CN103684560A - Robust pre-coding method based on user fairness in multi-cell multi-user system - Google Patents

Abstract

The invention provides a robust pre-coding method based on user fairness in a multi-cell multi-user system. The method comprises the following steps that system parameters are set; MSEsk is defined to be the MSE of a k<th> user in an m<th> cell; the MSE of the k<th> user in the m<th> cell is defined when bounded errors exist in a channel; parameter defining is carried out; under the situation that bounded errors exist in channel information, a cost function is used for correcting the MSE; and a slack variable is introduced, and a subproblem with the existing bounded errors is converted into a GEVP problem to be solved. According to the method, influence from the bounded errors can be effectively handled, the fairness of users is guaranteed, feedback expenditure is lowered through a distributed algorithm, and good bit-error-rate performance is obtained.

Description

Robust pre-coding method based on user fairness in the multi-user system of many communities

Technical field

What the present invention relates to is a kind of method of wireless communication technology field, the robust pre-coding method based on user fairness in the multi-user system of specifically a kind of many communities.

Background technology

In recent years, along with the develop rapidly of wireless communication technology, the requirement of radio communication high traffic, two-forty and spectral efficient is day by day urgent.In Next-Generation Wireless Communication Systems, frequency duplex factor as one is 1, has serious presence of intercell interference (Inter-Cell Interference, ICI).As the key technology that suppresses ICI, the multi-cell communication systems of cooperating with each other in a plurality of base stations becomes one of study hotspot.According to the degree of base station collaboration, be divided into Combined Treatment (Joint Processing, JP) and coordinates beam shaping (Coordinated Beamforming, CBF).In JP pattern, data message and channel condition information (Channel State Information, CSI) are shared in the base station of cooperating with each other; In CBF pattern, CSI is only shared in the base station of cooperating with each other.Here consider CBF pattern.

At present, the signal processing method of multi-cell cooperating transmission is mainly considered from two angles: the performance that 1) raising system is total; 2) guarantee the fairness between user.

In prior art, disclose H.Dahrouj and W.Yu document " the Coordinated beamforming for the multi-cell multi-antenna wireless system cooperative beam of the multi-cell multi-antenna wireless system (be shaped); " IEEE Trans.Wireless Commun., vol.9, no.5, pp.1748-1759, May2010, according to the up-downgoing antithesis of many communities TDD system, the total transmitted power problem of maximization under SINR restrictive condition is changed into ascending power optimization problem, utilize Lagrange duality theory to realize distributed solving.Q.J.Shi, M.Razaviyayn, Z.Q.Luo, the document of and C.He " An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel (the maximized distributed iterative weighted least mean square of MIMO interference broadcast channel and utilance error approach), " IEEE Trans.on Signal Process., vol.59, no.9, pp.4331 – 4340, Sept.2011, utilizing the WMMSE(Weighted Minimum Mean Square Error that is related to design iteration of weighted sum mean square error and weighted sum rate) algorithm solves the weighted sum rate maximization problems of MIMO broadcast interference channel.H.Park, S.Park, H.Kong, the document of and I.Lee " the weighted sum MSE(Mean Square Error in Weighted sum MSE minimization under per-BS power constraint for network MIMO systems(MIMO network system under each base station power restriction, mean square deviation) minimize), " IEEE Commun.Letters, vol.16, no.3, pp.360-363, Mar.2012, structure Lagrangian, utilize KKT (Karush-Kuhn-Tucker) condition, solve the weighted sum MSE minimization problem under each base station power restriction.T.M.Kim, F.Sun, the document of and A.J.Paulraj " the MMSE precoding of the low complex degree in Low-complexity MMSE precoding for coordinated multipoint with per-antenna power constraint(multipoint cooperative under each antenna power restriction), " IEEE Signal Process.Letters, vol.20, no.4, pp.395-398, April2013, based on leaking MMSE method, total MSE problem under each antenna power restriction is changed into distributed distributed optimization problem, utilize Lagrange duality method and KKT condition, obtain the precoding algorithm of low complex degree.

Y.Huang, G.Zheng, M.Bengtsson, K.Wong, L.Yang, the document of B.Ottersten " the distributed many community beam forming design of Distributed multicell beamforming design approaching pareto boundary with max-min fairness(based on progressive Pareto circle of max-min fairness), " IEEE Trans.Wireless Commun., vol.11, no.8, pp.2921-2933, Aug.2012, fairness based on user, solve minimax speed problem, adopt approximate up-downgoing Dual Method, the distributed beam forming algorithm that has proposed a kind of iteration approaches Pa Letuo circle.

