CN110350962B - Multi-cell large-scale MIMO two-stage precoding method based on Givens transformation - Google Patents

Multi-cell large-scale MIMO two-stage precoding method based on Givens transformation Download PDF

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CN110350962B
CN110350962B CN201910584502.6A CN201910584502A CN110350962B CN 110350962 B CN110350962 B CN 110350962B CN 201910584502 A CN201910584502 A CN 201910584502A CN 110350962 B CN110350962 B CN 110350962B
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CN110350962A (en
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黄学军
王雪宁
黄秋实
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Nanjing University of Posts and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • 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
    • H04B7/0413—MIMO systems
    • H04B7/0452—Multi-user MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • 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
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03891—Spatial equalizers
    • H04L25/03898—Spatial equalizers codebook-based design
    • H04L25/0391—Spatial equalizers codebook-based design construction details of matrices

Abstract

The invention discloses a Givens transformation-based multi-cell large-scale MIMO two-stage precoding method, which comprises the following steps: s1, constructing a multi-cell large-scale MIMO system; s2, respectively generating a user received signal model and channel matrixes in multiple cells and cells according to the system model; s3, calculating null space of interference channels between cells by using QR decomposition based on Givens transformation, and respectively generating pre-precoding matrixes by orthogonal bases of the null space to eliminate interference between different cells; s4, calculating null space of interference channels between users in the cell, generating post precoding matrixes by orthogonal basis of the null space respectively, and eliminating interference between users in the cell.

Description

Multi-cell large-scale MIMO two-stage precoding method based on Givens transformation
Technical Field
The invention relates to a coding method, in particular to a multi-cell large-scale coding method, and belongs to the technical field of communication.
Background
The large-scale Multiple-Input Multiple-Output (Massive MIMO) technology is one of the key technologies of 5G, and the capacity of a mobile communication system is further improved by adopting a large-scale antenna array and a multi-user beam forming principle. However, in practical applications, the large-scale MIMO technology still faces some challenges, and especially in a multi-cell scenario, when the number of cells and the number of users increase, the problem of the complexity surge of the precoding algorithm is urgently solved. The precoding algorithm of the large-scale MIMO mainly comprises nonlinear precoding, linear precoding and other low-complexity improvement algorithms. Nonlinear precoding, such as Dirty Paper Coding (DPC), can achieve an upper bound close to the theoretical capacity, with the disadvantage of extremely high algorithm complexity. Linear precoding utilizes the asymptotic orthogonality property of massive MIMO channels, and can obtain higher channel capacity with lower complexity, but such algorithms all involve the inversion problem of Hermitian matrix, and the complexity of inversion operation increases with the increase of the number of users. In order to further reduce the complexity, researchers have proposed a series of low-complexity iterative algorithms, but the low-complexity iterative algorithms have the problems of poor error rate performance and high delay. Subsequently, a Joint Spatial Division Multiplexing (JSDM) scheme has been proposed, which reduces the channel dimension according to user packets and performs two-stage precoding, but the Block Diagonalization (BD) algorithm adopted by the scheme includes multiple SVD decompositions.
In summary, how to provide a multi-cell massive MIMO two-stage precoding scheme with lower complexity and better system capacity and error code performance based on the prior art also becomes a problem to be solved by researchers in the industry at present.
Disclosure of Invention
The invention aims to provide a Givens transformation-based multi-cell large-scale MIMO two-stage precoding method which can effectively eliminate channel interference between adjacent cells and between users in the cells
The purpose of the invention is realized as follows: a multi-cell large-scale MIMO two-stage precoding method based on Givens transformation comprises the following steps:
s1, constructing a multi-cell large-scale MIMO system, and dividing cells according to geographical positions, wherein the system comprises a large-scale antenna base station and a user terminal;
s2, respectively generating a user received signal model and channel matrixes in multiple cells and cells according to the system model;
s3, calculating null space of interference channels between cells by using QR decomposition based on Givens transformation, and respectively generating pre-precoding matrixes by orthogonal bases of the null space to eliminate interference between different cells;
s4, calculating the null space of the interference channel between the users in the cell, and respectively generating post-precoding matrixes by the orthogonal basis of the null space to eliminate the interference between the users in the cell.
