CN108631829A - Joint Power distribution, precoding and coding/decoding method and its base station - Google Patents
Joint Power distribution, precoding and coding/decoding method and its base station Download PDFInfo
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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
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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
- H04B7/0426—Power distribution
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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
- H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
- H04L25/024—Channel estimation channel estimation algorithms
Abstract
A kind of joint Power distribution of present invention offer, precoding and coding/decoding method and its base station, are suitable for multiple-input and multiple-output Non-orthogonal Multiple and access (MIMO NOMA) system.The method of the present invention includes the following steps：(1) precoder corresponding to each group is decomposed into the first precoder and is multiplied by the second precoder；(2) mean square error (mean squared error, MSE) function of the decoded signal of all user apparatus in each group is obtained；(3) power allocation factor of each group is calculated in the case of the maximum value of all MSE functions in minimizing a group；And (4) obtain the second precoder and decoder of each group in the case where overall transmission power is limited according to the calculated power allocation factor of institute by minimizing the MSE functions summation of the decoded signal of all user apparatus in all groups.
Description
Technical field
The present invention relates to one kind being suitable for downlink multiple-input and multiple-output-Non-orthogonal Multiple access (multiple
Input multiple output non-orthogonal multiple access, MIMO-NOMA) joint work(in system
Rate distribution, precoding and coding/decoding method and the base station using the method.
Background technology
With the development of science and technology, the significantly improving in terms of capacity due to NOMA systems, has become next generation communication system
The foreground technology of system development.
In NOMA systems, user's multiplexing can carry out in the power domain of transmission end, then use company in receiving terminal
Continuous property interference eliminates (successive interference cancellation, SIC) technology and opens multi-user signal separation
Come.Therefore, base station will configure more transimission power for the subscriber signal with poor channel conditions, and be with preferable letter
The subscriber signal of road condition configures less transimission power, to promote being successfully decoded for two users.
On the other hand, since MIMO technology can increase by using space multiplexing (spatial multiplexing) and diversity
The advantages of beneficial (diversity gains), significantly increases system performance, therefore existing is at present combined MIMO with NOMA
Technology (i.e. MIMO-NOMA systems), further to improve system performance.
Although known MIMO-NOMA systems can promote system performance, current technology is directly by MIMO-NOMA systems
Transmission channel be decomposed into multiple parallel single-input single-output (SISO) NOMA transmission channels, not by the space of MIMO technology
Multiplexing and diversity gain account for.
Therefore, how in MIMO-NOMA systems really using the advantages of space multiplexing and diversity gain come provide preferably
System performance, one of be a topic of concern to those skilled in the art in fact.
Invention content
In view of this, a kind of joint Power distribution of present invention offer, precoding and coding/decoding method, the method are in multi input
Mean square error (the mean-squared of system is considered in multi output-Non-orthogonal Multiple access (MIMO-NOMA) system
Error, MSE) performance is proposed for power distribution, precoder and the design of decoder.
A kind of joint Power distribution of present invention offer, precoding and coding/decoding method, pass suitable for a MIMO-NOMA systems
Send message to the base station of 2K user apparatus, it includes two that wherein the 2K user apparatus, which is distinguished into K group and each group,
A user apparatus, and one in two user apparatus is strong user, another is weak user.The method includes following step
Suddenly：(1) precoder corresponding to each group is decomposed into the first precoder and is multiplied by the second precoder, wherein first is pre-
Encoder is generated with code block diagonal precoding technique；(2) it is associated with strong user in each group of acquirement and passes through the first decoder
It decodes the first MSE functions of the first signal and decodes the 2nd MSE functions of second signal by the second decoder, and be associated with
Weak user decodes the 3rd MSE functions of second signal by third decoder；(3) in the case of given second precoder,
It is counted under conditions of the maximum value in minimizing the first MSE functions, the 2nd MSE functions and the 3rd MSE functions for each group
Calculate the power allocation factor α corresponding to each groupk, whereinAnd (4) according to these power allocation factors,
Pass through all first MSE functions for minimizing K group and all 3rd MSE functions in the case where overall transmission power limits
Summation obtains the second precoder, the first decoder and the third decoder corresponding to each group.
In one embodiment of this invention, further include being thought highly of according to the second precoding newly obtained after above-mentioned steps (4)
Multiple step (3) and (4), until the summation convergence of all first MSE functions and all 3rd MSE functions of K group, in the hope of
The optimum solution of power allocation factor, the second precoder, the first decoder, the second decoder and third decoder.
In one embodiment of this invention, the antenna number of above-mentioned base station is more than the K-1 corresponding to any of K group
The dimension summation of the characteristic vector space of a interference channel matrix.
In one embodiment of this invention, above-mentioned first signal and second signal include the parallel data of more synchronous drivings
Symbol.
In one embodiment of this invention, above-mentioned " in the case of given second precoder, for each group most
It is calculated under conditions of maximum value in first MSE functions of smallization, the 2nd MSE functions and the 3rd MSE functions and corresponds to each group
Power allocation factor αk" the step of include：For each group in minimizing the first MSE functions and the 2nd MSE functions
The power allocation factor α corresponding to each group is calculated under conditions of maximum valuek；And minimizing first for each group
The power allocation factor α corresponding to each group is calculated under conditions of maximum value in MSE functions and the 3rd MSE functionsk。
In one embodiment of this invention, above-mentioned " in the case of given second precoder, for each group most
It is calculated under conditions of maximum value in first MSE functions of smallization, the 2nd MSE functions and the 3rd MSE functions and corresponds to each group
Power allocation factor αk" the step of further include：It is equal with the 2nd MSE functions to limit the first MSE functions, and limits the first MSE
Function is equal with the 3rd MSE functions, and power allocation factor α is associated with to obtainkQuadratic equation；The quadratic equation is asked
Solution, to obtain power allocation factor αkTwo solution；And select the greater as power allocation factor α in two solutionsk's
Optimum solution.
