CN103023544A - Low-complexity interference alignment method of multiple input multiple output (MIMO)interference channel system - Google Patents

Abstract

The invention discloses a low-complexity interference alignment method for a MIMO interference channel system in the technical field of communication. Firstly, obtain the interference channel matrix from the base station of other cells to the user in this cell, and randomly initialize the precoding matrix of the base station; obtain the interference covariance matrix of the user according to the precoding matrix and the interference channel matrix, and then obtain the orthogonal basis of the receiving interference subspace ; Then update the precoding matrix according to the orthogonal basis of the received interference subspace, when the updated precoding matrix does not meet the convergence condition, recalculate the orthogonal basis of the received interference subspace; otherwise, according to the updated precoding matrix that satisfies the convergence condition The precoding matrix obtains the orthogonal base of the final receiving interference subspace; then obtains the post-processing matrix according to the orthogonal base of the final receiving interference subspace; finally, the signal is subjected to zero-forcing processing through the post-processing matrix to obtain the signal after interference elimination . The invention has simple process and high accuracy, and can reduce calculation complexity while maintaining system data throughput.

Description

A Low-Complexity Interference Alignment Method for MIMO Interfering Channel Systems

technical field

The invention relates to the field of communication technology, in particular to a low-complexity interference alignment method for a MIMO interference channel system.

Background technique

The pursuit of higher transmission rate and higher spectral efficiency is a long-standing topic in the field of wireless communication. Multiple-antenna technology (Multiple Input Multiple Output, MIMO) introduces additional spatial freedom for wireless communication by configuring multiple antennas at the transmitting end and receiving end, thereby greatly improving the spectrum utilization and throughput of the system. In wireless networks, in addition to noise and fading factors, the impact of interference on communication is increasingly prominent. Now, the basic framework of 4G has been established. Because its basic multiple access method is based on OFDMA (Orthogonal Frequency Division Multiple Access) frequency division multiple access, multi-users in the cell are no longer the focus of research. However, due to the multiplexing of subcarriers in adjacent cells, inter-cell interference, especially the interference of edge users becomes a prominent problem. How to effectively eliminate the interference effect has become an important research topic. While introducing multi-antenna technology into the next-generation communication system, it is generally expected to use a frequency reuse factor of 1 for networking, which will inevitably cause co-channel interference (Co-Channel Interference, CCI), especially at the edge of the cell. users, seriously weakens the high spectrum efficiency brought by multi-antenna technology. The existing interference suppression technologies, such as interference randomization, interference deletion, and interference management, cannot solve this problem well. It is urgent to study more advanced Interference suppression technology to further improve spectral efficiency. Coordinated Multi Point (CoMP) technology is introduced in LTE-Advanced, which suppresses the interference of multi-antenna systems between cells through the cooperation between various base stations and users, and Interference Alignment (IA) is used as COMP Compared with traditional interference suppression technology, it has shown great advantages and research potential.

However, the traditional interference alignment technology requires the transmitter to have global channel state information, and it is too theoretical and unrealistic; non-ideal channel state information will significantly degrade system performance, and at the same time cannot achieve the effect of reducing interference. The inherent shortcomings of interference alignment techniques have inspired the development of more practical techniques. Then reduce the computational complexity of the actual system as much as possible, as the research and development direction of interference alignment technology in the future.

仍然是学术界未解决的问题。但是，如果退而求其次，不追求准确的闭式解，而是寻求一个非常接近的数值解的话，是有办法来求得的。分布式干扰对齐方法（EVD-IA方法）随机初始化一个数值解，利用TDD模式下通信系统信道的互易性，随着基站和用户之间迭代更新预编码矩阵和后处理矩阵，使数值解逐渐逼近准确的闭式解，使得干扰功率达到极小，但是此技术受限于1)系统的信道互易性，只能工作在TDD模式下的通信系统，2)使用了二阶的特征值分解算法，使整个系统的计算复杂度较高。针对EVD-IA方法的缺点，提出了交替最小化干扰对齐方法（AM-IA方法），不需要利用信道的互易性，利用基于子空间和矩阵之间的距离为理论知识，交替迭代更新发射端预编码矩阵和用户干扰子空间，使得干扰信号矩阵尽可能得对齐于干扰子空间，但是此技术缺点是使用了二阶的特征值分解算法，使整个系统的计算复杂度较高，不利于在实际系统中的应用和硬件实现。The interference alignment problem of the MIMO Gaussian interference channel is actually attributed to the solution formula, and a set of base station precoding and user postprocessing matrices are obtained. Unfortunately, how to solve the system of equations

