CN103067062A - Base station antenna selecting method based on interference alignment in multi-cell system - Google Patents

Abstract

The invention discloses a base station antenna selecting method based on interference alignment in a multi-cell system, and mainly solves the problems that an existing multi-antenna interference alignment technology is relatively high in system hardware cost, and the base station antenna selecting method based on interference alignment can only be used in a network comprising 3 cells. The method comprises the following implementation steps of: estimating state information of channels from various base stations to users in the resident cells; initiating base station antenna selection schemes of the various cells; along a system and capacity increase optimizing direction, under the condition that other base station antenna selection schemes are unchanged, determining the optimal base station selection schemes of the various cells in sequence by using partial iterative interference alignment; and performing multi-cell interference coordination by adopting traditional iterative interference alignment. The base station antenna selecting method is applicable to an LTE (Long Term Evolution) network oriented to commercial use with a plurality of cells, is low in computation complexity, can reduce the system hardware cost, and realizes compromise between system and capacity and computation complexity.

Description

The antenna for base station system of selection of aliging based on interference in the multi-cell system

Technical field

The invention belongs to wireless communication technology field, further relate to the antenna for base station system of selection of aliging based on interference in a kind of multi-cell system, can be used for the LTE network that business is used.

Background technology

In order to improve the capacity of cellular system, the Next-Generation Wireless Communication Systems take the LTE network as representative requires to realize as far as possible that the full rate of neighbor cell is multiplexing, i.e. the spectrum reuse factor is 1.Therefore, with respect to noise and decline, presence of intercell interference becomes the principal element that affects systematic function.How effectively carrying out many Inter-Cell Interference Coordination, the interference of particularly eliminating Cell Edge User has caused widely to be paid close attention to.Disturbing alignment is a kind of interference coordination technique that proposes recent years, it can will snap to from the interference signal of other base stations a sub spaces that receives signal space at receiver user, useful signal from respective base station is projected to another interference-free subspace, thereby effectively disturb inhibition, improve power system capacity.

The scholars such as K.Gomadam are at article " Approaching the Capacity of Wireless Networksthrough Distributed Interference Alignment " (Proceedings of the IEEE GlobalTelecommunications Conference, Miami, USA, propose a kind of distributed iterative 2008:1-5) and disturbed alignment schemes (be called traditional iteration and disturb alignment), be applicable to the interference coordination of many residential quarters multiple-input and multiple-output (MIMO) network.The method is the pre-coding matrix of random initializtion base station at first, then according to disturbing the interference of revealing minimum principle Iterative Design user to suppress the pre-coding matrix of matrix and base station until convergence.The weak point that the method exists is: although user's antenna number is generally less in the mimo system, but a fairly large number of antenna of base station possible configuration, the method is not considered the increase along with antenna for base station quantity, the radio frequency link that comprises the elements such as digital-to-analogue/analog to digital converter, low-converter, low noise amplifier also will increase gradually, thereby increases the problem of system hardware cost.

The people such as J.G.Klotz are at article " Antenna Selection Criteria for Interference Alignment " (Proceedings of IEEE International Symposium on Personal, Indoor and Mobile RadioCommunications, Istanbul, Turkey, proposed 2010:527-531) for adopting non-iteration to disturb the antenna for base station system of selection of 3 cell systems of alignment, to reduce the system hardware cost, obtain simultaneously system and volumetric properties and promote.The main performing step of the method is: the first, and all days line options situation that all alternative antenna subsets of utilizing poor searching method to travel through 3 base stations are combined into; The second, for each day line options situation, carry out non-iteration and disturb alignment, and computing system and capacity or each user's useful and interference signal vector space chordal distance with; The 3rd, select the antenna selecting plan of each base station optimum according to maximization system and capacity criterion or maximization chordal distance criterion, the antenna of choosing is connected on the corresponding radio frequency link; The 4th, realize non-iteration interference alignment.The weak point that the method exists is: disturb alignment in view of non-iteration and can only finish the interference coordination of 3 residential quarters, this method is only applicable to comprise the system of 3 residential quarters, therefore uses to have limitation, can not expand to the system of many residential quarters.

Summary of the invention

The object of the invention is to overcome above-mentioned the deficiencies in the prior art, propose in a kind of multi-cell system based on the antenna for base station system of selection of disturbing alignment, reduce the system hardware cost, obtain a day line options gain, simultaneously with range of application from 3 cell extension to a plurality of residential quarters.

For achieving the above object, the thinking of the inventive method is:

Do not fix and more characteristics for carrying out the multiplexing number of cells of full rate in the LTE system, the inventive method adopts iteration to disturb alignment to carry out the interference coordination of a plurality of cell systems; Owing to determining that the antenna for base station selection scheme of each residential quarter optimum is a combinatorial optimization problem, finding the solution this combinatorial optimization problem need to repeatedly search for various days line options situations that are combined into by each cell base station, therefore in each day line options situation search procedure, adopt the traditional iteration that comprises repeatedly iteration to disturb alignment can cause the computation complexity of method higher; The inventive method adopts following two modes to reduce respectively the number of times of various days line options situations of search and the computation complexity in each search procedure: first, optimization direction along system and capacity increase, in the situation that keep other antenna for base station selection schemes constant, successively the antenna for base station selection scheme of each residential quarter is optimized, thereby reduces the number of times of finding the solution various days line options situations of search in the combinatorial optimization problem; The second, when optimizing the antenna for base station selection scheme of each residential quarter, adopt the part iteration of only carrying out the several times iteration to disturb alignment, then computing system and capacity, rather than finish traditional iteration and disturb alignment, thereby reduce the computation complexity of each search procedure; According to the antenna for base station selection scheme of each residential quarter optimum, the inventive method adopts traditional iteration to disturb alignment to realize many Inter-Cell Interference Coordination at last.