But, in real system, be difficult to obtain desirable channel condition information (Channel State Information, CSI), need to consider to have the transmission of CSI error robustness.According to the feature of CSI error, can set up respectively statistical error model and Bounded Errors model.Consider Bounded Errors model, C.Shen, K.Wang, the document of Z.Qiu and C.Chi " the robust cooperative beam in the many cell wireless system of Worst-case SINR constrained robust coordinated beamforming for multicell wireless systems(under the poorest SINR restriction is shaped), " in proc.IEEE Int.Conf.Commun. (ICC), Kyoto, Japan, May2011, adopt positive semidefinite planning (Semidefinite Program, SDP) and S-process (S-Procedure), solve the gross power minimization problem under the poorest SINR restriction.A.Tajer, N.Prasad, the document of and X.Wang " Progressive linear precoder design of robust in the transmission of Robust linear precoder design for multi-cell downlink transmission(multi-cell downlink), " IEEE Trans.Signal Process., vol.59, no.1, pp.235-251, Jan.2011, consider respectively many cell scenario of alone family, each community and each community multi-user, consider minimum SINR problem and dual problem thereof under the lower maximization of each base station power restriction worst condition, set up the equivalence relation of former problem and dual problem, adopt second order cone planning (Second-Order Cone, SOC) solve each the cell power minimization problem under worst condition SINR restriction, according to the equivalence relation of former problem and dual problem, obtain beam forming vector or beam forming matrix, the MSE optimization problem of worst condition is transformed to generalized eigenvalue problem (Generalized Eigenvalue Problem, GEVP) to be solved.The above-mentioned analysis to Bounded Errors model, all adopts centralized algorithm.

Summary of the invention

Technical problem to be solved by this invention is to propose the robust pre-coding method based on user fairness in the multi-user system of a kind of many communities, the present invention considers the Power Limitation of each base station in Bounded Errors situation, the MSE of Yi Duo community multi-user system maximum is minimised as optimization aim, according to leaking criterion, structure cost function, the Min-Max MSE problem of Ba Duo community changes into the Min-Max MSE subproblem of corresponding each base station, introduce slack variable, utilize Schur supplementary set theorem (Schur complement lemma) and S-to process (S-procedure) subproblem is transformed to generalized eigenvalue problem (generalized eigenvalue problem, GEVP), obtain distributed precoding and guarantee the BER performance of system.

The present invention is achieved by the following technical solutions, robust pre-coding method based on user fairness in the multi-user system of a kind of many communities, it is characterized in that, as channel, there is the Performance evaluation criterion of Bounded Errors in the optimization problem under worst condition, consider the Power Limitation of user fairness and each base station, the MSE of Yi Duo community multi-user system maximum is minimised as optimization aim, according to leaking criterion, structure cost function, the Min-Max MSE problem of Ba Duo community changes into the Min-Max MSE subproblem of corresponding each base station, introduce slack variable, utilize Schur supplementary set theorem and S-to process subproblem is transformed to generalized eigenvalue problem, obtain distributed pre-coding matrix, specifically comprise the following steps:

Step 1, arranges system parameters: M is counted in cooperation cell, and there are a base station, the antenna number N of each base station in each community _t, the number of users K of each base station service, each user has a reception antenna, the power constraint P of m base station _m, wherein: m=1 ..., M, the covariance of k user's of m community the multiple gaussian additive noise of zero-mean

wherein: k=1 ..., K, m base station is to k user's of n community estimation channel condition information

channel Bounded Errors matrix Δ _mnk, wherein: m, n=1 ..., M;

Step 2, definition MSE _mkbe k user's of m community MSE,

$\begin{array}{c}{\mathrm{MSE}}_{\mathrm{mk}}\left(\right\{f_{n1},...,f_{\mathrm{nK}}{\}}_{n=1}^M,\left\{h_{\mathrm{nmk}}{\}}_{n=1}^M\right)\\ =E\left\{(y_{\mathrm{mk}}-s_{\mathrm{mk}})(y_{\mathrm{mk}}-s_{\mathrm{mk}}{)}^H\right\}\\ ={\left|\right|h_{\mathrm{mmk}}^H{f}_{\mathrm{mk}}-1\left|\right|}^2+\underset{i=1,i\&NotEqual;k}{\overset{K}{\mathrm{\&Sigma;}}}{\left|\right|h_{\mathrm{mmk}}^H{f}_{\mathrm{mi}}\left|\right|}^2+\underset{n=1,n\&NotEqual;m}{\overset{M}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|\right|h_{\mathrm{nmk}}^H{f}_{\mathrm{ni}}\left|\right|}^2+{\mathrm{\&sigma;}}_{\mathrm{mk}}^2\end{array}$

Wherein:

be n base station to k user's of m community actual channel state information, wherein: m, n=1 ..., M, k=1 ..., K,

be m the precoding vector of base station to k user of m community, wherein: k=1 ..., K, m=1 ..., M;

