CN102025462B - Block diagonalization precoding method used in MU-MIMO (Multiuser-Multiple Input Multiple Output) system down link - Google Patents

Abstract

The invention relates to a BD (Block Diagonalization) precoding method used in an MU-MIMO (Multi-User-Multiple Input Multiple Output) system down link. The method comprises the following steps of: step 1, carrying out channel estimation by all users according to received pilot frequency data so as to obtain the MIMO channel matrix of the respective current base station side to users; step 2, obtaining the MIMO channel state information of all user sides by the base station side through channel reciprocity in a TDD (Time Division Duplex) mode; step 3, calculating the null space orthogonal basis of the interference channel matrix of the users by the base station side; step 4, calculating the precoding matrix of individual user according to calculated null space orthogonal basis of the interference channel matrix; and step 5, orderly traversing all the users, and repeating steps 3 and 4 to obtain the precoding matrix of all the users. The invention has the advantage of effectively reducing algorithm complexity under the condition of ensuring that the system performance has no losses.

Description

Block diagonalization method for precoding in the MU-MIMO system down link

Technical field

The invention belongs to wireless communication technology field, particularly block diagonalization (Block-diagonalization, the BD) precoding technique in multi-user's multiple-input and multiple-output (being called for short MU-MIMO) system down link.

Background technology

Multiple-input and multiple-output (being called for short MIMO) technology can improve diversity gain and the availability of frequency spectrum of wireless communication system greatly under the prerequisite that does not increase frequency spectrum resource and transmitting power.The at present research of mimo system expands to multi-multipoint multi-user MIMO system (MU-MIMO) from point-to-point alone family.In multi-user's multiple-input and multiple-output (MIMO) system, base station end (being called for short BS) transmits to a plurality of users simultaneously, because a plurality of users share same Time And Frequency resource, will inevitably introduce multi-user's common-channel interference (being called for short CCI).But be difficult to mutually cooperation between each user, therefore in the MU-MIMO system down link, can carry out preliminary treatment by precoding at the base station end and eliminate CCI between the user.

Under time division duplex multiplexing (being called for short TDD) pattern, the base station end can be known by channel reciprocity user's channel information.When the antenna sum of user side is less than or equal to number of transmit antennas (the user antenna total quantity of communicating by letter is less than the number of transmit antennas of base station), according to the block diagonalization method for precoding, the base station end is according to channel condition information (the Channel State Information of all users in the system, CSI) pre-coding matrix of designing, can eliminate the CCI between the multi-user fully, reach good systematic function.

With the BD method for precoding of analyzing in the MU-MIMO system down link, the MU-MIMO system condition is set as for convenience of explanation:

Be that number of transmit antennas is not less than the reception antenna number.Base station end number of transmit antennas is N _t, total number of users is K, and the span of user k is 1≤k≤K arbitrarily, and the reception antenna number of expression user k is n _k, n _k〉=1, for simplifying the analysis, suppose that the data fluxion that each user of the present invention communicates equates with each user's reception antenna number respectively.

BD method for precoding in the existing MU-MIMO system down link mainly contains:

Method 1: traditional BD method for precoding.Mainly comprise the steps:

1. calculate

Wherein Interference channel matrix for any user k; In the formula, rank (g) representing matrix get order computing, H _kThe channel matrix that represents any user k, [g] ^TThe transposition of representing matrix.Interference channel matrix to any user

Carry out singular value decomposition (SingularValue Decomposition, SVD), namely

Wherein

Be Left singular matrix,

Be

The singular value diagonal matrix,

With

Be respectively

Right singular matrix before Row and after

Row, [g] H

The conjugate transpose of representing matrix.According to matrix theory knowledge, can prove

Be The kernel orthogonal basis.

2. obtain to eliminate fully the equivalent channel matrix of interference user CCI:

3. be the precoding gain of obtaining the equivalent channel matrix maximum of zero CCI, equivalent channel carried out SVD again decompose

With

Represent respectively left singular matrix, singular value diagonal matrix and the right singular matrix of equation left end matrix after SVD decomposes.

4. thereby the pre-coding matrix that obtains each user is:

Wherein

For

Front n _kRow.

5. the pre-coding matrix of whole system is: W _s=[W ₁W ₂K W _K].

