CN110086515A - A kind of MIMO-NOMA system uplink Precoding Design method - Google Patents

Abstract

The invention discloses a kind of MIMO-NOMA system uplink Precoding Design methods, in the proposed solution, firstly, according to each user data stream configuration, subscriber signal propagation distance and antenna for base station number, by user from closely to being far divided into multiple groups；Secondly, the pre-coding matrix of same group of user of co-design and least mean-square error (MMSE) balanced device of base station improve the power efficiency of system, user job multiplexer mode in same group, difference group user job removes the interference for having demodulated user group using serial interference deleting technique in NOMA mode.Again, in the Precoding Design of same group of user, Precoding Design is divided into beamforming matrix design and power distribution matrix design, the invention proposes the closed solutions of beamforming matrix and power distribution matrix design；Compared to traditional sub-clustering MIMO-NOMA transmission plan, the present invention proposes that system transmitting power consumption can be significantly reduced in MIMO-NOMA pre-coding scheme.

Description

A kind of MIMO-NOMA system uplink Precoding Design method

Technical field

The invention discloses a kind of MIMO-NOMA system uplink Precoding Design method, it is related to multiple access in wireless communication and connects Enter technical field.

Background technique

The supported concurrent connection number of conventional orthogonal multi-address system is limited to governable orthogonal resource block number mesh, is difficult Meets the needs of third generation mobile communication system is to huge connection number.In recent years, non-orthogonal multiple accesses (NOMA) technology because of it It can support higher throughput of system and more concurrent connection numbers, and the extensive concern by academia and industry.NOMA It include mainly power domain and code domain, the present invention is directed power domain NOMA.In new power domain, NOMA utilizes channel between user Strong and weak difference deletes (SIC) by the supercomposed coding of transmitting terminal and the serial interference of receiving end to distinguish different user, one The concurrent transmission of multiple users is realized in a sky time/frequency source block.

Multiple-input, multiple-output (MIMO) technology is the key technology of lifting system spectrum efficiency or reliability, is future mobile communications In the technology that will use.Therefore, it is necessary to which NOMA concept is expanded to base station and uses the situation of configuration multiple antennas per family, formed MIMO-NOMA system.NOMA is to solve huge connectivity problem in future wireless system and improve system spectrum effect with merging for MIMO The effective ways of rate.However, in the case where wirelessly communicating complex jamming environment, to reach the specific service quality of user, biggish wink When transmission power be to restrict one of the major obstacle of MIMO-NOMA application.

In Uplink MIMO-NOMA system, traditional transmission mode is the sub-clustering NOMA scheme based on signal alignment technology. In traditional sub-clustering NOMA scheme, the basic thought of MIMO-NOMA transmission is that user is divided into several clusters, and wherein the number of cluster is not More than antenna for base station number, every cluster includes the channel user weak with channel by force.For uplink, first passes through user and prelist Code, the same direction will be snapped to cluster subscriber signal, interferes between cluster and is eliminated by the balanced device of base station, and subscriber signal is logical in cluster SIC receiver is crossed to be separated.In above-mentioned sub-clustering NOMA transmission plan, uplink user precoding is used respectively with base station equalizer It is interfered between cluster to carry out signal alignment and inhibit, this design method may create the problem that (1) if between two cluster user wave beams Angle very little, most of useful signal can be also lost during AF panel between cluster.In this way, dry in order to reach scheduled letter The transient transmission power than threshold value, needed of making an uproar can increased dramatically.(2) balanced device of precoding and receiving end does not have co-design, Influence the power efficiency of transmitter.

Summary of the invention

The present invention provides a kind of MIMO-NOMA system uplink Precoding Design side for the defects of above-mentioned background technique Method, proposes the MIMO-NOMA innovation structure based on user grouping collaboration optimization, and new method is significant special with " grouping " and " collaboration " Sign is interfered using serial/parallel mixing and is deleted, overcome the limitation of traditional structure, realize the combination of MIMO-NOMA.

