阅读说明：本技术 一种基于不完全信道下多用户双向mimo中继系统的预编码方法 (A kind of method for precoding based on the two-way MIMO relay system of multi-user under endless all channel ) 是由 禹永植 侯培迟 郭立民 于 2019-08-28 设计创作，主要内容包括：本发明公开了一种基于不完全信道下多用户双向MIMO中继系统的预编码方法,属于无线中继通信技术领域。本发明首先分别计算第k个信源和第k个用户在两个时隙内接收的总信号；在非理想信道状态下,建立信道模型；然后根据系统模型和信道模型,构建MIMO中继系统的收发预编码算法的优化问题表示式；再求解第k个信源接收滤波矩阵W<Sub>1,k</Sub>和第k个用户接收滤波矩阵W<Sub>2,k</Sub>；根据最大功率约束条件,优化第k个信源预编码矩阵B<Sub>1,k</Sub>；再优化中继转发矩阵；通过通过平方约束二次规划问题优化第k个用户预编码矩阵；最后进行联合迭代至收敛,得到优化后的预编码矩阵；该算法考虑非理想的信道状态信息,可以更加切合实际的通信系统,有效提高系统的性能。(The invention discloses a kind of method for precoding based on the two-way MIMO relay system of multi-user under endless all channel, belong to wireless relay communication technical field.The present invention calculates separately k-th of information source and k-th of user received resultant signal in two time slots first；Under imperfect channel state, channel model is established；Then according to system model and channel model, the optimization problem expression of the transmitting-receiving precoding algorithms of MIMO relay system is constructed；K-th of signal source receiving filtering matrix W is solved again 1,k It accepts filter matrix W with k-th of user 2,k ；According to maximum power constraint condition, optimize k-th of information source pre-coding matrix B 1,k ；Re-optimization relay forwarding matrix；By optimizing k-th of user's pre-coding matrix by a square constraint quadratic programming problem；It finally carries out Joint iteration extremely to restrain, the pre-coding matrix after being optimized；The algorithm considers nonideal channel state information, can more realistic communication system, effectively improve the performance of system.)

1. a kind of method for precoding based on the two-way MIMO relay system of multi-user under endless all channel, which is characterized in that include Following steps:

Step 1: k-th of information source and k-th of user received resultant signal in two time slots are calculated separately；

Step 2: under imperfect channel state, channel model is established；

Step 3: according to system model and channel model, the signal mean square error table at k-th of information source and k-th of user is calculated It is minimised as target up to formula, and with system and mean square error, the optimization for constructing the transmitting-receiving precoding algorithms of MIMO relay system is asked Inscribe expression；

Step 4: by MSE_1,kAnd MSE_2,kLocal derviation method is asked to solve k-th of signal source receiving filtering matrix W respectively_1,kAnd kth A user accepts filter matrix W_2,k(k=1,2 ..., K)；

Step 5: according to maximum power constraint condition, optimize k-th of information source pre-coding matrix B_1,k；

Step 6: k-th of information source pre-coding matrix B is fixed_1,k, k-th of user's pre-coding matrix B_2,k, the filter of k-th signal source receiving Wave matrix W_1,kIt accepts filter matrix W with k-th of user_2,k(k=1,2 ..., K), by the optimization of standard semi definite programming problem After forwarding matrix F；

Step 7: fixed relay forwards matrix F, k-th of information source pre-coding matrix B_1,k, signal source receiving filtering matrix W_1,kAnd user Accept filter matrix W_2,k(k=1,2 ..., K) optimizes k-th of user's pre-coding matrix by a square constraint quadratic programming problem B₂,_k；

Step 8: combined relaying forwards matrix F, k-th of information source pre-coding matrix B_1,k, k-th of user's pre-coding matrix B_2,k, letter Source accepts filter matrix W_1,kIt accepts filter matrix W with user_2,kIt carries out Joint iteration extremely to restrain, the precoding square after being optimized Battle array；If maximum number of iterations is I_max, iteration ends thresholding is ε, the number of iterations n；Rule of judgmentAnd | |F⁽ⁿ⁺¹⁾-F⁽ⁿ⁾| |≤ε n > I_maxWhether meet, satisfaction then terminates iteration；Otherwise, step 4 is jumped to, it is straight to continue iteration To meeting the condition of convergence.