It is in one embodiment of this invention, above-mentioned that " the first MSE functions of limitation are equal with the 2nd MSE functions, and limit first
MSE functions are equal with the 3rd MSE functions, and power allocation factor α is associated with to obtainkQuadratic equation " the step of further include：
To have comprising power allocation factor αkInverse matrix with Taylor expansion (Taylor expansion) approximation.
In one embodiment of this invention, above-mentioned " in the case of given second precoder, for each group most
It is calculated under conditions of maximum value in first MSE functions of smallization, the 2nd MSE functions and the 3rd MSE functions and corresponds to each group
Power allocation factor αk" the step of further include：By power allocation factor αkOptimum solution substitute into above-mentioned inverse matrix, to examine
Whether corresponding inverse matrix meets the condition of convergence of Taylors approximation, and be arranged in the case where condition is not satisfied power distribution because
Sub- αkFor a fixed value.
In one embodiment of this invention, above-mentioned " according to these power allocation factors, the case where overall transmission power limits
Under by minimize K group all first MSE functions and all 3rd MSE functions summation come obtain each group it is right
The step of the second precoder, the first decoder and third decoder answered " includes：The case where giving the second precoder
Under, it is obtained in each group by the summation of all first MSE functions and all 3rd MSE functions that minimize K group
Strong user and the first decoder and third decoder corresponding to weak user；And it is decoded according to these first decoders and third
Device passes through all first MSE functions for minimizing K group and all 3rd MSE letters in the case where overall transmission power limits
Several summations obtains the second precoder corresponding to each group.
In one embodiment of this invention, above-mentioned " according to these first decoders and third decoder, in overall transmission power
It is each to obtain by minimizing the summation of all first MSE functions and all 3rd MSE functions of K group in the case of limitation
The second precoder method corresponding to a group " includes：Using Caro need-Ku En-Plutarch (Karush-Kuhn-Tucker,
KKT) condition obtains each institute of group of all first MSE functions and the summation of all 3rd MSE functions that minimize K group
Corresponding second precoder.
The present invention provides a kind of base station, is suitable for MIMO-NOMA systems；This base station include transmission circuit, storage circuit and
Processing circuit.Transmission circuit includes more antennas, to transmit a message to 2K user apparatus, the wherein 2K user apparatus quilt
It includes two user apparatus to be distinguished into K group and each group, and one in two user apparatus is strong user, another
A is weak user.Storage circuit stores multiple program codes.Processing circuit couples transmission circuit and storage circuit, and is configured
To execute：(1) precoder corresponding to each group is decomposed into the first precoder and is multiplied by the second precoder, wherein the
One precoder is generated with code block diagonal precoding technique；(2) it is associated with strong user in each group of acquirement and passes through the first solution
Code device decodes the first MSE functions of the first signal and decodes the 2nd MSE functions of second signal, Yi Jiguan by the second decoder
It is coupled to the 3rd MSE functions that weak user decodes second signal by third decoder；(3) the case where giving the second precoder
Under, for each group under conditions of the maximum value in minimizing the first MSE functions, the 2nd MSE functions and the 3rd MSE functions
Calculate the power allocation factor α corresponding to each groupk, whereinAnd (4) according to power allocation factor αk,
Overall transmission power is obtained in the case of limiting by minimizing the summation of the first MSE functions and the 3rd MSE functions of K group
The second precoder, the first decoder corresponding to each group and third decoder.
In one embodiment of this invention, above-mentioned processing circuit is further configured to execute：According to second newly obtained
Precoder repeats step (3) and (4), until the summation of all first MSE functions and all 3rd MSE functions of K group
Convergence, in the hope of the best of power allocation factor, the second precoder, the first decoder, the second decoder and third decoder
Solution.
In one embodiment of this invention, the antenna number of above-mentioned transmission circuit is more than corresponding to any of K group
K-1 interference channel matrix characteristic vector space dimension summation.
In one embodiment of this invention, above-mentioned first signal and second signal include the parallel data of more synchronous drivings
Symbol.
In one embodiment of this invention, above-mentioned processing circuit is further configured to execute：For each group most
Under conditions of maximum value in first MSE functions of smallization and the 2nd MSE functions calculate corresponding to each group power distribution because
Sub- αk；And for the calculating pair under conditions of the maximum value in minimizing the first MSE functions and the 3rd MSE functions of each group
It should be in the power allocation factor α of each groupk。
In one embodiment of this invention, above-mentioned processing circuit is further configured to execute：Limit the first MSE functions with
2nd MSE functions are equal, and the first MSE functions of limitation are equal with the 3rd MSE functions, and power allocation factor α is associated with to obtaink
Quadratic equation；The quadratic equation is solved, to obtain power allocation factor αkTwo solution；And in two solutions
Select the greater as power allocation factor αkOptimum solution.
In one embodiment of this invention, above-mentioned processing circuit is further configured to execute：Power distribution will be associated with
Factor-alphakInverse matrix with Taylor expansion approximation.