Still an unsolved problem in academia. However, if you settle for the second best, instead of pursuing an accurate closed-form solution, but seek a very close numerical solution, there is a way to obtain it. The distributed interference alignment method (EVD-IA method) randomly initializes a numerical solution, uses the reciprocity of the communication system channel in TDD mode, and updates the precoding matrix and post-processing matrix iteratively between the base station and the user, so that the numerical solution gradually Approaching the exact closed-form solution makes the interference power extremely small, but this technology is limited by 1) the channel reciprocity of the system, and can only work in the communication system in TDD mode, 2) uses the second-order eigenvalue decomposition Algorithm, the computational complexity of the whole system is high. Aiming at the shortcomings of the EVD-IA method, an Alternate Minimization Interference Alignment Method (AM-IA method) is proposed, which does not need to use the reciprocity of the channel, and uses the theoretical knowledge based on the distance between the subspace and the matrix to update the emission alternately and iteratively. end precoding matrix and user interference subspace, so that the interference signal matrix is aligned to the interference subspace as much as possible, but the disadvantage of this technology is that it uses the second-order eigenvalue decomposition algorithm, which makes the calculation complexity of the whole system higher, which is not conducive to Applications and hardware implementations in real systems.

Contents of the invention

(1) Technical problems to be solved

The technical problem to be solved by the present invention is how to reduce the computational complexity of the system while maintaining the system throughput in the MIMO interference channel system.

(2) Technical solution

In order to solve the above technical problems, the technical solution of the present invention provides a low-complexity interference alignment method for a MIMO interference channel system, characterized in that the method includes:

S1: Obtain the interference channel matrix from other cell base stations to users in this cell, and randomly initialize the precoding matrix of the base station;

S2: Calculate the interference covariance matrix of the user according to the precoding matrix and the interference channel matrix, and then obtain the orthogonal basis of the receiving interference subspace;

S3: Update the precoding matrix according to the orthogonal basis of the received interference subspace, and when the updated precoding matrix does not meet the convergence condition, return to step S2; otherwise, obtain the final precoding matrix according to the updated precoding matrix that meets the convergence condition Orthogonal basis of received interference subspace of ;

S4: Obtain a post-processing matrix according to the orthogonal basis of the final received interference subspace;

S5: Perform zero-forcing processing on the signal through the post-processing matrix to obtain the signal after the interference is eliminated.

Described step S2 specifically comprises:

S21: Calculate and obtain an interference covariance matrix of each user according to the precoding matrix and the interference channel matrix;

S22: Decompose the interference covariance matrix to obtain a first unitary matrix;

S23: Select a specified column of the first unitary matrix as an orthogonal basis of the received interference subspace.

Described step S3 specifically comprises:

S31: Calculate a distance matrix between the interference channel matrix and an orthogonal basis of the received interference subspace;

S32: Decompose the distance matrix to obtain a second unitary matrix;

S33: Select the setting column of the second unitary matrix as the updated precoding matrix;

S34: Calculate whether the updated precoding matrix satisfies the convergence condition. If the convergence condition is not satisfied, replace the precoding matrix with the updated precoding matrix, and return to step S2; otherwise, according to the updated precoding matrix The orthogonal basis of the final receiving interference subspace is obtained.

The calculation formula of the interference covariance matrix is:

${\mathrm{<span\; class="notranslate">\; D.</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&NotEqual;</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}{\overset{\mathrm{<span\; class="notranslate">\; K</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}$

in:

为干扰协方差矩阵；

is the interference covariance matrix;

为干扰信道矩阵；

is the interference channel matrix;

V _k is a precoding matrix;

K is the total number of base stations;

k is the kth base station;

k _u is the k _uth user.

The convergence condition is:

A difference matrix between the updated precoding matrix and the precoding matrix is smaller than a set matrix.