Step 3, k user's of m community mean square error when definition channel exists Bounded Errors ${\stackrel{\&OverBar;}{\mathrm{MSE}}}_{\mathrm{mk}}={\mathrm{MSE}}_{\mathrm{mk}}({\{f_{n1},...,f_{\mathrm{nK}}\}}_{n=1}^M,{\{{\hat{H}}_{\mathrm{nmk}}+{\mathrm{\&Delta;}}_{\mathrm{nmk}}\}}_{n=1}^M),$ According to leaking criterion, the angle of other community users being disturbed from user, is used this user to substitute mean square error MSE to the distracter of other community users _mkin the distracter to this user during other cooperative base station service respective cell user, use

substitute $\underset{n=1,n\&NotEqual;m}{\overset{M}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|\right|{({\hat{h}}_{\mathrm{nmk}}+{\mathrm{\&Delta;}}_{\mathrm{nmk}})}^H{f}_{\mathrm{ni}}\left|\right|}^2,$ The cost function ξ that structure is revised _mk;

Step 4, defines m base station and to the pre-coding matrix of all transmission data is

according to the character of matrix product, to the cost function ξ revising _mkcarry out re, plural number asked to changing into column vector with computing and asking norm computing of mould,

be deformed into

wherein: k=1 ..., K, m, n=1 ..., M;

Step 5, channel information exists under bounded error condition, uses cost function ξ _mkas the mean square error of revising, the Min-Max MSE optimization problem of multi-cell system is changed into M completely independently subproblem;

The Min-Max MSE optimization problem of described Duo community multi-user system is:

$\begin{array}{c}\underset{\left\{f_{\mathrm{mk}}\right\}}{\min \mathrm{imize}}\underset{\{k,m\}}{\max }\underset{\left\{{\mathrm{\&Delta;}}_{\mathrm{nmk}}\right\}}{\max }{\stackrel{\&OverBar;}{\mathrm{MSE}}}_{\mathrm{mk}}\\ \mathrm{subjectto}\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}\mathrm{tr}\left(f_{\mathrm{mi}}{f}_{\mathrm{mi}}^H\right)\&le;P_m,\&ForAll;m=1,...,M\end{array}$

Subproblem is:

$\begin{array}{c}\underset{F_M}{\min \mathrm{imize}}\underset{k}{\max }\underset{\left\{{\mathrm{\&Delta;}}_{\mathrm{nmk}}\right\}}{\max }{\mathrm{\&xi;}}_{\mathrm{mk}}\\ \mathrm{subjectto}\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}\mathrm{tr}\left(f_{\mathrm{mi}}{f}_{\mathrm{mi}}^H\right)\&le;P_m,\&ForAll;m=1,...,M\end{array};$

Step 6, introduces slack variable, according to Schur supplementary set theorem (Schur complement lemma) and S-, processes (S-Procedure), the subproblem that has Bounded Errors is changed into GEVP problem and obtain distributed precoding matrix.

Described Schur supplementary set theorem is:

Suppose that Hermitian matrix X can Partitioning Expression of A be

$X=\left[\begin{array}{cc}A& B\\ B^H& C\end{array}\right]$

Wherein, A, C are square formation.If C is positive definite matrix, the positive semi-definite sufficient and necessary condition of X is

$A-{\mathrm{BC}}^{-1}{B}^H>=0$

That is, if

? $X>=0\&DoubleLeftRightArrow;A-{\mathrm{BC}}^{-1}{B}^H>=0;$

Described S-processes:

For Hermitian matrix A and given matrix B, C, condition

$A\&GreaterEqual;B^H\mathrm{\&Omega;C}+C^H{\mathrm{\&Omega;}}^{H}B,\&ForAll;\mathrm{\&Omega;}:\left|\right|\mathrm{\&Omega;}\left|\right|\&le;\mathrm{\&rho;}$

The necessary and sufficient condition of setting up is to have λ >=0, makes

$\left[\begin{array}{cc}A-{\mathrm{\&lambda;C}}^{H}C& -{\mathrm{\&rho;B}}^H\\ -\mathrm{\&rho;B}& \mathrm{\&lambda;I}\end{array}\right]>=0$

Described GEVP problem refers to:

$\begin{array}{cc}\underset{F_m,a_m,b_m,{\mathrm{\&lambda;}}_m}{\min \mathrm{imize}}& a_m\end{array}$

$s.t\left[\begin{array}{ccc}{a}_m& b_{\mathrm{mk}}& {\mathrm{\&sigma;}}_{\mathrm{mk}}\\ b_{\mathrm{mk}}^H& a_m{I}_M& 0\\ {\mathrm{\&sigma;}}_{\mathrm{mk}}& 0& a_m\end{array}\right]>=0$

