CN109922487B - Resource allocation method under downlink MIMO-NOMA network - Google Patents

Resource allocation method under downlink MIMO-NOMA network Download PDF

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CN109922487B
CN109922487B CN201910245323.XA CN201910245323A CN109922487B CN 109922487 B CN109922487 B CN 109922487B CN 201910245323 A CN201910245323 A CN 201910245323A CN 109922487 B CN109922487 B CN 109922487B
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CN109922487A (en
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朱晓荣
张晓逸
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Nanjing University of Posts and Telecommunications
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Nanjing University of Posts and Telecommunications
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Abstract

The invention discloses a resource allocation method under a downlink MIMO-NOMA network, which is characterized in that user clustering is carried out on the basis of channel state information analysis of users, multidimensional resources such as space, frequency spectrum and power are comprehensively considered by taking multidimensional resource allocation research under the downlink MIMO-NOMA network as a main line, network performance is measured by effective capacity, a multidimensional resource allocation model under the downlink MIMO-NOMA network is established, and optimal multidimensional resource allocation is rapidly realized by using the characteristics of convergence and low complexity of an alternating iteration optimization theory. The invention fully considers the characteristics of beam directivity, service diversity and the like, meets the beam directivity by user clustering, meets the service diversity by effective capacity, and realizes the multi-dimensional resource allocation under the downlink MIMO-NOMA network.

Description

Resource allocation method under downlink MIMO-NOMA network
Technical Field
The invention relates to a multi-dimensional resource allocation method based on user clustering in a downlink MIMO-NOMA network, belonging to the technical field of network resource allocation.
Background
The 5G is a new generation mobile communication system developed for the demand of mobile communication after 2020, and according to the development rule of mobile communication, the 5G needs to have higher spectrum efficiency and network capacity to meet the exponentially increasing user demand. Non-orthogonal multiple access (NOMA) is an alternative multiple access technology of 5G, and can effectively improve the spectrum efficiency. Different from the conventional Orthogonal Multiple Access (OMA), NOMA enables multiple users to share the same time-frequency resource through power domain multiplexing, and meanwhile, a Serial Interference Cancellation (SIC) technology is adopted at a receiving end to decode step by step to obtain signals so as to eliminate simultaneous same-frequency interference.
In the Multiple-input Multiple-output (MIMO) technology, spatial multiplexing is realized by using multi-antenna transmission at a transmitting end and a receiving end, and network capacity is improved on the premise of not increasing frequency spectrum resources and transmitting power. In order to further improve the performance of NOMA, MIMO technology is applied to NOMA to form a MIMO-NOMA network. Compared with the traditional LTE network, the network increases the resource reuse of a space domain and a power domain, and can remarkably improve the spectrum efficiency and the network capacity through a resource allocation algorithm with excellent performance. But the resources in the MIMO-NOMA network include multidimensional resources such as space, spectrum and power, and the resource allocation faces a serious challenge.
The method comprises the steps of clustering users based on channel state information analysis of the users, taking multidimensional resource allocation research under a downlink MIMO-NOMA network as a main line, comprehensively considering multidimensional resources such as space, frequency spectrum and power, measuring network performance by Effective Capacity (EC), establishing a multidimensional resource allocation model under the downlink MIMO-NOMA network, and having great practical significance for realizing the multidimensional resource allocation under the optimal downlink MIMO-NOMA network.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects in the prior art, the invention provides a resource allocation method under a downlink MIMO-NOMA network, which is characterized in that the method is used for clustering users on the basis of channel state information analysis of the users, takes multidimensional resource allocation research under the downlink MIMO-NOMA network as a main line, comprehensively considers multidimensional resources such as space, frequency spectrum, power and the like, measures network performance by EC, establishes a multidimensional resource allocation model under the downlink MIMO-NOMA network, and quickly realizes optimal multidimensional resource allocation by utilizing the characteristics of convergence and low complexity of an alternating iteration optimization theory.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the technical scheme that:
a resource allocation method under a downlink MIMO-NOMA network comprises the following steps:
step 1), clustering users: acquiring channel state information and cell information of users, and performing user clustering on each cell by combining the channel state information of the users, so that the users in the clusters occupy the same wave beam, share the same time-frequency resource, and determine the optimal user clustering;
step 2), beam allocation: analyzing the beam forming process, and determining the optimal beam distribution quantity by utilizing the zero forcing beam forming theory as the user clustering distribution beam direction obtained in the step 1);
step 3), problem formation: introducing EC as an index for measuring network performance, and establishing an optimization problem by taking the EC of the maximized user as a target;
step 4), channel allocation: under the given condition of power distribution, converting the optimization problem obtained in the step 3) into an equivalent maximum weighted bipartite graph matching problem, and solving by using the Hungarian algorithm to obtain the optimal channel distribution
Step 5), power distribution: under the condition of assuming given channel allocation, converting the optimization problem obtained in the step 3) into an equivalent Lagrange dual problem, and solving by utilizing a sub-gradient algorithm to obtain optimal transmission power allocation;
step 6), alternately and iteratively optimizing: and alternately iterating the step 4) and the step 5) until the effective capacity of the user tends to converge, so as to obtain the optimal channel allocation and power allocation.