Concrete steps of the present invention are as follows:

(1) estimates that each base station is to the channel condition information of this community user

Base station k sends pilot frequency information for this community user k, and user k estimates each antenna of base station k to the channel condition information of self, and feeds back to base station k, k=1 wherein ..., B, B are the residential quarter number; Base station k determines channel matrix according to the channel condition information of this community user feedback

Wherein N and M represent respectively the antenna number of base station k and user k,

The expression complex field;

(2) each cell-site antenna selection scheme of initialization

The antenna selecting plan ω of initialization base station k _kFor having the matrix of maximum F-norm

Corresponding alternative antenna is selected vector, ω _kComputing formula as follows:

${\mathrm{\ω}}_k=\arg \underset{l\∈\{1,...,C_N^{N_f}\}}{\max }{|\left|H_{\mathrm{kk}}^{{\mathrm{\φ}}_l}\right||}_F^2,$

Wherein, k=1 ..., B,

Expression line options scheme on the same day is φ _lThe time according to channel matrix H _KkThe base station k that determines is to the channel matrix of this community user, φ _lL alternative antenna of expression base station selected vector, Select the index variables of vector for alternative antenna, N _fBe the rf chain way of base station,

Expression is chosen N from the N number _fThe number of combinations of number, || || _FThe F-norm of representing matrix; The antenna selecting plan of each base station is combined into B cell-site antenna selection set omega={ ω ₁, ω ₂..., ω _B;

(3) along the optimization direction of system and capacity increase, in the situation that keep other antenna for base station selection schemes constant, utilize the part iteration to disturb alignment to determine successively the antenna for base station selection scheme of each residential quarter optimum:

3.1) to select the index variables l of vector be 1 to the initialization alternative antenna, system and the capacity C of simultaneously initialization maximum _MaxBe 0;

3.2) with the antenna for base station selection scheme ω of residential quarter 1 ₁Be updated to alternative antenna and select vectorial φ _l, keep the antenna selecting plan of other base stations constant, simultaneously the 1st element in B the cell-site antenna selection set omega is updated to φ _l

3.3) according to above-mentioned antenna selecting plan, carry out the part iteration and disturb alignment, the base station pre-coding matrix and the user that design each residential quarter disturb the inhibition matrix, are implemented as follows:

3.3a) pre-coding matrix of random initializtion base station k

K=1 wherein ..., B, d represent that the base station sends the dimension of data flow;

3.3b) initialization iterations indicator variable c is 1;

3.3c) determine the interference covariance matrix of user k ' when the c time iteration

K '=1 wherein ..., B;

3.3d) reveal minimum principle according to disturbing, according to above-mentioned interference covariance matrix

The interference of design user k ' when the c time iteration suppresses matrix

K '=1 wherein ..., B, υ _dD characteristic value characteristic of correspondence vector of { } representing matrix minimum;

3.3e) suppress matrix according to above-mentioned interference

Determine the interference covariance matrix of base station k when the c time iteration

K '=1 wherein ..., B, k=1 ..., B;

3.3f) reveal minimum principle according to disturbing, according to above-mentioned interference covariance matrix

The pre-coding matrix of design base station k when the c time iteration

K=1 wherein ..., B;

3.3g) value of iterations indicator variable c adds 1, if c≤N _Ite, then return step 3.3c, proceed iteration; Otherwise, jump to step 3.4, obtain N _IteThe pre-coding matrix of base station k after the inferior iteration

Suppress matrix with the interference of user k '

K=1 wherein ..., B, k '=1 ..., B, N _IteDisturb the iterations of alignment for the part iteration;

3.4) determine that base station k ' is to the equivalent channel of user k ' And the interference covariance matrix of user k '

Wherein

Be illustrated in antenna selecting plan ω _{K '}Base station k ' arrives the channel matrix of user k ' in the situation, Expression N _IteThe pre-coding matrix of base station k ' after the inferior iteration, k '=1 ..., B;

3.5) equivalent channel of disturbing alignment to obtain according to the part iteration

Disturb and suppress matrix

And interference covariance matrix

Computing system and capacity

Wherein

Be the capacity of user k ', k '=1 wherein ..., B;

3.6) if C ^Ω＞C _Max, C then is set _Max=C ^Ω, and the optimum alternative antenna of order is selected the index variables l of vector ^*=l, namely optimum alternative antenna is selected vector Otherwise, C _MaxRemain unchanged;

3.7) alternative antenna selects the value of the index variables l of vector to add 1, if

Then return step 3.2, continue other alternative antenna of traversal and select vector; Otherwise, skip to step 3.8;

3.8) determine the antenna for base station selection scheme of residential quarter 1 optimum

3.9) according to the described method of step 3.1 to 3.8, determine that successively residential quarter 2 is to the antenna for base station selection scheme of residential quarter B optimum ${\mathrm{\ω}}_2^{*},{\mathrm{\ω}}_3^{*},...,{\mathrm{\ω}}_B^{*};$

3.10) the antenna for base station selection scheme of above-mentioned each residential quarter optimum is combined into B optimum cell-site antenna selection set ${\mathrm{\Ω}}^{*}=\{{\mathrm{\ω}}_1^{*},{\mathrm{\ω}}_2^{*},...,{\mathrm{\ω}}_B^{*}\};$

(4) adopt traditional iteration to disturb alignment to carry out many coordinating district interferences:

4.1) select set omega according to B cell-site antenna of above-mentioned optimum ^*, carrying out iterations is N _ITraditional iteration disturb alignment, the base station pre-coding matrix and the user that design each residential quarter disturb the inhibition matrix;

4.2) disturb the pre-coding matrix of alignment design and interference to suppress matrix according to above-mentioned traditional iteration, each cell base station and user transmit and receive data respectively, carry out many coordinating district interferences, eliminate presence of intercell interference.

The present invention has following advantage:

1. the present invention is owing to utilizing iteration to disturb alignment to carry out many coordinating district interferences, and the antenna for base station of realizing each residential quarter optimum is selected, overcome the existing shortcoming that can only in comprising 3 subzone networks, use based on the antenna for base station system of selection of disturbing alignment, with range of application from 3 cell extension to a plurality of residential quarters, the LTE network of using applicable to the business with a plurality of residential quarters;

2. the present invention is owing to the optimization direction along system and capacity increase, in the constant situation of the antenna for base station selection scheme that keeps other residential quarters, determine successively the antenna for base station selection scheme of each residential quarter optimum, reduced the number of times of searching for various days line options situations, and in the search procedure of each day line options situation, adopt the less part iteration of iterations to disturb alignment, thereby greatly reduced computation complexity;

3. the present invention has reduced the rf chain way of base station because antenna for base station is selected, thereby reduces the system hardware cost, obtains simultaneously a day line options gain;

4. the present invention can the adjustment member iteration disturb the iterations of alignment, thereby reaches the compromise of system and capacity and computation complexity.

Description of drawings

Fig. 1 is the B cell system illustraton of model that the present invention is suitable for;

Fig. 2 is general flow chart of the present invention;

Fig. 3 is the sub-process figure that determines the antenna for base station selection scheme of each residential quarter optimum among the present invention;

Fig. 4 is the sub-process figure that the part iteration is disturbed alignment among the present invention;

Fig. 5 is the present invention and the system of random antenna for base station system of selection and poor search base station antenna selecting method and the simulation comparison figure that capacity changes with signal to noise ratio.