As a further limitation of the present invention, S1 specifically includes the following steps:
constructing a multi-cell large-scale MIMO system, grouping users according to geographical positions, and constructingIn the multi-cell massive MIMO downlink model, M massive MIMO antenna arrays respectively serve M cells, each cell considers a user group, the base station and the cells are respectively denoted by b and g, and b, g is 1,2, …, M. The total number of users of the system is K ═ ΣgKgIn which K isgIndicating the number of multi-antenna user terminals contained in the g-th cell. The number of base station antennas is NtThe number of the user terminal antennas is Nr。
As a further limitation of the present invention, S2 specifically includes the following steps:
s21, respectively generating multi-cell channel matrixes according to the system model, wherein the multi-cell channel matrixes comprise a channel matrix of the whole system and a channel matrix of each cell; for the g cell, its channel matrix is
Figure BDA0002113991320000021
Wherein, the matrix
Figure BDA0002113991320000022
Representing the channel matrix between base station b and cell g, Hb,gCan be split into KgSub-matrix
Figure BDA0002113991320000023
K-th representing base station b and cell ggChannel matrix between users, satisfy
Figure BDA0002113991320000031
Wherein
Figure BDA0002113991320000032
Representing user k in cell ggThe channel covariance matrix of (a);
s22, generating a user received signal model by the channel matrix, wherein the signal received by the cell g from the base station b is
yb,g＝(Hb,g)Hxb+ng
Wherein:
Figure BDA0002113991320000033
signal vector representing the antenna array transmission of base station b, sb ∈ Cd×1Is a valid data symbol stream vector, d is the dimension of the valid signal, d ≦ min { M, Kg}；
Figure BDA0002113991320000034
For the total pre-coding matrix, the sum of the pre-coding matrices,
Figure BDA0002113991320000035
representing a precoding matrix, Pb∈Cr×dRepresenting a post-precoding matrix; n isgRepresenting the noise interference experienced by cell g.
As a further limitation of the present invention, S3 specifically includes the following steps:
s31, first neglecting the interference between users in the cell, regarding the cell as a whole, at this time the system can be regarded as a multi-user MIMO channel, and the total received signal of the cell g is expressed as
Figure BDA0002113991320000036
The first two terms in the formula represent effective signals and interference from adjacent cells respectively, and the purpose of pre-precoding is to find out an interference channel Hb′,gTo generate a set of bases B of the null spaceb′Eliminating the interference term in the formula;
s32, converting the channel matrix H of each cellgSplicing to obtain the channel matrix of the whole system
Figure BDA0002113991320000037
Carrying out QR decomposition on the obtained product: h ═ Q · R, where
Figure BDA00021139913200000312
Is an orthogonal matrix, and the matrix is,
Figure BDA0002113991320000038
is an upper triangular matrix;
s33, because the channel matrix H is non-square matrix, and for convenient analysis, taking its conjugate transpose HHPseudo-inverse of (2):
Figure BDA0002113991320000039
order to
Figure BDA00021139913200000310
And partitioning by cell, L ═ L1,L2,…,LM]Wherein L isgIs the sub-matrix of L corresponding to cell g,
Figure BDA00021139913200000311
s34, defining the channel matrix without the sub-matrix of the cell as the interference channel matrix of the cell g:
Hg′＝[H1,H2,…Hg-1,Hg+1,…,HM]
the nature of the pseudo-inverse can be used to determine
Figure BDA0002113991320000041
The elements of the non-principal diagonal in the formula are all 0, i.e.
