in further detail.

Step 1, estimate the channel matrix involved in precoding.

Using the channel estimation method in the multi-user MIMO system, the downlink channel matrix of each user is estimated to form a joint user channel matrix.

Perform conjugate transposition on the joint user channel matrix to obtain the joint user channel matrix after the conjugate transposition.

Step 2, performing QR decomposition on the joint user-channel matrix after conjugate transposition.

QR decomposition is performed on the joint user-channel matrix after conjugate transposition to obtain an orthogonal matrix and an upper triangular matrix used to represent the joint user-channel matrix.

Step 3, find the pseudo-inverse of the joint user-channel matrix.

Invert the conjugate transpose of the upper triangular matrix to obtain the lower triangular matrix after inversion.

Multiply the inverted lower triangular matrix with the orthogonal matrix to obtain the pseudo-inverse of the joint user-channel matrix.

Step 4, constructing the first half of the precoding matrix.

In the first step, the upper triangular matrix of the joint user channel matrix is divided into several sub-matrices equal to the number of users, and the obtained sub-matrix is used as the upper triangular matrix of each user.

Step 2: Select an unprocessed user among all the users participating in the precoding, calculate the inverse of the conjugate transpose of the upper triangular matrix of the selected user, and obtain the lower triangular matrix after inversion of the selected user.

Step 3: Multiply the lower triangular matrix after the inversion of the selected user by the orthogonal matrix of the joint user channel matrix to obtain the pseudo inverse of the null space of the selected user channel matrix.

Step 4: Utilize the QR decomposition based on Givens transform to decompose the pseudo-inverse of the null space of the channel matrix of the selected user to obtain the orthogonal matrix and upper triangular matrix of the selected user decomposition.

The formula of the QR decomposition based on Givens transform is as follows:

where QL _k denotes the pseudo-inverse of the null space of the channel matrix of the selected k-th user, Represents the orthogonal matrix obtained by performing QR decomposition based on Givens transform on the selected kth user, Represents the upper triangular matrix obtained by performing QR decomposition based on Givens transform on the selected kth user.

Step 5, judge whether all users have traversed, if so, execute step 6 of this step, otherwise, execute step 2 of this step.

Step 6: Extract the orthogonal matrix decomposed by each user to form a block diagonal matrix, and use the block diagonal matrix as the first half of the joint precoding matrix.

The orthogonal matrix decomposed by each user is extracted, and the expression of forming a block diagonal matrix is as follows:

where W ^o represents the block diagonalization matrix, Represents the extracted orthogonal matrix decomposed by the nth user, and N represents the total number of users.

Step 5, construct the second half of the precoding matrix.

Step 1: Select an unprocessed user among all users participating in precoding, and multiply the orthogonal matrix decomposed by the selected user with the downlink channel matrix of the selected user to obtain the equivalent single-user channel of the selected user matrix.

Step 2: Singular value decomposition is performed on the equivalent single-user channel matrix of the selected user to obtain the left unitary matrix of the selected user and the right unitary matrix of the selected user.

Step 3: The first x right singular vectors of the right unitary matrix of the selected user are used as the second half of the precoding matrix of the selected user, and the conjugate transpose of the left unitary matrix of the selected user is used as the reception of the selected user matrix, x denotes the rank of the equivalent single-user channel matrix for the selected user.

Step 4, judge whether all users have been traversed, if so, execute step 5 of this step, otherwise, execute step 1 of this step.

In step 5, the second half of the precoding matrix of each user is combined into the second half of the joint precoding matrix.

Step 6, obtaining the final joint precoding matrix.

The first half of the joint precoding matrix is multiplied by the second half of the joint precoding matrix to obtain the final joint precoding matrix.

With reference to the simulation diagram of accompanying drawing 2, the effect of the present invention is further described in detail.

(1) Simulation conditions:

The simulation experiment of the present invention is carried out under the condition that the hardware environment is Intel(R) Core(TM) i3-4170 CPU@3.70GHz, and the software environment is a 64-bit Windows operating system. The simulation parameters are set as follows: use Matlab software to generate random input signals, 180 bits per frame, and transmit a total of 100,000 frames; QPSK modulation is used, and the channel matrix elements are independent and identically distributed complex Gaussian random variables with zero mean unit variance. The bit error rate simulation is carried out respectively for the traditional block diagonalization method in the prior art, the block diagonalization method based on Gram-Schmidt orthogonalization and the method proposed by the present invention.

(2) Simulation content and result analysis:

Figure 2(a) shows that the number of transmitting antennas is 6, the number of users is 3, and the number of antennas per user is 2, using the method of the present invention and the block pair based on Gram-Schmidt orthogonalization in the prior art Bit error rate simulation for the cornerization method and the traditional block diagonalization method. In Fig. 2 (a), abscissa represents signal-to-noise ratio, and ordinate represents bit error rate, and in Fig. 2 (a), the curve represented with rhombus mark represents the curve that adopts bit error rate and signal-to-noise ratio that the inventive method gains to change, with The curves marked with squares represent the curves of BER and SNR changes obtained by using the block diagonalization method based on Gram-Schmidt orthogonalization, and the curves marked with circles represent the curves obtained by using the traditional block diagonalization method The curve of bit error rate and signal-to-noise ratio. As can be seen from Fig. 2 (a), the bit error rate of the block diagonalization method based on Gram-Schmidt orthogonalization is equal to the bit error rate of the traditional block diagonalization method, while the bit error rate of the method of the present invention is higher than The bit error rate of the block diagonalization method based on Gram-Schmidt orthogonalization is about 2-4 dB lower than that of the traditional block diagonalization method.