Method 2: based on the BD method for precoding of QR decomposition.Mainly comprise the steps:

1. right

Carrying out QR decomposes:

The interference channel Matrix Conjugate transposition that represents any user k,

Expression

Carry out the orthogonal matrix after QR decomposes,

With

Respectively expression

Before

Row and after

Row.

2. obtain to eliminate the equivalent channel matrix of CCI:

3. be the precoding gain of obtaining the equivalent channel matrix maximum of zero CCI, equivalent channel carried out SVD again decompose

With

Represent respectively left singular matrix, singular value diagonal matrix and the right singular matrix of equation left end matrix after SVD decomposes.

4. thereby the pre-coding matrix that obtains each user is:

Wherein

For

Front n _kRow; So, the pre-coding matrix of whole system is: W _s=[W ₁W ₂K W _K].

The major defect of the BD method for precoding in the existing MU-MIMO system down link is that computational complexity is high.Method 1 described traditional BD method needs twice SVD to decompose.Although at the method 2 described BD method for precoding that decompose based on QR, replaced the SVD decomposition with the QR decomposition, complexity decreases, and is still higher.Because existing methodical these deficiencies cause the transmitting terminal in communication system that the complexity that signal carries out precoding is increased the linear predictive coding Efficiency Decreasing.Therefore, the complexity of the BD method of MU-MIMO system still has the space of reduction.The below makes a concrete analysis of above-mentioned two kinds of existing methodical complexities:

Table 1:MU-MIMO system parameter setting

Number of transmit antennas	N t
		Each user's reception antenna number	n
Each user's transmission data fluxion	n
		Total number of users	K

Definition N _r=n * K and

1. the analysis of complexity of traditional BD method for precoding

Table 2: traditional BD method for precoding analysis of complexity step table

2. the analysis of complexity of the BD method for precoding that decomposes based on QR

Table 3: based on the BD method for precoding analysis of complexity step table of QR decomposition

From above analysis of complexity to the BD method for precoding the existing MU-MIMO system down link, we can find out that the major defect of these methods is that computational complexity is high, and the complexity of algorithm directly affects communication system hardware configuration demand.Because the existence of such deficiency, so that the practical application of existing BD method for precoding has just obtained larger restriction.Based on the requirement of using, those skilled in the art is devoted to seek the BD pre-coding scheme of low complex degree.

Summary of the invention

The objective of the invention is the computational complexity for the BD method for precoding that reduces existing MU-MIMO system, proposed the BD method for precoding in the MU-MIMO system down link.

To achieve these goals, technical scheme of the present invention is: the BD method for precoding in the MU-MIMO system down link comprises step:

Step 1: each user carries out channel estimating to obtain self current base station end to user's mimo channel matrix according to the pilot data that receives;

Under the step 2:TDD pattern, the base station end is known the mimo channel state information of each user side by channel reciprocity;

Step 3: the base station end calculates the kernel orthogonal basis of user's interference channel matrix;

Step 4: the pre-coding matrix that calculates unique user according to the kernel orthogonal basis of the interference channel matrix that calculates;

Step 5: travel through successively all users, repeating step 3 and 4 obtains all users' pre-coding matrix.

The concrete steps of above-mentioned steps 3 comprise step by step following:

31. the base station end utilizes the GSO method to calculate any user's interference channel matrix according to the mimo channel gain of knowing each user from user side

Orthogonal basis

32. according to the interference channel matrix

Orthogonal basis

And null space basis

Relation: I is N _t* N _tThe unit matrix of dimension, the base station end calculates user's interference channel matrix

Null space basis

Between product form

33. the base station is for matrix

Before

Column vector is utilized GSO method (the similar above-mentioned steps 3 of concrete operations) again, obtains the null space basis of any user's interference channel matrix Footnote j is used for representing the traversal to all users,

The reception antenna summation that represents all users.