Figure BDA0002113991320000042
I.e. the interference matrix H for any cell gg' to a word, all are
(Hg′)HQ(Rg H)-1＝(Hg′)HQLg＝0
I.e. the matrix QLgIs a matrix HgZero space of' for QLgPerforming a Givens transform-based QR decomposition:
Figure BDA0002113991320000043
wherein the content of the first and second substances,
Figure BDA0002113991320000044
in order to form an upper triangular matrix,
Figure BDA0002113991320000045
is an orthogonal matrix and is a matrix QLgA set of orthonormal bases, thus
Figure BDA0002113991320000046
Wherein
Figure BDA0002113991320000047
Is a reversible matrix, thereby
Figure BDA0002113991320000048
S35, in summary, the
Figure BDA0002113991320000049
Is a precoding matrix of a cell, i.e. a pre-precoding matrix
Figure BDA00021139913200000410
The precoding matrix of the whole system is
Figure BDA00021139913200000411
As a further limitation of the present invention, S4 specifically includes the following steps:
s41, after the interference between the adjacent cells is eliminated, the k-th user of the cell g receives the signal of
Figure BDA00021139913200000412
The second term in the formula is inter-user interference within a cell, where H is definedg,k-effThe k-th user representing cell g is passingPre-precoded equivalent channel, and Hg,k-eff＝(Hg,g,k)HBg，Pg,kRepresenting a post-precoding matrix corresponding to the kth user of the cell g; sg,kA vector formed by effective data which represents that the cell g sends to the user k; n isg,kRepresenting the noise interference of user k in cell g;
s42, defining the interference channel of a single user in each independent cell in the equivalent model as:
Figure BDA00021139913200000413
method for eliminating interference between users and interference channel H by repeating pre-coding method of S3g,k' the null space is QLkThen to the matrix QLkIs decomposed
Figure BDA00021139913200000414
Order to
Figure BDA00021139913200000415
Is the precoding matrix of a single user k in a cell, i.e. the postprecoding matrix
Figure BDA0002113991320000051
The post-precoding matrix of cell g is
Figure BDA0002113991320000052
Compared with the prior art, the invention adopting the technical scheme has the following technical effects: under a multi-cell large-scale MIMO system model, the invention provides a Givens transformation-based two-stage precoding scheme, which shares user distribution information in a multi-cell joint processing mode, processes an interference channel by using QR decomposition based on Givens transformation, respectively obtains null spaces of the interference channels between cells and between users in the cells, respectively generates two-stage precoding matrixes by orthogonal bases of the null spaces, and eliminates interference between different cells and between users; compared with the precoding scheme based on the existing traditional BD algorithm, the multi-cell large-scale MIMO two-stage precoding based on the scheme has the advantages of obviously reduced algorithm complexity, lower Bit Error Rate (BER) and higher system and rate.
Drawings
FIG. 1 is a system model diagram of the method of the present invention.
FIG. 2 is a comparison of computational complexity between the method of the present invention and a conventional method.
Fig. 3 is a comparison chart of the error rate of the method of the present invention and the conventional method when the number of base station antennas is 32, the number of users in a cell is 4, and the number of user antennas is 2.
Fig. 4 is a comparison chart of the error rate of the method of the present invention and the conventional method when the number of base station antennas is 128, the number of users in a cell is 16, and the number of user antennas is 2.
Fig. 5 is a system and rate comparison diagram for different coding schemes.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
the invention as shown in fig. 1 provides a Givens transformation-based multi-cell massive MIMO two-stage precoding method, which comprises the following steps.
S1, constructing a multi-cell large-scale MIMO system, dividing cells according to geographical positions, wherein the system comprises a large-scale antenna base station and a user terminal, establishing a multi-cell large-scale MIMO downlink model, wherein M large-scale MIMO antenna arrays respectively serve M cells, each cell considers a user group, the base station and the cells are respectively represented by b and g, and b and g are 1,2, … and M; the total number of users of the system is K ═ ΣgKgIn which K isgIndicating the number of multi-antenna user terminals contained in the g cell; the number of base station antennas is NtThe number of the user terminal antennas is Nr。
S2, respectively generating a user received signal model and channel matrixes in multiple cells and cells according to the system model; the method specifically comprises the following steps:
s21, the multi-cell channel matrix includes the channel matrix of the whole system and the channel matrix of each cell, for the g cell, the channel matrix is
Figure BDA0002113991320000061
Wherein the matrix
Figure BDA0002113991320000062
Representing the channel matrix between base station b and cell g, Hb,gCan be split into KgSub-matrix
Figure BDA0002113991320000063
K-th representing base station b and cell ggChannel matrices between individual users, i.e.
