CN110086515B - Uplink precoding design method of MIMO-NOMA system - Google Patents

Uplink precoding design method of MIMO-NOMA system Download PDF

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CN110086515B
CN110086515B CN201910339175.8A CN201910339175A CN110086515B CN 110086515 B CN110086515 B CN 110086515B CN 201910339175 A CN201910339175 A CN 201910339175A CN 110086515 B CN110086515 B CN 110086515B
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CN110086515A (en
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王鸿
宋荣方
胡晗
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Nanjing University of Posts and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
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Abstract

The invention discloses an uplink precoding design method of a MIMO-NOMA system, in the proposed scheme, firstly, users are divided into a plurality of groups from near to far according to the configuration of each user data stream, the propagation distance of user signals and the number of base station antennas; secondly, a precoding matrix of the same group of users and a Minimum Mean Square Error (MMSE) equalizer at a base station are jointly designed to improve the power efficiency of the system, the users in the same group work in a multiplexing mode, the users in different groups work in a NOMA mode, and the interference of a demodulated user group is removed by adopting a serial interference cancellation technology. Thirdly, in the precoding design of the same group of users, the precoding design is divided into the beam forming matrix design and the power distribution matrix design, and the invention provides a closed solution of the beam forming matrix and the power distribution matrix design; compared with the traditional clustering MIMO-NOMA transmission scheme, the MIMO-NOMA precoding scheme provided by the invention can obviously reduce the transmission power consumption of the system.

Description

Uplink precoding design method of MIMO-NOMA system
Technical Field
The invention discloses an uplink precoding design method of a MIMO-NOMA system, and relates to the technical field of multiple access in wireless communication.
Background
The number of concurrent connections supportable by the conventional orthogonal multiple access system is limited by the number of available orthogonal resource blocks, which is difficult to satisfy the requirement of the new generation mobile communication system for a huge number of connections. In recent years, non-orthogonal multiple access (NOMA) technology has received much attention from both academic and industrial circles because it can support higher system throughput and a greater number of concurrent connections. NOMA mainly comprises a power domain and a code domain, and the present invention is directed to power domain NOMA. In a new power domain, the NOMA distinguishes different users by using the difference of channel strength among users through superposition coding of a sending end and Serial Interference Cancellation (SIC) of a receiving end, and realizes the concurrent transmission of a plurality of users on one space-time frequency resource block.
A Multiple Input Multiple Output (MIMO) technology is a key technology for improving the spectrum efficiency or reliability of a system, and is a technology that will be adopted in future mobile communication. Therefore, it is necessary to extend the NOMA concept to the case where multiple antennas are configured for both the base station and the user, forming a MIMO-NOMA system. The fusion of NOMA and MIMO is an effective method for solving the problem of huge connection in future wireless communication and improving the spectrum efficiency of a system. However, in the complex interference environment of wireless communication, in order to achieve the user-specific service quality, the larger instantaneous transmission power is one of the main obstacles restricting the application of MIMO-NOMA.
In an uplink MIMO-NOMA system, a conventional transmission method is a clustered NOMA scheme based on a signal alignment technology. In the conventional clustered NOMA scheme, the basic idea of MIMO-NOMA transmission is to divide users into several clusters, wherein the number of clusters is no more than the number of base station antennas, and each cluster contains users with strong and weak channels. For the uplink, user precoding is firstly carried out, the user signals in the same cluster are aligned to the same direction, the inter-cluster interference is eliminated through an equalizer of a base station, and the user signals in the cluster are separated through a SIC receiver. In the above-mentioned clustered NOMA transmission scheme, the uplink user precoding and the base station equalizer are respectively used for signal alignment and inter-cluster interference suppression, and this design method may cause the following problems: (1) if the angle between the beams of two clusters of users is small, most of the useful signal will be lost in the inter-cluster interference suppression process. Thus, the instantaneous transmit power required to reach the predetermined signal to interference and noise ratio threshold increases dramatically. (2) Precoding and an equalizer at a receiving end are not jointly designed, and power efficiency of a transmitter is influenced.