The calculation formula of the post-processing matrix is:

${\mathrm{<span\; class="notranslate">\; W</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{{\mathrm{<span\; class="notranslate">\; N</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; :</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; :</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; h</span>}}$

in:

is the postprocessing matrix;

为长度

的单位阵；

is the length

the unit matrix;

为最终的接收干扰子空间的正交基；

is the orthogonal basis of the final received interference subspace;

为接收天线的数目；

is the number of receiving antennas;

d _k is the number of data streams transmitted by base station k.

(3) Beneficial effects

列为接收干扰子空间的正交基；依据最小化欧氏距离准则，根据其他小区到本小区内用户的干扰信道矩阵信息和接收干扰子空间，获得各基站的干扰信道矩阵与干扰子空间的正交基的距离；之后，依据各基站的干扰信道矩阵与干扰子空间的正交基的距离，根据基于修正的Gram-Schmidt方法使用排序QR分解算法，获得酉矩阵和对角线元素递增的上三角矩阵；依据酉矩阵，选取最后的d_k列为新的各个基站预编码矩阵；直到收敛为止，最终，根据接收干扰子空间的正交基，得到用户的后处理矩阵。由于使用了基于修正的Gram-Schmidt方法的排序QR分解算法，把搜索顺序的过程融进计算干扰信道矩阵QR分解过程中，在每一次正交化步骤之前，对信道矩阵的列进行排列，选取的准则就是列向量范数最小的列向量最先进行QR分解，因此降低了系统各用户信道矩阵的维数，从而使SQRD-IA方案在低维度下进行计算，有效降低了传统AM-IA方案的计算复杂度。在随着迭代次数的增加，进一步增大了系统吞吐量而且接收干扰有显著地减少，并且与传统AM-IA方案基本保持一致的迭代效果，从而提升了此方法在实际应用中的可行性。The present invention adopts the sorting QR decomposition algorithm based on the modified Gram-Schmidt method to approach the eigenvalue decomposition algorithm in the AM-IA algorithm, and adopts the method of cyclically iterating the base station precoding matrix and the post-reception processing matrix to seek a A numerical solution very close to the closed-form solution. First, through channel estimation, obtain the channel information from the base station of the cell to the users in the cell, and the interference channel matrix information from other cells to the users in the cell, and randomly initialize the precoding matrix of each base station; according to the precoding matrix of each base station and other The interference channel matrix information from the cell to the user in the cell is obtained to obtain the interference covariance matrix of each user; then, according to the interference covariance matrix of each user, the sorting QR decomposition algorithm is used according to the modified Gram-Schmidt method to obtain the unitary matrix and An upper triangular matrix with increasing diagonal elements; according to a unitary matrix, select the first

is listed as the orthogonal basis of the receiving interference subspace; according to the minimum Euclidean distance criterion, according to the interference channel matrix information of other cells to the users in this cell and the receiving interference subspace, the interference channel matrix and the interference subspace of each base station are obtained Orthogonal base distance; After that, according to the distance between the interference channel matrix of each base station and the orthogonal base of the interference subspace, according to the modified Gram-Schmidt method using the sorting QR decomposition algorithm, the unitary matrix and the diagonal element increment are obtained The upper triangular matrix; according to the unitary matrix, select the last d _k column as the new precoding matrix of each base station; until convergence, finally, according to the orthogonal basis of the received interference subspace, the post-processing matrix of the user is obtained. Due to the use of the sorted QR decomposition algorithm based on the modified Gram-Schmidt method, the process of searching the order is integrated into the process of calculating the QR decomposition of the interference channel matrix. Before each orthogonalization step, the columns of the channel matrix are arranged, and the selection The criterion is that the column vector with the smallest norm of the column vector is QR decomposed first, thus reducing the dimensionality of the channel matrix of each user in the system, so that the SQRD-IA scheme can be calculated in a low dimension, effectively reducing the traditional AM-IA scheme computational complexity. As the number of iterations increases, the system throughput is further increased and the reception interference is significantly reduced, and the iteration effect is basically consistent with the traditional AM-IA scheme, thus improving the feasibility of this method in practical applications.