To achieve the above object, The technical solution adopted by the invention is as follows: a kind of MIMO-NOMA system uplink precoding is set Meter method, which comprises the following steps:

S1. according to each user data stream configuration and antenna for base station number, by user according to the propagation between user and base station Distance is by being closely divided into multiple groups to remote；

S2. after the completion of user grouping, the total reception subscriber signal y of base station,

Wherein, H_k,uIndicate the channel matrix between user [k, u] and base station, D_k,uFor the pre-coding matrix of user [k, u], x_k,uFor the transmitting signal of user [k, u], H_JChannel matrix between interference source and base station, z_JFor the interference signal of interference source, n For the white Gaussian noise signal of system, it is 0, variances sigma that each of which element, which obeys mean value,²For multiple Gauss distribution, user [k, u] For u-th of user of kth group,

And write the received subscriber signal y in base station as matrix form as unit of group,

Wherein,Indicate sytem matrix,Indicate signal to Amount,For vector x_k,uTransposition；

S3. the received each group of subscriber signal y order of demodulation in base station in setting grouping NOMA transmission plan, obtains each group User's demodulated signal

S4. pre-coding matrix optimizing problem P0 model is established, optimization problem P0 is the minimum power problem of modeling, mesh Scalar functions are to minimize total transmission power, and restrictive condition is the minimum-rate demand for guaranteeing each user, and optimized variable is each The pre-coding matrix of user；

S5. in order to inhibit the interference for not demodulating user group and interference source from other and implement simultaneously to same group of subscriber signal Row demodulation, designs each group sytem matrixGeneral decomposed form:

Sytem matrix H_kIt is the matrix synthesized by all subscriber channels of kth group with precoding product matrix, Q_kIt is that kth group is used The interference at family and the covariance matrix of noise, Ξ_kIt is a unitary matrice, for the direction of wave beam where controlling each data flow, Λ_k It is a diagonal matrix, for controlling the power distribution between data flow；

S6. according to sytem matrix H in S5_kDecomposed form, calculate pre-coding matrix D_k,uGeneral decomposed form；

S7. according to pre-coding matrix D_k,uGeneral decomposed form, equivalence conversion S4 in minimum power problem, will prelist The optimization problem P0 of code matrix modeling is decomposed into beamforming matrix and power distribution matrix combined optimization problem；

S8. substep solves conversion postwave beam shaping matrix optimizing problem and power distribution matrix optimizing problem in S7, first Successively design beamforming matrix { Ξ_k,uEach column vector, and based on the beamforming matrix { Ξ designed_k,u, design is most Excellent power distribution matrix { Λ_k,u}。

S9. by the optimal beam forming matrix { Ξ acquired in S8_k,uAnd optimal power allocation matrix { Λ_k,uBe updated to In S6 in the expression formula of pre-coding matrixIt can be obtained the user's pre-coding matrix for needing to optimize D_k,u, wherein H_k,uFor the channel matrix between user [k, u] and base station, the information known to system can be obtained by channel estimation It arrives, Q_kInterference and noise covariance matrix for kth group user.

Further, in S1, each group of total number of users according to flow amount be less than antenna for base station number, i.e., to user grouping when need to expire Sufficient the following conditions:Wherein, U_kFor the number of users that kth group includes, l_k,uData flow is sent for user [k, u] Number, N_AFor the number of antennas of base station.

Further, in S2, interference signal z_JCovariance matrix meetWherein, E { } is to ask expectation computing, P_JFor the maximum transmission power of interference source,For N_J×N_JUnit matrix,For matrix z_J's Conjugate transposition.

Further, in S3, the implementation criterion of order of demodulation according to user's propagation distance by closely to far successively packet design, Since the mean power intensity of first group of subscriber signal is most strong, a kind of last mean power intensity of subscriber signal is most weak, so The implementation criterion of order of demodulation are as follows: receive the 1st group of subscriber signal of parallel demodulation in signal y from total first, demodulating the 1st group of user When signal, other group of signal is regarded as noise, delete the 1st group of subscriber signal in signal from total receive after the completion of demodulation, then from deleting Except demodulating the 2nd group of subscriber signal in total reception signal y after modulated signal, and so on, until demodulation last group of user letter Number, kth group user's demodulated signalIt indicates are as follows:

Wherein, K indicates that (i.e. last group of user is not present K group because the signal of all user groups in front has all been deleted The interference of other users group, therefore K group demodulation signal has different representations from other groups), R_kBelieve as kth group user Number balanced device；

Due to that can be made using least mean-square error (MMSE) receiver each for specific pre-coding matrix Data flow obtains optimal Signal to Interference plus Noise Ratio, MMSE balanced device R_kIt can be designed as:

Wherein, MMSE is least mean-square error, as 1≤k≤K-1,Work as k=K,

Further, in S4, in the case where meeting the minimum-rate demand condition of each user, the expression formula of optimization problem P0 Are as follows:

Wherein, Tr { } is the operation of Matrix Calculating mark,For the minimum-rate demand of user [k, u], SINR_k,u,iFor user The Signal to Interference plus Noise Ratio of [k, u] i-th of data flow,

SINR_k,u,iBy user's demodulated signalWith MMSE balanced device R_kIt obtains, indicates are as follows:

Wherein, D_k,u[i] indicates D_k,uI-th column,For matrixInversion operation.

Further, in S6, the pre-coding matrix D of user [k, u]_k,uDecomposed form are as follows:

Wherein, Ξ_k,uIt is unitary matrice Ξ_kSubmatrix, for the direction of wave beam where controlling each data flow, Λ_k,uIt is pair Angular moment battle array Λ_kSubmatrix, for controlling the power distribution between data flow；

Wherein, the beamforming matrix Ξ of user [k, u]_k,uIt is by unitary matrice Ξ_k?It arranges toThe submatrix of composition is arranged, i.e.,Power distribution matrix Λ_k,uPair Angle element is by diagonal matrix Λ_k?A diagonal element is toA diagonal element composition, i.e.,Ξ_k[i] representing matrix Ξ_kI-th column, [Λ_k]_i,jTable Show matrix Λ_kThe i-th row jth column element, diag { } representing matrix diagonalization operation.

Further, in S7, according to the pre-coding matrix decomposed form of user in S6 [k, u], the expression formula of Signal to Interference plus Noise Ratio Simplify are as follows:

Optimization problem P0 equivalence is converted into optimization problem P1:

Wherein, matrixFirst restrictive condition indicates the minimum-rate of user Demand, second restrictive condition are to guarantee beamforming matrix { Ξ_k,uComposition composite matrix Ξ_kFor unitary matrice.

Further, in S8, two stages that are divided into of optimization problem P1 are solved after converting in S7, including beam forming square Battle array { Ξ_k,uAnd power distribution matrix { Λ_k,uSolve；

To beamforming matrix { Ξ_k,uSolve:

Design beamforming matrix { Ξ_k,uTenth of the twelve Earthly Branches vector Ξ_k,u[i], tenth of the twelve Earthly Branches vector Ξ_k,u[i] are as follows:

Wherein,v_min (X) the corresponding singular value vector of minimum non-zero singular value of representing matrix X；

To power distribution matrix { Λ_k,uSolve:

By solving all tenth of the twelve Earthly Branches vector Ξ_k,u[i] determines { Ξ_k,u, it obtainsInto And obtain Π_k,uDiagonal element { [Π_k,u]_i,i}；

For given { [Π_k,u]_i,i, optimization problem P1 equivalence is converted into optimization problem P2, as follows:

Introduce Lagrange multiplier { θ_k,u, construct Auxiliary goal functionAre as follows:

FunctionIt is rightLocal derviation is asked to indicate are as follows:

When optimization problem P2 takes optimal value, it can obtainAnd optimization problem P2 restrictive condition takes equal sign, i.e.,It acquiresOptimal value are as follows:

Wherein, M_k,uIndicate diagonal matrix Λ_k,uThe number of middle nonzero element, (x)⁺Operation is expressed as form: when x >= 0, (x)⁺=x, when x < 0, (x)⁺=0；

Obtain optimal power allocation matrix Λ_k,u, be one byFor diagonal element group At diagonal matrix, i.e.,

The utility model has the advantages that Precoding Design through the invention, it can be with the pre-coding matrix of same group of user of combined optimization, together When can effectively adjust the direction that each user emits signal beam forming matrix, and the transmitting function to each customer traffic Rate carries out optimum allocation, and then can promote transmission power utilization efficiency；Under the premise of guaranteeing each user's minimum transmission rate, Regardless of user is to send individual traffic or multiple data flows, the transmitting power consumption of system can be substantially reduced by proposing a plan.