The concrete operations of above-mentioned steps 31 are:

311. the interference channel matrix

Can obtain by the row piecemeal:

312. being used GSO (Gram-Schmidt Orthogonalization), the column vector group obtains corresponding orthonormal vector group β ₁, β ₂, L, β _Nt:

${\mathrm{\β}}_1=\frac{{\mathrm{\α}}_1}{\left|\right|{\mathrm{\α}}_1\left|\right|}$

${\mathrm{\β}}_i=\frac{{\mathrm{\α}}_i-\underset{j=1}{\overset{i-1}{\mathrm{\Σ}}}({\mathrm{\α}}_i,{\mathrm{\β}}_j)}{\left|\right|{\mathrm{\α}}_i-\underset{j=1}{\overset{i-1}{\mathrm{\Σ}}}({\mathrm{\α}}_i,{\mathrm{\β}}_j)\left|\right|}i=\mathrm{2,3},L{N}_t$

Thereby 313. obtain orthogonal basis

The concrete steps of above-mentioned steps 4 comprise step by step following:

41. the base station is with user's channel matrix H _kKernel orthogonal basis with its corresponding interference matrix

Multiply each other, can obtain user's zero and disturb equivalent channel matrix

42. be the precoding gain of obtaining the equivalent channel matrix maximum of zero CCI, the base station is to the equivalent block diagonalization channel matrix of user's zero CCI

Be SVD and decompose, obtain the front n of right unitary matrice of the equivalent channel matrix of zero CCI _kRow;

43. the base station to the right unitary matrice of the equivalent channel matrix of the kernel orthogonal basis of user's interference channel matrix and its corresponding zero CCI before n _kRow are made the phase multiplication, with the result of the product pre-coding matrix as the user.

The invention has the beneficial effects as follows: in order to improve cell throughout, the MU-MIMO system has become the study hotspot of many broadband wireless communications standards, and multi-user's CCI becomes the bottleneck that the restriction system throughput further improves.The BD precoding technique can effectively be eliminated CCI, and multiple implementation method is arranged, and diverse ways brings different performances to system.The present invention is based on BD and can eliminate the principle of CCI fully, propose a kind of new method and obtain the kernel orthogonal basis that to eliminate CCI, guaranteeing that systematic function is not subjected to the situation of any loss, can effectively reduce algorithm complex, the complexity that this can reduce the user side hardware configuration undoubtedly also meets the principle that the communication designer communicates system.Method of the present invention is according to all users' mimo channel information, utilize Schimidt orthogonalization (Gram-Schmidt Orthogonalization, GSO) and SVD decompose and calculate successively each user's pre-coding matrix, can obviously reduce the computational complexity of the BD method for precoding in the MU-MIMO system down link.Simultaneously, the method that the present invention proposes, in the MU-MIMO system down link, the process that is to ask for pre-coding matrix from the main difference of existing method for precoding is different, contrast existing method for precoding, the present invention need to not make Secretary in interface standard and other side, therefore has good transplantability.

Description of drawings

Fig. 1 is the structural representation of MU-MIMO system down link.

Fig. 2 is the main flow chart of the specific embodiment of the invention.

Fig. 3 is at N _tUnder the system configuration of=8, n=2, under the condition of different user number, the computational complexity comparison diagram of the method for the specific embodiment of the invention and art methods.

Fig. 4 is at N _tUnder the system configuration of=16, n=2, under the condition of different user number, the method for the specific embodiment of the invention and the computational complexity comparison diagram that decomposes the BD method based on QR.

Fig. 5 is under different signal to noise ratio snr conditions, the method for the specific embodiment of the invention and the capacity comparison figure of art methods.

Embodiment

The present invention is described further below in conjunction with the drawings and specific embodiments.When implementation is described in detail, simultaneously the rudimentary knowledge of embodiment is done and briefly introduced, because this part content all is based on prior art, therefore do not do detailed expansion and describe, but this does not affect those of ordinary skill in the art's the understanding of the present invention and enforcement.

With analysis method for precoding of the present invention, the MU-MIMO system condition is done following setting for convenience of explanation: as shown in Figure 1,

Be that transmitting antenna (Antenna) number is not less than the reception antenna number.Under tdd mode, definition N _tBe base station end number of transmit antennas, total user (User) number is K, and (1≤k≤K) has n to user k arbitrarily _k(n _k〉=1) root reception antenna and n _kCircuit-switched data stream (Data streams) carries out data communication.Base station end of same time carries out transfer of data to K user.All users that the base station covers among the figure (from User 1 to User K) estimate separately channel matrix by pilot tone.According to the channel reciprocity under the tdd mode, all users' channel matrix can be known in the base station, through precoder data message is sent to antenna end again and is sent to the user.For simplifying the analysis, suppose that the data fluxion that each user of the present invention communicates equates with each user's reception antenna number respectively, and base station end transmit power allocations adopts average power allocation.