In one embodiment of this invention, above-mentioned processing circuit is further configured to execute：By power allocation factor αk
Optimum solution substitute into above-mentioned inverse matrix, to examine whether corresponding inverse matrix meets the condition of convergence of Taylors approximation, and not
Power allocation factor α is set in the case of meeting the conditionkFor a fixed value.
In one embodiment of this invention, above-mentioned processing circuit is further configured to execute：In given second precoding
It is each to obtain by minimizing the summation of all first MSE functions and all 3rd MSE functions of K group in the case of device
Strong user and the first decoder and third decoder corresponding to weak user in a group；And according to these first decoders with
Third decoder, in the case where overall transmission power is limited by minimizing all first MSE functions and all the of K group
The summation of three MSE functions obtains the second precoder corresponding to each group.
In one embodiment of this invention, above-mentioned processing circuit is further configured to execute：- Ku En-is needed using Caro
All first MSE functions of K group of Plutarch (KKT) condition acquirement minimum are each with the summation of all 3rd MSE functions
The second precoder corresponding to group.
Based on above-mentioned, a kind of joint Power distribution of proposition of the embodiment of the present invention, precoding and coding/decoding method and its base station；This
Invention obtains the precoder that can eliminate inter-group interference by code block diagonal technology first, by the MIMO- of multiple groups
NOMA channel decomposings are multiple parallel single group MIMO-NOMA channels；The present invention and the MSE for considering MIMO-NOMA systems
Performance successively forms two optimization problems, to obtain certain level for power allocation factor and precoder with decoder
MSE performances；In addition, the present invention more by iterative algorithm obtain the final optimal power contribution factor, best precoder and
Best decoder, further to promote MSE performances.Comprehensive speech, the present invention can be effectively improved the performance of MIMO-NOMA systems,
Preferable transmission quality is provided.
For the features and advantages of the present invention can be clearer and more comprehensible, spy is for embodiment and is described in detail with the accompanying drawings as follows.
Description of the drawings
Fig. 1 is that the extensive MIMO-NOMA systems of downlink multigroup group depicted in an embodiment according to the present invention are shown
It is intended to.
Fig. 2 is joint Power distribution, precoding and the coding/decoding method flow chart depicted in an embodiment according to the present invention.
Fig. 3 is according to equivalent K parallel single group MIMO-NOMA channel schematic diagrames depicted in Fig. 1.
【Symbol description】
1_1、1_2、2_1、2_2、…、K_1、K_2：User apparatus
100：The extensive MIMO-NOMA systems of downlink multigroup group
110：Base station
C_1、C_2、…、C_K：Group
S210、S220、S230、S240：Step
Specific implementation mode
Fig. 1 is the extensive MIMO-NOMA systems of downlink multigroup group depicted in an embodiment according to the present invention
Schematic diagram.In an embodiment of the present invention, the extensive MIMO-NOMA systems 100 of downlink include base station 110 be distinguished into
K group 2K user apparatus (i.e. group C_1, C_2 ..., C_K and user apparatus 1_1,1_2 ..., K_1, K_2), wherein K
≥1.The transmission range of different groups does not overlap each other, and each group includes to share identical transmission end spatial coherence matrix
Two user apparatus.Present invention assumes that channel state information (the channel state of the known overall situation (global)
Information), the channel matrix H between base station 110 and 2K user apparatus can also be obtainedk,i(k=1 ..., K, i=
1,2) information.In addition to this, base station 110 is configured with NTRoot antenna, and user apparatus 1_1,1_2 ..., K_1, K_2 each
Then it is configured with NRRoot antenna, wherein NT>>NR。
In the present embodiment, user apparatus 1_1,1_2 ..., K_1, K_2 can for example realize for (but not limited to) movement station,
Advanced movement station (advanced mobile station), server, user terminal, desktop PC, laptop computer,
Network computer, work station, personal digital assistant (personal digital assistant), tablet computer (tablet
Personal computer), scanner, telephone device, pager, camera, TV, handheld video game device, music dress
It sets, wireless sensor etc., the present invention is limited not to this.
In the present embodiment, base station 110 may include (but not limited to)：For example, eNB, household eNB (Home eNB), advanced
Base station (advanced base station), base station transceiver system (base transceiver system), access point, one's original domicile
Base station (home base station), repeater, intermediate node, intermediate equipment and/or satellite-based communication base station, but
The embodiment of the present invention is not limited to this.
From hardware point, base station 110 can include at least (but not limited to) transmission circuit, processing circuit and optionally select
Storage circuit.Transmission circuit may include transmitter circuit, acceptor circuit, analog to digital (analog-to-digital, A/
D) converter, D/A converter, low noise amplification, mixing, filtering, impedance matching, transmission line, power amplification, one or more antennas
Circuit and local storage medium element (but the present invention is not limited thereto).Storage circuit be, for example, memory, hard disk or it is any its
It may be configured to record multiple program codes or module to store the element of data.
Processing circuit is configured to processing digital signal and executes method proposed in the exemplary embodiments of the present invention
Function, processing routine or method and step.Processing circuit is optionally coupled to memory circuit to store program code, device is matched
Set, codebook, buffering or permanent data etc..The function of processing circuit can be used such as microprocessor, microcontroller, dsp chip,
The programmable units such as FPGA are implemented.The function of processing circuit also can use independent electronic or IC to implement, and processing circuit
Hardware or software implementation can be used.