2. a kind of precoding side based on the two-way MIMO relay system of multi-user under endless all channel according to claim 1 Method, which is characterized in that the step 1 the following steps are included:

Step 1-1: in first transmission time slot, relay node is received from k-th of information source node and k-th of user simultaneously SignalWithWherein,For the transmitting of k-th of information source node Signal and satisfaction For the transmitting signal and satisfaction of k-th of user WithThe respectively pre-coding matrix of k-th of information source and k-th of user；Relay node is first Reception signal y in a time slot_rIt indicates are as follows:

Wherein,WithThe MIMO of respectively k-th of information source node and k-th of user to relay node Channel matrix,For the multiple AWGN at relay node, and meet At relay node Noise power；

The then reception signal y at relay node_rFurther it is rewritten into:

Step 1-2: in second transmission time slot, relay node passes through relay forwarding matrixTo reception signal y_rInto Row enhanced processing obtains signal x_r, then signal x_rIt is expressed with the power limitation condition of relay node are as follows:

Wherein, P_rFor transmission power maximum at relay node；Power limitation condition at k-th of information source node and k-th of user Meet respectivelyWithP_s1And P_s2It is respectively defined as k-th of information source node and k-th Maximum transmission power at user；Reception signal in second transmission time slot, at k-th of information source nodeWith Reception signal at k-th of userIt respectively indicates as follows:

Wherein,WithRespectively relay node is believed to k-th The mimo channel matrix of source node and k-th of user；In addition,For the multiple AWGN and satisfaction at k-th of information source node For the multiple AWGN and satisfaction at k-th of user WithIt is the noise power at k-th of information source node and k-th of user；

The information signal oneself emitted in previous time slot is individually subtracted in 1-3: k-th information source node of step and k-th of user, letter The reception signal of k-th of information source node and k-th of user after changeWithIt is expressed as

Wherein,With It makes an uproar for equivalent at k-th of information source node Sound, the equivalent noise at k-th of user areK-th of user's sheet is not considered Body considers that the adjacent interference from other users isDefinitionFor k-th of information source section The matrix that accepts filter at point,For the matrix that accepts filter at k-th of user；Then at k-th of information source node pair All users emit signal s₂Estimation signal beSignal s is emitted to information source at k-th of user₁Estimation signal For

3. a kind of precoding side based on the two-way MIMO relay system of multi-user under endless all channel according to claim 1 Method, which is characterized in that the channel model in the step 2 are as follows:

Definition WithTo estimate channel square Battle array, ∑_iAnd ∑_jIt is the correlation coefficient matrix of each node antennas, Φ_iAnd Φ_jIt is the correlation system of each node transmitting antenna Matrix number, correlation coefficient matrix assume to meet positive semidefinite and known；Wherein,ΔH_iWith ΔG_jIt is channel estimation errors matrix, element obeys independent CN (0, σ respectively²)。

4. a kind of precoding side based on the two-way MIMO relay system of multi-user under endless all channel according to claim 1 Method, which is characterized in that the step 3 comprises the steps of:

The MSE matrix of signal waveform estimation at 3-1: k-th information source node of step and k-th of user directly gives respectively, Simplified expression formula is as follows:

Wherein,It is k-th Equivalent noise at information source nodeCovariance matrix；

Equivalent noise at a userCovariance matrix；

Wherein,

Step 3-2: according to step 3-1, under all node power restrictive conditions, the multi-user based on MSMSE design criteria is double It is expressed as follows to the joint precoding problem of MIMO AF relay communications system:

5. a kind of precoding side based on the two-way MIMO relay system of multi-user under endless all channel according to claim 1 Method, which is characterized in that the W in the step 4_1,kIt accepts filter matrix W with k-th of user_2,k(k=1,2 ..., K) are as follows:

Wherein, the solution of receiving end matrix is converted into fixed fixed relay forwarding matrix F, k-th of information source pre-coding matrix B_1,kWith K-th of family pre-coding matrix B_2,kSolve k-th of signal source receiving filtering matrix W_1,kIt accepts filter matrix W with k-th of user_2,k(k =1,2 ..., K) subproblem because power limit is not present in receiving end, directly to MSE_1,kAnd MSE_2,kIt asks respectively inclined It leads: byWith

6. a kind of precoding side based on the two-way MIMO relay system of multi-user under endless all channel according to claim 1 Method, which is characterized in that k-th of information source pre-coding matrix B in the step 5_1,kAre as follows:

The user of information source end does not influence to each other, independent mutually, therefore information source end matrix B_1,kIt need to meet for diagonal matrix form, And meet power constraintsAssuming that each information source configures its maximum power, then:

So maximum power should be arranged in each user.

7. a kind of precoding side based on the two-way MIMO relay system of multi-user under endless all channel according to claim 1 Method, which is characterized in that the step 6 comprises the steps of:

Step 6-1: MSE is obtained first_1,kAnd MSE_2,kExpression formula:

MSE_1,k(k=1,2 ..., K):

MSE_2,k(k=1,2 ..., K):

Wherein,With

Step 6-2: the expression formula in step 6-1 is brought at k-th of the information source node simplified in step 3 and k-th of user The MSE matrix of signal waveform estimation, obtains following rewriting form:

Wherein, for above formula, there is following variable replacement:

Power limitation condition at relay node is further rewritten into:

Step 6-3: it enablesIt is managed according to Shu Er complement fixed, the joint based on MSMSE is excellent Change problem is converted into the standard SDP problem about relaying transmitting-receiving matrix F:

Wherein, p_1,kMeet p_1,k≥MSE_1,k, p_2,kMeet p_2,k≥MSE_2,k；Out-trunk, which is solved, with CVX Optimization Toolbox receives and dispatches square The optimal value of battle array F.

8. a kind of precoding side based on the two-way MIMO relay system of multi-user under endless all channel according to claim 1 Method, which is characterized in that the step 7 comprises the steps of:

Step 7-1: it enablesThe vector variable for converting CVX for matrix variables to solve；According to algorithmWith pre-coding matrix B_2,kRelated MSE_1,kExpression formula conversion are as follows:

Wherein,D_kkIt is by matrix D_kFromRow ToThe matrix of row composition；In addition, defining following variable replacement:

Step 7-2: according to step 7-1, the combined optimization problem based on MSMSE is converted into about equivalent variable b₂Standard QCQP Problem:

Wherein,SimultaneouslyAlsoEquivalent variable b is solved using CVX Optimization Toolbox₂ Optimal value, further according toInverse operation, solve the pre-coding matrix B of k-th of user_2,kOptimal value.

Technical field

The invention belongs to wireless relay communication technical fields, in particular to a kind of two-way based on multi-user under endless all channel The method for precoding of MIMO relay system.

Background technique

In recent years, with the rapid development of the 5th third-generation mobile communication, it is equipped with the multiuser MIMO relay system of multiple antennas Precoding research more and more attention has been paid to.MIMO technology is that one kind does not need to increase wireless frequency bandwidth, but can provide class again It is similar to increase the communication technology method that bandwidth equally brings same gain effect, and relayed communications technology can improve spectrum utilization effect Rate.The combination of MIMO technology and relayed communications technology is the trend of modern age Development of Wireless Communications, it can give full play to MIMO technology The diversity gain that the spatial multiplex gains and relayed communications of offer provide.In the following mobile network, base station and user are all made of The receiving and transmitting signal of multiple antennas, precoding can not only eliminate the interference between multiple antennas, multi-user, while can reduce at mobile station The complexity of reason, therefore, academia are absorbed in the precoding problem of research multiuser MIMO relay system.