K user's mimo channel matrix is

$H_k=\left(\begin{array}{ccc}{h}_{11}& K& h_{{1N}_t}\\ M& O& M\\ h_{n_{k}1}& L& h_{n_k{N}_t}\end{array}\right)$ Formula (1)

k _NmIn the representation formula (2) each, be the m transmit antennas to the channel impulse response of n root reception antenna, its envelope is obeyed independent identically distributed Rayleigh decline.

The signal that k user receives is

y _k=H _kWs+z _kFormula (3)

S is the transmitting data vector, comprises K user's data flow.W is pre-coding matrix.z _kThat zero-mean and variance are δ ²Additive white Gaussian noise.

As shown in Figure 2, the BD method for precoding of the MU-MIMO system of present embodiment comprises step:

Step 1: each user carries out channel estimating to obtain self current base station end to user's mimo channel matrix according to the pilot data that receives;

Under the step 2:TDD pattern, the base station end is known the mimo channel state information of each user side by channel reciprocity;

Step 3: the base station end calculates the kernel orthogonal basis of user's interference channel matrix; The concrete steps of step 3 comprise step by step following:

31. the base station end utilizes GSO (Gram-Schmidt Orthogonalization, Schimidt orthogonalization) method to calculate any user's interference channel matrix according to the mimo channel gain of knowing each user from user side

Orthogonal basis Concrete operations are:

311. the interference channel matrix

Can obtain by the row piecemeal:

312. being used the GSO method, the column vector group obtains corresponding orthonormal vector group β ₁, β ₂, L, β _Nt:

${\mathrm{\β}}_1=\frac{{\mathrm{\α}}_1}{\left|\right|{\mathrm{\α}}_1\left|\right|}$

${\mathrm{\β}}_i=\frac{{\mathrm{\α}}_i-\underset{j=1}{\overset{i-1}{\mathrm{\Σ}}}({\mathrm{\α}}_i,{\mathrm{\β}}_j)}{\left|\right|{\mathrm{\α}}_i-\underset{j=1}{\overset{i-1}{\mathrm{\Σ}}}({\mathrm{\α}}_i,{\mathrm{\β}}_j)\left|\right|}i=\mathrm{2,3},L{N}_t;$

Thereby 313. obtain orthogonal basis

32. according to the interference channel matrix

Orthogonal basis

And null space basis

Relation:

I is N _t* N _tThe unit matrix of dimension, the base station end calculates user's interference channel matrix Null space basis

Between product form

33. the base station is for matrix

Before

Column vector is utilized the GSO method again, obtains the null space basis of any user's interference channel matrix

Footnote j is used for representing the traversal to all users, The reception antenna summation that represents all users.

Step 4: the pre-coding matrix that calculates unique user according to the kernel orthogonal basis of the interference channel matrix that calculates; The concrete steps of step 4 comprise step by step following:

41. the base station is with user's channel matrix H _kKernel orthogonal basis with its corresponding interference matrix

Multiply each other, can obtain user's zero and disturb equivalent channel matrix

42. be the precoding gain of obtaining the equivalent channel matrix maximum of zero CCI, the base station is to the equivalent block diagonalization channel matrix of user's zero CCI Be SVD and decompose, obtain the front n of right unitary matrice of the equivalent channel matrix of zero CCI _kRow;

43. the base station to the right unitary matrice of the equivalent channel matrix of the kernel orthogonal basis of user's interference channel matrix and its corresponding zero CCI before n _kRow are made the phase multiplication, with the result of the product pre-coding matrix as the user.

Step 5. travels through all users successively, and repeating step 3 and 4 obtains all users' pre-coding matrix.

Next, utilize its corresponding user of Linear precoding matrix who constructs each good user to transmit and multiply each other, then by base station end antenna transmission, so far, can finish the system flow of whole linear predictive coding.