Figure BDA0002113991320000064
Assuming that line-of-sight propagation is not considered, the matrix
Figure BDA0002113991320000065
Satisfy the requirement of
Figure BDA0002113991320000066
Wherein
Figure BDA0002113991320000067
Representing user k in cell ggThe channel covariance matrix of (a); will have equal or similar
Figure BDA0002113991320000068
The users of the cell are divided into the same cell, and the channel covariance matrix of each cell is Rb,gUser channels between different cells are considered to be uncorrelated with each other; according to the single-loop model, users in the same group are located in a scattering ring with radius r, the distance between the scattering ring and the base station center is d, the included angle θ between the scattering ring center and the x-axis is called the user angle of Arrival (AOA), and Δ ═ arctan (r/d) is the angle spread of the transmitted signal (Angula)r Spread, AS). Assuming that the received power follows a uniform distribution, the channel covariance matrix R is nowb,gWith respect to only theta and delta, the (i, j) th element thereof can be expressed as
Figure BDA0002113991320000069
1≤i,j≤Nt
Wherein k (α) ═ 2 π/λ (cos α, sin α)TDenotes the signal vector with angle of arrival α, λ denotes the carrier wavelength, uiAnd ujTwo-dimensional coordinates of the ith and jth antennas. Using the Karhunen-Loeve notation, submatrix
Figure BDA00021139913200000610
Can be expressed as
Figure BDA00021139913200000711
Wherein
Figure BDA0002113991320000071
Represents Rb,gR is R, is the eigenvector matrix corresponding to the principal eigenvalue of (the eigenvalue significantly greater than zero)b,gNumber of principal eigenvalues, Λb,gIs formed by Rb,gThe r-order diagonal matrix formed by the main eigenvalues of (1),
Figure BDA0002113991320000072
and is
Figure BDA0002113991320000073
S22, generating a user received signal model by the channel matrix; cell g receives a signal from base station b as
yb,g＝(Hb,g)Hxb+ng
Wherein:
Figure BDA0002113991320000074
signal vector, s, representing the antenna array transmission of base station bb∈Cd×1Is a valid data symbol stream vector, d is the dimension of the valid signal, d ≦ min { M, Kg}；
Figure BDA0002113991320000075
For the total pre-coding matrix, the sum of the pre-coding matrices,
Figure BDA0002113991320000076
representing a precoding matrix, Pb∈Cr×dRepresenting a post-precoding matrix; n isgRepresenting the noise interference experienced by cell g.
S3, calculating null space of interference channels between cells by using QR decomposition based on Givens transformation, and respectively generating pre-precoding matrixes by orthogonal bases of the null space to eliminate interference between different cells;
s31, first neglecting the interference between users in the cell, regarding the cell as a whole, at this time the system can be regarded as a multi-user MIMO channel, and the total received signal of the cell g is expressed as
Figure BDA0002113991320000077
The first two terms in the formula represent effective signals and interference from adjacent cells respectively, and the purpose of pre-precoding is to find out an interference channel Hb′,gTo generate a set of bases B of the null spaceb′Eliminating the interference term in the formula;
s32, converting the channel matrix H of each cellgSplicing to obtain the channel matrix of the whole system
Figure BDA0002113991320000078
Carrying out QR decomposition on the obtained product: h ═ Q · R, where
Figure BDA0002113991320000079
Is an orthogonal matrix, and the matrix is,
Figure BDA00021139913200000710
is an upper triangular matrix;
s33, because the channel matrix H is non-square matrix, and for convenient analysis, taking its conjugate transpose HHPseudo-inverse of (2):
Figure BDA0002113991320000081
order to
Figure BDA0002113991320000082
And partitioning by cell, L ═ L1,L2,…,LM]Wherein L isgIs the sub-matrix of L corresponding to cell g,
Figure BDA0002113991320000083
s34, defining the channel matrix without the sub-matrix of the cell as the interference channel matrix of the cell g:
Hg′＝[H1,H2,…Hg-1,Hg+1,…,HM]
the nature of the pseudo-inverse can be used to determine
Figure BDA0002113991320000084
The elements of the non-principal diagonal in the formula are all 0, i.e.