Disclosure of Invention
Aiming at the defects in the background art, the invention provides an uplink precoding design method of an MIMO-NOMA system, and provides an MIMO-NOMA innovative structure based on user grouping cooperative optimization.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows: a method for designing uplink precoding in a MIMO-NOMA system is characterized by comprising the following steps:
s1, dividing users into a plurality of groups from near to far according to the propagation distance between the users and a base station according to the configuration of each user data stream and the number of base station antennas;
s2, after the user grouping is finished, the base station receives the user signal y,
Figure BDA0002040136640000021
wherein Hk,uRepresents the user [ k, u ]]Channel matrix with base station, Dk,uFor a user k, u]Of the precoding matrix xk,uFor a user k, u]Of the transmission signal HJIs a channel matrix between the interference source and the base station, zJIs the interference signal of an interference source, n is the Gaussian white noise signal of a system, and each element of the Gaussian white noise signal obeys the mean value of 0 and the variance sigma2Is a complex Gaussian distribution, user [ k, u ]]For the kth group of the u-th user,
and writes user signals y received by the base station in a matrix form in units of groups,
Figure BDA0002040136640000022
wherein the content of the first and second substances,
Figure BDA0002040136640000023
a matrix of the system is represented,
Figure BDA0002040136640000024
a vector of signals is represented by a vector of signals,
Figure BDA0002040136640000025
is a vector xk,uTransposing;
s3, setting the demodulation sequence of each group of user signals received by the base station in the grouped NOMA transmission scheme to obtain each group of user demodulation signals
Figure BDA0002040136640000026
S4, establishing a precoding matrix optimization problem P0 model, wherein the optimization problem P0 is a power minimization problem of modeling, the objective function is to minimize the total transmitting power, the limiting condition is to ensure the minimum speed requirement of each user, and the optimization variable is the precoding matrix of each user;
s5. to suppress signals from other non-demodulated usersInterference of group and interference source and parallel demodulation of user signals in the same group, designing system matrix of each group
Figure BDA0002040136640000031
General decomposition form of (a):
Figure BDA0002040136640000032
system matrix HkIs a matrix composed of the k-th group of all user channels and the precoding product matrix, QkIs the covariance matrix of interference and noise of the k group of users, xikIs a unitary matrix for controlling the direction of the beam in which each data stream is located, ΛkIs a diagonal matrix for controlling the power distribution among the data streams;
s6, according to the system matrix H in S5kIn the form of decomposition of (A), calculating a precoding matrix Dk,uA general decomposition form;
s7, according to the pre-coding matrix Dk,uThe general decomposition form of the method is equivalent to the power minimization problem in the S4, and the optimization problem P0 of the precoding matrix modeling is decomposed into a joint optimization problem of a beam forming matrix and a power distribution matrix;
s8, solving the optimization problem of the transformed beamforming matrix and the optimization problem of the power distribution matrix in step S7, and firstly designing the beamforming matrix { xi-k,uAre based on the designed beamforming matrix { xi }k,uDesign the optimal power distribution matrix { Λ }k,u}。
S9, the obtained optimal beamforming matrix { xi ] in S8k,uAnd the optimal power allocation matrix Λk,uSubstituting into the expression of precoding matrix in S6
Figure BDA0002040136640000033
The user precoding matrix D needing to be optimized can be obtainedk,uWherein H isk,uFor a user k, u]A channel matrix with the base station, which is system-aware information, obtainable by channel estimation, QkInterference and noise covariance matrix for the kth group of users.
Further, in S1, the total number of data streams of each group of users is less than the number of base station antennas, that is, the following conditions need to be satisfied when grouping the users:
Figure BDA0002040136640000034
wherein, UkFor the number of users included in the kth group, lk,uFor a user k, u]Number of data streams to send, NAIs the number of antennas of the base station.
Further, in S2, the interference signal zJSatisfies the covariance matrix
Figure BDA0002040136640000035
Wherein E {. is the expectation operation, PJIs the maximum transmit power of the interferer,
Figure BDA0002040136640000036
is NJ×NJThe unit matrix of (a) is,
Figure BDA0002040136640000037
is a matrix zJThe conjugate transpose of (c).