In this example, it is assumed that the channel of the extensive MIMO-NOMA systems of downlink 100 is geometric monocycle
(one-ring) scattering model, and the antenna that 110 end of base station is arranged is uniform linear array (uniform linear array).
Since two user apparatus in each group share identical channel resource, so it is considered herein that two in k-th of group
User apparatus also shares identical spatial correlation matrix Rk,k∈{1,....,K}.Based on above-mentioned, it is located at incidence angle (angle of
arrival)θkAnd the channel co-variation moment matrix corresponding to k-th of group with angular spread (angular spread) Δ
(covariancematrix) (m, p) a element can be expressed as：
Wherein λ D are the minimum range between the antenna at 110 end of base station.
According to equation (1), the channel matrix H corresponding to i-th of user apparatus in k-th of groupk,iIt can be expressed as：
Wherein i ∈ { 1,2 }, k ∈ { 1 ..., K },To followDistribution quickly declines
Fall (fast-fading) complex-valued Gaussian (Gaussian) matrix, ΙMThe unit matrix of M × M is represented,Represent space
Correlation matrix RkHave rkThe diagonal matrix of a non-zero characteristic value, andFor spatial correlation matrix RkFeature vector
The matrix constituted；Here, rkAlternatively referred to as channel matrix Hk,iCharacteristic vector space dimension.
It should be noted that definition of the embodiment of the present invention has larger Nice Fu Luobin norm (Frobenius norm) square
The user apparatus (i.e. user apparatus 1_1,2_1 ..., K_1) of channel matrix be strong user, and there is smaller Nice Fu Luobin model
The user apparatus of several squares of channel matrix is weak user (i.e. user apparatus 1_2,2_2 ..., K_2), that is,
For k-th of group, base station 110 will have power allocation factor αkStrong user signal vectorWith
With power allocation factor 1- αkWeak user signal vectorIt is combined into the multiplexing on power domain
(multiplexing) signal vector, as follows：
Wherein sk,1With sk,2Vector dimension LkRepresent the number of the parallel data symbol of synchronous driving.
By signal vector xkIt is multiplied by precoderIt can then be indicated in the signal vector of 110 end of base station transmission
For：
And the received signal vector of i-th of user apparatus in k-th of group, it can be expressed as：
WhereinFor example, Additive White Gaussian Noise (additive white Gaussian noise,
AWGN), but the present invention is not limited thereto.
If above-mentioned received signal vector is unfolded, can be expressed as：
Wherein the right Section 3 of equation (6) is (inter- between the group caused by the signal vector by other groups
Cluster it) interferes, the right first item is the signal vector of strong user (i.e. for (intra-cluster) in the group of weak user
Interference), and the signal vector that the right Section 2 is weak user (i.e. for being interfered in the group of strong user).
To develop the space multiplexing and diversity gain potentiality of MIMO-NOMA systems, the present invention considers MIMO-NOMA systems
MSE performances are proposed for the relevant system design of power distribution, precoder and decoder of user apparatus.
Fig. 2 be depicted in an embodiment according to the present invention joint Power distribution, precoding and coding/decoding method flow
Figure, the method can be executed by base station 110, and each step therein is illustrated hereinafter with reference to the system architecture of Fig. 1.
In step S210, by the precoder F corresponding to each groupkIt is decomposed into the first precoder and is multiplied by second in advance
Encoder, wherein the first precoder is generated with code block diagonal (block diagonalization) precoding technique.
In the present embodiment, the precoder F proposedkIncluding to eliminate the first precoder of inter-group interferenceWith promoting the second precoder of MSE performancesIt can be expressed as：
Fk=QkWk, k ∈ 1 ..., and K } equation (7)
Wherein N represents the dimension of the kernel of an equivalent channel matrix, this parameter will be in the first precoder Q belowk
Design in illustrate.
According to equation (6) and (7), the interference of i-th of user apparatus of first of group of signal pair of k-th of group can be with
It is expressed asTo eliminate inter-group interference, the of k-th of group of the invention
One precoder QkDesign will make corresponding signal vector xkVia channel matrix Hl,iReach two users of first of group
It is 0 when the receiving terminal of device；That is, QkDesign will meet following zero interference condition：Hl,iQk=0 (i.e.), l, k ∈ { 1 ..., K }, l ≠ k.
Based on above-mentioned, base station 110 will generate the first precoder using the precoder designing technique of code block diagonal
Qk.Specifically, in the program of code block diagonal, the signal vector x of k-th of group is collected firstkOther groups are generated
Distracter corresponding to K-1 interference channel matrix (Hl,i, l ∈ { 1 ..., K }, l ≠ k) all feature vectors, and by its
It is expressed as matrix Dimension beWhereinWhenWhen,N (be equal to) a 0 singular value and corresponding kernel (null
It space) can be by rightIt executes following singular value decomposition (singular value decomposition, SVD) and obtains：
WhereinIt is to includeThe diagonal matrix of a non-zero singular value,WithRespectively
It is the matrix that corresponding left singular vector is constituted with right singular vector, andCan further withWithIt is expressed as
Above-mentioned matrixThe vector space (spanned vector space) that is transformed into of N number of row vector be matrixKernel.
It is worth noting that, in order to ensure matrixKernel exist, and can completely eliminate inter-group interference, pass
The antenna number of sending end must satisfy following condition：
Wherein rlFor interference channel matrix Hl,iCharacteristic vector space dimension, and LkSynchronous driving is represented to k-th group
The parallel data symbol number of any user of group；Due to Lk>=1, so inequality (9) means that the antenna number of transmission end must
The dimension summation of the characteristic vector space of K-1 interference channel matrix corresponding to any of K group must be more than.