Figure BDA0002113991320000085
I.e. the interference matrix H for any cell gg' to a word, all are
(Hg′)HQ(Rg H)-1＝(Hg′)HQLg＝0
I.e. the matrix QLgIs a matrix Hg' null space; for QLgPerforming a Givens transform-based QR decomposition:
Figure BDA0002113991320000086
wherein the content of the first and second substances,
Figure BDA0002113991320000087
in order to form an upper triangular matrix,
Figure BDA0002113991320000088
is an orthogonal matrix and is a matrix QLgA set of orthonormal bases; thus, it is possible to provide
Figure BDA0002113991320000089
Wherein
Figure BDA00021139913200000810
Is a reversible matrix, thereby
Figure BDA00021139913200000811
S35, in summary, the
Figure BDA00021139913200000812
Is a precoding matrix of a cell, i.e. a pre-precoding matrix
Figure BDA00021139913200000813
The precoding matrix of the whole system is
Figure BDA00021139913200000814
S4, calculating null space of interference channels between users in the cell, and generating post-precoding matrices from orthogonal bases of the null space, respectively, to eliminate interference between users in the cell, which specifically includes:
s41, after the interference between the adjacent cells is eliminated, the users in each cell are only interfered by the signals sent to other users in the cell, and the system model can be equivalent to a combination of multiple independent multi-user MIMO channels. The k-th user of the cell g now receives a signal of
Figure BDA00021139913200000815
The second term in the equation is inter-user interference within the cell. Wherein, is defined asg,k-effRepresents the equivalent channel of the k-th user of the cell g after pre-precoding, and Hg,k-eff＝(Hg,g,k)HBg，Pg,kRepresenting a post-precoding matrix corresponding to the kth user of the cell g; sg,kA vector formed by effective data which represents that the cell g sends to the user k; n isg,kRepresenting the noise interference of user k in cell g;
s42, defining the interference channel of each user in each independent cell in the equivalent model as
Figure BDA0002113991320000097
At this time, the method similar to the pre-coding is used again to eliminate the interference between users and the interference channel Hg,k' the null space is QLkThen to the matrix QLkIs decomposed
Figure BDA0002113991320000091
Order to
Figure BDA0002113991320000092
Is the precoding matrix of a single user k in a cell, i.e. the postprecoding matrix
Figure BDA0002113991320000093
The post-precoding matrix of cell g is
Figure BDA0002113991320000094
S43, the Interference between users is eliminated, the user Signal-to-Noise Ratio is improved, and the system capacity is improved, at this time, the Signal-to-Interference plus Noise Ratio (SINR) of the kth user in the cell g is
Figure BDA0002113991320000095
Wherein, the denominator polynomial respectively corresponds to the intra-cell interference, the extra-cell interference and the noise, and the reachable rate of the user k is
Cg,k＝log(1+SINRg,k)
System capacity of
Figure BDA0002113991320000096
The performance of the method of the invention is analyzed in combination with simulation experiments.
Let the number of users K in each cellgAre all equal. The size of the total channel matrix H of the system is MNt×MKgNrThe size of the interference channel matrix of each cell is MNt×(M-1)KgNrAfter eliminating the inter-cell interference, the size of the equivalent channel matrix of each user is Nt×KgNrThe size of the equivalent interference matrix is Nt×(Kg-1)Nr，
The total operands of the proposed scheme when using a QR decomposition based on a Givens transform are
ψG＝8(MKgNr)2MNt+4(MKgNr)3/3+24(MKgNr)2MNt-8(MKgNr)3+8(KgNr)2Nt+4(KgNr)3/3+24(KgNr)2Nt-8(KgNr)3]
Fig. 2 compares the computational complexity of the conventional BD precoding scheme under multiple cells, the QR decomposition scheme based on Schmidt orthogonalization, and the precoding scheme proposed herein as a function of the number of users in a cell. Without loss of generality, assume that the number of cells M is 3Number of base station antennas NtNumber of user terminal antennas N of 64rIs 1. It can be seen that the complexity of the scheme herein is significantly reduced under both QR decompositions compared to using the conventional BD precoding algorithm, which is reduced by nearly an order of magnitude when the number of users in a cell exceeds 16. Compared with a QR decomposition scheme based on Schmidt orthogonalization, the complexity of the Givens-QR transformation scheme is reduced to a certain extent when the number of users is increased.