Further, in S3, the implementation criteria of the demodulation order are grouped and designed from near to far according to the propagation distance of the users, and since the average power strength of the first group of user signals is strongest and the average power strength of the last group of user signals is weakest, the implementation criteria of the demodulation order are: firstly, demodulating the 1 st group of user signals in parallel from the total received signal y, when demodulating the 1 st group of user signals, regarding other groups of signals as noise, deleting the 1 st group of user signals from the total received signal after the demodulation is finished, then demodulating the 2 nd group of user signals from the total received signal y after the modulated signal is deleted, and so on until the last group of user signals are demodulated, and the kth group of user demodulated signals
Figure BDA0002040136640000041
Expressed as:
Figure BDA0002040136640000042
Figure BDA0002040136640000043
wherein, K represents the K group (i.e. the last group of users, since the signals of all the previous user groups are deleted and there is no interference from other user groups, the demodulated signals of the K group have different representation forms from other groups), RkAn equalizer as a kth group of user signals;
since the Minimum Mean Square Error (MMSE) receiver can be used to obtain the optimal signal-to-interference-and-noise ratio for each data stream for a specific precoding matrix, the MMSE equalizer RkCan be designed as follows:
Figure BDA0002040136640000044
wherein MMSE is the minimum mean square error, when K is more than or equal to 1 and less than or equal to K-1,
Figure BDA0002040136640000049
when K is equal to K, the first group of the symbols,
Figure BDA0002040136640000045
further, in S4, under the condition of satisfying the minimum rate requirement of each user, the expression of the optimization problem P0 is:
Figure BDA0002040136640000046
wherein Tr {. is matrix tracing operation,
Figure BDA0002040136640000047
for a user k, u]Minimum rate requirement, SINRk,u,iFor a user k, u]Ith data streamThe signal-to-interference-and-noise ratio of (c),
SINRk,u,idemodulation of signals by users
Figure BDA0002040136640000048
And MMSE equalizer RkObtained, expressed as:
Figure BDA0002040136640000051
wherein D isk,u[i]Represents Dk,uThe (c) th column of (a),
Figure BDA0002040136640000052
is a matrix
Figure BDA0002040136640000053
The inversion operation of (1).
Further, in S6, the user [ k, u ]]Of the precoding matrix Dk,uThe decomposition form is:
Figure BDA0002040136640000054
wherein xik,uIs the unitary matrix xikFor controlling the direction of the beam on which each data stream is located, Λk,uIs a diagonal matrix ΛkThe sub-matrix is used for controlling power distribution among data streams;
wherein, the user [ k, u]Xi of the beamforming matrixk,uIs formed by the unitary matrix xikTo (1) a
Figure BDA0002040136640000055
Is listed to the first
Figure BDA0002040136640000056
Submatrices of columns, i.e.
Figure BDA0002040136640000057
Power distribution matrix Λk,uIs formed by a diagonal matrixΛkTo (1) a
Figure BDA0002040136640000058
Diagonal element to
Figure BDA0002040136640000059
A diagonal element composition, i.e.
Figure BDA00020401366400000510
Ξk[i]The representation matrix xikColumn i, [ lambda ]k]i,jRepresentation matrix ΛkRow i and column j of (1), diag { · } represents a matrix diagonalization operation.
Further, in S7, according to the precoding matrix decomposition form of user [ k, u ] in S6, the expression of the signal to interference plus noise ratio is simplified as follows:
Figure BDA00020401366400000511
the optimization problem P0 is equivalently transformed into the optimization problem P1:
Figure BDA00020401366400000512
wherein, the matrix
Figure BDA00020401366400000513
The first constraint is to ensure that the beamforming matrix { xi ] represents the minimum rate requirement for the user, and the second constraint is to ensure that the beamforming matrix { xi-k,uXi composed ofkIs a unitary matrix.
Further, in S8, the transformed optimization problem P1 in S7 is solved in two stages, including the beamforming matrix { Ξ |)k,uA and a power allocation matrix Λk,uSolving;
pair beamforming matrix { xi-k,uSolving:
design beamforming matrix { xi-k,uXi's unitary vector xik,u[i]Mean vector xik,u[i]Comprises the following steps:
Figure BDA0002040136640000061
wherein the content of the first and second substances,
Figure BDA0002040136640000062
vmin(X) representing a singular value vector corresponding to a minimum non-zero singular value of the matrix X;
to power distribution matrix { Lambdak,uSolving:
by solving all unitary vectors xik,u[i]Determining { xi-k,uGet it
Figure BDA0002040136640000063
Thereby obtaining pik,uDiagonal element { [ II { [k,u]i,i}；
For a given { [ Π { [k,u]i,iThe optimization problem P1 is equivalently transformed into the optimization problem P2, as follows:
Figure BDA0002040136640000064
introducing Lagrange multiplier thetak,uConstructing an auxiliary objective function
Figure BDA0002040136640000065
Comprises the following steps:
Figure BDA0002040136640000066
function(s)
Figure BDA0002040136640000067
To pair
Figure BDA0002040136640000068
The partial derivative is expressed as:
Figure BDA0002040136640000069
when the optimization problem P2 takes an optimal value, the optimal value can be obtained
Figure BDA00020401366400000610
And the optimization problem P2 constraint takes equal sign, i.e.
Figure BDA00020401366400000611
To obtain
Figure BDA00020401366400000612
The optimal values of (a) are:
Figure BDA00020401366400000613
wherein M isk,uRepresenting diagonal matrix Λk,uNumber of non-zero elements in (x)+The operation is represented in the form: when x is more than or equal to 0, (x)+X when<0，(x)+＝0；
Obtaining an optimal power distribution matrix Lambdak,uWhich is a mixture of
Figure BDA0002040136640000071
Diagonal matrices formed for diagonal elements, i.e.