Embodiment

Below in conjunction with accompanying drawing the present invention is done further detailed description.

With reference to Fig. 1, in the B cell system, user of the base station of each residential quarter service, the antenna number of base station and rf chain way are respectively N and N _f, user's antenna number and radio frequency link number average are M.The sequence number of residential quarter represents with k, and k=1 ..., B, then base station k and user k represent respectively base station and the user of residential quarter k.The system that a plurality of users are arranged for each residential quarter, for example can adopting, time-multiplexed mode is reduced to the system that each time slot only has a user.Suppose N＞N _f, N need to be chosen in each base station from all N antenna _fIndividual antenna, and be connected on the corresponding radio frequency link, so the alternative antenna of base station set Φ comprises

Individual alternative antenna is selected vector, can be expressed as

Wherein

Expression is chosen N from the N number _fThe number of combinations of number, φ _lRepresent that l alternative antenna select vector, it is the long column vector of N, and its element value is 0 or 1, and l is the index variables that alternative antenna is selected vector.Sequence number is that the element of i is that 1 to represent i antenna of base station selected in the column vector, otherwise not selected.

Expression base station k is to the channel matrix of user k ', wherein ω _kThe antenna selecting plan that expression base station k chooses from alternative antenna is selected to gather,

The expression complex field.

With reference to Fig. 2, performing step of the present invention comprises as follows:

Step 1 estimates that each base station is to the channel condition information of this community user.

1a) base station k sends to user k

Inferior pilot frequency information is chosen each time some antennas and they is connected to radio frequency link transmission pilot frequency information, wherein chooses N the 1st time from all N antenna _fIndividual antenna, the 2nd time from remaining N-N _fChoose N in the individual antenna _fIndividual antenna, the 3rd time from remaining N-2N _fChoose N in the individual antenna _fIndividual antenna, until the Inferiorly choose last remaining antenna, thereby guarantee that all antennas all can once be connected to radio frequency link at certain and send pilot frequency information, k=1 wherein ..., B,

Representative rounds up to scalar x;

1b) user k estimates base station k respective antenna to the channel condition information of self each antenna by the pilot frequency information that receives at every turn, and with corresponding channel matrix feedback to base station k, k=1 wherein ..., B;

1c) base station k obtains its all antennas to the channel coefficients of each antenna of user according to the channel matrix of each time feedback, and channel coefficients is formed channel matrix

K=1 wherein ..., B.

Step 2, each cell-site antenna selection scheme of initialization.

2a) according to channel matrix H _KkSelect vectorial φ with alternative antenna _l, determine to work as φ _lBase station k is to the channel matrix of this community user during as antenna selecting plan

Wherein, k=1 ..., B,

Diag{ φ _lRepresent that the element on the leading diagonal is column vector φ _lThe diagonal matrix of corresponding element, function

The submatrix that expression is made of the non-zero row of matrix;

2b) the antenna selecting plan ω of initialization base station k _kMatrix for the F-norm of maximum

Corresponding alternative antenna is selected vector, and computing formula is as follows:

${\mathrm{\ω}}_k=\arg \underset{l\∈\{1,...,C_N^{N_f}\}}{\max }{|\left|H_{\mathrm{kk}}^{{\mathrm{\φ}}_l}\right||}_F^2,$

Wherein, k=1 ..., B, || || _FThe F-norm of representing matrix;

2c) antenna selecting plan with above-mentioned each base station is combined into B cell-site antenna selection set omega={ ω ₁, ω ₂..., ω _B.

Step 3 along the optimization direction of system and capacity increase, in the situation that keep other antenna for base station selection schemes constant, utilizes the part iteration to disturb alignment to determine successively the antenna for base station selection scheme of each residential quarter optimum.

With reference to Fig. 3, being achieved as follows of this step:

3.1) to select the index variables l of vector be 1 to the initialization alternative antenna, system and the capacity C of simultaneously initialization maximum _MaxBe 0;

3.2) with the antenna for base station selection scheme ω of residential quarter 1 ₁Be updated to alternative antenna and select vectorial φ _l, keep the antenna selecting plan of other base stations constant, simultaneously the 1st element in B the cell-site antenna selection set omega is updated to φ _l

3.3) according to above-mentioned antenna selecting plan, carry out the part iteration and disturb alignment, the base station pre-coding matrix and the user that design each residential quarter disturb the inhibition matrix:

With reference to Fig. 4, being implemented as follows of this step:

3.3a) pre-coding matrix of random initializtion base station k And satisfy

K=1 wherein ..., B, () ^HThe conjugate transpose of representing matrix, I _nThe unit matrix of expression n * n dimension, d represents that the base station sends the dimension of data flow;

3.3b) initialization iterations indicator variable c is 1;

3.3c) according to scholars such as K.Gomadam at article " Approaching the Capacity of WirelessNetworks through Distributed Interference Alignment " (Proceedings of the IEEE GlobalTelecommunications Conference, Miami, USA, training method 2008:1-5) is determined the interference covariance matrix of user k ' when the c time iteration

$Q_{k^{\′},c}^{\mathrm{\Ω}}=\underset{k=1,k\≠k^{\′}}{\overset{B}{\mathrm{\Σ}}}\frac{P_k}{d}{H}_{k^{\′}k}^{{\mathrm{\ω}}_k}{V}_{k,c-1}^{\mathrm{\Ω}}{\left(V_{k,c-1}^{\mathrm{\Ω}}\right)}^H{\left(H_{k^{\′}k}^{{\mathrm{\ω}}_k}\right)}^H,$

Wherein, k '=1 ..., B, P _kThe transmitting power of expression base station k,

The pre-coding matrix of base station k when being illustrated in the c-1 time iteration;

3.3d) reveal minimum principle according to disturbing, according to above-mentioned interference covariance matrix

The interference of design user k ' when the c time iteration suppresses matrix K '=1 wherein ..., B, υ _dD characteristic value characteristic of correspondence vector of { } representing matrix minimum;

3.3e) according to scholars such as K.Gomadam at article " Approaching the Capacity of WirelessNetworks through Distributed Interference Alignment " (Proceedings of the IEEE GlobalTelecommunications Conference, Miami, USA, training method 2008:1-5) is determined the interference covariance matrix of base station k when the c time iteration