Description of drawings

Fig. 1 is the flowchart of the low-complexity interference alignment method of the MIMO interference channel system of the present invention;

FIG. 2 is a transmission schematic diagram of an embodiment of a low-complexity interference alignment method for a MIMO interference channel system according to the present invention;

Fig. 3 has provided the antenna configuration (8,8,3) of each end of the system, K=4, under the condition of different signal-to-noise ratios, the comparative graph of the system capacity based on the SQRD-IA method of the present invention and the AM-IA scheme ;

K=4，SNR＝30dB,不同的迭代次数的条件下，基于本发明的SQRD-IA方案和AM-IA方案的系统容量的收敛性比较曲线图；Figure 4 shows the antenna configuration at each end

K=4, SNR=30dB, under the condition of different number of iterations, the comparative graph of the convergence of the system capacity based on the SQRD-IA scheme of the present invention and the AM-IA scheme;

Detailed ways

In order to make the purpose, content and advantages of the present invention clearer, the embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings.

The low-complexity interference alignment method of the MIMO interference channel system proposed by the present invention is described as follows in conjunction with the accompanying drawings and embodiments:

As shown in Figure 1, the present invention comprises the following steps:

S1: Through channel estimation, obtain the channel matrix from the base station of this cell to the users in this cell, and the interference channel matrix from other cells to users in this cell, and randomly initialize the precoding matrix of the base station;

系统配置为

系统中第k个基站到第k_u个用户的信道矩阵为

k=1,…,K;k_u=1,…,K_u，系统的噪声系数为σ，基站k发送信号S_k；Assuming that the system includes K base stations and K _u users, the number of transmitting antennas of the kth base station is M _k , the number of data streams transmitted by the kth base station is d _k , and the number of receiving antennas of the _kth user is

The system configuration is

The channel matrix from the kth base station to the k _uth user in the system is

k=1,…,K; k _u =1,…,K _u , the noise figure of the system is σ, base station k sends signal S _k ;

k=1,…,K;k_u=1,…,K_u;k≠k_u，并且随机初始化各个基站的预编码矩阵

第k_u个用户的接收信号为 $y_{k_u}=H_{k_u,k}{V}_k{S}_k+\underset{k=1,k\&NotEqual;k_u}{\overset{K}{\mathrm{\&Sigma;}}}{H}_{k_u,k}{V}_k{S}_k+n_{k_u};$ Through channel estimation, obtain the channel information from the base station of the cell to the user of the cell k=1,...,K;k _u =1,...,K _u ;k=k _u , and interference channel matrix information from other cells to users in this cell

k=1,…,K;k _u =1,…,K _u ;k≠k _u , and randomly initialize the precoding matrix of each base station

The received signal of the k _uth user is ${\mathrm{the\; y}}_{k_u}=h_{k_u,k}{V}_k{S}_k+\underset{k=1,k\&NotEqual;k_u}{\overset{K}{\mathrm{\&Sigma;}}}{h}_{k_u,k}{V}_k{S}_k+{\mathrm{no}}_{k_u};$

S2: Calculate the interference covariance matrix of the user according to the precoding matrix and the interference channel matrix, and then obtain the orthogonal basis of the receiving interference subspace;

S21: Calculate and obtain an interference covariance matrix of each user according to the precoding matrix and the interference channel matrix;

k=1,…,K;k_u=1,…,K_u;k≠k_u，获得各用户的干扰协方差矩阵：According to the precoding matrix V _k of each base station and the interference channel matrix information from other cells to users in this cell

k=1,…,K;k _u =1,…,K _u ;k≠k _u , to obtain the interference covariance matrix of each user:

${\mathrm{<span\; class="notranslate">\; D.</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&NotEqual;</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}{\overset{\mathrm{<span\; class="notranslate">\; K</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}$

in:

is the interference covariance matrix;

为干扰信道矩阵；

is the interference channel matrix;

V _k is a precoding matrix;

K is the total number of base stations;

k is the kth base station;

k _u is the k _uth user.