The specific steps of the step 1) are as follows:
step 11), dividing users of the cell n into G groups based on the average channel gain of the users, and recording the G groups as the G groups
Figure BDA0002010896190000021
Wherein
Figure BDA0002010896190000022
Is the set of users in the G-th group in cell n, G ═ 1, 2.
Figure BDA0002010896190000023
Inner user
Figure BDA0002010896190000024
The channel gain vector on subcarrier u is noted as
Figure BDA0002010896190000025
Wherein the content of the first and second substances,
Figure BDA0002010896190000026
is the user in antenna m
Figure BDA0002010896190000027
Channel gain, M, over subcarrier unRepresents the number of antennas in cell n; user' s
Figure BDA0002010896190000028
Is expressed as the average channel gain vector
Figure BDA0002010896190000029
Defining users
Figure BDA00020108961900000210
And the user
Figure BDA00020108961900000211
The average channel gain correlation coefficient between is:
Figure BDA00020108961900000212
wherein the content of the first and second substances,
Figure BDA00020108961900000213
and
Figure BDA00020108961900000214
are respectively average channel gain vectors
Figure BDA00020108961900000215
And
Figure BDA00020108961900000216
the evaluation index of whether the user can be divided into a cluster is defined as the minimum correlation coefficient rho when
Figure BDA00020108961900000217
Then the user
Figure BDA00020108961900000218
And the user
Figure BDA00020108961900000219
Can be divided into one cluster;
step 12), setting the initial value of g as 1; from
Figure BDA00020108961900000220
In randomly selecting a user
Figure BDA00020108961900000221
Step 13), g is g + 1; if G > G, go to step 14), otherwise go from
Figure BDA00020108961900000222
Is selected so that
Figure BDA00020108961900000223
Maximum and satisfy
Figure BDA00020108961900000224
To a user
Figure BDA00020108961900000225
If there are users who satisfy the condition
Figure BDA00020108961900000226
Turning to the step 12), otherwise, turning to the step 13 from g';
step 14), g is g + 1; if G > G, go to step 14), otherwise go from
Figure BDA00020108961900000227
Is selected so that
Figure BDA00020108961900000228
Maximum and satisfy
Figure BDA0002010896190000031
To a user
Figure BDA0002010896190000032
If there are users who satisfy the condition
Figure BDA0002010896190000033
Go to step 12), otherwise go to step 13);
step 15), dividing the users obtained by traversing into a cluster, deleting the users from the G group, and repeating the steps 11) -13) until all the users are divided; the users who get cell n are divided into LnA cluster of
Figure BDA0002010896190000034
Wherein C isnlIs the user set of the ith cluster in the cell n and is recorded as
Figure BDA0002010896190000035
|CnlIs | CnlThe number of users.