$\left[\begin{array}{ccc}{b}_{\mathrm{mmk}}-{\mathrm{\&lambda;}}_{\mathrm{mmk}}& {\hat{h}}_{\mathrm{mmk}}^H{F}_m-e_K& 0\\ F_m^H{\hat{h}}_{\mathrm{mmk}}-e_K& b_{\mathrm{mmk}}{I}_K& -{\mathrm{\&epsiv;}}_{\mathrm{mmk}}{F}_m^H\\ 0& -{\mathrm{\&epsiv;}}_{\mathrm{mmk}}{F}_m& {\mathrm{\&lambda;}}_{\mathrm{mmk}}{I}_{\mathrm{Nt}}\end{array}\right]>=0$

$\left[\begin{array}{ccc}{b}_{\mathrm{mnk}}-{\mathrm{\&lambda;}}_{\mathrm{mmk}}& {\hat{h}}_{\mathrm{mnk}}^H{F}_m& 0\\ F_m^H{\hat{h}}_{\mathrm{mnk}}& b_{\mathrm{mnk}}{I}_K& -{\mathrm{\&epsiv;}}_{\mathrm{mnk}}{F}_m^H\\ 0& -{\mathrm{\&epsiv;}}_{\mathrm{mnk}}{F}_m& {\mathrm{\&lambda;}}_{\mathrm{mnk}}{I}_{\mathrm{Nt}}\end{array}\right]>=0\&ForAll;n\&NotEqual;m$

$\mathrm{tr}\left(F_m{F}_m^H\right)\&le;P_m$

Wherein: a _m, λ _mnk, b _mnkfor the slack variable of introducing, b _mk=[b _m1k..., b _mMk].

Compared with prior art, proposed by the invention for the robust beam forming algorithm based on user fairness in the multi-user system of many communities, consider the Power Limitation of each base station, optimize the MSE that channel information exists bounded error condition Xia Duo community multi-user system maximum, according to leaking criterion, structure cost function, the Min-Max MSE problem of Ba Duo community changes into the Min-Max MSE subproblem of corresponding each base station, introduce slack variable, utilize Schur supplementary set theorem (Schur complement lemma) and S-to process (S-procedure) subproblem is transformed to generalized eigenvalue problem (Generalized Eigenvalue Problem, GEVP) pre-coding matrix of Computation distribution formula, Bounded Errors is had compared with strong robustness, local CSI is only used in each base station, reduced feedback overhead, and guaranteed the BER performance of system.

Accompanying drawing explanation

By reading the detailed description of non-limiting example being done with reference to the following drawings, it is more obvious that other features, objects and advantages of the present invention will become:

The schematic diagram of Tu1Wei Duo community multi-user system; Wherein, BS represents base station (base station, BS), and MS represents user (mobile station, MS).

Fig. 2 is scene M=2, N _tduring=4, K=2, adopt respectively the MSE performance comparison diagram of centralized (Centralized) algorithm of Min-Max MSE in method provided by the invention and prior art.

Fig. 3 is scene M=2, N _tduring=4, K=2, adopt respectively the BER performance comparison diagram of centralized (Centralized) algorithm of method provided by the invention and Lagrange (Lagrangian) algorithm based on sum MSE of the prior art and Min-Max MSE.

Embodiment

Below in conjunction with specific embodiment, the present invention is described in detail.Following examples will contribute to those skilled in the art further to understand the present invention, but not limit in any form the present invention.It should be pointed out that to those skilled in the art, without departing from the inventive concept of the premise, can also make some distortion and improvement.These all belong to protection scope of the present invention.

Method for precoding based on user fairness in the multi-user system of many communities disclosed in this invention, consider the Power Limitation of user fairness and each base station, with channel information, exist multi-user system maximum MSE in Bounded Errors Duo community to be minimised as optimization aim, according to leaking criterion, structure cost function, the Min-Max MSE problem of Ba Duo community changes into the Min-Max MSE subproblem of corresponding each base station, introduce slack variable, utilize Schur supplementary set theorem (Schur complement lemma) and S-to process (S-procedure) subproblem is transformed to generalized eigenvalue problem (generalized eigenvalue problem, GEVP), obtain distributed pre-coding matrix, described channel information exists the Min-Max MSE optimization problem of Bounded Errors Duo community multi-user system to be:

$\begin{array}{c}\underset{\left\{f_{\mathrm{mk}}\right\}}{\min \mathrm{imize}}\underset{\{k,m\}}{\max }\underset{\left\{{\mathrm{\&Delta;}}_{\mathrm{nmk}}\right\}}{\max }{\stackrel{\&OverBar;}{\mathrm{MSE}}}_{\mathrm{mk}}\\ \mathrm{subjectto}\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}\mathrm{tr}\left(f_{\mathrm{mi}}{f}_{\mathrm{mi}}^H\right)\&le;P_m,\&ForAll;m=1,...,M\end{array}$

Wherein:

${\stackrel{\&OverBar;}{\mathrm{MSE}}}_{\mathrm{mk}}={\left|\right|({\hat{h}}_{\mathrm{mmk}}^H+{\mathrm{\&Delta;}}_{\mathrm{mmk}}^H)f_{\mathrm{mk}}-1\left|\right|}^2+\underset{i=1,i\&NotEqual;k}{\overset{K}{\mathrm{\&Sigma;}}}{\left|\right|({\hat{h}}_{\mathrm{mmk}}^H+{\mathrm{\&Delta;}}_{\mathrm{mmk}}^H)f_{\mathrm{mi}}\left|\right|}^2+\underset{n=1,n\&NotEqual;m}{\overset{M}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|\right|({\hat{h}}_{\mathrm{nmk}}^H+{\mathrm{\&Delta;}}_{\mathrm{nmk}}^H)f_{\mathrm{ni}}\left|\right|}^2+{\mathrm{\&sigma;}}_{\mathrm{mk}}^2$

Wherein:

that n base station is to k user's of m community estimation channel condition information, Δ _nmkbe channel errors vector and

f _mkm the precoding vector of base station to k user of m community,

the variance of the additive white Gaussian noise that receives of k user of m community, P _mit is the Power Limitation of m base station.

Method for designing of the present invention comprises the following steps:

The first step, system parameters is set: M is counted in cooperation cell, and there are a base station (base station, BS), the antenna number N of each base station in each community _t, the number of users K of each base station service, each user (mobile station, MS) has a reception antenna, the power constraint P of m base station _m, wherein: m=1 ..., M, the covariance of k user's of m community the multiple gaussian additive noise of zero-mean

wherein: k=1 ..., K, m base station is to k user's of n community estimation channel condition information

channel Bounded Errors matrix Δ _mnk, wherein: m, n=1 ..., M;

In the present embodiment, simulating scenes used is M=2, N _t=4, K=2.

In the present embodiment,

the random vector of obeying independent identically distributed Gaussian Profile,

wherein: m, n=1 ..., M, k=1 ..., K.

In the present embodiment, signal to noise ratio $\mathrm{SNR}=\frac{P_{\max }}{{\mathrm{\&sigma;}}_{\mathrm{mk}}^2},P_{\max }=10,P_m=P_{\max }(\&ForAll;m=1,...,M);$

Second step, definition MSE _mkbe k user's of m community MSE,

$\begin{array}{c}{\mathrm{MSE}}_{\mathrm{mk}}\left(\right\{f_{n1},...,f_{\mathrm{nK}}{\}}_{n=1}^M,\left\{h_{\mathrm{nmk}}{\}}_{n=1}^M\right)\\ =E\left\{(y_{\mathrm{mk}}-s_{\mathrm{mk}})(y_{\mathrm{mk}}-s_{\mathrm{mk}}{)}^H\right\}\\ ={\left|\right|h_{\mathrm{mmk}}^H{f}_{\mathrm{mk}}-1\left|\right|}^2+\underset{i=1,i\&NotEqual;k}{\overset{K}{\mathrm{\&Sigma;}}}{\left|\right|h_{\mathrm{mmk}}^H{f}_{\mathrm{mi}}\left|\right|}^2+\underset{n=1,n\&NotEqual;m}{\overset{M}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|\right|h_{\mathrm{nmk}}^H{f}_{\mathrm{ni}}\left|\right|}^2+{\mathrm{\&sigma;}}_{\mathrm{mk}}^2\end{array}$

Wherein: h _nmkbe n base station to k user's of m community actual channel state information, wherein: m, n=1 ..., M, k=1 ..., K, f _mkbe m the precoding vector of base station to k user of m community, wherein: k=1 ..., K, m=1 ..., M;

The 3rd step, definition $\stackrel{\&OverBar;}{\mathrm{MSE}}={\mathrm{MSE}}_{\mathrm{mk}}({\{f_{n1},...,f_{\mathrm{nK}}\}}_{n=1}^M,{\{{\hat{H}}_{\mathrm{nmk}}+{\mathrm{\&Delta;}}_{\mathrm{nmk}}\}}_{n=1}^M),$ According to leaking criterion, the angle from user to other area interference, the cost function that structure is revised,

$\begin{array}{c}{\mathrm{\&xi;}}_{\mathrm{mk}}={\left|\right|{({\hat{h}}_{\mathrm{mmk}}+{\mathrm{\&Delta;}}_{\mathrm{mmk}})}^H{f}_{\mathrm{mk}}-1\left|\right|}^2+\underset{i=1,i\&NotEqual;k}{\overset{K}{\mathrm{\&Sigma;}}}{\left|\right|{({\hat{h}}_{\mathrm{mmk}}+{\mathrm{\&Delta;}}_{\mathrm{mmk}})}^H{f}_{\mathrm{mi}}\left|\right|}^2\\ +\underset{n=1,n\&NotEqual;m}{\overset{M}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|\right|{({\hat{h}}_{\mathrm{mnk}}+{\mathrm{\&Delta;}}_{\mathrm{mnk}})}^H{f}_{\mathrm{mi}}\left|\right|}^2+{\mathrm{\&sigma;}}_{\mathrm{mk}}^2\end{array};$