S22: Decompose the interference covariance matrix to obtain a first unitary matrix;

根据基于修正的Gram-Schmidt方法使用排序QR分解算法，获得第一酉矩阵

和对角线元素递增的第一上三角矩阵

According to the interference covariance matrix of each user

Using the sorted QR decomposition algorithm based on the modified Gram-Schmidt method, the first unitary matrix is obtained

and a first upper triangular matrix with increasing diagonal elements

和对角线元素递增的第一上三角矩阵

The process of sorting QR decomposition based on the modified Gram-Schmidt method includes: rearranging the column vectors in the interference covariance matrix based on the determinant criterion, allowing the column vector with the smallest norm to be QR decomposed first, and the modified Gram-Schmidt method The Schmidt method performs QR decomposition on the reordered interference covariance matrix; finally obtains the first unitary matrix

and a first upper triangular matrix with increasing diagonal elements

The program flow of the sorting QR decomposition algorithm based on the modified Gram-Schmidt method is:

Initialization: R=0, $Q=\underset{k=1,k\&NotEqual;k_u}{\overset{K}{\mathrm{\&Sigma;}}}{h}_{k_u,k}{V}_k{V}_k^h{h}_{k_u,k}^h$

in:

M _k is the number of transmitting antennas of the kth base station;

r _{μ, μ} is the norm of matrix q _μ ;

q _μ is the remaining μ column of Q;

r _{μ, v} is the projection matrix;

k _μ , q _v , v and μ are set intermediate variables.

S23: Select a specified column of the first unitary matrix as an orthogonal basis of the received interference subspace.

最前的

列为接收干扰线性子空间的正交基

Since the data stream sent by the base station is d _k , in order to separate the desired signal and the interference signal of the user terminal as much as possible, the interference signal of the user k _u is aligned in a dimension of at most In the linear subspace of , select the first unitary matrix

the first

Orthogonal basis for receiving interference linear subspace

S3: Update the precoding matrix according to the orthogonal basis of the received interference subspace, and when the updated precoding matrix does not meet the convergence condition, return to step S2; otherwise, obtain the final precoding matrix according to the updated precoding matrix that meets the convergence condition Orthogonal basis of received interference subspace of ;

S31: Calculate a distance matrix between the interference channel matrix and an orthogonal basis of the received interference subspace;

k=1,…,K;k_u=1,…,K_u;k≠k_u和接收干扰线性子空间的正交基

获得各基站的干扰信道矩阵与干扰子空间的正交基的距离矩阵

According to the minimum Euclidean distance criterion, according to the interference channel matrix information from other cells to users in this cell

k=1,…,K; k _u =1,…,K _u ; k≠k _u and the orthogonal basis of the receiving interference linear subspace

Obtain the distance matrix of the interference channel matrix of each base station and the orthogonal base of the interference subspace

S32: Decompose the distance matrix to obtain a second unitary matrix;

根据基于修正的Gram-Schmidt方法使用排序QR分解算法，获得第二酉矩阵Q_k和对角线元素递增的第二上三角矩阵R_k；According to the distance matrix of the interference channel matrix of each base station and the orthogonal basis of the interference subspace

According to the modified Gram-Schmidt method based on the sorting QR decomposition algorithm, obtain the second unitary matrix Q _k and the second upper triangular matrix R _k with increasing diagonal elements;

S33: Select the setting column of the second unitary matrix as the updated precoding matrix;

Then, since the dimension of the receiving subspace occupied by the expected signal is d _k , according to the second unitary matrix Q _k , the last dk column is selected as the updated precoding matrix V _k , and the calculation formula is $V_k=Q_k^{m_k-d_k+1:m_k}.$

S34: Calculate whether the updated precoding matrix satisfies the convergence condition. If the convergence condition is not satisfied, replace the precoding matrix with the updated precoding matrix and return to step S2; otherwise, according to the updated precoding matrix The orthogonal basis of the final receiving interference subspace is obtained.

The convergence condition is that a difference matrix between the updated precoding matrix and the precoding matrix is smaller than a set matrix. The setting matrix can be flexibly set according to the actual situation, as long as the interference leakage is satisfied Less than 10 ^-8 is enough.

的计算公式为：The interference leak

The calculation formula is:

${\mathrm{<span\; class="notranslate">\; IL</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; trace</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}{\mathrm{<span\; class="notranslate">\; W</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}<span\; class="notranslate">\; )</span>$

为后处理矩阵；trace()表示求矩阵的迹。in:

is the post-processing matrix; trace() means to find the trace of the matrix.