The specific steps of the step 2) are as follows:
step 21), the users of the cell n obtained according to step 1 are divided into LnAn individual cluster
Figure BDA0002010896190000036
Wherein C isnlIs the user set of the l-th cluster in the cell n
Figure BDA0002010896190000037
Cell recordingn is the vector of the transmitted signal on channel u
Figure BDA0002010896190000038
Wherein
Figure BDA0002010896190000039
Is CnlThe superposition coded signal transmitted on channel u,
Figure BDA00020108961900000310
is allocated on channel u
Figure BDA00020108961900000311
Power ratio of (A) to (B)
Figure BDA00020108961900000312
Figure BDA00020108961900000313
Is that
Figure BDA00020108961900000314
A transmit signal on channel u; the beamforming matrix for cell n on channel u is
Figure BDA00020108961900000315
Wherein
Figure BDA00020108961900000316
Is CnlA beam vector on channel u; the transmitted signal of cell n on channel u is:
Figure BDA00020108961900000317
step 22), mixing
Figure BDA00020108961900000318
Is shown as
Figure BDA00020108961900000319
Wherein
Figure BDA00020108961900000320
For eliminating CnlInter-cluster interference experienced by the inner user on channel u,
Figure BDA00020108961900000321
for determining C on channel unlAllocated power, defining users
Figure BDA00020108961900000322
The channel gain vector on channel u is
Figure BDA00020108961900000323
Assuming that the number of transmitting antennas is greater than or equal to the number of receiving antennas, the inter-cluster interference is completely eliminated, CnlInter-cluster interference experienced by an inner user on channel u is divided by C in cell nnlUser generation, definition of other clusters
Figure BDA00020108961900000324
Is dividing C in cell nnlChannel gain matrix on channel u for users in other clusters, wherein
Figure BDA00020108961900000325
Is CnlA channel gain matrix for the inner user on channel u;
step 23), for
Figure BDA00020108961900000326
Singular value decomposition to obtain
Figure BDA00020108961900000327
Wherein
Figure BDA00020108961900000328
Is that
Figure BDA00020108961900000329
Front K ofn-|CnlL left singular vectors, corresponding
Figure BDA00020108961900000330
A non-zero singular value of;
Figure BDA00020108961900000331
is that
Figure BDA00020108961900000332
Rear M ofn-Kn+|CnlL left singular vectors, corresponding
Figure BDA00020108961900000333
And zero singular value of
Figure BDA00020108961900000334
Order to
Figure BDA00020108961900000335
Is equal to
Figure BDA00020108961900000336
Sum of medium anisotropy
Figure BDA00020108961900000337
By using
Figure BDA00020108961900000338
Elimination of CnlInter-cluster interference experienced by the inner user on channel u,
Figure BDA00020108961900000339
is formed by
Figure BDA00020108961900000340
Is used to form a matrix of singular values of,
Figure BDA0002010896190000041
is that
Figure BDA0002010896190000042
Right singular matrix of (a).
The specific steps of the step 3) are as follows:
step 31) utilizing
Figure BDA0002010896190000043
Elimination of CnlAfter inter-cluster interference experienced by the inner user on channel u,
Figure BDA0002010896190000044
the received signal of the terminal on channel u is:
Figure BDA0002010896190000045
wherein the first term is
Figure BDA0002010896190000046
The second term is intra-cluster interference, the third term is inter-zone interference,
Figure BDA0002010896190000047
is noise that follows a complex gaussian distribution;
step 32), because the users in the cluster occupy the same wave beam and share the same time-frequency resource, the SIC technology is utilized to decode the user signals step by step according to the sequence of increasing the channel gain; hypothesis CnlThe channel gain vector of the inner user on the channel u satisfies
Figure BDA0002010896190000048
The decoding order of SIC is
Figure BDA0002010896190000049
Figure BDA00020108961900000410
The terminal decodes the user by SIC technology
Figure BDA00020108961900000411
After the signal of (2), the user
Figure BDA00020108961900000412
The signal to interference plus noise ratio on channel u is:
Figure BDA00020108961900000413
step 33), obtaining the user by utilizing the Shannon formula
Figure BDA00020108961900000414
The transmission rate on channel u is:
Figure BDA00020108961900000415
step 34), introducing EC as an index for measuring network performance,
Figure BDA00020108961900000416
EC of (a) is expressed as:
Figure BDA00020108961900000417
wherein the content of the first and second substances,
Figure BDA00020108961900000418
is a user
Figure BDA00020108961900000419
QoS index of (E [. cndot.)]Represents expectation in view of
Figure BDA00020108961900000420
Time of flight
Figure BDA00020108961900000421
The above equation is therefore Taylor expanded at 1 as:
Figure BDA00020108961900000422
ignoring the higher order terms of the above, the simplified EC expression is:
Figure BDA00020108961900000423
since the above formula is only
Figure BDA0002010896190000051
Is a random variable, so it would be desirable to develop:
Figure BDA0002010896190000052
wherein
Figure BDA0002010896190000053
Is the sub-carrier indicator, if CnlOccupying sub-carrier u then
Figure BDA0002010896190000054
Otherwise, the reverse is carried out
Figure BDA0002010896190000055
Will be provided with
Figure BDA0002010896190000056
Substituting the expression to obtain:
Figure BDA0002010896190000057
wherein
Figure BDA0002010896190000058
Step 35) of jointly optimizing the subcarrier indication factors
Figure BDA0002010896190000059
Inter-cluster power allocation
Figure BDA00020108961900000510
And between users in the clusterPower distribution ratio
Figure BDA00020108961900000511
Obtaining an optimization problem aiming at maximizing EC of users in a downlink multi-cell MIMO-NOMA network:
Figure BDA00020108961900000512
Figure BDA00020108961900000513
Figure BDA00020108961900000514
Figure BDA00020108961900000515
Figure BDA00020108961900000516
Figure BDA00020108961900000517
wherein the content of the first and second substances,
Figure BDA00020108961900000518
is a user
Figure BDA00020108961900000519
Minimum EC requirements of (a);
Figure BDA00020108961900000520
is the maximum transmit power of cell n; defining variables
Figure BDA00020108961900000521
Using variables
Figure BDA00020108961900000522
Replacing variables
Figure BDA00020108961900000523
And
Figure BDA00020108961900000524
a simplified optimization problem P2 is obtained:
Figure BDA0002010896190000061
Figure BDA0002010896190000062
Figure BDA0002010896190000063
Figure BDA0002010896190000064
Figure BDA0002010896190000065
the specific steps of the step 4) are as follows:
step 41) assuming that the transmission power is evenly distributed to the users, the optimization problem P2 is simplified as follows:
Figure BDA0002010896190000066
Figure BDA0002010896190000067
Figure BDA0002010896190000068
Figure BDA0002010896190000069
construct weighted bipartite graph F ═ VC×VSE), in which VCAnd VSSet of vertices, V, representing clusters and subcarriers, respectivelyCVertex v in (1)C(n, l) represents Cnl，VSVertex v in (1)S(u) denotes the subcarrier u, E denotes the connection VCAnd VSE (n, l, u) in E represents a connecting vertex vC(n, l) and vertex vS(u) the weight defining the edge e (n, l, u) is
Figure BDA00020108961900000610
A match definition for graph F is a set of pairs of non-adjacent edges, i.e., any two edges in a match cannot share the same vertex, and according to the definition, the optimization problem P3 is transformed into a maximum weighted bipartite graph matching problem, i.e., a match E is found in graph F*So that E*The sum of the weights of the middle edges is maximum, the classical Hungarian algorithm is utilized to directly solve,
step 42), construct weighted bipartite graph F ═ VC×VSE), in which VCSet of vertices, V, representing all clustersSVertex set representing all subcarriers, E represents connection VCAnd VSUsing Hungarian algorithm to solve to obtain a matching E*；
Step 43), judging whether P3 is satisfied (C1), and if not, reconstructing a weighted bipartite graph F '((V)'C×V'SAnd E '), wherein V'CRepresents a set of vertices, V ', of clusters that do not satisfy P3 (C1)'SRepresents a vertex set of unmatched subcarriers, E 'represents a connection V'CAnd V'SThe edge set is solved by using Hungarian algorithm to obtain a matching E'*Repeating step 42) until P3(C1) is satisfied;
step (ii) of44) Judging whether unmatched subcarriers exist or not, and if the unmatched subcarriers exist, reconstructing a weighted bipartite graph F ″ (V)C×V'SE') in which VCSet of vertices, V ', representing all clusters'SVertex set representing unmatched subcarriers, E' representing connection VCAnd V'SThe edge set is solved by using Hungarian algorithm to obtain a matching E'*And repeating the step 43) until the sub-carriers are allocated.