When the equal sign in inequality (9) is set up, matrixThe dimension of kernel be
In the present embodiment, the matrix V pushed away with inequality (9) according to equation (8)kIt will be as the of k-th of group
One precoder Qk, that is,：
Thus, which base station 110 can be by using the first precoder Q of equation (10)k(k ∈ 1 ..., K }) eliminate
Inter-group interference in equation (6).Then, the MIMO- of multiple groups of the extensive MIMO-NOMA systems of downlink 100
NOMA channels will can be broken down into K parallel single group MIMO-NOMA channels.
Fig. 3 is according to equivalent K parallel single group MIMO-NOMA channel schematic diagrames depicted in Fig. 1.In this situation
Under, the received signal vector of i-th of user apparatus in k-th of group can be expressed as：
According to equation (11), for being interfered in the group of two user apparatus in k-th of group, strong user can be by holding
Row SIC removes the signal vector of weak user, and the signal vector of strong user can be considered as noise and directly decoded out by weak user
Received signal vector.It is extensive for the downlink multigroup group proposed in next explanation based on above-mentioned
The design of MIMO-NOMA systems 100 will focus mainly on the MSE Study on Performance of two user apparatus in single group.
In step S220, obtains and be associated with strong user decodes the first signal by the first decoder the in each group
One MSE functions and the 2nd MSE functions that second signal is decoded by the second decoder, and be associated with weak user and pass through third solution
3rd MSE functions of code device decoding second signal.
In the present embodiment, if applying the first decoder D in k-th of groupk,11, the second decoder Dk,12And third solution
Code device Dk,22To restore signal vector (i.e. the first signal s of strong userk,1) with signal vector (the i.e. second signal of weak user
sk,2), then it can be expressed as in strong user and the MSE of the received signal vector of weak user terminal：
Equation (12) indicates that the strong user in k-th of group first passes through the second decoder Dk,12Decode the signal of weak user
sk,2The 2nd corresponding MSE functions Jk,12, equation (13) indicate k-th of group in strong user in the hypothesis with perfect SIC
Under (i.e.) pass through the first decoder Dk,11Decode itself signal sk,1Corresponding
One MSE functions Jk,11, and equation (14) indicates that the weak user in k-th of group passes through third decoder Dk,22Decode itself letter
Number sk,2The 3rd corresponding MSE functions Jk,22。
In one embodiment of this invention, in order to seek the first decoder Dk,11, the second decoder Dk,12And third decoder
Dk,22Optimum solution corresponding to MSE functions, equation (11) is substituted into equation (12)-(14), and result is unfolded as follows：
WhereinWithRespectively strong user and the equivalent channel corresponding to weak user
Matrix.
In the present embodiment, by peer-to-peer (15)-(17) the second decoding can be derived using matrix partial differential rule
Device Dk,12, the first decoder Dk,11And third decoder Dk,22Closed type (closed-form) optimum solution, be expressed as down
RowAnd
It should be noted that the second decoder Dk,12, the first decoder Dk,11And third decoder Dk,22Optimum solution can also adopt
It obtains in other ways, the present invention is limited not to this.It should also be noted that present invention assumes that global channel can be obtained
Status information, therefore the second decoder Dk,12, the first decoder Dk,11And third decoder Dk,22Optimum solution can be taken by base station 110
It must be resent to user apparatus, or also can directly be calculated by user apparatus, the present invention is limited not to this.
By above-mentioned second decoder Dk,12, the first decoder Dk,11And third decoder Dk,22Optimum solution substitute into respectively
Formula (15)-(17) are associated with the MSE J of strong user and the signal vector of weak userk,12、Jk,11And Jk,22(i.e. second, first and
3rd MSE functions) it can be rewritten as respectively：
In step S230, in the case of given second precoder, the first MSE letters are being minimized for each group
Calculated under conditions of maximum value in number, the 2nd MSE functions and the 3rd MSE functions power distribution corresponding to each group because
Son.
In the present embodiment, two user apparatus in single group can not only decode the signal vector of itself,
And strong user can also restore the signal vector of weak user among the SIC processes that NOMA is transmitted.Therefore, the present invention is to be associated with
The power allocation factor of two user apparatus in each group has formulated an optimized problem-and has been directed to k-th of group,
Given second precoder WkIn the case of be based on above-mentioned MSEAndTo calculate power allocation factor αk；This one
Optimized problem aims at the maximum MSE for minimizing the received signal vector in all decoding programs, as follows：
Wherein the restrictive condition of (24) formula indicates that above-mentioned optimization problem follows NOMA principles, also that is, the signal of weak user
The transimission power of vector must be more than transimission power (the 1- α of the signal vector of strong userk>αk)。
To seek the solution of above-mentioned optimization problem, herein by MSEAndTo power allocation factor αkIt is inclined
Differential representation is as follows：
Wherein
Since the derivative of equation (25) always has positive value, so MSEWithFor power allocation factor αkIt is stringent
Increasing function；In addition, according toFor a negative definite (negative
Definite) matrix, this, which also results in the derivative in equation (26), always has negative value, and leads to MSEFor power distribution because
Sub- αkStrictly decreasing function.Therefore, existIn the case of, MSEAndIt will intersect there are two tools
Point.