Detailed description of the invention

Fig. 1 is system architecture illustraton of model；

Fig. 2 is that the grouping proposed cooperates with optimization architecture figure compared with traditional sub-clustering framework；

Fig. 3 is that system always emits power consumption diagram when each user transmits 1 data flow；

Fig. 4 is that system always emits power consumption diagram when each user transmits 2 data flows；

Fig. 5 is the cumulative distribution function figure for always emitting power consumption when each user transmits 1 data flow；

Fig. 6 is the cumulative distribution function figure for always emitting power consumption when each user transmits 2 data flows.

Specific embodiment

The implementation of technical solution is described in further detail with reference to the accompanying drawing.Following embodiment is only used for more clear Illustrate to Chu technical solution of the present invention, and not intended to limit the protection scope of the present invention.

As shown in Fig. 1~2, the present invention considers that covering radius is the cellular uplink transmitting scene of R, and base station is in covering The heart, U user are evenly distributed in coverage area, and user and base station transceiver end number of antennas are all N_A.Base station, which receives, comes from U The uplink signal of a user, while the also interference by the external disturbance source signal of a random distribution.The antenna number of interference source Mesh is N_J, base station is d at a distance from external interference source_J。

S1. according to each user data stream configuration and antenna for base station number, by user according to the propagation between user and base station Distance is by being closely divided into multiple groups to remote；

U user is divided into K group from small to large according to user's propagation distance, kth group includes U_kA user, and just like ShiShimonoseki System: if k < k', d_k,u<d_k',u', d here_k,uIndicate the transmission range in kth group between u-th of user and base station.Due to the present invention What is considered is NOMA scene, therefore there are following relationshipsWherein, l_k,uData are sent for user [k, u] Flow amount；The following conditions need to be met when user grouping in the present invention:Require each group of total number of users evidence Flow amount is less than antenna for base station number, and each group of subscriber signal can be in base station parallel processing in this way.

S2. after the completion of user grouping, the expression formula of base station received signal is obtained, meanwhile, for the ease of subsequent precoding point Group design, needs to be write base station received signal as matrix form as unit of group.

After the completion of user grouping, base station received signal y can be indicated are as follows:

Wherein, H_k,uIndicate the channel matrix between user [k, u] and base station, D_k,uFor the pre-coding matrix of user [k, u], x_k,uFor the transmitting signal of user [k, u], H_JChannel matrix between interference source and base station, z_JFor the interference signal of interference source, n For the white Gaussian noise signal of system, it is 0, variances sigma that each of which element, which obeys mean value,²For multiple Gauss distribution.Interference signal z_J Covariance matrix meetWherein, E { } is to ask expectation computing, P_JFor the maximum hair of interference source Power is penetrated,For N_J×N_JUnit matrix,For matrix z_JConjugate transposition.

For the ease of subsequent precoding packet design, need as unit of group as to be write base station received signal

Following matrix form:

Wherein, the sytem matrix of kth groupThe signal vector of kth groupFor vector x_k,uTransposition.

S3. grouping collaboration NOMA proposed by the present invention and traditional sub-clustering NOMA scheme are as shown in Fig. 2, setting grouping NOMA is passed Transmission scheme each group subscriber signal order of demodulation, obtains the expression formula of each group of user's demodulated signalIt is grouped NOMA transmission plan Implement criterion: the 1st group of subscriber signal of parallel demodulation in signal y is received from total first, when demodulating the 1st group of subscriber signal, by it He organizes signal and regards noise as, the 1st group of subscriber signal is deleted in signal from total receive after the completion of demodulation, then after deleting modulated signal Total reception signal y in demodulate the 2nd group of subscriber signal, and so on, until demodulation last group of subscriber signal；Design so solution The reason of adjusting order is according to user's propagation distance by closely to being far successively grouped, the mean power intensity of first group of subscriber signal is most By force, a kind of last mean power intensity of subscriber signal is most weak.