In practical communication system, under imperfect channel state, it is contemplated that the presence of channel errors and Antenna Correlation, text Offer Chen Xiaomin, Zhu Yimin, Su Junxu, based on incomplete channel state information in et al. uplink multi-users MIMO relay system Precoding algorithms [J] electronics and information journal, 2016,38 (8): 1908-1912. has studied the up channel under one-way transmission Joint precoding.

Summary of the invention

It is prelisted the purpose of the present invention is to provide a kind of based on the two-way MIMO relay system of multi-user under endless all channel Code method；The present invention considers a multiuser MIMO two-way relay communication system, and model is by K transmitting end subscriber, K reception End subscriber and a relay node composition, as shown in Figure 1.It is N that transmitting end subscriber, which is equipped with identical antenna number,_s, receiving end use Being equipped with identical antenna number per family is N_k, relay node outfit N_rA antenna.To simplify the analysis, it is assumed that relay node is using in AF After agreement.

The purpose of the present invention is achieved through the following technical solutions:

A kind of method for precoding based on the two-way MIMO relay system of multi-user under endless all channel comprising the steps of:

Step 1: k-th of information source and k-th of user received resultant signal in two time slots are calculated separately；

Step 2: under imperfect channel state, channel model is established；

Step 3: according to system model and channel model, the signal mean square error at k-th of information source and k-th of user is calculated Poor expression formula, and target is minimised as with system and mean square error, construct the excellent of the transmitting-receiving method for precoding of MIMO relay system Change problem representation formula；

Step 4: by MSE_1,kAnd MSE_2,kLocal derviation method is asked to solve k-th of signal source receiving filtering matrix W respectively_1,kWith K-th of user accepts filter matrix W_2,k(k=1,2 ..., K)；

Step 5: according to maximum power constraint condition, optimize k-th of information source pre-coding matrix B_1,k；

Step 6: k-th of information source pre-coding matrix B is fixed_1,k, k-th of user's pre-coding matrix B_2,k, k-th of information source connect Receive filtering matrix W_1,kIt accepts filter matrix W with k-th of user_2,k(k=1,2 ..., K), it is excellent by standard semi definite programming problem Change relay forwarding matrix F；

Step 7: fixed relay forwards matrix F, k-th of information source pre-coding matrix B_1,k, signal source receiving filtering matrix W_1,kWith User accepts filter matrix W_2,k(k=1,2 ..., K) optimizes k-th of user's precoding by a square constraint quadratic programming problem Matrix B_2,k；

Step 8: combined relaying forwards matrix F, k-th of information source pre-coding matrix B_1,k, k-th of user's pre-coding matrix B_2,k, signal source receiving filtering matrix W_1,kIt accepts filter matrix W with user_2,kJoint iteration is carried out extremely to restrain, it is pre- after being optimized Encoder matrix；If maximum number of iterations is I_max, iteration ends thresholding is ε, the number of iterations n；Rule of judgmentAnd | | F⁽ⁿ⁺¹⁾-F⁽ⁿ⁾| |≤ε n > I_maxWhether meet, satisfaction then terminates iteration；Otherwise, it jumps to Step 4 continues iteration until meeting the condition of convergence.

The step 1 the following steps are included:

Step 1-1: in first transmission time slot, relay node is received from k-th of information source node and k-th simultaneously The signal of userWithWherein,For k-th information source node Emit signal and satisfactionFor the transmitting signal and satisfaction of k-th of user WithThe respectively pre-coding matrix of k-th of information source and k-th of user； Reception signal y of the relay node in first time slot_rIt indicates are as follows:

Wherein,WithRespectively k-th of information source node and k-th of user arrive relay node Mimo channel matrix,For the multiple AWGN at relay node, and meet For relay node The noise power at place；

The then reception signal y at relay node_rFurther it is rewritten into:

Step 1-2: in second transmission time slot, relay node passes through relay forwarding matrixTo reception signal y_rIt amplifies processing and obtains signal x_r, then signal x_rIt is expressed with the power limitation condition of relay node are as follows:

Wherein, P_rFor transmission power maximum at relay node；Power limit at k-th of information source node and k-th of user Condition processed meets respectivelyWithP_s1And P_s2Be respectively defined as k-th of information source node and Maximum transmission power at k-th of user；Reception signal in second transmission time slot, at k-th of information source nodeWith the reception signal at k-th of userIt respectively indicates as follows:

Wherein,WithRespectively relay node is to kth The mimo channel matrix of a information source node and k-th of user；In addition,For the multiple AWGN at k-th of information source node and Meet For the multiple AWGN and satisfaction at k-th of user WithIt is the noise power at k-th of information source node and k-th of user；

The information letter oneself emitted in previous time slot is individually subtracted in 1-3: k-th information source node of step and k-th of user Number, the reception signal of simplified k-th of information source node and k-th of userWithIt indicates are as follows:

Wherein,With For at k-th of information source node etc. Noise is imitated, the equivalent noise at k-th of user isK-th of use is not considered Family itself considers that the adjacent interference from other users isDefinitionBelieve for k-th The matrix that accepts filter at source node,For the matrix that accepts filter at k-th of user；Then k-th of information source node Place emits signal s to all users₂Estimation signal beSignal s is emitted to information source at k-th of user₁Estimation Signal is

Channel model in the step 2 are as follows:

Definition WithTo estimate channel Matrix, ∑_iAnd ∑_jIt is the correlation coefficient matrix of each node antennas, Φ_iAnd Φ_jIt is the correlation of each node transmitting antenna Coefficient matrix, correlation coefficient matrix assume to meet positive semidefinite and known；Wherein,ΔH_i With Δ G_jIt is channel estimation errors matrix, element obeys independent CN (0, σ respectively²)。

The step 3 comprises the steps of:

The MSE matrix of signal waveform estimation at 3-1: k-th information source node of step and k-th of user respectively directly to Out, simplified expression formula is as follows:

Wherein, For the equivalent noise at k-th of information source nodeCovariance matrix；

For the equivalent noise at k-th of userCovariance matrix；

Wherein,

Step 3-2: multi-purpose based on MSMSE design criteria under all node power restrictive conditions according to step 3-1 The joint precoding problem of the two-way MIMO AF relay communications system in family is expressed as follows:

W in the step 4_1,kIt accepts filter matrix W with k-th of user_2,k(k=1,2 ..., K) are as follows:

Wherein, the solution of receiving end matrix is converted into fixed fixed relay forwarding matrix F, k-th of information source pre-coding matrix B_1,kWith k-th of family pre-coding matrix B_2,kSolve k-th of signal source receiving filtering matrix W_1,kIt accepts filter matrix with k-th of user W_2,kThe subproblem of (k=1,2 ..., K), because power limit is not present in receiving end, directly to MSE_1,kAnd MSE_2,kRespectively Seek local derviation: byWith

K-th of information source pre-coding matrix B in the step 5_1,kAre as follows:

The user of information source end does not influence to each other, independent mutually, therefore information source end matrix B_1,kIt need to meet for diagonal matrix shape Formula, and meet power constraintsK=1,2 ..., K；Assuming that each information source configures its maximum power, Then:So maximum power should be arranged in each user.

The step 6 comprises the steps of:

Step 6-1: MSE is obtained first_1,kAnd MSE_2,kExpression formula:

MSE_1,k(k=1,2 ..., K):

MSE_2,k(k=1,2 ..., K):

Wherein,With

Step 6-2: the expression formula in step 6-1 is brought into k-th of the information source node simplified in step 3 and k-th of user The MSE matrix of the signal waveform estimation at place, obtains following rewriting form:

Wherein, for above formula, there is following variable replacement:

Power limitation condition at relay node is further rewritten into:

Step 6-3: it enablesIt is managed according to Shu Er complement fixed, the connection based on MSMSE It closes optimization problem and is converted into the standard SDP problem for receiving and dispatching matrix F about relaying:

Wherein, p_1,kMeet p_1,k≥MSE_1,k, p_2,kMeet p_2,k≥MSE_2,k；Out-trunk is solved with CVX Optimization Toolbox to receive Send out the optimal value of matrix F.