${\stackrel{\‾}{Q}}_{k,c}^{\mathrm{\Ω}}=\underset{k^{\′}=1,k^{\′}\≠k}{\overset{B}{\mathrm{\Σ}}}\frac{P_{k^{\′}}}{d}{\left(H_{k^{\′}k}^{{\mathrm{\ω}}_k}\right)}^H{U}_{k^{\′},c}^{\mathrm{\Ω}}{\left(U_{k^{\′},c}^{\mathrm{\Ω}}\right)}^H{H}_{k^{\′}k}^{{\mathrm{\ω}}_k},$

Wherein, k=1 ..., B, P _{K '}The transmitting power of expression user k ', value equates with the transmitting power of this cell base station;

3.3f) reveal minimum principle according to disturbing, according to above-mentioned interference covariance matrix

The pre-coding matrix of design base station k when the c time iteration K=1 wherein ..., B;

3.3g) value of iterations indicator variable c adds 1, if c≤N _Ite, then return step 3.3c, proceed iteration; Otherwise, jump to step 3.4, obtain N _IteThe pre-coding matrix of base station k after the inferior iteration Suppress matrix with the interference of user k '

K=1 wherein ..., B, k '=1 ..., B, N _IteDisturb the iterations of alignment for the part iteration, and satisfy N _Ite≤ N _I, N _IThe iterations empirical value that the expression tradition disturbs the alignment convergence to need is preferably 30;

3.4) according to scholars such as K.Gomadam at article " Approaching the Capacity of WirelessNetworks through Distributed Interference Alignment " (Proceedings of the IEEE GlobalTelecommunications Conference, Miami, USA, training method 2008:1-5) determines that base station k ' is to the equivalent channel of user k ' And the interference covariance matrix of user k '

$Q_{k^{\′}}^{\mathrm{\Ω}}=\underset{k=1,k\≠k^{\′}}{\overset{B}{\mathrm{\Σ}}}\frac{P_k}{d}{H}_{k^{\′}k}^{{\mathrm{\ω}}_k}{V}_{k,N_{\mathrm{ite}}}^{\mathrm{\Ω}}{\left(V_{k,N_{\mathrm{ite}}}^{\mathrm{\Ω}}\right)}^H{\left(H_{k^{\′}k}^{{\mathrm{\ω}}_k}\right)}^H,$

Wherein, k '=1 ..., B, wherein

Be illustrated in antenna selecting plan ω _{K '}Base station k ' is to the channel matrix of user k ' in the situation;

3.5) equivalent channel of disturbing alignment to obtain according to the part iteration

Disturb and suppress matrix

And interference covariance matrix

Computing system and capacity C ^Ω:

$C^{\mathrm{\Ω}}=\underset{k^{\′}=1}{\overset{B}{\mathrm{\Σ}}}{C}_{k^{\′}}^{\mathrm{\Ω}}=\underset{k^{\′}=1}{\overset{B}{\mathrm{\Σ}}}{\log }_2|I_d+\frac{P_{k^{\′}}{\left(U_{k^{\′},N_{\mathrm{ite}}}^{\mathrm{\Ω}}\right)}^H{H}_{k^{\′}{k}^{\′}}^{{\mathrm{\ω}}_{k^{\′}}}{V}_{k^{\′},N_{\mathrm{ite}}}^{\mathrm{\Ω}}{\left(V_{k^{\′},N_{\mathrm{ite}}}^{\mathrm{\Ω}}\right)}^H{\left(H_{k^{\′}{k}^{\′}}^{{\mathrm{\ω}}_{k^{\′}}}\right)}^{\text{H}}{U}_{k^{\′}{,N}_{\mathrm{ite}}}^{\mathrm{\Ω}}/d}{{\left(U_{k^{\′}{,N}_{\mathrm{ite}}}^{\mathrm{\Ω}}\right)}^H({\mathrm{\σ}}^2{I}_M+Q_{k^{\′}}^{\mathrm{\Ω}})U_{k^{\′},N_{\mathrm{ite}}}^{\mathrm{\Ω}}}|,$

Wherein, k '=1 ..., B, σ ²The variance of white Gaussian noise in the channel, || the determinant of representing matrix, bodge are bit/s/Hz;

3.6) if C ^Ω＞C _Max, C then is set _Max=C ^Ω, and the optimum alternative antenna of order is selected the index variables l of vector ^*=l, namely optimum alternative antenna is selected vector

Otherwise, C _MaxRemain unchanged;

3.7) alternative antenna selects the value of the index variables l of vector to add 1, if Then return step 3.2, other alternative antenna that continue among the basic alternative antenna set of the traversal Φ are selected vector; Otherwise, skip to step 3.8;

3.8) determine the antenna for base station selection scheme of residential quarter 1 optimum

3.9) according to the described method of step 3.1 to 3.8, determine that successively residential quarter 2 is to the antenna for base station selection scheme of residential quarter B optimum ${\mathrm{\ω}}_2^{*},{\mathrm{\ω}}_3^{*},...,{\mathrm{\ω}}_B^{*};$

3.10) the antenna for base station selection scheme of above-mentioned each residential quarter optimum is combined into B optimum cell-site antenna selection set ${\mathrm{\Ω}}^{*}=\{{\mathrm{\ω}}_1^{*},{\mathrm{\ω}}_2^{*},...,{\mathrm{\ω}}_B^{*}\}.$

Step 4 adopts traditional iteration to disturb alignment to carry out many coordinating district interferences.

4.1) select set omega according to B cell-site antenna of above-mentioned optimum ^*, carrying out iterations is N _ITraditional iteration disturb alignment, the base station pre-coding matrix and the user that design each residential quarter disturb the inhibition matrix:

4.1a) pre-coding matrix of random initializtion base station k

And satisfy

K=1 wherein ..., B, () ^HThe conjugate transpose of representing matrix, I _nThe unit matrix of expression n * n dimension, d represents that the base station sends the dimension of data flow;

4.1b) initialization iterations indicator variable m is 1;

4.1c) according to scholars such as K.Gomadam at article " Approaching the Capacity of WirelessNetworks through Distributed Interference Alignment " (Proceedings of the IEEE GlobalTelecommunications Conference, Miami, USA, training method 2008:1-5) is determined the interference covariance matrix of user k ' when the m time iteration

$Q_{k^{\′},m}^{{\mathrm{\Ω}}^{*}}=\underset{k=1,k\≠k^{\′}}{\overset{B}{\mathrm{\Σ}}}\frac{P_k}{d}{H}_{k^{\′}k}^{{\mathrm{\ω}}_k^{*}}{V}_{k,m-1}^{{\mathrm{\Ω}}^{*}}{\left(V_{k,m-1}^{{\mathrm{\Ω}}^{*}}\right)}^H{\left(H_{k^{\′}k}^{{\mathrm{\ω}}_k^{*}}\right)}^H,$