Fig. 3 shows bit error rate simulation comparison of three precoding schemes when a base station is equipped with 32 antennas, each cell contains 4 users, and each user is equipped with 2 antennas. It can be seen from the figure that although the algorithm complexity of the QR decomposition scheme based on Schmidt orthogonalization is obviously lower than that of the BD precoding scheme adopting SVD decomposition, the error rate performance of the QR decomposition scheme and the BD precoding scheme are close, and the curves are basically overlapped. While the bit error rate performance of the proposed scheme is better than the former two, this benefits from the efficiency of Givens transform in processing sparse matrices of channels, and the resulting orthogonal matrices have better orthogonality.
Fig. 4 shows bit error rate simulation comparison of three precoding schemes when a base station is equipped with 128 antennas, each cell contains 16 users, and each user is equipped with 2 antennas. It can be seen that the error rate performance of the scheme is still better, and as can be seen by comparing fig. 4 with fig. 3, the more the number of antennas at the base station end and the number of users in a cell are, the more the precoding scheme has the advantage of the error rate performance.
FIG. 5 shows the system and rate simulation comparison of three precoding schemes when a base station is equipped with 100 antennas, each cell contains 30 users, and each user is equipped with 1 antenna; it can be seen from fig. 5 that the system and rate of the precoding scheme proposed herein are higher, and the advantages are more obvious as the signal to interference and noise ratio increases.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications or substitutions within the technical scope of the present invention are included in the scope of the present invention, and therefore, the scope of the present invention should be subject to the protection scope of the claims.

Claims (1)

1. A Givens transformation-based multi-cell large-scale MIMO two-stage precoding method is characterized by comprising the following steps:
s1, constructing a multi-cell large-scale MIMO system, and dividing cells according to geographical positions, wherein the system comprises a large-scale antenna base station and a user terminal, and S1 specifically comprises the following steps:
constructing a multi-cell large-scale MIMO system, grouping users according to geographical positions, establishing a multi-cell large-scale MIMO downlink model, wherein M large-scale MIMO antenna arrays respectively serve M cells, each cell considers a user group, a base station and the cells are respectively represented by b and g, and b and g are 1,2, … and M; the total number of users of the system is K ═ sigmagKgIn which K isgIndicating the number of multi-antenna user terminals contained in the g cell; the number of base station antennas is NtThe number of the user terminal antennas is Nr；
S2, respectively generating a user received signal model and channel matrixes in multiple cells and cells according to the system model, wherein S2 specifically comprises the following steps:
s21, respectively generating multi-cell channel matrixes according to the system model, wherein the multi-cell channel matrixes comprise a channel matrix of the whole system and a channel matrix of each cell; for the g cell, its channel matrix is
Figure FDA0003356627120000011
Wherein, the matrix
Figure FDA0003356627120000012
Representing the channel matrix between base station b and cell g, Hb,gCan be split into KgSub-matrix
Figure FDA0003356627120000013
K-th representing base station b and cell ggChannel matrix between users, satisfy
Figure FDA0003356627120000014
Wherein
Figure FDA0003356627120000015
Representing user k in cell ggThe channel covariance matrix of (a);
s22, generating a user received signal model by the channel matrix, wherein the signal received by the cell g from the base station b is
yb,g＝(Hb,g)Hxb+ng
Wherein:
Figure FDA0003356627120000016
signal vector, s, representing the antenna array transmission of base station bb∈Cd×1Is a valid data symbol stream vector, d is the dimension of the valid signal, d ≦ min { M, Kg}；
Figure FDA0003356627120000017
For the total pre-coding matrix, the sum of the pre-coding matrices,
Figure FDA0003356627120000018