The step 7 comprises the steps of:

Step 7-1: it enablesThe vector variable for converting CVX for matrix variables to solve；According to operation RuleWith pre-coding matrix B_2,kRelated MSE_1,kExpression formula conversion are as follows:

Wherein,D_kkIt is by matrix D_kFromRow is to theThe matrix of row composition；In addition, defining following variable replacement:

Step 7-2: according to step 7-1, the combined optimization problem based on MSMSE is converted into about equivalent variable b₂Standard QCQP problem:

Wherein, Simultaneously AlsoEquivalent change is solved using CVX Optimization Toolbox Measure b₂Optimal value, further according toInverse operation, solve the pre-coding matrix B of k-th of user_2,kOptimization Value.

The beneficial effects of the present invention are:

Present invention firstly provides based on multi-emitting end/multi-user end transmitted in both directions MIMO relaying system under endless all channel The method for precoding of system.The research under dual transfer mode is relayed for existing multiuser MIMO, it is non-ideal to propose consideration Method for precoding of the multiple source to multi-user system, more realistic communication system under channel status, improve the property of system Energy.

Detailed description of the invention

Fig. 1 is the two-way MIMO relay communications system of multi-user of the present invention.

Specific embodiment

The present invention is directed to the two-way relay communication system under semiduplex mode, proposes a kind of based on multi-purpose under endless all channel The method for precoding of the two-way MIMO relay system in family.User terminal accept filter matrix optimization then by information source end MSE_1,kWith User terminal MSE_2,kLocal derviation method is asked to solve direct solution optimized expression formula respectively；Information source end pre-coding matrix according to power about Beam condition directly obtains its expression formula；The optimization of user's pre-coding matrix and relay forwarding matrix is established using MSMSE as criterion Optimization aim equation, and user's pre-coding matrix optimizing problem is converted to a QCQP problem and optimizes processing, relaying turns The optimization of hair matrix is then that the SDP problem for the standard that is converted to is solved；Finally by relay forwarding matrix, information source precoding square Battle array, user's pre-coding matrix and the matrix Joint iteration that accepts filter obtain optimal pre-coding matrix to restraining.This method considers Nonideal channel state information, can more realistic communication system, effectively improve the performance of system.

The present invention is further described in detail below:

A kind of method for precoding based on the two-way MIMO relay system of multi-user under endless all channel, model are emitted by K End subscriber, K reception end subscriber and a relay node composition, as shown in Figure 1.Transmitting end subscriber is equipped with identical antenna number For N_s, receive end subscriber be equipped with identical antenna number be N_k, relay node outfit N_rA antenna.To simplify the analysis, it is assumed that relaying Node uses AF trunk protocol.Feature of the invention is as follows:

1, imperfect channel state information is considered under the system model of multi-emitting end/multi-user end transmitted in both directions；

2, incomplete channel state information is considered, in relay forwarding matrix, information source pre-coding matrix, user's pre-coding matrix Under combining with the matrix that accepts filter, optimization aim equation is established with MSMSE design criteria；

3, k-th of signal source receiving filtering matrix W_1,kIt accepts filter matrix W with k-th of user_2,k(k=1,2 ..., K) pass through To information source end MSE₁With user terminal MSE_2,kLocal derviation method is asked to solve respectively；

4, according to maximum power constraint condition, optimize k-th of information source pre-coding matrix B_1,k；

5, k-th of user's pre-coding matrix B_2,kIt is optimized by QCQP problem, relay forwarding matrix F passes through SDP problem It optimizes；

6, pass through k-th of information source pre-coding matrix B of joint_1,k, k-th of user's pre-coding matrix B_2,k, relay forwarding matrix F, k-th of signal source receiving filtering matrix W_1,kIt accepts filter matrix W with k-th of user_2,kIt is iterated optimization, reaches and solved It is required that.