Figure BDA0002040136640000072
Has the advantages that: through the precoding design of the invention, the precoding matrix of the same group of users can be optimized in a combined manner, and simultaneously, the direction of the beam forming matrix of the signal transmitted by each user can be effectively adjusted, and the transmitting power of each user data stream can be optimally distributed, so that the transmitting power utilization efficiency can be improved; on the premise of ensuring the minimum transmission rate of each user, the proposal can obviously reduce the transmission power consumption of the system no matter whether the user sends a single data stream or a plurality of data streams.
Drawings
FIG. 1 is a diagram of a system architecture model;
FIG. 2 is a diagram comparing the proposed packet co-optimization architecture with a conventional clustering architecture;
FIG. 3 is a diagram of the total transmission power consumption of the system when each user transmits 1 data stream;
FIG. 4 is a diagram of the total transmit power consumption of the system when each user transmits 2 data streams;
fig. 5 is a graph of the cumulative distribution function of the total transmission power consumption when each user transmits 1 data stream;
fig. 6 is a graph of a cumulative distribution function of total transmission power consumption when each user transmits 2 data streams.
Detailed Description
The following describes the embodiments in further detail with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
As shown in FIGS. 1-2, the present invention considers the cellular uplink transmission scenario with coverage radius R, the base station is the center of coverage, U users are uniformly distributed in the coverage area, and the number of the user and the base station transceiver antennas are both NA. The base station receives uplink signals from U users and is interfered by an external interference source signal which is randomly distributed. The number of antennas of the interference source is NJThe distance between the base station and the external interference source is dJ。
S1, dividing users into a plurality of groups from near to far according to the propagation distance between the users and a base station according to the configuration of each user data stream and the number of base station antennas;
dividing U users into K groups according to the propagation distance of the users from small to large, wherein the K group comprises UkIndividual users, and the following relationships: if k is<k'，dk,u<dk',u'Where d isk,uIndicating the transmission distance between the u-th user in the k-th group and the base station. Since the present invention considers a NOMA scenario, the following relationship exists
Figure BDA0002040136640000081
Wherein lk,uFor a user k, u]The number of data streams to send; the following conditions are required to be satisfied when the users are grouped in the invention:
Figure BDA0002040136640000082
i.e. the total number of data streams per group of users is required to be less than the number of base station antennas so that each group of user signals can be processed in parallel at the base station.
And S2, after the grouping of the users is finished, obtaining an expression of the base station received signals, and simultaneously, in order to facilitate the subsequent precoding grouping design, writing the base station received signals into a matrix form by taking a group as a unit.
After the user grouping is completed, the base station receives the signal y as follows:
Figure BDA0002040136640000083
wherein Hk,uRepresents the user [ k, u ]]Channel matrix with base station, Dk,uFor a user k, u]Of the precoding matrix xk,uFor a user k, u]Of the transmission signal HJIs a channel matrix between the interference source and the base station, zJIs the interference signal of an interference source, n is the Gaussian white noise signal of a system, and each element of the Gaussian white noise signal obeys the mean value of 0 and the variance sigma2Is a complex gaussian distribution. Interference signal zJSatisfies the covariance matrix
Figure BDA0002040136640000084
Wherein E {. is the expectation operation, PJIs the maximum transmit power of the interferer,
Figure BDA00020401366400000810
is NJ×NJThe unit matrix of (a) is,
Figure BDA0002040136640000085
is a matrix zJThe conjugate transpose of (c).
In order to facilitate the design of subsequent pre-coding groups, the signals received by the base station need to be written into groups
The following matrix:
Figure BDA0002040136640000086
wherein the system matrix of the k-th group
Figure BDA0002040136640000087
Signal vector of kth group
Figure BDA0002040136640000088
Is a vector xk,uThe transposing of (1).
S3, the grouping cooperation NOMA scheme and the traditional clustering NOMA scheme provided by the invention are shown in figure 2, and the demodulation sequence of each group of user signals of the grouping NOMA transmission scheme is set to obtain the expression of each group of user demodulated signals
Figure BDA0002040136640000089
Packet NOMA transmission scheme implementation criteria: firstly, demodulating a 1 st group of user signals in parallel from a total received signal y, regarding other groups of signals as noise when demodulating the 1 st group of user signals, deleting the 1 st group of user signals from the total received signal after the demodulation is finished, demodulating a 2 nd group of user signals from the total received signal y after the modulated signal is deleted, and so on until the last group of user signals are demodulated; the reason for designing such demodulation order is that the average power strength of the first group of user signals is strongest and the average power strength of the last user signal is weakest, which are grouped in sequence from near to far according to the propagation distance of the users.