representing a precoding matrix, Pb∈Cr×dRepresenting a post-precoding matrix; n isgRepresenting the noise interference experienced by cell g;
s3, calculating null space of interference channels between cells by using QR decomposition based on Givens transformation, and respectively generating pre-precoding matrixes by orthogonal bases of the null space to eliminate interference between different cells; the method specifically comprises the following steps:
s31, first neglecting the interference between users in the cell, regarding the cell as a whole, at this time the system can be regarded as a multi-user MIMO channel, and the total received signal of the cell g is expressed as
Figure FDA0003356627120000021
The first two terms in the formula represent effective signals and interference from adjacent cells respectively, and the purpose of pre-precoding is to find out an interference channel Hb′,gTo generate a set of bases B of the null spaceb′Eliminating the interference term in the formula;
s32, converting the channel matrix H of each cellgSplicing to obtain the channel matrix of the whole system
Figure FDA0003356627120000022
Carrying out QR decomposition on the obtained product: h ═ Q · R, where
Figure FDA0003356627120000023
Is an orthogonal matrix, and the matrix is,
Figure FDA0003356627120000024
is an upper triangular matrix;
s33, because the channel matrix H is non-square matrix, and for convenient analysis, taking its conjugate transpose HHPseudo-inverse of (2):
Figure FDA0003356627120000025
order to
Figure FDA0003356627120000026
And partitioning by cell, L ═ L1,L2,…,LM]Wherein L isgIs the sub-matrix of L corresponding to cell g,
Figure FDA0003356627120000027
s34, defining the channel matrix without the sub-matrix of the cell as the interference channel matrix of the cell g:
Hg′＝[H1,H2,…Hg-1,Hg+1,…,HM]
the nature of the pseudo-inverse can be used to determine
Figure FDA0003356627120000028
The elements of the non-principal diagonal in the formula are all 0, i.e.
Figure FDA0003356627120000029
I.e. the interference matrix H for any cell gg' to a word, all are
(Hg′)HQ(Rg H)-1＝(Hg′)HQLg＝0
I.e. the matrix QLgIs a matrix HgZero space of' for QLgPerforming a Givens transform-based QR decomposition:
Figure FDA0003356627120000031
wherein the content of the first and second substances,
Figure FDA0003356627120000032
in order to form an upper triangular matrix,
Figure FDA0003356627120000033
is an orthogonal matrix and is a matrix QLgA set of orthonormal bases, thus
Figure FDA0003356627120000034
Wherein
Figure FDA0003356627120000035
Is a reversible matrix, thereby
Figure FDA0003356627120000036
S35, in summary, the
Figure FDA0003356627120000037
Is a precoding matrix of a cell, i.e. a pre-precoding matrix
Figure FDA0003356627120000038
The precoding matrix of the whole system is
Figure FDA0003356627120000039
S4, calculating null space of interference channels among users in the cell, and respectively generating post-precoding matrixes by orthogonal bases of the null space to eliminate interference among the users in the cell; the method specifically comprises the following steps:
s41, after the interference between the adjacent cells is eliminated, the k-th user of the cell g receives the signal of
Figure FDA00033566271200000310
The second term in the formula is inter-user interference within a cell, where H is definedg,k-effRepresents the equivalent channel of the k-th user of the cell g after pre-precoding, and Hg,k-eff＝(Hg,g,k)HBg，Pg,kRepresenting a post-precoding matrix corresponding to the kth user of the cell g; sg,kA vector formed by effective data which represents that the cell g sends to the user k; n isg,kRepresenting the noise interference of user k in cell g;
s42, defining the interference channel of a single user in each independent cell in the equivalent model as:
Figure FDA00033566271200000311
method for eliminating interference between users and interference channel H by repeating pre-coding method of S3g,k' the null space is QLkThen to the matrix QLkIs decomposed
Figure FDA00033566271200000312
Order to
Figure FDA00033566271200000313
Is the precoding matrix of a single user k in a cell, i.e. the postprecoding matrix
Figure FDA00033566271200000314
The post-precoding matrix of cell g is
Figure FDA0003356627120000041
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