Step 1: k-th of information source and k-th of user received resultant signal in two time slots are calculated separately；

In first transmission time slot, relay node receives the letter from k-th of information source node and k-th of user simultaneously NumberWithWherein,For the transmitting signal of k-th of information source node And meet For the transmitting signal and satisfaction of k-th of user WithThe respectively pre-coding matrix of k-th of information source and k-th of user.Relay node is first Reception signal y in a time slot_rIt may be expressed as:

Wherein,WithRespectively k-th of information source node and k-th of user are to relay node Mimo channel matrix,For the multiple AWGN at relay node, and meet For relaying section Noise power at point.

The then reception signal y at relay node_rIt can further be rewritten into:

In second transmission time slot, relay node passes through relay forwarding matrixTo reception signal y_rIt carries out Enhanced processing obtains signal x_r, then signal x_rIt can be expressed as with the power limitation condition of relay node:

Wherein, P_rFor transmission power maximum at relay node.Power limit at k-th of information source node and k-th of user Condition processed meets respectivelyWithP_s1And P_s2Be respectively defined as k-th of information source node and Maximum transmission power at k-th of user.Reception signal in second transmission time slot, at k-th of information source nodeWith the reception signal at k-th of userIt respectively indicates as follows:

Wherein,WithRespectively relay node is to kth The mimo channel matrix of a information source node and k-th of user.In addition,For the multiple AWGN at k-th of information source node and MeetFor the multiple AWGN and satisfaction at k-th of user WithIt is the noise power at k-th of information source node and k-th of user.

The information signal oneself emitted in previous time slot is individually subtracted in k-th of information source node and k-th of user, after simplifying K-th of information source node and k-th of user reception signalWithIt may be expressed as:

Wherein,With For at k-th of information source node etc. Noise is imitated, the equivalent noise at k-th of user isK-th of use is not considered Family itself considers that the adjacent interference from other users isDefinitionBelieve for k-th The matrix that accepts filter at source node,For the matrix that accepts filter at k-th of user.Then k-th of information source node Place emits signal s to all users₂Estimation signal beSignal s is emitted to information source at k-th of user₁Estimation Signal is

Step 2: under imperfect channel state, channel model is established；

In practical communication system, since each node can not obtain accurate channel information, in endless all channel shape Under state, it is contemplated that the presence of channel estimation errors and Antenna Correlation, channel matrix can be indicated with kronecker model.It is fixed Justice WithTo estimate channel matrix, ∑_iWith ∑_jIt is the correlation coefficient matrix of each node antennas, Φ_iAnd Φ_jIt is the correlation coefficient matrix of each node transmitting antenna, Correlation coefficient matrix assumes to meet positive semidefinite and known.Since channel estimation methods have some limitations in reality, Channel state information can not be obtained completely, it is therefore desirable to consider influence of the channel estimation errors to system.Therefore channel model It is represented by

Wherein,ΔH_iWith Δ G_jIt is channel estimation errors matrix, element is obeyed solely respectively Vertical CN (0, σ²)。

Step 3: according to system model and channel model, the signal mean square error at k-th of information source and k-th of user is calculated Poor (Mean Square Error, MSE) expression formula, and with system and mean square error (Minimum Sum Mean Square Error, MSMSE) it is minimised as target, construct the optimization problem expression of the transmitting-receiving method for precoding of MIMO relay system；

The MSE matrix of signal waveform estimation at k-th of information source node and k-th of user can directly give respectively, letter Expression formula after change is as follows:

Wherein,It is k-th Equivalent noise at information source nodeCovariance matrix；

For the equivalent noise at k-th of userCovariance matrix.