Using R_kAs the balanced device of kth group subscriber signal, the detection signal of such kth group userIt can be expressed as

Due to that can be made using least mean-square error (MMSE) receiver each for specific pre-coding matrix Data flow obtains optimal Signal to Interference plus Noise Ratio, MMSE balanced device R_kIt can indicate are as follows:

Wherein, as 1≤k≤K-1,When

S4. pre-coding matrix optimizing model is established, objective function is to minimize total transmission power, and restrictive condition is to protect Demonstrate,prove the minimum-rate demand of each user；

At this point, minimum power problem is modeled as optimization problem in the case where meeting the minimum-rate demand condition of each user P0:

Wherein, Tr { } is the operation of Matrix Calculating mark,For the minimum-rate demand of user [k, u], SINR_k,u,iFor user The Signal to Interference plus Noise Ratio of [k, u] i-th of data flow can detect signal by user in S3With MMSE balanced device R_kExpression formula obtain It arrives, can indicate are as follows:

Wherein, D_k,u[i] indicates D_k,uI-th column,For matrixInversion operation.

S5. each group sytem matrix is separately designedGeneral decomposed form, wherein H_k,u For u-th of user of kth group to the channel matrix between base station, sytem matrix H_kIt is to be multiplied by all subscriber channels of kth group with precoding The matrix of product matrix synthesis.

In the present invention, sytem matrix H_kTarget there are two designing: one inhibits not demodulating user group from other and do Disturb the interference in source, secondly, parallel demodulation is implemented to same group of subscriber signal；To meet two above target, sytem matrix H_kDesign It is for following general decomposed form

Wherein, Ξ_kIt is a unitary matrice, for the direction of wave beam where controlling each data flow, i.e. referred to as beam forming square Battle array, Λ_kIt is that a diagonal matrix for controlling the power distribution between data flow becomes power distribution matrix.

S6. according to sytem matrix H in S5_kDecomposed form, obtain u-th of user D of pre-coding matrix kth group_k,uGeneral point Solution form；

According to sytem matrix H in S5_kDesign form, the pre-coding matrix of user [k, u] can correspondingly design as follows Decomposed form:

Wherein, the beamforming matrix Ξ of user [k, u]_k,uIt is by matrix Ξ_k?It arranges to The submatrix of composition is arranged, i.e.,Power distribution matrix Λ_k,uDiagonal element It is by diagonal matrix Λ_k?A diagonal element is toA diagonal element composition, i.e.,Here, Ξ_k[i] representing matrix Ξ_kI-th column, [Λ_k]_i,jRepresenting matrix Λ_kThe i-th row jth column element, diag { } representing matrix diagonalization operation.

S7. according to precoding D_k,uGeneral decomposed form, equivalence conversion S4 in minimum power problem, by precoding square Battle array optimization problem is decomposed into beamforming matrix and power distribution matrix optimizing problem.

According to the Precoding Design form of user in S6 [k, u],

The expression formula of Signal to Interference plus Noise Ratio simplifies are as follows:

Correspondingly, optimization problem P0 can equivalence be converted into optimization problem P1, it is as follows:

Wherein, matrixFirst restrictive condition indicates the minimum-rate of user Demand, second restrictive condition are to guarantee beamforming matrix { Ξ_k,uComposition composite matrix Ξ_kFor unitary matrice.

S8. optimization problem after converting in substep solution S7, successively designs each column vector of beamforming matrix first, and Based on the beamforming matrix designed, optimal power distribution matrix is designed.