Wherein, k '=1 ..., B, P _kThe transmitting power of expression base station k, The pre-coding matrix of base station k when being illustrated in the m-1 time iteration, Be illustrated in antenna selecting plan

Base station k is to the channel matrix of user k ' in the situation;

4.1d) reveal minimum principle according to disturbing, according to above-mentioned interference covariance matrix

The interference of design user k ' when the m time iteration suppresses matrix

K '=1 wherein ..., B, υ _dD characteristic value characteristic of correspondence vector of { } representing matrix minimum;

4.1e) according to scholars such as K.Gomadam at article " Approaching the Capacity of WirelessNetworks through Distributed Interference Alignment " (Proceedings of the IEEE GlobalTelecommunications Conference, Miami, USA, training method 2008:1-5) is determined the interference covariance matrix of base station k when the m time iteration

${\stackrel{\‾}{Q}}_{k,m}^{{\mathrm{\Ω}}^{*}}=\underset{k^{\′}=1,k^{\′}\≠k}{\overset{B}{\mathrm{\Σ}}}\frac{P_{k^{\′}}}{d}{\left(H_{k^{\′}k}^{{\mathrm{\ω}}_k^{*}}\right)}^H{U}_{k^{\′},m}^{{\mathrm{\Ω}}^{*}}{\left(U_{k^{\′},m}^{{\mathrm{\Ω}}^{*}}\right)}^H{H}_{k^{\′},k}^{{\mathrm{\ω}}_k^{*}},$

Wherein, k=1 ..., B, P _kThe transmitting power of ' expression user k ', its value equates with the transmitting power of this cell base station;

4.1f) reveal minimum principle according to disturbing, according to above-mentioned interference covariance matrix The pre-coding matrix of design base station k when the m time iteration

K=1 wherein ..., B;

4.1g) value of iterations variable m adds 1, if m≤N _I, then return step 4.1c, proceed iteration; Otherwise iterative process finishes, and obtains the pre-coding matrix of base station k

Suppress matrix with the interference of user k '

K=1 wherein ..., B, k '=1 ..., B jumps to step 4.2;

4.2) disturb the pre-coding matrix of alignment design and interference to suppress matrix according to above-mentioned traditional iteration, each cell base station and user transmit and receive data respectively, carry out many coordinating district interferences, eliminate presence of intercell interference.

Advantage of the present invention further specifies by following computation complexity analysis and simulation result:

1) computation complexity analysis

Before analyzing computation complexity of the present invention, the computation complexity of the poor search base station antenna selecting method of given first.Poor search base station antenna selecting method is the most direct a kind of method, namely travel through by all alternative antenna of all base stations and select various days synthetic line options situations of Vector Groups, then disturb alignment to select so that the antenna for base station selection scheme of a kind of each residential quarter of system and capacity maximum by traditional iteration.Owing in the system B base station arranged, and each base station having

Individual alternative antenna is selected vector, so the number of times of various days line options situations of the method search is

In each search procedure, carrying out iterations is N _ITraditional iteration disturb alignment, disturb the computation complexity of alignment to be in each search procedure:

${\mathrm{BN}}_I[O\left(N_f^3\right)+O\left(M^3\right)]+{\mathrm{BN}}_I\left[2(B-1)(O\left(N_f^{2}M\right)+O\left(N_f{M}^2\right))\right].$

Therefore, the poor total computation complexity of search base station antenna selecting method is:

${\mathrm{BN}}_I{\left(C_N^{N_f}\right)}^B[O\left(N_f^3\right)+O\left(M^3\right)+2(B-1(O\left(N_f^{2}M\right)+O\left(N_f{M}^2\right))].$

The present invention is along the optimization direction of system and capacity increase, in the situation that keep other antenna for base station selection schemes constant, successively the antenna selecting plan of each base station is optimized, the number of times that the not possible situation of limit institute, so the present invention is searched for various days line options situations is

In each search procedure, the present invention adopts the part iteration to disturb alignment, has reduced the iterations that disturbs alignment, disturbs the computation complexity of alignment to be in each search procedure:

Disturb the computation complexity that aligns to compare in the computation complexity of matrix F-norm and the each search procedure in the step 2 very little, so this part complexity can be ignored.Consideration step 4 is carried out the computation complexity that traditional iteration is disturbed alignment, and the total computation complexity of the present invention can be expressed as:

$(B^2{N}_{\mathrm{ite}}{C}_N^{N_f}+{\mathrm{BN}}_I)[O\left(N_f^3\right)+O\left(M^3\right)+2(B-1)(O\left(N_f^{2}M\right)+O\left(N_f{M}^2\right))],$

Further abbreviation is:

${\mathrm{BN}}_I(1+\mathrm{\θ}{\mathrm{BC}}_N^{N_f})[O\left(N_f^3\right)+O\left(M^3\right)+2(B-1)(O\left(N_f^{2}M\right)+O\left(N_f{M}^2\right))],$

Wherein, θ=N _Ite/ N _IBe the part iteration factor, its span is 0＜θ≤1.Because in B＞1 and

Condition under

Less than Especially B or

When larger

Much smaller than

Therefore the present invention is lower with respect to poor search base station antenna selecting method computation complexity.

2) emulation experiment

2.1) simulated conditions:

Adopt the MATLAB simulation software, emulation 1000 times.The rf chain way N of the antenna number N=4 of residential quarter number B=4, base station, base station _f=3, the iterations of user's antenna and rf chain way M=3, the dimension d=1 that sends data flow, traditional iteration interference alignment is N _I=30.The transmitting power of supposing each cell base station equates, all is P, and the variances sigma of Gaussian noise ²=1, then power P has represented the signal to noise ratio snr of each community user in the system.

2.2) emulation content and result:

Disturb the iterations N of alignment in the part iteration _Ite=1,5,10, under 30 conditions, system and capacity to the present invention and random antenna for base station system of selection and poor search base station antenna selecting method carry out Monte-Carlo Simulation with the signal to noise ratio snr situation of change, obtain corresponding simulation comparison figure, as shown in Figure 5, wherein abscissa represents signal to noise ratio snr, and ordinate represents system and capacity.