By the use of RkAs equalizers for the k-th group of users' signals, so that the detection signals of the k-th group of users
Figure BDA0002040136640000091
Can be expressed as
Figure BDA0002040136640000092
Figure BDA0002040136640000093
Since the Minimum Mean Square Error (MMSE) receiver can be used to obtain the optimal signal-to-interference-and-noise ratio for each data stream for a specific precoding matrix, the MMSE equalizer RkCan be expressed as:
Figure BDA0002040136640000094
wherein, when K is more than or equal to 1 and less than or equal to K-1,
Figure BDA0002040136640000095
when in use
Figure BDA0002040136640000096
S4, establishing a precoding matrix optimization model, wherein the objective function is to minimize the total transmitting power, and the limiting condition is to ensure the minimum speed requirement of each user;
at this time, under the condition of satisfying the minimum rate requirement of each user, the power minimization problem is modeled as an optimization problem P0:
Figure BDA0002040136640000097
wherein Tr {. is matrix tracing operation,
Figure BDA0002040136640000098
for a user k, u]Minimum rate requirement, SINRk,u,iFor a user k, u]Signal-to-interference-and-noise ratio of ith data stream, which can be detected by user in S3
Figure BDA0002040136640000099
And MMSE equalizer RkThe expression of (a) is obtained and can be expressed as:
Figure BDA00020401366400000910
wherein D isk,u[i]Represents Dk,uThe (c) th column of (a),
Figure BDA00020401366400000911
is a matrix
Figure BDA00020401366400000912
The inversion operation of (1).
S5, respectively designing each group of system matrix
Figure BDA0002040136640000101
In a general decomposed form, wherein Hk,uIs a channel matrix from the kth user to the base station, a system matrix HkIs a matrix synthesized by all user channels of the kth group and a precoding product matrix.
In the present invention, the system matrix HkTwo goals are designed: firstly, interference from other non-demodulated user groups and interference sources is suppressed, and secondly, parallel demodulation is carried out on the same group of user signals; to meet the above two objectives, the system matrix HkDesigned in a general decomposed form as follows
Figure BDA0002040136640000102
Wherein xikIs a unitary matrix for controlling the direction of the beam in which each data stream is located, called beamforming matrix, ΛkIs a diagonal matrix used to control the power distribution among the data streams, i.e., is a power distribution matrix.
S6, according to the system matrix H in S5kTo obtain the kth group of the precoding matrix, the u-th user Dk,uA general decomposition form;
according to the system matrix H in S5kIn the design form of (1), user [ k, u ]]The precoding matrix of (a) can be designed accordingly as follows:
Figure BDA0002040136640000103
wherein, the user [ k, u]Xi of the beamforming matrixk,uIs formed by matrix xikTo (1) a
Figure BDA0002040136640000104
Is listed to the first
Figure BDA0002040136640000105
Submatrices of columns, i.e.
Figure BDA0002040136640000106
Power distribution matrix Λk,uIs formed by a diagonal matrix ΛkTo (1) a
Figure BDA0002040136640000107
Diagonal element to
Figure BDA0002040136640000108
A diagonal element composition, i.e.
Figure BDA0002040136640000109
Here, xik[i]The representation matrix xikColumn i, [ lambda ]k]i,jRepresentation matrix ΛkRow i and column j of (1), diag { · } represents a matrix diagonalization operation.
S7, according to the precoding Dk,uThe general decomposition form of (1) equivalently transforms the power minimization problem in S4, and decomposes the precoding matrix optimization problem into the beamforming matrix and power allocation matrix optimization problem.
According to the precoding scheme of the user k, u in S6,
Figure BDA0002040136640000111
the expression of the signal to interference and noise ratio is simplified as follows:
Figure BDA0002040136640000112
accordingly, optimization problem P0 may be equivalently transformed into optimization problem P1, as follows:
Figure BDA0002040136640000113
wherein, the matrix
Figure BDA0002040136640000114
The first constraint is to ensure that the beamforming matrix { xi ] represents the minimum rate requirement for the user, and the second constraint is to ensure that the beamforming matrix { xi-k,uXi composed ofkIs a unitary matrix.
And S8, solving the optimization problem after conversion in the S7 step by step, firstly sequentially designing each column vector of the beam forming matrix, and designing an optimal power distribution matrix based on the designed beam forming matrix.