Based on the above results, in the present embodiment, the optimization problem of (24) formula can be decomposed into minimum by base station 110
MSEWithIn maximum value (i.e.) and minimum MSEWith(i.e.) in maximum value two sub-problems.
In the case, base station 110 can also be by being respectively set MSEAnd MSETo obtain
Power allocation factor αk, as shown below：
It should be noted that the items of equation (27) and (28) have following features value characteristic：
Wherein
Based on features described above matter characteristic, equation (27) and (28) can be rewritten as：
However, equation (32) and (33) show power allocation factor αkPosition is in inverse matrixWithin, this
It will be so that power allocation factor αkOptimum solution be not easy to acquire.In order to solve this problem, the present invention uses Taylor expansion
(Taylor expansion) carrys out approximate correlation in power allocation factor αkInverse matrix, the wherein Taylor corresponding to the inverse matrix
Approximation can be expressed asIt is worth noting that, if above-mentioned inverse matrix meets Taylors approximation item
Part：||BA-1||<1 (or | | A-1B||<1), thus it is ensured that corresponding Taylor expansion convergence.
In the present embodiment, base station 110 is arrangedAndTo obtain following Taylors approximation formula：
After equation (34) is substituted into equation (32) and (33), it can respectively obtain：
Based on equation (35) and (36) and enable And Base station 110 obtains power allocation factor α via quadratic equation solutionkTwo solutionAnd
As shown below：
It should be noted that according to the MSE characteristics in equation (25) and (26), there is the power allocation factor relatively having a bowel movement to compare
In another, by with smaller MSE values, therefore selection is had the power relatively having a bowel movement by base station 110 in equation (37) and (38)
Distribution factor is as power allocation factor αk, as shown below：
It should be noted that the power allocation factor obtained according to above-mentioned Taylor expansionIt must satisfy corresponding inverse square
The Taylors approximation condition of battle array.Therefore, base station 110 needs further by this by power allocation factorSubstitute into the Thailand of corresponding inverse matrix
Approximate condition is strangled, to check whether to restrain.When(or) when, in equation
(39) solution obtained in is disabled, this also implies that corresponding channel condition is mutually on duty；In the case, base station 110 will
Power allocation factor is setFor a fixed value, such as
According to above-mentioned, in the present embodiment, power distribution of the base station 110 for two user apparatus in k-th of group
The factorIt can be expressed as：
It is worth noting that, the power allocation factor of equation (40)Mean all decoding journeys in k-th of group
The MSE performances of sequence can at least reach certain level.
In step S240, according to the power allocation factor obtained, pass through in the case where an overall transmission power limits
The summation of the first MSE functions and the 3rd MSE functions that minimize all groups prelists to obtain second corresponding to each group
Code device, the first decoder and third decoder.
In the present embodiment, base station 110 is according to the power allocation factor obtained in step S230Formed one with
Second precoder Wk, the first decoder Dk,11And third decoder Dk,22Come the optimization problem indicated, wherein k ∈ 1 ...,
K}.This optimization problem is to limit P in a given overall transmission powerTIn the case of, minimize all groups equation (16) with
(17) the MSE J described ink,11With Jk,22Summation obtain corresponding to the best second pre- of each group k ∈ { 1 ..., K }
Encoder Wk, best first decoder Dk,11And best third decoder Dk,22, as shown below：
It is worth noting that, the restrictive condition of (41) formula is not related to the first decoder Dk,11With third decoder Dk,22, therefore
In given second precoder WkIn the case of, above-mentioned optimization problem can be expressed as：
It enables the corresponding gradient of object function of (42) formula be equal to zero (or using method in step S220), can directly obtain
The optimum solution of the first decoder as described in equation (19) and (20) differenceWith the optimum solution of third decoder
Then, in the optimum solution of given first decoderWith the optimum solution of third decoderIn the case of, it is above-mentioned
Minimize MSE J of all groups described in equation (16) and (17)k,11And Jk,22Summation obtain corresponding to each group
The best second precoder W of group k ∈ { 1 ..., K }kOptimization problem can be expressed as：
To solve this optimization problem, Caro, which can be used, needs-Ku En-Plutarch (KKT) condition, and corresponding Lagrange
(Lagrangian) function can be expressed as：
Wherein λ >=0 is the Lagrange's multiplier (Lagrangianmultiplier) of the restrictive condition in (43) formula.Cause
This, the KKT conditions of above-mentioned optimization problem can be expressed as：
Wherein H'k,1=Hk,1QkWith H'k,2=Hk,2Qk(do not include the second precoder Wk) be associated with respectively strong user with
The equivalent channel matrix of weak user.
Based on equation (45a), the second precoderOptimum solution can be expressed as：
According to equation (46) it is known that the second precoderPower (i.e.) tight corresponding to λ
Lattice successively decrease；Therefore, the upper bound of best λ is as follows：
WhereinAndAccording to inequality (47), meet the overall transmission power of (43) formula
Limit PTBest λ can pass through two points of (bisection) search methods and obtain.
In short, joint Power according to fig. 2 is distributed, precoding and coding/decoding method, downlink multigroup group are extensive
MIMO-NOMA systems 100 can get the preliminary optimal power contribution factor, best precoder and best decoder to reduce
The MSE of system.But it in other embodiments of the present invention, can also be according to the second precoder obtained in step S240 most
Good solutionIt is iteratively performed step S230~S240, until all groups are in the first MSE functions of strong user terminal and in weak use
The summation of the 3rd MSE functions at family end restrains, to obtain the final power allocation factor α that can minimize system MSEk, second
Precoder Wk, the first decoder Dk,11, the second decoder Dk,12And third decoder Dk,22Optimum solution.