As can be seen from Figure 5, system and the volumetric properties of random antenna for base station system of selection are the poorest, because random device is just chosen at random antenna for base station and accessed the respective radio-frequency link, are difficult to obtain a day line options gain.Poor search base station antenna selecting method has traveled through by all alternative antenna of all base stations and has selected various days synthetic line options situations of Vector Groups, and adopts traditional iteration to disturb the method for alignment, has therefore obtained optimum system and capacity.When signal to noise ratio snr is increased to 30dB from 0dB, system of the present invention and capacity all a little less than poor search base station antenna selecting method apparently higher than system and the capacity of random antenna for base station system of selection.The present invention is at N _IteConcrete system and volumetric properties situation when getting different value: work as N _IteWhen getting minimum value 1, poor-performing of the present invention, the optimal performance that the poor search base station antenna selecting method of distance obtains is far away, because N _IteToo little, the part iteration has been disturbed the iteration of only aliging once, but the performance of this moment still is better than the performance of random antenna for base station system of selection; Work as N _IteWhen getting maximum 30, the present invention obtains the optimal performance that can reach, and this optimal performance is close to the performance of poor search base station antenna selecting method.Work as N _IteGet respectively 5 and at 10 o'clock, performance of the present invention is with respect to N _IteThe performance of getting at 1 o'clock is obviously promoted.N particularly _IteGot 10 o'clock, the present invention can obtain almost and N _IteGet 30 o'clock same performances, and iterations is with respect to N _IteGet 30 o'clock less, show N _Ite=10 can obtain the compromise of system and capacity and computation complexity.

The analysis showed that of simulation result and computation complexity, the present invention can reduce computation complexity effectively, obtain simultaneously close to poor search base station antenna selecting method and volumetric properties.In addition, the present invention disturbs the iterations of alignment, the compromise of realization system and capacity and computation complexity by the adjustment member iteration.

Claims (10)

1. In the multi-cell system based on the antenna for base station system of selection of disturbing alignment, comprise the steps:

   (1) estimates that each base station is to the channel condition information of this community user

   Base station k sends pilot frequency information for this community user k, and user k estimates each antenna of base station k to the channel condition information of self, and feeds back to base station k, k=1 wherein ..., B, B are the residential quarter number; Base station k determines channel matrix according to the channel condition information of this community user feedback

   

   Wherein N and M represent respectively the antenna number of base station k and user k,

   

   The expression complex field;

   (2) each cell-site antenna selection scheme of initialization

   The antenna selecting plan ω of initialization base station k _kFor having the matrix of maximum F-norm

   

   Corresponding alternative antenna is selected vector, ω _kComputing formula as follows:

   ${\mathrm{\ω}}_k=\arg \underset{l\∈\{1,...,C_N^{N_f}\}}{\max }{|\left|H_{\mathrm{kk}}^{{\mathrm{\φ}}_l}\right||}_F^2,$

   Wherein, k=1 ..., B,

   

   Expression line options scheme on the same day is φ _lThe time according to channel matrix H _KkThe base station k that determines is to the channel matrix of this community user, φ _lL alternative antenna of expression base station selected vector,

   

   Select the index variables of vector for alternative antenna, N _fBe the rf chain way of base station,

   

   Expression is chosen N from the N number _fThe number of combinations of number, || || _FThe F-norm of representing matrix; The antenna selecting plan of each base station is combined into B cell-site antenna selection set omega={ ω ₁, ω ₂..., ω _B;

   (3) along the optimization direction of system and capacity increase, in the situation that keep other antenna for base station selection schemes constant, utilize the part iteration to disturb alignment to determine successively the antenna for base station selection scheme of each residential quarter optimum:

   3.1) to select the index variables l of vector be 1 to the initialization alternative antenna, system and the capacity C of simultaneously initialization maximum _MaxBe 0;

   3.2) with the antenna for base station selection scheme ω of residential quarter 1 ₁Be updated to alternative antenna and select vectorial φ _l, keep the antenna selecting plan of other base stations constant, simultaneously the 1st element in B the cell-site antenna selection set omega is updated to φ _l

   3.3) according to above-mentioned antenna selecting plan, carry out the part iteration and disturb alignment, the base station pre-coding matrix and the user that design each residential quarter disturb the inhibition matrix, are implemented as follows:

   3.3a) pre-coding matrix of random initializtion base station k

   

   K=1 wherein ..., B, d represent that the base station sends the dimension of data flow;

   3.3b) initialization iterations indicator variable c is 1;

   3.3c) determine the interference covariance matrix of user k ' when the c time iteration K '=1 wherein ..., B;

   3.3d) reveal minimum principle according to disturbing, according to above-mentioned interference covariance matrix The interference of design user k ' when the c time iteration suppresses matrix

   

   K '=1 wherein ..., B, υ _dD characteristic value characteristic of correspondence vector of { } representing matrix minimum;

   3.3e) suppress matrix according to above-mentioned interference

   

   Determine the interference covariance matrix of base station k when the c time iteration

   

   K '=1 wherein ..., B, k=1 ..., B;

   3.3f) reveal minimum principle according to disturbing, according to above-mentioned interference covariance matrix The pre-coding matrix of design base station k when the c time iteration

   

   K=1 wherein ..., B;

   3.3g) value of iterations indicator variable c adds 1, if c≤N _Ite, then return step 3.3c, proceed iteration; Otherwise, jump to step 3.4, obtain N _IteThe pre-coding matrix of base station k after the inferior iteration

   

   Suppress matrix with the interference of user k '

   

   K=1 wherein ..., B, k '=1 ..., B, N _IteDisturb the iterations of alignment for the part iteration;

   3.4) determine that base station k ' is to the equivalent channel of user k '

   

   And the interference covariance matrix of user k '

   

   Wherein

   

   Be illustrated in antenna selecting plan ω _{K '}Base station k ' arrives the channel matrix of user k ' in the situation, Expression N _IteThe pre-coding matrix of base station k ' after the inferior iteration, k '=1 ..., B;

   3.5) equivalent channel of disturbing alignment to obtain according to the part iteration Disturb and suppress matrix

   

   And interference covariance matrix

   

   Computing system and capacity

   

   Wherein Be the capacity of user k ', k '=1 wherein ..., B;

   3.6) if C ^Ω＞C _Max, C then is set _Max=C ^Ω, and the optimum alternative antenna of order is selected the index variables l of vector ^*=l, namely optimum alternative antenna is selected vector

   

   Otherwise, C _MaxRemain unchanged;

   3.7) alternative antenna selects the value of the index variables l of vector to add 1, if

   

   Then return step 3.2, continue other alternative antenna of traversal and select vector; Otherwise, skip to step 3.8;

   3.8) determine the antenna for base station selection scheme of residential quarter 1 optimum

   