The optimization problem P1 after transformation in S7 is solved in two stages, namely, the beamforming matrix { xi ] is solved firstk,uSolving the power distribution matrix { Lambda }k,u}。
8a) Beamforming matrix { xi-k,uSolving:
from the optimization problem P1, an objective function can be determined, the objective function being with respect to { [ Π { [k,u]i,iA monotonically increasing function of }; for the beamforming matrix solution, design { xi ] in turnk,uEach column of { [ Π ] is minimizedk,u]i,iXi while satisfying { xik,uThe orthogonality between each column; specifically, each matrix xi is first designed in turnk,uColumn 1 of (1), then designing each matrix xi in turnk,uThe 2 nd column in the middle, analogize in turn, until the unitary vectors of all users are designed; in order to ensure the orthogonality of the unitary matrix, a beamforming matrix { xi ] is designedk,uThe ith vector xi ofk,u[i]Then, xi is satisfiedk,u[i]In an orthogonal subspace of designed complete unitary vectors, i.e. xik,u[i]⊥Σk,u,iWherein the matrix Σk,u,iIs caused by xik,u[i]The synthetic matrix being composed of unitary vectors before the design is completed, i.e.
Figure BDA0002040136640000115
Under the above conditions, xik,u[i]Is designed in the following form that,
Figure BDA0002040136640000121
wherein i is more than or equal to 1 and less than or equal to lk,uAnd in order to make [ pik,u]iiMinimization, wk,u,iThe design is as follows:
Figure BDA0002040136640000122
wherein v ismin(X) a singular value vector corresponding to the smallest non-zero singular value of the matrix X, and repeating the above unitary vector xik,u[i]And calculating until unitary matrixes of all users are designed.
8b) Power distribution matrix Λk,uSolving:
through the above steps, the { xik,uAre correspondingly obtainable
Figure BDA0002040136640000123
Further obtaining pik,uDiagonal element { [ II { [k,u]i,i}. For a given { [ Π { [k,u]i,i}, optimization problem P1 may equivalently be transformed into optimization problem P2, as follows:
Figure BDA0002040136640000124
the optimization problem P2 is solved by using the lagrange multiplier method. Introducing Lagrange multiplier thetak,uAnd constructing an auxiliary objective function as follows:
Figure BDA0002040136640000125
function(s)
Figure BDA0002040136640000126
To pair
Figure BDA0002040136640000127
The partial derivative can be expressed as:
Figure BDA0002040136640000128
when the optimization problem P2 takes an optimal value, the optimal value can be obtained
Figure BDA0002040136640000129
And the optimization problem P2 constraint takes equal sign, i.e.
Figure BDA00020401366400001210
To obtain
Figure BDA00020401366400001211
The optimal values of (a) are:
Figure BDA0002040136640000131
wherein M isk,uRepresenting diagonal matrix Λk,uNumber of non-zero elements in (x)+The operation is represented in the form: when x is more than or equal to 0, (x)+X when<0，(x)+＝0。
Finally obtaining the optimal power distribution matrix Lambdak,uWhich is a mixture of
Figure BDA0002040136640000132
Diagonal matrices formed for diagonal elements, i.e.
Figure BDA0002040136640000133
S9, the obtained optimal beamforming matrix { xi ] in S8k,uAnd the optimal power allocation matrix Λk,uSubstituting into the expression of precoding matrix in S6
Figure BDA0002040136640000134
The user precoding matrix D needing to be optimized can be obtainedk,uWherein H isk,uFor a user k, u]A channel matrix with the base station, which is system-aware information, obtainable by channel estimation, QkThe interference and noise covariance matrix for the kth group of users can be solved by the expression in S4.
The performance of the uplink precoding design method of the MIMO-NOMA system based on the grouping cooperative optimization provided by the invention is explained through Monte Carlo simulation experiments. The system parameters are as follows: cell radius R is 500m, and external interference source transmitting power PJ1dBm, white Gaussian noise power σ2-99dBm, path loss exponent β 3.5, number of subscriber groups K2, number of base station antennas NANumber of user antennas N-8ANumber N of external aggressor antennas, 8J＝1。
Fig. 3 shows the total transmission power consumption of the system when each user transmits 1 data stream, and the system has 16 concurrent users; fig. 4 shows the total transmission power consumption of the system when each user transmits 2 data streams simultaneously, and the system has 8 concurrent users; as can be seen from fig. 3 and fig. 4, the method of the present invention can greatly reduce the transmission power consumption of the system. Compared with the traditional clustering NOMA, the total emission power consumption of the scheme provided by the invention is reduced by more than 5dBm when each user transmits 1 data stream, and is reduced by more than 15dBm when each user transmits 2 data streams.