In the present embodiment, according to the second precoder W obtained in step S240kOptimum solution, can directly make
Acquired equation (37), (38) and (40) the update power allocation factor α in step S230k, so that in k-th of group
Two user apparatus have rational MSE performances.Then, updated power allocation factor αkAlso it can be used directly in step
Acquired equation (18)-(20) update the first decoder D with equation (46) in S240k,11, the second decoder Dk,12, third solution
Code device Dk,22And the second precoder Wk, to be further reduced the MSE of system.Above-mentioned iterative process will be repeatedly carried out, until being
The MSE summations convergence of all users in system, to obtain the final optimal power contribution factor, best that can minimize system MSE
Precoder and best decoder.
In conclusion a kind of joint Power distribution of proposition of the embodiment of the present invention, precoding and coding/decoding method and its base station；This
Invention obtains the precoder that can eliminate inter-group interference by code block diagonal technology first, by the MIMO- of multiple groups
NOMA channel decomposings are multiple parallel single group MIMO-NOMA channels；The present invention and the MSE for considering MIMO-NOMA systems
Performance successively forms two optimization problems, to obtain certain level for power allocation factor and precoder with decoder
MSE performances；In addition, the present invention more by iterative algorithm obtain the final optimal power contribution factor, best precoder and
Best decoder, further to promote MSE performances.Comprehensive speech, the present invention can be effectively improved the performance of MIMO-NOMA systems,
Preferable transmission quality is provided.
Although the present invention is disclosed as above with embodiment, it is not limited to the present invention.Those skilled in the art,
Do not depart from the spirit and scope of the present invention, when can carry out it is appropriate change and retouch, so these, which are changed and retouched, should belong to this
The range that patent of invention covers.
Claims (20)
1. a kind of joint Power distribution, precoding and coding/decoding method are suitable for multiple-input and multiple-output-Non-orthogonal Multiple access
(MIMO-NOMA) base station of 2K user apparatus is transmitted a message in system, wherein the 2K user apparatus is distinguished into K group
Group and each group include two user apparatus, and one in two user apparatus is strong user, another is weak user,
The method includes：
(1) precoder corresponding to each group is decomposed into the first precoder and is multiplied by the second precoder, wherein
First precoder is generated with code block diagonal precoding technique；
(2) it obtains and is associated with the first mean square error that the strong user decodes the first signal by the first decoder in each group
Poor (MSE) function and the 2nd MSE functions that second signal is decoded by the second decoder, and the weak user is associated with by the
Three decoders decode the 3rd MSE functions of the second signal；
(3) give second precoder in the case of, for each group minimize the first MSE functions,
The power distribution corresponding to each group is calculated under conditions of maximum value in 2nd MSE functions and the 3rd MSE functions
Factor-alphak, whereinAnd
(4) according to the power allocation factor αk, in the case where an overall transmission power is limited by minimizing the K group
All first MSE functions and all 3rd MSE functions summation come obtain corresponding to each group this is second pre-
Encoder, first decoder and the third decoder.
2. the method as described in claim 1, wherein further including after step (4)：
According to second precoder repeat step (3) and (4), until the K group all first MSE functions and own
The summations of 3rd MSE functions restrains, with obtain the power allocation factor, second precoder, first decoder, this
The optimum solution of two decoders and the third decoder.
3. the method as described in claim 1, the wherein antenna number of the base station are more than corresponding to any of the K group
The dimension summation of the characteristic vector space of K-1 interference channel matrix.
4. the method as described in claim 1, wherein first signal and the second signal include the parallel of more synchronous drivings
Data symbol.
5. the method as described in claim 1 exists wherein in the case where giving second precoder for each group
It minimizes to calculate under conditions of the maximum value in the first MSE functions, the 2nd MSE functions and the 3rd MSE functions and correspond to
The power allocation factor α of each groupkThe step of include：
It is calculated under conditions of minimizing the first MSE functions with maximum value in the 2nd MSE functions for each group
Corresponding to the power allocation factor α of each groupk；And
It is calculated under conditions of minimizing the first MSE functions with maximum value in the 3rd MSE functions for each group
Corresponding to the power allocation factor α of each groupk。
6. method as claimed in claim 5 exists wherein in the case where giving second precoder for each group
It minimizes to calculate under conditions of the maximum value in the first MSE functions, the 2nd MSE functions and the 3rd MSE functions and correspond to
The power allocation factor α of each groupkThe step of further include：
It is equal with the 2nd MSE functions to limit the first MSE functions, and limits the first MSE functions and the 3rd MSE function phases
Deng, with obtain be associated with power allocation factor αkQuadratic equation；
The quadratic equation is solved, to obtain power allocation factor αkTwo solution；And
Select the greater as power allocation factor α in two solutionskOptimum solution.
7. method as claimed in claim 6, wherein to limit the first MSE functions equal with the 2nd MSE functions, and limiting should
First MSE functions are equal with the 3rd MSE functions, and power allocation factor α is associated with to obtainkThe quadratic equation step
Suddenly further include：
Power allocation factor α will be associated withkAn inverse matrix with Taylor expansion (Taylor expansion) approximation.