   3.9) according to the described method of step 3.1 to 3.8, determine that successively residential quarter 2 is to the antenna for base station selection scheme of residential quarter B optimum ${\mathrm{\ω}}_2^{*},{\mathrm{\ω}}_3^{*},...,{\mathrm{\ω}}_B^{*};$

   3.10) the antenna for base station selection scheme of above-mentioned each residential quarter optimum is combined into B optimum cell-site antenna selection set ${\mathrm{\Ω}}^{*}=\{{\mathrm{\ω}}_1^{*},{\mathrm{\ω}}_2^{*},...,{\mathrm{\ω}}_B^{*}\};$

   (4) adopt traditional iteration to disturb alignment to carry out many coordinating district interferences:

   4.1) select set omega according to B cell-site antenna of above-mentioned optimum ^*, carrying out iterations is N _ITraditional iteration disturb alignment, the base station pre-coding matrix and the user that design each residential quarter disturb the inhibition matrix;

   4.2) disturb the pre-coding matrix of alignment design and interference to suppress matrix according to above-mentioned traditional iteration, each cell base station and user transmit and receive data respectively, carry out many coordinating district interferences, eliminate presence of intercell interference.
2. 2. the antenna for base station system of selection of aliging based on interference in the multi-cell system according to claim 1, wherein the described base station k of step (1) sends pilot frequency information to user k, and be to carry out in the following manner: base station k divides

   

   The inferior user k of giving sends pilot frequency information, chooses each time some antennas and they are connected to radio frequency link to send pilot frequency information, wherein chooses N the 1st time from all N antenna _fIndividual antenna, the 2nd time from remaining N-N _fChoose N in the individual antenna _fIndividual antenna, the 3rd time from remaining N-2N _fChoose N in the individual antenna _fIndividual antenna, until the

   

   Inferiorly choose last remaining antenna, thereby guarantee that all antennas all can once be connected to radio frequency link at certain and send pilot frequency information, k=1 wherein ..., B, B are the residential quarter number, N and N _fRepresent antenna number and the rf chain way of base station, and N＞N _f,

   

   Representative rounds up to scalar x.
3. 3. the antenna for base station system of selection of aliging based on interference in the multi-cell system according to claim 1, the channel matrix in the wherein said step (2)

   

   Determine with following formula:

   

   Wherein, k=1 ..., B, B are the residential quarter number, H _KkBe the channel matrix of base station k to this community user, φ _lL alternative antenna of expression base station selected vector, and it is the column vector that N grows, and the element value is whether 1 or 0 not represent respective antenna selected in this vector,

   

   For alternative antenna is selected vector index variable, N and N _fRepresent antenna number and the rf chain way of base station, and N＞N _f,

   

   Expression is chosen N from the N number _fThe number of combinations of number, Diag{ φ _lRepresent that the element on the leading diagonal is column vector φ _lThe diagonal matrix of corresponding element, function

   

   The submatrix that expression is made of the non-zero row of matrix.
4. 4. the antenna for base station system of selection of aliging based on interference in the multi-cell system according to claim 1, the pre-coding matrix in the wherein said step (3.3a)

   

   Satisfy condition: K=1 wherein ..., B, B are the residential quarter number, Ω is that the B cell-site antenna is selected set, N _fThe rf chain way of expression base station, d represents that the base station sends the dimension of data flow, () ^HThe conjugate transpose of representing matrix, I _nThe unit matrix of expression n * n dimension,

   

   The expression complex field.
5. In the multi-cell system according to claim 1 based on the antenna for base station system of selection of disturbing alignment, the interference covariance matrix of user k ' when the c time iteration in the wherein said step (3.3c)

   

   Its computing formula is as follows:

   $Q_{k^{\′},c}^{\mathrm{\Ω}}=\underset{k=1,k\≠k^{\′}}{\overset{B}{\mathrm{\Σ}}}\frac{P_k}{d}{H}_{k^{\′}k}^{{\mathrm{\ω}}_k}{V}_{k,c-1}^{\mathrm{\Ω}}{\left(V_{k,c-1}^{\mathrm{\Ω}}\right)}^H{\left(H_{k^{\′}k}^{{\mathrm{\ω}}_k}\right)}^H,$

   Wherein, k '=1 ..., B, B are the residential quarter number, Ω is that B cell-site antenna selected set, P _kThe transmitting power of expression base station k, d represents that the base station sends the dimension of data flow, The pre-coding matrix of base station k when being illustrated in the c-1 time iteration,

   

   Be illustrated in antenna selecting plan ω _kBase station k is to the channel matrix of user k ', () in the situation ^HThe conjugate transpose of representing matrix.
6. In the multi-cell system according to claim 1 based on the antenna for base station system of selection of disturbing alignment, the interference covariance matrix of base station k when the c time iteration in the wherein said step (3.3e)

   

   Its computing formula is as follows:

   ${\stackrel{\‾}{Q}}_{k,c}^{\mathrm{\Ω}}=\underset{k^{\′}=1,k^{\′}\≠k}{\overset{B}{\mathrm{\Σ}}}\frac{P_{k^{\′}}}{d}{\left(H_{k^{\′}k}^{{\mathrm{\ω}}_k}\right)}^H{U}_{k^{\′},c}^{\mathrm{\Ω}}{\left(U_{k^{\′},c}^{\mathrm{\Ω}}\right)}^H{H}_{k^{\′}k}^{{\mathrm{\ω}}_k},$

   Wherein, k=1 ..., B, B are the residential quarter number, Ω is that B cell-site antenna selected set, P _{K '}The transmitting power of expression user k ', value equate with the transmitting power of this cell base station, and d represents the dimension of base station transmission data flow,

   

   The interference of user k ' suppresses matrix when being illustrated in the c time iteration,

   

   Be illustrated in antenna selecting plan ω _kBase station k is to the channel matrix of user k ', () in the situation ^HThe conjugate transpose of representing matrix.
7. 7. the antenna for base station system of selection of aliging based on interference in the multi-cell system according to claim 1, the part iteration in the wherein said step (3.3g) is disturbed the iterations N of alignment _IteNeed to satisfy N _Ite≤ N _I, N wherein _IThe iterations empirical value that the expression tradition disturbs the alignment convergence to need is preferably 30.
8. 8. the antenna for base station system of selection of aliging based on interference in the multi-cell system according to claim 1, the interference covariance matrix of the user k ' in the wherein said step (3.4) Its computing formula is as follows:

   $Q_{k^{\′}}^{\mathrm{\Ω}}=\underset{k=1,k\≠k^{\′}}{\overset{B}{\mathrm{\Σ}}}\frac{P_k}{d}{H}_{k^{\′}k}^{{\mathrm{\ω}}_k}{V}_{k,N_{\mathrm{ite}}}^{\mathrm{\Ω}}{\left(V_{k,N_{\mathrm{ite}}}^{\mathrm{\Ω}}\right)}^H{\left(H_{k^{\′}k}^{{\mathrm{\ω}}_k}\right)}^H,$

   Wherein, k '=1 ..., B, B are the residential quarter number, Ω is that B cell-site antenna selected set, P _kThe transmitting power of expression base station k, d represents that the base station sends the dimension of data flow,

   

   Be illustrated in N _IteThe pre-coding matrix of base station k after the inferior iteration,

   

   Be illustrated in antenna selecting plan ω _kBase station k is to the channel matrix of user k ', () in the situation ^HThe conjugate transpose of representing matrix.
9. 9. the antenna for base station system of selection of aliging based on interference in the multi-cell system according to claim 1, the capacity in the wherein said step (3.5) Its computing formula is as follows:

   $C_{k^{\′}}^{\mathrm{\Ω}}={\log }_2|I_d+\frac{P_{k^{\′}}{\left(U_{k^{\′},N_{\mathrm{ite}}}^{\mathrm{\Ω}}\right)}^H{H}_{k^{\′}{k}^{\′}}^{{\mathrm{\ω}}_{k^{\′}}}{V}_{k^{\′},N_{\mathrm{ite}}}^{\mathrm{\Ω}}{\left(V_{k^{\′},N_{\mathrm{ite}}}^{\mathrm{\Ω}}\right)}^H{\left(H_{k^{\′}{k}^{\′}}^{{\mathrm{\ω}}_{k^{\′}}}\right)}^{\text{H}}{U}_{k^{\′}{,N}_{\mathrm{ite}}}^{\mathrm{\Ω}}/d}{{\left(U_{k^{\′}{,N}_{\mathrm{ite}}}^{\mathrm{\Ω}}\right)}^H({\mathrm{\σ}}^2{I}_M+Q_{k^{\′}}^{\mathrm{\Ω}})U_{k^{\′},N_{\mathrm{ite}}}^{\mathrm{\Ω}}}|,$

   Wherein, k '=1 ..., B, B are the residential quarter number, Ω is that B cell-site antenna selected set, P _{K '}The transmitting power of expression base station k ', d represents that the base station sends the dimension of data flow,

   

   With

   

   Represent respectively N _IteThe interference of the pre-coding matrix of base station k ' and user k ' suppresses matrix after the inferior iteration, Be illustrated in antenna selecting plan φ _{K '}Base station k ' arrives the channel matrix of user k ' in the situation,

   

   The interference covariance matrix of expression user k ', () ^HThe conjugate transpose of representing matrix, σ ²The variance of white Gaussian noise in the channel, I _nThe unit matrix of expression n * n dimension, M is user's antenna number, || the determinant of representing matrix, bodge are bit/s/Hz.
10. 10. the antenna for base station system of selection of aliging based on interference in the multi-cell system according to claim 1, wherein described B the cell-site antenna according to optimum of step (4.1) selected set omega ^*, carrying out iterations is N _ITraditional iteration disturb alignment, the base station pre-coding matrix and the user that design in each residential quarter disturb the inhibition matrix, carry out as follows:

    4.1a) pre-coding matrix of random initializtion base station k

    

    And satisfy

    

    K=1 wherein ..., B, B represent residential quarter number, N _fRepresent the rf chain way of base station, d represents that the base station sends the dimension of data flow, () ^HThe conjugate transpose of representing matrix, I _nThe unit matrix of expression n * n dimension,

    

    The expression complex field;

    4.1b) initialization iterations variable m is 1;

    4.1c) determine the interference covariance matrix of user k ' when the m time iteration

    $Q_{k^{\′},m}^{{\mathrm{\Ω}}^{*}}=\underset{k=1,k\≠k^{\′}}{\overset{B}{\mathrm{\Σ}}}\frac{P_k}{d}{H}_{k^{\′}k}^{{\mathrm{\ω}}_k^{*}}{V}_{k,m-1}^{{\mathrm{\Ω}}^{*}}{\left(V_{k,m-1}^{{\mathrm{\Ω}}^{*}}\right)}^H{\left(H_{k^{\′}k}^{{\mathrm{\ω}}_k^{*}}\right)}^H,$

    Wherein, k '=1 ..., B, P _kThe transmitting power of expression base station k, The pre-coding matrix of base station k when being illustrated in the m-1 time iteration,

    

    Be illustrated in antenna selecting plan

    

    Base station k is to the channel matrix of user k ' in the situation;

    4.1d) reveal minimum principle according to disturbing, according to above-mentioned interference covariance matrix

    

    The interference of design user k ' when the m time iteration suppresses matrix

    

    K '=1 wherein ..., B, d characteristic value characteristic of correspondence vector of υ d{} representing matrix minimum;

    4.1e) suppress matrix according to above-mentioned interference

    

    Determine the interference covariance matrix of base station k when the m time iteration

    

    ${\stackrel{\‾}{Q}}_{k,m}^{{\mathrm{\Ω}}^{*}}=\underset{k^{\′}=1,k^{\′}\≠k}{\overset{B}{\mathrm{\Σ}}}\frac{P_{k^{\′}}}{d}{\left(H_{k^{\′}k}^{{\mathrm{\ω}}_k^{*}}\right)}^H{U}_{k^{\′},m}^{{\mathrm{\Ω}}^{*}}{\left(U_{k^{\′},m}^{{\mathrm{\Ω}}^{*}}\right)}^H{H}_{k^{\′},k}^{{\mathrm{\ω}}_k^{*}},$

    Wherein, k=1 ..., B, k '=1 ..., B, P _{K '}The transmitting power of expression user k ', value equates with the transmitting power of this cell base station;

    4.1f) reveal minimum principle according to disturbing, according to above-mentioned interference covariance matrix

    

    The pre-coding matrix of design base station k when the m time iteration

    

    K=1 wherein ..., B;

    4.1g) value of iterations variable m adds 1, if m≤N _I, N wherein _IThe iterations empirical value that the expression tradition disturbs the alignment convergence to need is preferably 30, then returns step 4.1c, proceeds iteration; Otherwise iterative process finishes, and obtains the pre-coding matrix of base station k

    

    Suppress matrix with the interference of user k '

    

    K=1 wherein ..., B, k '=1 ..., B.

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