Fig. 5 is a cumulative distribution function of total transmission power consumption when each user transmits 1 data stream, and fig. 6 is a cumulative distribution function of total transmission power consumption when each user transmits 2 data streams; as can be seen from fig. 5 and fig. 6, the cumulative distribution function of the total transmission power consumption of the NOMA method proposed by the present invention is always located at the left side of the traditional clustered NOMA scheme, which means that the transmission power value of the NOMA method proposed by the present invention is concentrated in a smaller value area, but the transmission power fluctuation range of the traditional clustered NOMA scheme is larger, which means that the speed of converging the cumulative distribution function of the total transmission power consumption to 1 is slower.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (3)

1. A method for designing uplink precoding in a MIMO-NOMA system is characterized by comprising the following steps:
s1, dividing users into a plurality of groups from near to far according to the propagation distance between the users and a base station according to the configuration of each user data stream and the number of base station antennas;
s2, after the user grouping is finished, the base station receives the user signal y,
Figure FDA0003191793300000011
wherein Hk,uRepresents the user [ k, u ]]Channel matrix with base station, Dk,uFor a user k, u]Of the precoding matrix xk,uFor a user k, u]Of the transmission signal HJIs a channel matrix between the interference source and the base station, zJIs the interference signal of the interference source, n is the Gaussian white noise signal of the system, user [ k, u]For the kth group of the u-th user,
and writes user signals y received by the base station in a matrix form in units of groups,
Figure FDA0003191793300000012
wherein the content of the first and second substances,
Figure FDA0003191793300000013
a matrix of the system is represented,
Figure FDA0003191793300000014
a vector of signals is represented by a vector of signals,
Figure FDA0003191793300000015
is a vector xk,uTransposing;
s3, setting the demodulation sequence of each group of user signals received by the base station in the grouped NOMA transmission scheme to obtain each group of user demodulation signals
Figure FDA0003191793300000016
S4, establishing a precoding matrix optimization problem P0 model, wherein the optimization problem P0 is a power minimization problem of modeling;
s5, designing each group of system matrix
Figure FDA0003191793300000017
General decomposition form of (a):
Figure FDA0003191793300000018
wherein Q iskIs the covariance matrix of interference and noise of the k group of users, xikIs a unitary matrix for controlling the direction of the beam in which each data stream is located, ΛkIs a diagonal matrix for controlling the power distribution among the data streams;
s6, according to the system matrix H in S5kIn the form of decomposition of (A), calculating a precoding matrix Dk,uA general decomposition form;
s7, according to the pre-coding matrix Dk,uThe general decomposition form of the method is equivalent to the power minimization problem in the S4, and the optimization problem P0 of the precoding matrix modeling is decomposed into a joint optimization problem of a beam forming matrix and a power distribution matrix;
s8, step-by-step solving of converted wave beams in S7Firstly, designing a beam forming matrix { xi ] in turn to optimize a forming matrix and a power distribution matrixk,uAre based on the designed beamforming matrix { xi }k,uDesign the optimal power distribution matrix { Λ }k,u},
S9, the obtained optimal beamforming matrix { xi ] in S8k,uAnd the optimal power allocation matrix Λk,uSubstituting into the expression of precoding matrix in S6
Figure FDA0003191793300000021
Obtaining a user precoding matrix D to be optimizedk,uAnd in S3, the implementation criteria of the demodulation order are: firstly, demodulating the 1 st group of user signals in parallel from the total received signal y, when demodulating the 1 st group of user signals, regarding other groups of signals as noise, deleting the 1 st group of user signals from the total received signal after the demodulation is finished, then demodulating the 2 nd group of user signals from the total received signal y after the modulated signal is deleted, and so on until the last group of user signals are demodulated, and the kth group of user demodulated signals
Figure FDA0003191793300000022
Expressed as:
Figure FDA0003191793300000023
Figure FDA0003191793300000024
wherein R iskAn equalizer as a kth group of user signals;
MMSE equalizer R designed to obtain optimal SINRk：
Figure FDA0003191793300000025
Wherein the MMSEIs the minimum mean square error, when K is more than or equal to 1 and less than or equal to K-1,
Figure FDA0003191793300000031
when K is equal to K, the first group of the symbols,
Figure FDA0003191793300000032
in S4, the expression of the optimization problem P0 is:
P0
Figure FDA0003191793300000033
wherein Tr {. is matrix tracing operation,
Figure FDA0003191793300000034
for a user k, u]Minimum rate requirement, SINRk,u,iFor a user k, u]The signal to interference plus noise ratio of the ith data stream,
SINRk,u,idemodulation of signals by users
Figure FDA0003191793300000035
And MMSE equalizer RkObtained, expressed as:
Figure FDA0003191793300000036
wherein D isk,u[i]Represents Dk,uThe (c) th column of (a),
Figure FDA0003191793300000037
is a matrix
Figure FDA0003191793300000038
In S6, user [ k, u ]]The decomposition form of the precoding matrix is as follows:
Figure FDA0003191793300000039
wherein xik,uIs the unitary matrix xikFor controlling the direction of the beam on which each data stream is located, Λk,uIs a diagonal matrix ΛkThe sub-matrix is used for controlling power distribution among data streams;
wherein, the user [ k, u]Xi of the beamforming matrixk,uIs formed by the unitary matrix xikTo (1) a
Figure FDA00031917933000000310
Is listed to the first
Figure FDA00031917933000000311
Submatrices of columns, i.e.