The 4th step, m base station of definition to the pre-coding matrix of all transmission data are

according to the character of matrix product, to ξ _mkcarry out re,

$\begin{array}{c}{\mathrm{\&xi;}}_{\mathrm{mk}}={({\hat{h}}_{\mathrm{mmk}}+{\mathrm{\&Delta;}}_{\mathrm{mmk}})}^H\left(\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}{f}_{\mathrm{mi}}{f}_{\mathrm{mi}}^H\right){({\hat{h}}_{\mathrm{mmk}}+{\mathrm{\&Delta;}}_{\mathrm{mmk}})-({\hat{h}}_{\mathrm{mmk}}+{\mathrm{\&Delta;}}_{\mathrm{mmk}})}^H{f}_{\mathrm{mi}}-f_{\mathrm{mk}}^H({\hat{h}}_{\mathrm{mmk}}+{\mathrm{\&Delta;}}_{\mathrm{mmk}})\\ +\underset{n=1,n\&NotEqual;m}{\overset{M}{\mathrm{\&Sigma;}}}\left[{({\hat{h}}_{\mathrm{mnk}}+{\mathrm{\&Delta;}}_{\mathrm{mnk}})}^H\left(\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}{f}_{\mathrm{mi}}{f}_{\mathrm{mi}}^H\right)({\hat{h}}_{\mathrm{mnk}}+{\mathrm{\&Delta;}}_{\mathrm{mnk}})\right]+1+{\mathrm{\&sigma;}}_{\mathrm{mk}}^2\\ ={\left|\right|{({\hat{h}}_{\mathrm{mmk}}+{\mathrm{\&Delta;}}_{\mathrm{mmk}})}^H{F}_m-e_k\left|\right|}^2\underset{n=1,n\&NotEqual;m}{\overset{M}{\mathrm{\&Sigma;}}}{\left|\right|{({\hat{h}}_{\mathrm{mnk}}+{\mathrm{\&Delta;}}_{\mathrm{mnk}})}^H{f}_m\left|\right|}^2+{\mathrm{\&sigma;}}_{\mathrm{mk}}^2\end{array}$

The 5th step, channel information exist under bounded error condition, use cost function ξ _mkas the mean square error of revising, the Min-Max MSE optimization problem of multi-cell system is changed into M completely independently subproblem;

Described subproblem is:

$\begin{array}{c}\underset{F_M}{\min \mathrm{imize}}\underset{k}{\max }\underset{\left\{{\mathrm{\&Delta;}}_{\mathrm{nmk}}\right\}}{\max }{\mathrm{\&xi;}}_{\mathrm{mk}}\\ \mathrm{subjectto}\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}\mathrm{tr}\left(f_{\mathrm{mi}}{f}_{\mathrm{mi}}^H\right)\&le;P_m,\&ForAll;m=1,...,M\end{array};$

The 6th step, introducing slack variable, process (S-Procedure) according to Schur supplementary set theorem (Schur complement lemma) and S-, exists the subproblem of Bounded Errors to change into GEVP problem channel information;

Described GEVP problem is:

$\begin{array}{cc}\underset{F_m,a_m,b_m,{\mathrm{\&lambda;}}_m}{\min \mathrm{imize}}& a_m\end{array}$

$s.t\left[\begin{array}{ccc}{a}_m& b_{\mathrm{mk}}& {\mathrm{\&sigma;}}_{\mathrm{mk}}\\ b_{\mathrm{mk}}^H& a_m{I}_M& 0\\ {\mathrm{\&sigma;}}_{\mathrm{mk}}& 0& a_m\end{array}\right]>=0$

$\left[\begin{array}{ccc}{b}_{\mathrm{mmk}}-{\mathrm{\&lambda;}}_{\mathrm{mmk}}& {\hat{h}}_{\mathrm{mmk}}^H{F}_m-e_K& 0\\ F_m^H{\hat{h}}_{\mathrm{mmk}}-e_K& b_{\mathrm{mmk}}{I}_K& -{\mathrm{\&epsiv;}}_{\mathrm{mmk}}{F}_m^H\\ 0& -{\mathrm{\&epsiv;}}_{\mathrm{mmk}}{F}_m& {\mathrm{\&lambda;}}_{\mathrm{mmk}}{I}_{\mathrm{Nt}}\end{array}\right]>=0$