8. the method for claim 7, existing for each group wherein in the case where giving second precoder
It minimizes to calculate under conditions of the maximum value in the first MSE functions, the 2nd MSE functions and the 3rd MSE functions and correspond to
The power allocation factor α of each groupkThe step of further include：
By power allocation factor αkThe optimum solution substitute into the inverse matrix, to examine whether the inverse matrix meets the Thailand
It strangles and the approximate condition of convergence is unfolded, and power allocation factor α is set in the case where condition is not satisfiedkFor fixed value.
9. the method as described in claim 1, wherein according to power allocation factor αk, the case where the overall transmission power limits
Under it is each to obtain this by minimizing the summation of all first MSE functions and all 3rd MSE functions of the K group
The step of second precoder, first decoder and the third decoder corresponding to group includes：
In the case where giving second precoder, by minimizing all first MSE functions of the K group and owning
The summation of 3rd MSE functions obtains first decoder corresponding to each group and the third decoder；And
According to first decoder and the third decoder, in the case where the overall transmission power is limited by minimizing the K
All first MSE functions of group and the summation of all 3rd MSE functions come obtain corresponding to each group this
Two precoders.
10. method as claimed in claim 9, wherein according to first decoder and the third decoder, in total transmission work(
Rate limit in the case of by minimizing the summations of all first MSE functions and all 3rd MSE functions of the K group
Include to obtain the second precoder method corresponding to each group：
- Ku En-Plutarch (KKT) condition is needed to obtain all first MSE functions of the minimum K group and own using Caro
Second precoder corresponding to each group of the summation of 3rd MSE functions.
11. a kind of base station is suitable for multiple-input and multiple-output-Non-orthogonal Multiple and accesses (MIMO-NOMA) system, this base station includes：
Transmission circuit, including more antennas, to transmit a message to 2K user apparatus, wherein the 2K user apparatus is distinguished
Include two user apparatus at K group and each group, and one in two user apparatus is strong user, another is
Weak user；
Storage circuit stores multiple program codes；And
Processing circuit couples the transmission circuit and the storage circuit, and is configured to execute following operation：
(1) precoder corresponding to each group is decomposed into the first precoder and is multiplied by the second precoder, wherein
First precoder is generated with code block diagonal precoding technique；
(2) it obtains and is associated with the first MSE letters that the strong user decodes the first signal by the first decoder in each group
Number and the 2nd MSE functions that second signal is decoded by the second decoder, and be associated with the weak user and pass through third decoder
Decode the 3rd MSE functions of the second signal；
(3) give second precoder in the case of, for each group minimize the first MSE functions,
The power distribution corresponding to each group is calculated under conditions of maximum value in 2nd MSE functions and the 3rd MSE functions
Factor-alphak, wherein
(4) according to the power allocation factor αk, in the case where overall transmission power is limited by minimizing the K group
The summation of all first MSE functions and all 3rd MSE functions come obtain corresponding to each group this second prelist
Code device, first decoder and the third decoder.
12. base station as claimed in claim 11, the wherein processing circuit are further configured to execute：
According to second precoder repeat above-mentioned (3) and (4), until the K group all first MSE functions and own
The summations of 3rd MSE functions restrains, with obtain the power allocation factor, second precoder, first decoder, this
The optimum solution of two decoders and the third decoder.
13. base station as claimed in claim 11, the wherein antenna number of the transmission circuit are more than institute of any of the K group
The dimension summation of the characteristic vector space of corresponding K-1 interference channel matrix.
14. base station as claimed in claim 11, wherein first signal and the second signal include more synchronous drivings and
Row data symbol.
15. base station as claimed in claim 11, the wherein processing circuit are further configured to execute：
It is calculated under conditions of minimizing the first MSE functions with maximum value in the 2nd MSE functions for each group
Corresponding to the power allocation factor α of each groupk；And
It is calculated under conditions of minimizing the first MSE functions with maximum value in the 3rd MSE functions for each group
Corresponding to the power allocation factor α of each groupk。
16. base station as claimed in claim 15, the wherein processing circuit are further configured to execute：
It is equal with the 2nd MSE functions to limit the first MSE functions, and limits the first MSE functions and the 3rd MSE function phases
Deng, with obtain be associated with power allocation factor αkA quadratic equation；
The quadratic equation is solved, to obtain power allocation factor αkTwo solution；And
Select the greater as power allocation factor α in two solutionskOptimum solution.
17. base station as claimed in claim 16, the wherein processing circuit are further configured to execute：
Power allocation factor α will be associated withkAn inverse matrix with Taylor expansion approximation.
18. base station as claimed in claim 17, the wherein processing circuit are further configured to execute：
By power allocation factor αkThe optimum solution substitute into the inverse matrix, to examine whether the inverse matrix meets the Thailand
It strangles and the approximate condition of convergence is unfolded, and power allocation factor α is set in the case where condition is not satisfiedkFor a fixed value.
19. base station as claimed in claim 11, the wherein processing circuit are further configured to execute：
In the case where giving second precoder, by minimizing all first MSE functions of the K group and owning
The summation of 3rd MSE functions obtains first decoder corresponding to each group and the third decoder；And
According to first decoder and the third decoder, in the case where the overall transmission power is limited by minimizing the K
All first MSE functions of group and the summation of all 3rd MSE functions come obtain corresponding to each group this
Two precoders.
20. base station as claimed in claim 19, the wherein processing circuit are further configured to execute：
- Ku En-Plutarch (KKT) condition is needed to obtain all first MSE functions of the minimum K group and own using Caro
Second precoder corresponding to each group of the summation of 3rd MSE functions.
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