S4: Obtain a post-processing matrix according to the orthogonal basis of the final received interference subspace;

得到用户的后处理矩阵：According to the orthogonal basis of the converged receiving interference subspace

Get the user's postprocessing matrix:

${\mathrm{<span\; class="notranslate">\; W</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{{\mathrm{<span\; class="notranslate">\; N</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; :</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}^{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; :</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; h</span>}}$

in:

为后处理矩阵；

is the postprocessing matrix;

的单位阵 is the length

unit matrix

为最终的接收干扰子空间的正交基；

is the orthogonal basis of the final received interference subspace;

为接收天线的数目；

is the number of receiving antennas;

d _k is the number of data streams transmitted by base station k.

S5: Perform zero-forcing processing on the signal through the post-processing matrix to obtain the signal after the interference is eliminated.

The conditions for interference alignment are achieved by postprocessing the matrix:

${\mathrm{<span\; class="notranslate">\; W</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; k</span>}$

$\mathrm{<span\; class="notranslate">\; rank</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}$

The signal after the interference is eliminated is:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; S</span>}}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; \&NotEqual;</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}{\overset{\mathrm{<span\; class="notranslate">\; K</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; W</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}$

$<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; u</span>}}}$

So far, the work of interference alignment optimization has been completed.

In summary, the present invention proposes a low-complexity interference alignment method in a MIMO interference channel system, which has the advantage of low complexity and is applicable to systems with any antenna configuration and number of users. Due to the use of the sorted QR decomposition algorithm based on the modified Gram-Schmidt method, the process of searching the order is integrated into the process of calculating the QR decomposition of the interference channel matrix. Before each orthogonalization step, the columns of the channel matrix are arranged, and the selection The criterion is that the column vector with the smallest norm of the column vector is QR decomposed first, thus reducing the dimension of the channel matrix of each user in the system and effectively reducing the computational complexity of the interference alignment technology.

A comparison between the SQRD-IA scheme of the present invention and the AM-IA scheme will be given below to make the advantages and features of the present invention more obvious.

而言，矩阵相加运算的计算复杂度为：2mn(flops)，对m×n和n×p矩阵乘法的计算复杂度为2mnp(flops)，矩阵范数||G||_F运算的计算复杂度为：4mn(flop)，而对m×m的是矩阵而言，广义的特征值分解的计算复杂度为4m³/3+17m³(flops)，QR分解算法的计算复杂度为：2m³(flops)，其中，相对于广义的QR分解方法，本算法的运算量仅多了矩阵Q的列排序。基于修正的Gram-Schmidt方法的排序QR分解算法的计算复杂度略高于广义的QR分解算法为2m³+m(m-1)/2(flops)。For the sake of simplicity, it can be approximately considered that the complex number matrix operation complexity is 6 times the corresponding operation complexity of the real number matrix. One flop is represented as a floating-point operation. For a real matrix of size m×n

In other words, the computational complexity of matrix addition operation is: 2mn (flops), the computational complexity of m×n and n×p matrix multiplication is 2mnp (flops), the calculation of matrix norm ||G|| _F operation The complexity is: 4mn (flop), and for the m×m matrix, the computational complexity of the generalized eigenvalue decomposition is 4m ³ /3+17m ³ (flops), and the computational complexity of the QR decomposition algorithm is: 2m ³ (flops), among them, compared with the generalized QR decomposition method, the calculation amount of this algorithm is only more than the column sorting of matrix Q. The computational complexity of the sorting QR decomposition algorithm based on the modified Gram-Schmidt method is slightly higher than that of the generalized QR decomposition algorithm, which is 2m ³ +m(m-1)/2(flops).

The following is a comparison of the computational complexity of the SQRD-IA scheme and the AM-IA scheme, as shown in Table 1.

Table 1 Computational complexity comparison of the two algorithms

It can be seen from Table 1 that, compared with the interference alignment method of the AM-IA scheme, the computational complexity of the SQRD-IA scheme of the present invention is reduced by 51%, which will facilitate the application of the method of the present invention in actual communication systems.