Under the MU-MIMO system parameter setting shown in the table 1, the analysis of complexity of the inventive method:

The analysis of complexity step table of table 4 the inventive method

From analysis of complexity table 1 to table 4, can find out why the inventive method can make complexity obviously reduce, and key is that the complexity of asking for the kernel orthogonal basis has obtained obvious minimizing.Under the MU-MIMO system parameter setting shown in the table 1, the method for the specific embodiment of the invention and the contrast of the computational complexity of art methods are as follows:

1. in traditional BD method, decompose to obtain the kernel orthogonal basis by SVD, and the computation complexity of SVD decomposition itself is larger, especially when number of users was more, its complexity was considerable, and total computing floating number is calculated as:

$K[24N_t^2{N}_r^{\%}+48{\mathrm{<figure-callout\; id="3"\; label="N\; t"\; filenames="HDA0000038545160000021.png,HDA0000038545160000022.png"\; state="\{\{state\}\}">N</figure-callout>}}_t^{}+16n{N}_t(N_t-N_r^{\%})+24n{(N_t-N_r^{\%})}^2+48{(N_t-N_r^{\%})}^3]$

2. in the BD method based on the QR decomposition, decompose by the interference user matrix being carried out QR, replaced the SVD decomposition, complexity reduces to some extent, and total computing floating number is calculated as:

$K[{8\mathrm{<figure-callout\; id="3"\; label="N\; t"\; filenames="HDA0000038545160000021.png,HDA0000038545160000022.png"\; state="\{\{state\}\}">N</figure-callout>}}_t^{}+16n{N}_t(N_t-N_r^{\%})+{24n}^2{(N_t-N_r^{\%})\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000038545160000011.png,HDA0000038545160000022.png"\; state="\{\{state\}\}">n</figure-callout>}}^2+{48n}^3]$

3. in the BD method for precoding of the present invention, use a kind of brand-new kernel orthogonal basis method of asking for, ask for the kernel orthogonal basis based on the GSO method of low complex degree, can bring the obvious reduction of the method complexity, total computing floating number is calculated as:

$K[{8N}_t{\mathrm{<figure-callout\; id="2"\; label="N\; r\; \%"\; filenames="HDA0000038545160000011.png,HDA0000038545160000022.png"\; state="\{\{state\}\}">N</figure-callout>}}_{r\%}^2+8N_r^{<figure-callout\; id="2"\; label="\%\; N\; t"\; filenames="HDA0000038545160000011.png,HDA0000038545160000022.png"\; state="\{\{state\}\}">\%</figure-callout>}{N}_t^{}{}_2^{}+N_t+8N_t{(N_t-N_r^{\%})}^2+16{\mathrm{nN}}_t(N_t-N_r^{\%})+24n{(N_t-N_r^{\%})}^2+48{(N_t-N_r^{\%})}^3]$

The present invention will be described in detail with the form of instantiation below in conjunction with accompanying drawing 3, accompanying drawing 4 and accompanying drawing 5.

In accompanying drawing 3, with number of users K as independent variable, the BD algorithm that provided traditional BD algorithm, decomposes based on QR and the complexity contrast simulation of the inventive method.The system emulation condition is: base station transmit antennas is counted N _t=8, number of users domain of variation K=2: 4, each user's reception antenna is counted n=2.As can be seen from the figure, traditional BD algorithm decompose owing to relate to SVD, and SVD decomposition itself just has higher complexity, thus can cause the complexity of the method very high, and constantly increase along with the increase of number of users.The complexity of the BD algorithm that decomposes based on QR for the BD algorithm, has obvious reduction, and along with the increase of number of users, complexity does not become strictly increasing trend.Take full advantage of the helpfulness that QR decomposes.The inventive method can be on the basis of above-mentioned two kinds of methods, and the complexity performance of optimization system more further reduces the complexity of algorithm itself, meets us and carries out the improved thought of algorithm.

Accompanying drawing 4 be 16 at the antenna for base station number, every user antenna number is 2, number of users rises to the BD method of decomposing based on QR that obtains under 8 the system configuration and the complexity performance simulation of the inventive method from 2.This analogous diagram further illustrates the inventive method and compares superior performance with the BD method of decomposing based on QR.As can be seen from the figure, the inventive method almost in all number of users domain of variation, has the performance advantage of obvious reduction complexity.