Figure FDA00031917933000000312
Power distribution matrix Λk,uIs formed by a diagonal matrix ΛkTo (1) a
Figure FDA00031917933000000313
Diagonal element to
Figure FDA00031917933000000314
A diagonal element composition, i.e.
Figure FDA00031917933000000315
Ξk[i]The representation matrix xikColumn i, [ lambda ]k]i,jRepresentation matrix ΛkRow i and column j of (1), diag {. cndot.) represents a matrix diagonalization operation, in S7, according to user [ k, u ] in S6]The expression of the signal to interference and noise ratio is simplified as follows:
Figure FDA00031917933000000316
the optimization problem P0 is equivalently transformed into the optimization problem P1:
P1
Figure FDA0003191793300000041
wherein, the matrix
Figure FDA0003191793300000042
The first constraint is to ensure that the beamforming matrix { xi ] represents the minimum rate requirement for the user, and the second constraint is to ensure that the beamforming matrix { xi-k,uXi composed ofkFor the unitary matrix, the transformed optimization problem P0 in the step-by-step solution S7 includes a beam forming matrix { xi-k,uA and a power allocation matrix Λk,uSolving;
pair beamforming matrix { xi-k,uSolving:
design Pair beamforming matrix { xi-k,uXi's unitary vector xik,u[i]Mean vector xik,u[i]Comprises the following steps:
Figure FDA0003191793300000043
wherein the content of the first and second substances,
Figure FDA0003191793300000044
1≤i≤lk,u，vmin(X) representing a singular value vector corresponding to a minimum non-zero singular value of the matrix X;
to power distribution matrix { Lambdak,uSolving:
by solving all unitary vectors xik,u[i]Determining { xi-k,uGet it
Figure FDA0003191793300000045
Thereby obtaining pik,uDiagonal element { [ II { [k,u]i,i}；
For a given { [ Π { [k,u]i,iThe optimization problem P1 is equivalently transformed into the optimization problem P2, as follows:
P2
Figure FDA0003191793300000046
introducing Lagrange multiplier thetak,uAnd constructing an auxiliary objective function lambda as:
Figure FDA0003191793300000047
function Λ pair
Figure FDA0003191793300000051
The partial derivative is expressed as:
Figure FDA0003191793300000052
when the optimization problem P2 takes an optimal value, the optimal value can be obtained
Figure FDA0003191793300000053
And the optimization problem P2 constraint takes equal sign, i.e.
Figure FDA0003191793300000054
To obtain
Figure FDA0003191793300000055
The optimal values of (a) are:
Figure FDA0003191793300000056
wherein M isk,uRepresenting diagonal matrix Λk,uNumber of non-zero elements in (x)+The operation is represented in the form: when x is more than or equal to 0, (x)+X, when x < 0, (x)+＝0；
Obtaining an optimal power distribution matrix Lambdak,uWhich is a mixture of
Figure FDA0003191793300000057
Diagonal matrices formed for diagonal elements, i.e.
Figure FDA0003191793300000058
2. The uplink precoding design method of the MIMO-NOMA system according to claim 1, wherein in S1, the total number of data streams for each group of users is less than the number of base station antennas, that is, the following conditions are satisfied when grouping users:
Figure FDA0003191793300000059
wherein, UkFor the number of users included in the kth group, lk,uFor a user k, u]Number of data streams to send, NAIs the number of antennas of the base station.
3. The method of claim 1, wherein in S2, the interference signal z isJSatisfies the covariance matrix
Figure FDA00031917933000000510
Wherein E {. is the expectation operation, PJIs the maximum transmit power of the interferer,
Figure FDA00031917933000000511
is NJ×NJThe unit matrix of (a) is,
Figure FDA00031917933000000512
is a matrix zJThe conjugate transpose of (c).
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