In addition, as shown in Figure 3, in the system configuration (M _k , N _k , d _k )=(8,8,3), K=4, under different SNR conditions, the SQRD-IA scheme of the present invention and The comparison curve of the system capacity of the AM-IA scheme; as can be seen from the figure, the system capacity of the SQRD-IA scheme of the present invention is slightly lower than that of the AM-IA scheme.

As shown in Figure 4, under the conditions of system configuration (M _k , N _k , d _k )=(8,8,3), K=4, different signal-to-noise ratios and iteration times, the SQRD-IA of the present invention Scheme and the system iterative convergence speed comparison graph of AM-IA scheme; As can be seen from the figure, the SQRD-IA scheme of the present invention is compared with the AM-IA scheme, before 500 iterations, the convergence rate of the two algorithms is slightly different. Reduced, the two algorithms converged at 500 iterations, and the performance tended to be stable and basically consistent;

The above is only a preferred embodiment of the present invention, for those of ordinary skill in the art, without departing from the technical principle of the present invention, some improvements and deformations can also be made, and these improvements and deformations should also be regarded as protection scope of the present invention.

Claims (6)

1.MIMO the low complex degree of interference channel system disturbs alignment schemes, it is characterized in that the method comprises:

S1: obtain other cell base stations to the interference channel matrix of this community user, and the pre-coding matrix of random initializtion base station;

S2: get user's interference covariance matrix according to described pre-coding matrix and interference channel Matrix Calculating, and then obtain receiving the orthogonal basis of interference space;

S3: the orthogonal basis according to described reception interference space upgrades pre-coding matrix, when the pre-coding matrix after upgrading does not satisfy the condition of convergence, returns step S2; Otherwise, obtain the orthogonal basis of final reception interference space according to the pre-coding matrix after the renewal of satisfying the condition of convergence;

S4: the orthogonal basis according to final reception interference space obtains the reprocessing matrix;

S5: by the reprocessing matrix signal is carried out ZF and process, the signal after the interference that is eliminated.

2. method according to claim 1 is characterized in that, described step S2 specifically comprises:

S21: the interference covariance matrix that obtains each user according to described pre-coding matrix and described interference channel matrix computations;

S22: described interference covariance matrix is decomposed, obtain the first unitary matrice;

S23: the orthogonal basis that receives interference space is classified in the appointment of choosing the first unitary matrice as.

3. method according to claim 2 is characterized in that, described step S3 specifically comprises:

S31: calculate the distance matrix between the orthogonal basis of described interference channel matrix and described reception interference space;

S32: described distance matrix is decomposed, obtain the second unitary matrice;

S33: the pre-coding matrix after the renewal is classified in the setting of choosing the second unitary matrice as;

S34: whether the pre-coding matrix that calculates after the described renewal satisfies the condition of convergence, when not satisfying the condition of convergence, replaces described pre-coding matrix with the pre-coding matrix after upgrading, and returns step S2; Otherwise, obtain the orthogonal basis of final reception interference space according to the pre-coding matrix after upgrading.

4. method according to claim 2 is characterized in that, the computing formula of described interference covariance matrix is:

$D_{k_u}=\underset{k=1,k\&NotEqual;k_u}{\overset{K}{\mathrm{\&Sigma;}}}{H}_{k_u,k}{V}_k{V}_k^H{H}_{k_u,k}^H$

Wherein:

Be interference covariance matrix;

Be the interference channel matrix;

V _kBe pre-coding matrix;

K is total number of base;

K is k base station;

k _uBe k _uIndividual user.

5. method according to claim 2 is characterized in that, the described condition of convergence is:

Poor matrix between pre-coding matrix after the described renewal and the described pre-coding matrix is less than setting matrix.

6. method according to claim 2 is characterized in that, the computing formula of described reprocessing matrix is:

$W_{k_u}=I_{N_{k_u}}-Q_{k_u}^{1:N_{k_u}-d_k}{\left(Q_{k_u}^{1:N_{k_u}-d_k}\right)}^H$

Wherein:

Be the reprocessing matrix;

Be length Unit matrix;

Orthogonal basis for final reception interference space;

Number for reception antenna;

d _kNumber of data streams for base station k emission.

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