Figure 2(b) shows that the number of transmitting antennas is 18, the number of users is 6, and the number of antennas per user is 3, using the method of the present invention and the block pair based on Gram-Schmidt orthogonalization in the prior art Bit error rate simulation for the cornerization method and the traditional block diagonalization method. In Fig. 2 (b), abscissa represents signal-to-noise ratio, and ordinate represents bit error rate, and in Fig. 2 (b), the curve represented with rhombus mark represents the curve that adopts bit error rate and signal-to-noise ratio that the inventive method gains to change, with The curves marked with squares represent the curves of BER and SNR changes obtained by using the block diagonalization method based on Gram-Schmidt orthogonalization, and the curves marked with circles represent the curves obtained by using the traditional block diagonalization method The curve of bit error rate and signal-to-noise ratio. As can be seen from the bit error simulation results in Fig. 2 (b), the bit error rate of the method of the present invention is lower than that of the block diagonalization method based on Gram-Schmidt orthogonalization and the traditional block diagonalization method The bit error rate is about 3-5 dB. Combining FIG. 2(a) and FIG. 2(b), it can be seen that as the number of antennas and the number of users increase, the bit error rate of the method of the present invention decreases more.

To sum up, the method of the present invention can reduce the bit error rate and computational complexity on the basis of eliminating interference among users in a multi-user communication system, improve the quality of signals received by users, and enhance the stability of the system. As the number of antennas and the number of users increase, the bit error rate of the method of the present invention decreases more.

Claims (3)

1. a kind of interference elimination method that block diagonalization precoding is converted based on Givens, is comprised the following steps：

(1) channel matrix of participation precoding is estimated：

(1a) uses channel estimation methods, estimates the down channel matrix of all users for participating in precoding, constitutes federated user Channel matrix；

(1b) carries out conjugate transposition to federated user channel matrix, obtains the federated user channel matrix after conjugate transposition；

(2) QR decomposition is carried out to the federated user channel matrix after conjugate transposition：

QR decomposition is carried out to the federated user channel matrix after conjugate transposition, is obtained for representing federated user channel matrix just Hand over matrix and upper triangular matrix；

(3) pseudoinverse of federated user channel matrix is sought：

(3a) to being inverted after upper triangular matrix conjugate transposition, the lower triangular matrix after being inverted；

With orthogonal matrix be multiplied lower triangular matrix after inverting by (3b), obtains the pseudoinverse of federated user channel matrix；

(4) first half of pre-coding matrix is constructed：

The upper triangular matrix of federated user channel matrix is divided into the several submatrixs equal with number of users by (4a), will The submatrix for arriving as each user upper triangular matrix；

(4b) optional untreated user in the user of all participation precodings, the upper triangular matrix to selected user is asked Conjugate transposition it is inverse, obtain the lower triangular matrix after selected user is inverted；

Lower triangular matrix after (4c) inverts selected user is multiplied with the orthogonal matrix of federated user channel matrix, obtains selected The pseudoinverse of subscriber channel matrix kernel；

(4d) is decomposed using the QR based on Givens conversion, and the pseudoinverse to selected user channel matrix kernel is decomposed, and obtains institute From orthogonal matrix and upper triangular matrix that family is decomposed；

(4e) judges whether all users have traveled through, if so, then performing step (4f), otherwise, performs step (4b)；

(4f) extracts the orthogonal matrix of each user decomposition, and blocking diagonalizable matrix is pre- using block diagonalization matrix as joint The first half of encoder matrix；

(5) latter half of pre-coding matrix is constructed：

(5a) optional untreated user, the orthogonal matrix that selected user is decomposed in the user of all participation precodings With the down channel matrix multiple of selected user, the equivalent single user channel matrix of selected user is obtained；

(5b) carries out singular value decomposition to the equivalent single user channel matrix of selected user, obtain the left unitary matrice of selected user with The right unitary matrice of selected user；

(5c) by the preceding x right singular vector of the right unitary matrice of selected user, as the latter half of of selected user pre-coding matrix Point, the conjugate transposition of the left unitary matrice of selected user as selected user receiving matrix, x represents the equivalent alone of selected user The order of family channel matrix；

(5d) judges whether to have traveled through all users, if so, then performing step (5e), otherwise, performs step (5a)；

(5e) latter half of each user's pre-coding matrix is constituted the latter half of joint pre-coding matrix；

(6) final joint pre-coding matrix is obtained：

By the first half for combining pre-coding matrix and the latter half multiplication for combine pre-coding matrix, obtain it is final combine prelist Code matrix.

2. the interference elimination method that block diagonalization precoding is converted based on Givens according to claim 1, its feature exists In the formula that the QR based on Givens conversion described in step (4d) is decomposed is as follows：

${\mathrm{QL}}_k={\stackrel{\‾}{Q}}_k{\stackrel{\‾}{R}}_k$

Wherein, QL_kThe pseudoinverse of the channel matrix kernel of k-th selected user is represented,Represent to k-th selected user Carry out the QR based on Givens conversion and decompose the orthogonal matrix for obtaining,Expression is based on to k-th selected user The QR of Givens conversion decomposes the upper triangular matrix for obtaining.

3. the interference elimination method that block diagonalization precoding is converted based on Givens according to claim 1, its feature exists In, the orthogonal matrix of each user decomposition is extracted described in step (4f), the expression formula of blocking diagonalizable matrix is as follows：

$W^o=\[{\stackrel{\‾}{Q}}_1,{\stackrel{\‾}{Q}}_2,...,{\stackrel{\‾}{Q}}_n,...,{\stackrel{\‾}{Q}}_N\]$

Wherein, W^oBlock diagonalization matrix is represented,The orthogonal matrix that extracted nth user decomposes is represented, N represents that user is total Number.