Wherein:

According to above-mentioned analysis, under all node power restrictive conditions, the multi-user based on MSMSE design criteria is two-way The joint precoding problem of MIMOAF relay communications system can be expressed as follows:

Step 4: directly by MSE_1,kAnd MSE_2,kLocal derviation method is asked to solve k-th of signal source receiving filtering matrix respectively W_1,kIt accepts filter matrix W with k-th of user_2,k(k=1,2 ..., K)；

The solution of receiving end matrix can be converted into fixed fixed relay forwarding matrix F, k-th of information source pre-coding matrix B_1,k With k-th of family pre-coding matrix B_2,kSolve k-th of signal source receiving filtering matrix W_1,kIt accepts filter matrix W with k-th of user_2,k The subproblem of (k=1,2 ..., K) can be directly to (11) MSE because power limit is not present in receiving end_1,k(12) MSE_2,kLocal derviation is sought respectively: byWithIt is available:

Step 5: according to maximum power constraint condition, optimize k-th of information source pre-coding matrix B_1,k；

The user of information source end does not influence to each other, independent mutually, therefore information source end matrix B_1,kIt need to meet for diagonal matrix shape Formula, and meet power constraintsK=1,2 ..., K.Assuming that each information source configures its maximum power, then

So maximum power should be arranged in each user, it may be assumed that

Step 6: k-th of information source pre-coding matrix B is fixed_1,k, k-th of user's pre-coding matrix B_2,k, k-th of information source connect Receive filtering matrix W₁It accepts filter matrix W with k-th of user_2,k(k=1,2 ..., K) passes through standard semi definite programming (Semi- Definite Programming, SDP) problem optimization relay forwarding matrix F；

MSE_1,k(k=1,2 ..., K):

MSE_2,k(k=1,2 ..., K):

Wherein,WithBring expression formula (21)-(23) into table Up in formula (11), expression formula (24)-(27) are brought into expression formula (12), MSE_1,kAnd MSE_2,kExpression formula can further be rewritten into Following form:

Wherein, for expression formula (28) and (29), there is following variable replacement:

Power limitation condition at relay node can be further rewritten into:

According to above-mentioned analysis, enableIt is managed, is based on according to Shu Er complement fixed Combined optimization problem (13)-(16) of MSMSE can be converted into the standard SDP problem about relay forwarding matrix F:

Wherein, p_1,kMeet p_1,k≥MSE_1,k, p_2,kMeet p_2,k≥MSE_2,k.Out-trunk is solved with CVX Optimization Toolbox to receive Send out the optimal value of matrix F.

Step 7: fixed relay forwards matrix F, k-th of information source pre-coding matrix B_1,k, k-th of signal source receiving filtering matrix W_1,kIt accepts filter matrix W with k-th of user_2,k(k=1,2 ..., K) passes through a square constraint quadratic programming (Quadratic Constraint Quadratic Programming, QCQP) k-th of user's pre-coding matrix B of problem optimization_2,k；

Firstly, enablingThe soluble vector variable of CVX is converted by matrix variables.According to operation method ThenWith pre-coding matrix B_2,kRelated MSE_1,kExpression formula can convert are as follows:

Wherein,D_kkIt is by matrix D_kFromRow is to theThe matrix of row composition.In addition, defining following variable replacement:

According to above-mentioned analysis, combined optimization problem (13)-(16) based on MSMSE can be converted into about equivalent variable b₂'s Standard QCQP problem:

Wherein,SimultaneouslyAlsoMake Equivalent variable b is solved with CVX Optimization Toolbox₂Optimal value, further according toInverse operation, solve kth The pre-coding matrix B of a user_2,kOptimal value.

Step 8: combined relaying forwards matrix F, k-th of information source pre-coding matrix B_1,k, k-th of user's pre-coding matrix B_2,k, k-th of signal source receiving filtering matrix W_1,kIt accepts filter matrix W with k-th of user_2,kIt is iterated to convergence, is optimized Pre-coding matrix afterwards.If maximum number of iterations is I_max, iteration ends thresholding is ε, the number of iterations n.Rule of judgmentAndOr n > I_maxWhether meet, satisfaction then terminates iteration；Otherwise, it jumps to Step 4 continues iteration until meeting the condition of convergence.

The foregoing is only a preferred embodiment of the present invention, is not intended to restrict the invention, for the skill of this field For art personnel, the invention may be variously modified and varied.All within the spirits and principles of the present invention, made any to repair Change, equivalent replacement, improvement etc., should all be included in the protection scope of the present invention.