Two stages that are divided into of optimization problem P1 solve after converting in S7, i.e., first solve beamforming matrix { Ξ_k,u, then Solve power distribution matrix { Λ_k,u}。

8a) beamforming matrix { Ξ_k,uSolve:

By optimization problem P1 objective function it was determined that objective function is about { [Π_k,u]_i,iMonotonically increasing function； Beamforming matrix is solved, by successively designing { Ξ_k,uEach column minimize { [Π_k,u]_i,i, meet simultaneously {Ξ_k,uOrthogonal property between each column；Specifically, each matrix Ξ is successively designed first_k,uIn the 1st column, then according to Each matrix of secondary design Ξ_k,uIn the 2nd column, and so on, until the tenth of the twelve Earthly Branches vector of all users all designs completion；In order to guarantee The orthogonality of unitary matrice, in design beamforming matrix { Ξ_k,uI-th of vector Ξ_k,uWhen [i], Ξ need to be met_k,u[i] is located at In the orthogonal subspaces for completing tenth of the twelve Earthly Branches vector through design, i.e. Ξ_k,u[i]⊥Σ_k,u,i, wherein matrix Σ_k,u,iIt is by Ξ_k,u[i] is set The composite matrix of tenth of the twelve Earthly Branches vector composition before is counted into, i.e.,

It, need to be by Ξ according to above-mentioned condition_k,u[i] is designed as following form,

Wherein, 1≤i≤l_k,u, and in order to make [Π_k,u]_iiIt minimizes, w_k,u,iIt is designed to following form:

Wherein, v_min(X) the corresponding singular value vector of minimum non-zero singular value of representing matrix X, repeat the above tenth of the twelve Earthly Branches to Measure Ξ_k,u[i] calculates step, until designing the unitary matrice of all users.

8b) power distribution matrix { Λ_k,uSolve:

{ Ξ can be determined by above step_k,u, it is correspondingly availableInto And available Π_k,uDiagonal element { [Π_k,u]_i,i}.For given { [Π_k,u]_i,i, optimization problem P1 of equal value can turn Optimization problem P2 is turned to, as follows:

By utilizing method of Lagrange multipliers, solving optimization problem P2.Introduce Lagrange multiplier { θ_k,u, construction auxiliary Objective function are as follows:

FunctionIt is rightAsk local derviation that can indicate are as follows:

When optimization problem P2 takes optimal value, it can obtainAnd optimization problem P2 restrictive condition takes equal sign, i.e.,It acquiresOptimal value are as follows:

Wherein, M_k,uIndicate diagonal matrix Λ_k,uThe number of middle nonzero element, (x)⁺Operation is expressed as form: when x >= 0, (x)⁺=x, when x < 0, (x)⁺=0.

Finally obtain optimal power allocation matrix Λ_k,u, be one byFor diagonal element The diagonal matrix of element composition, i.e.,

S9. by the optimal beam forming matrix { Ξ acquired in S8_k,uAnd optimal power allocation matrix { Λ_k,uBe updated to In S6 in the expression formula of pre-coding matrixIt can be obtained the user's pre-coding matrix for needing to optimize D_k,u, wherein H_k,uFor the channel matrix between user [k, u] and base station, the information known to system can be obtained by channel estimation It arrives, Q_kInterference and noise covariance matrix for kth group user can be solved by expression formula in S4.

In MIMO-NOMA system below by the grouping collaboration optimization proposed by the present invention of Monte-Carlo Simulation description of test The performance of row Precoding Design method.System parameter is as follows: radius of society R=500m, external interference source transmission power P_J= 1dBm, white Gaussian noise power σ²=-99dBm, path loss index β=3.5, user group number K=2, antenna for base station number N_A =8, user antenna number N_A=8, external interference source number of antennas N_J=1.

Fig. 3 gives system total transmitting power consumption when each user transmits 1 data flow, and there are 16 and hairs for system Family；System total transmitting power consumption when Fig. 4 gives each 2 data flows of user's simultaneous transmission, there are 8 concurrent users for system； It can be found that the present invention proposes that the transmitting power consumption of system can be greatly lowered in method from Fig. 3 and Fig. 4.Compared to tradition point Cluster NOMA, when each user transmits 1 data flow, the present invention, which proposes a plan, always emits power consumption reduction 5dBm or more, each When user transmits 2 data flows, the present invention, which proposes a plan, always emits power consumption reduction 15dBm or more.