$\left[\begin{array}{ccc}{b}_{\mathrm{mnk}}-{\mathrm{\&lambda;}}_{\mathrm{mmk}}& {\hat{h}}_{\mathrm{mnk}}^H{F}_m& 0\\ F_m^H{\hat{h}}_{\mathrm{mnk}}& b_{\mathrm{mnk}}{I}_K& -{\mathrm{\&epsiv;}}_{\mathrm{mnk}}{F}_m^H\\ 0& -{\mathrm{\&epsiv;}}_{\mathrm{mnk}}{F}_m& {\mathrm{\&lambda;}}_{\mathrm{mnk}}{I}_{\mathrm{Nt}}\end{array}\right]>=0\&ForAll;n\&NotEqual;m$

$\mathrm{tr}\left(F_m{F}_m^H\right)\&le;P_m$

Wherein: a _m, λ _mnk, b _mnkfor the slack variable of introducing, b _mk=[b _m1k..., b _mMk].

In embodiment corresponding to Fig. 2, reflected that channel exists the maximum MSE of Bounded Errors with the variation relation of SNR.In an embodiment, M=2, N _tduring=4, K=2, adopt respectively the MSE performance comparison diagram of centralized (Centralized) algorithm of Min-Max MSE in method provided by the invention and prior art.In figure, two cooperation cell are expressed as C ₁and C ₂.As seen from Figure 2, adopt the MSE performance of each community of robust pre-coding algorithm of the present embodiment close with the MSE performance of employing centralized algorithm.Adopt centralized algorithm, need cooperation cell shared channel state information (Channel state information, CSI); And the distributed precoding algorithm of employing the present embodiment, each base station only needs local channel condition information to be applicable to actual multi-cell cooperating system.

In embodiment corresponding to Fig. 3, adopt QPSK modulation, scene M=2, N _tduring=4, K=2, adopt respectively the BER performance comparison diagram of centralized (Centralized) algorithm of method provided by the invention and Lagrange (Lagrangian) algorithm based on sum MSE of the prior art and Min-Max MSE.As seen from Figure 3, adopt the channel information of the present embodiment to exist the distributed precoding algorithm based on user fairness in the multi-user system of Bounded Errors Duo community can effectively process Bounded Errors impact, reduce feedback overhead, obtain good BER performance.

Above specific embodiments of the invention are described.It will be appreciated that, the present invention is not limited to above-mentioned specific implementations, and those skilled in the art can make various distortion or modification within the scope of the claims, and this does not affect flesh and blood of the present invention.

Claims (3)

1. Robust pre-coding method based on user fairness in the multi-user system of 1.Yi Zhongduo community, it is characterized in that, as channel, there is the Performance evaluation criterion of Bounded Errors in the optimization problem under worst condition, consider the Power Limitation of user fairness and each base station, the MSE of Yi Duo community multi-user system maximum is minimised as optimization aim, according to leaking criterion, structure cost function, the Min-Max MSE problem of Ba Duo community changes into the Min-Max MSE subproblem of corresponding each base station, introduce slack variable, utilize Schur supplementary set theorem and S-to process subproblem is transformed to generalized eigenvalue problem, obtain distributed pre-coding matrix, specifically comprise the following steps:

   Step 1: system parameters is set, and M is counted in cooperation cell, there are a base station, the antenna number N of each base station in each community _t, the number of users K of each base station service, each user has a reception antenna, the power constraint P of m base station _m, wherein: m=1 ..., M, the covariance of k user's of m community the multiple gaussian additive noise of zero-mean

   

   wherein: k=1 ..., K, m base station is to k user's of n community estimation channel condition information

   

   channel Bounded Errors matrix Δ _mnk, wherein: m, n=1 ..., M;

   Step 2: definition MSE _mkbe k user's of m community MSE,

   $\begin{array}{c}{\mathrm{MSE}}_{\mathrm{mk}}\left(\right\{f_{n1},...,f_{\mathrm{nK}}{\}}_{n=1}^M,\left\{h_{\mathrm{nmk}}{\}}_{n=1}^M\right)\\ =E\left\{(y_{\mathrm{mk}}-s_{\mathrm{mk}})(y_{\mathrm{mk}}-s_{\mathrm{mk}}{)}^H\right\}\\ ={\left|\right|h_{\mathrm{mmk}}^H{f}_{\mathrm{mk}}-1\left|\right|}^2+\underset{i=1,i\&NotEqual;k}{\overset{K}{\mathrm{\&Sigma;}}}{\left|\right|h_{\mathrm{mmk}}^H{f}_{\mathrm{mi}}\left|\right|}^2+\underset{n=1,n\&NotEqual;m}{\overset{M}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|\right|h_{\mathrm{nmk}}^H{f}_{\mathrm{ni}}\left|\right|}^2+{\mathrm{\&sigma;}}_{\mathrm{mk}}^2\end{array}$