Accompanying drawing 5 is be used to being presented under the different signal to noise ratio conditions, traditional BD algorithm, the BD algorithm that decomposes based on QR and the volumetric properties comparison diagram of the inventive method.The simulated conditions that obtains accompanying drawing 5 is: the antenna for base station number is 8, and each user's antenna number is 2, and number of users is 4, and channel model is modeled as perfect single footpath Rayleigh channel.BS end signal transmitting power is 1.As shown in Figure 5, method of the present invention has identical power system capacity performance with the BD method for precoding that decomposes based on QR, is better than traditional BD precoding algorithm.And the algorithm complex of incidence of criminal offenses of the present invention is less than the BD precoding algorithm that decomposes based on QR.So, use incidence of criminal offenses of the present invention to carry out precoding, in the situation that guarantees system brought performance not suffer a loss, can reduce the complexity of algorithm, be a kind of more excellent design.

Those of ordinary skill in the art will appreciate that embodiment described here is in order to help reader understanding's principle of the present invention, should to be understood to that protection scope of the present invention is not limited to such special statement and embodiment.Those of ordinary skill in the art can make various other various concrete distortion and combinations that do not break away from essence of the present invention according to these technology enlightenments disclosed by the invention, and these distortion and combination are still in protection scope of the present invention.

Claims (1)

1.MU-MIMO the BD method for precoding in the system down link comprises step:

Step 1: each user carries out channel estimating to obtain self current base station end to user's mimo channel matrix according to the pilot data that receives;

Under the step 2:TDD pattern, the base station end is known the mimo channel state information of each user side by channel reciprocity;

Step 3: the base station end calculates the kernel orthogonal basis of user's interference channel matrix; This step comprises step by step following:

31. the base station end utilizes the GSO method to calculate any user's interference channel matrix according to the mimo channel gain of knowing each user from user side

Orthogonal basis

The concrete operations of above-mentioned steps 31 are:

311. the interference channel matrix

Can obtain by the row piecemeal:

312. being used GSO (Gram-Schmidt Orthogonalization), the column vector group obtains corresponding orthonormal vector group β ₁, β ₂..., β _Nt:

${\mathrm{\&beta;}}_1=\frac{{\mathrm{\&alpha;}}_1}{\left|\right|{\mathrm{\&alpha;}}_1\left|\right|}$

${\mathrm{\&beta;}}_i=\frac{{\mathrm{\&alpha;}}_i-\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}({\mathrm{\&alpha;}}_i,{\mathrm{\&beta;}}_j)}{\left|\right|{\mathrm{\&alpha;}}_i-\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}({\mathrm{\&alpha;}}_i,{\mathrm{\&beta;}}_j)\left|\right|},i=\mathrm{2,3},\&CenterDot;\&CenterDot;\&CenterDot;N_t;$

Thereby 313. obtain orthogonal basis

In the formula of step 31, under tdd mode, definition N _tBe base station end number of transmit antennas, total number of users is K, and arbitrarily (1≤k≤K) has n to user k _k(n _k〉=1) root reception antenna and n _kCircuit-switched data flows to row data communication;

32. according to the interference channel matrix

Orthogonal basis And null space basis

Relation:

I is N _t* N _tThe unit matrix of dimension, the base station end calculates user's interference channel matrix

Null space basis

Between product form

33. the base station is for matrix

Before

Column vector is utilized the GSO method again, obtains the null space basis of any user's interference channel matrix

Footnote j is used for representing the traversal to all users,

The reception antenna summation that represents all users;

Step 4: the pre-coding matrix that calculates unique user according to the kernel orthogonal basis of the interference channel matrix that calculates; The concrete steps of above-mentioned steps 4 comprise step by step following:

41. the base station is with user's channel matrix H _kKernel orthogonal basis with its corresponding interference matrix

Multiply each other, can obtain user's zero and disturb equivalent channel matrix

42. be the precoding gain of obtaining the equivalent channel matrix maximum of zero CCI, the base station is to the equivalent block diagonalization channel matrix of user's zero CCI

Be SVD and decompose, obtain the front n of right unitary matrice of the equivalent channel matrix of zero CCI _kRow;

43. the base station to the right unitary matrice of the equivalent channel matrix of the kernel orthogonal basis of user's interference channel matrix and its corresponding zero CCI before n _kRow are made the phase multiplication, with the result of the product pre-coding matrix as the user;

Step 5: travel through successively all users, repeating step 3 and 4 obtains all users' pre-coding matrix.

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