Fig. 5 is the cumulative distribution function for always emitting power consumption when each user transmits 1 data flow, and Fig. 6 is that each user passes Always emit the cumulative distribution function of power consumption when defeated 2 data flows；It can be found that the present invention proposes NOMA method from Fig. 5 and Fig. 6 The cumulative distribution function of total transmitting power consumption is always positioned at the left side of traditional sub-clustering NOMA scheme, illustrates that the present invention proposes NOMA method Transmission power level concentrates on lesser value region, however the transmission power fluctuation range of traditional sub-clustering NOMA scheme is larger, Show as always emit power consumption cumulative distribution function converge to 1 speed it is slower.

The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, without departing from the technical principles of the invention, several improvement and deformations can also be made, these improvement and deformations Also it should be regarded as protection scope of the present invention.

Claims (8)

1. a kind of MIMO-NOMA system uplink Precoding Design method, which comprises the following steps:

S1. according to each user data stream configuration and antenna for base station number, by user according to the propagation distance between user and base station By being closely divided into multiple groups to remote；

S2. after the completion of user grouping, the total reception subscriber signal y of base station,

Wherein, H_k,uIndicate the channel matrix between user [k, u] and base station, D_k,uFor the pre-coding matrix of user [k, u], x_k,u For the transmitting signal of user [k, u], H_JChannel matrix between interference source and base station, z_JFor the interference signal of interference source, n is The white Gaussian noise signal of system, user [k, u] are u-th of user of kth group,

And write the received subscriber signal y in base station as matrix form as unit of group,

Wherein,Indicate sytem matrix,Indicate signal vector, For vector x_k,uTransposition；

S3. the received each group of subscriber signal y order of demodulation in base station in setting grouping NOMA transmission plan, obtains each group of user Demodulated signal

S4. pre-coding matrix optimizing problem P0 model is established, optimization problem P0 is the minimum power problem of modeling；

S5. each group sytem matrix is designedGeneral decomposed form:

Wherein, Q_kIt is interference and the covariance matrix of noise of kth group user, Ξ_kIt is a unitary matrice, for controlling each data The direction of wave beam, Λ where stream_kIt is a diagonal matrix, for controlling the power distribution between data flow；

S6. according to sytem matrix H in S5_kDecomposed form, calculate pre-coding matrix D_k,uGeneral decomposed form；

S7. according to pre-coding matrix D_k,uGeneral decomposed form, equivalence conversion S4 in minimum power problem, by precoding square The optimization problem P0 of battle array modeling is decomposed into beamforming matrix and power distribution matrix combined optimization problem；

S8. substep solves conversion postwave beam shaping matrix optimizing problem and power distribution matrix optimizing problem in S7, first successively Design beamforming matrix { Ξ_k,uEach column vector, and based on the beamforming matrix { Ξ designed_k,u, it designs optimal Power distribution matrix { Λ_k,u}；

S9. by the optimal beam forming matrix { Ξ acquired in S8_k,uAnd optimal power allocation matrix { Λ_k,uBe updated in S6 In the expression formula of pre-coding matrixObtain the user's pre-coding matrix D for needing to optimize_k,u。

2. a kind of MIMO-NOMA system uplink Precoding Design method according to claim 1, which is characterized in that in S1, Each group of total number of users according to flow amount be less than antenna for base station number, i.e., to user grouping when need to meet the following conditions:Wherein, U_kFor the number of users that kth group includes, l_k,uNumber of data streams, N are sent for user [k, u]_AFor base The number of antennas stood.

3. a kind of MIMO-NOMA system uplink Precoding Design method according to claim 1, which is characterized in that in S2, Interference signal z_JCovariance matrix meetWherein, E { } is to ask expectation computing, P_JFor interference The maximum transmission power in source,For N_J×N_JUnit matrix,For matrix z_JConjugate transposition.