   Wherein: h _nmkbe n base station to k user's of m community actual channel state information, wherein: m, n=1 ..., M, k=1 ..., K, f _mkbe m the precoding vector of base station to k user of m community, wherein: k=1 ..., K, m=1 ..., M;

   Step 3: k user's of m community mean square error when definition channel exists Bounded Errors ${\stackrel{\&OverBar;}{\mathrm{MSE}}}_{\mathrm{mk}}={\mathrm{MSE}}_{\mathrm{mk}}({\{f_{n1},...,f_{\mathrm{nK}}\}}_{n=1}^M,{\{{\hat{H}}_{\mathrm{nmk}}+{\mathrm{\&Delta;}}_{\mathrm{nmk}}\}}_{n=1}^M),$ According to leaking criterion, the angle of other community users being disturbed from user, the interference with user to other community users

   

   substitute

   

   in the distracter of other community users to this user

   

   the cost function ξ that structure is revised _mk;

   Step 4: defining m base station to the pre-coding matrix of all transmission data is

   

   

   according to the character of matrix product, to the cost function ξ revising _mkcarry out re, plural number is asked to changing into column vector with computing and asking norm computing of mould;

   Step 5: channel information exists under bounded error condition, uses cost function ξ _mkas the mean square error of revising, the Min-Max MSE optimization problem of multi-cell system is changed into M completely independently subproblem;

   Step 6: introduce slack variable, process according to Schur supplementary set theorem and S-, the subproblem that has Bounded Errors is changed into GEVP problem solving.
2. 2. the robust pre-coding method based on user fairness in the multi-user system of many communities according to claim 1, is characterized in that, in described step 5, channel information exists the Min-Max MSE optimization problem of Bounded Errors Duo community multi-user system to refer to:

   $\begin{array}{c}\underset{\left\{f_{\mathrm{mk}}\right\}}{\min \mathrm{imize}}\underset{\{k,m\}}{\max }\underset{\left\{{\mathrm{\&Delta;}}_{\mathrm{nmk}}\right\}}{\max }{\stackrel{\&OverBar;}{\mathrm{MSE}}}_{\mathrm{mk}}\\ \mathrm{subjectto}\underset{i=1}{\overset{K}{\mathrm{\&Sigma;}}}\mathrm{tr}\left(f_{\mathrm{mi}}{f}_{\mathrm{mi}}^H\right)\&le;P_m,\&ForAll;m=1,...,M\end{array}.$
3. 3. the robust pre-coding method based on user fairness in the multi-user system of many communities according to claim 1,, it is characterized in that, the GEVP problem in described step 6 refers to:

   $\begin{array}{cc}\underset{F_m,a_m,b_m,{\mathrm{\&lambda;}}_m}{\min \mathrm{imize}}& a_m\end{array}$

   $s.t\left[\begin{array}{ccc}{a}_m& b_{\mathrm{mk}}& {\mathrm{\&sigma;}}_{\mathrm{mk}}\\ b_{\mathrm{mk}}^H& a_m{I}_M& 0\\ {\mathrm{\&sigma;}}_{\mathrm{mk}}& 0& a_m\end{array}\right]>=0$

   $\left[\begin{array}{ccc}{b}_{\mathrm{mmk}}-{\mathrm{\&lambda;}}_{\mathrm{mmk}}& {\hat{h}}_{\mathrm{mmk}}^H{F}_m-e_K& 0\\ F_m^H{\hat{h}}_{\mathrm{mmk}}-e_K& b_{\mathrm{mmk}}{I}_K& -{\mathrm{\&epsiv;}}_{\mathrm{mmk}}{F}_m^H\\ 0& -{\mathrm{\&epsiv;}}_{\mathrm{mmk}}{F}_m& {\mathrm{\&lambda;}}_{\mathrm{mmk}}{I}_{\mathrm{Nt}}\end{array}\right]>=0$

   $\left[\begin{array}{ccc}{b}_{\mathrm{mnk}}-{\mathrm{\&lambda;}}_{\mathrm{mmk}}& {\hat{h}}_{\mathrm{mnk}}^H{F}_m& 0\\ F_m^H{\hat{h}}_{\mathrm{mnk}}& b_{\mathrm{mnk}}{I}_K& -{\mathrm{\&epsiv;}}_{\mathrm{mnk}}{F}_m^H\\ 0& -{\mathrm{\&epsiv;}}_{\mathrm{mnk}}{F}_m& {\mathrm{\&lambda;}}_{\mathrm{mnk}}{I}_{\mathrm{Nt}}\end{array}\right]>=0\&ForAll;n\&NotEqual;m$

   $\mathrm{tr}(F_m{F}_m^H)\&le;P_m$

   Wherein: a _m, λ _mnk, b _mnkfor the slack variable of introducing, b _mk=[b _m1k..., b _mMk].

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