4. a kind of MIMO-NOMA system uplink Precoding Design method according to claim 1, which is characterized in that in S3, The implementation criterion of order of demodulation are as follows: receive the 1st group of subscriber signal of parallel demodulation in signal y from total first, demodulating the 1st group of user When signal, other group of signal is regarded as noise, delete the 1st group of subscriber signal in signal from total receive after the completion of demodulation, then from deleting Except demodulating the 2nd group of subscriber signal in total reception signal y after modulated signal, and so on, until demodulation last group of user letter Number, kth group user's demodulated signalIt indicates are as follows:

Wherein, R_kBalanced device as kth group subscriber signal；

Design obtains the MMSE balanced device R of optimal Signal to Interference plus Noise Ratio_k:

Wherein, MMSE is least mean-square error, as 1≤k≤K-1,Work as k=K,

5. a kind of MIMO-NOMA system uplink Precoding Design method according to claim 4, which is characterized in that in S4 In, the expression formula of optimization problem P0 are as follows:

Wherein, Tr { } is the operation of Matrix Calculating mark,For the minimum-rate demand of user [k, u], SINR_k,u,iFor user [k, u] The Signal to Interference plus Noise Ratio of i-th of data flow,

SINR_k,u,iBy user's demodulated signalWith MMSE balanced device R_kIt obtains, indicates are as follows:

Wherein, D_k,u[i] indicates D_k,uI-th column,For matrixInversion operation.

6. a kind of MIMO-NOMA system uplink Precoding Design method according to claim 5, which is characterized in that in S6, The pre-coding matrix decomposed form of user [k, u] are as follows:

Wherein, Ξ_k,uIt is unitary matrice Ξ_kSubmatrix, for the direction of wave beam where controlling each data flow, Λ_k,uIt is diagonal matrix Λ_kSubmatrix, for controlling the power distribution between data flow；

Wherein, the beamforming matrix Ξ of user [k, u]_k,uIt is by unitary matrice Ξ_k?It arranges toColumn group At submatrix, i.e.,Power distribution matrix Λ_k,uDiagonal element be by Diagonal matrix Λ_k?A diagonal element is toA diagonal element composition, i.e.,Ξ_k[i] representing matrix Ξ_kI-th column, [Λ_k]_i,jTable Show matrix Λ_kThe i-th row jth column element, diag { } representing matrix diagonalization operation.

7. a kind of MIMO-NOMA system uplink Precoding Design method according to claim 6, which is characterized in that in S7, According to the pre-coding matrix decomposed form of user in S6 [k, u], the expression formula of Signal to Interference plus Noise Ratio simplifies are as follows:

Optimization problem P0 equivalence is converted into optimization problem P1:

Wherein, matrixFirst restrictive condition indicates the minimum-rate demand of user, Second restrictive condition is to guarantee beamforming matrix { Ξ_k,uComposition composite matrix Ξ_kFor unitary matrice.

8. a kind of MIMO-NOMA system uplink Precoding Design method according to claim 7, which is characterized in that substep The optimization problem P0 solved after converting in S7 includes beamforming matrix { Ξ_k,uAnd power distribution matrix { Λ_k,uSolve；

To beamforming matrix { Ξ_k,uSolve:

Design is to beamforming matrix { Ξ_k,uTenth of the twelve Earthly Branches vector Ξ_k,u[i], tenth of the twelve Earthly Branches vector Ξ_k,u[i] are as follows:

Wherein,v_min(X) table Show the corresponding singular value vector of minimum non-zero singular value of matrix X；

To power distribution matrix { Λ_k,uSolve:

By solving all tenth of the twelve Earthly Branches vector Ξ_k,u[i] determines { Ξ_k,u, it obtainsAnd then To Π_k,uDiagonal element { [Π_k,u]_i,i}；

For given { [Π_k,u]_i,i, optimization problem P1 equivalence is converted into optimization problem P2, as follows:

Introduce Lagrange multiplier { θ_k,u, construct Auxiliary goal function L are as follows:

FunctionIt is rightLocal derviation is asked to indicate are as follows:

When optimization problem P2 takes optimal value, it can obtainAnd optimization problem P2 restrictive condition takes equal sign, i.e.,It acquiresOptimal value are as follows:

Wherein, M_k,uIndicate diagonal matrix Λ_k,uThe number of middle nonzero element, (x)⁺Operation is expressed as form: when x >=0, (x)⁺ =x, when x < 0, (x)⁺=0；

Obtain optimal power allocation matrix Λ_k,u, be one byFor diagonal element composition Diagonal matrix, i.e.,