The specific steps of the step 5) are as follows:
step 51), after the sub-carriers are allocated according to the step 4), the optimization problem P2 is simplified into:
Figure BDA0002010896190000071
Figure BDA0002010896190000072
Figure BDA0002010896190000073
step 52), obtaining the Lagrangian function of the optimization problem P4 according to the Lagrangian theory as follows:
Figure BDA0002010896190000074
where μ and v are lagrange multiplier vectors introduced according to the optimization problems P4(C1) and P4(C2), respectively,
Figure BDA0002010896190000075
and vnElements in μ and v, respectively, whose dual function is
Figure BDA0002010896190000076
Wherein sup {. is a supremum, and the lagrangian dual problem from which the optimization problem P4 is derived is:
Figure BDA0002010896190000077
s.t.C1:μ≥0,v≥0
step 53), updating simultaneously with a sub-gradient algorithm
Figure BDA0002010896190000078
And vnTo minimize L (μ, v). L (. mu.v) about variables
Figure BDA0002010896190000079
And vnThe sub-gradients of (a) are:
Figure BDA0002010896190000081
Figure BDA0002010896190000082
Figure BDA0002010896190000083
and vnThe update formulas of (a) are respectively:
Figure BDA0002010896190000084
Figure BDA0002010896190000085
where s is the number of iterations, phi(s)And
Figure BDA0002010896190000086
the update step sizes of mu and v in the s-th iteration process, {. cndot. }+＝max{·,0}；
Step 54), assume
Figure BDA0002010896190000087
Is the optimal solution of the optimization problem P4, and obtains mu by iteration of a sub-gradient algorithm*And v*After-utilization of
Figure BDA0002010896190000088
To pair
Figure BDA0002010896190000089
Is equal to 0 to obtain
Figure BDA00020108961900000810
The specific steps of the step 6) are as follows:
step 61) obtaining the optimal channel allocation under the fixed transmitting power according to the step 4);
step 62) obtaining the optimal transmission power distribution under the fixed channel according to the step 5);
step 63) repeats steps 61) and 62) until the effective capacity of the user tends to converge.
Preferably: the use of a decreasing step update scheme ensures that the algorithm converges quickly:
Figure BDA00020108961900000811
where a, b are constants, phi, with increasing s(s)And
Figure BDA00020108961900000812
gradually decreases.
Compared with the prior art, the invention has the following beneficial effects:
the invention carries out user clustering based on the analysis of the channel state information of the user, takes multidimensional resource allocation research under the downlink MIMO-NOMA network as a main line, comprehensively considers multidimensional resources such as space, frequency spectrum and power, and the like, measures the network performance by effective capacity, establishes a multidimensional resource allocation model under the downlink MIMO-NOMA network, and quickly realizes optimal multidimensional resource allocation by using the characteristics of convergence and low complexity of the alternating iterative optimization theory. The invention fully considers the characteristics of beam directivity, service diversity and the like, meets the beam directivity by user clustering, meets the service diversity by effective capacity, and realizes the multi-dimensional resource allocation under the downlink MIMO-NOMA network.
Drawings
Fig. 1 is a multi-dimensional resource allocation diagram based on user clustering in a downlink MIMO-NOMA network.
Fig. 2 is a schematic diagram of user clustering in a downlink MIMO-NOMA network.
Detailed Description
The present invention is further illustrated by the following description in conjunction with the accompanying drawings and the specific embodiments, it is to be understood that these examples are given solely for the purpose of illustration and are not intended as a definition of the limits of the invention, since various equivalent modifications will occur to those skilled in the art upon reading the present invention and fall within the limits of the appended claims.
A resource allocation method under a downlink MIMO-NOMA network is characterized in that user clustering is carried out on the basis of channel state information analysis of users, multidimensional resources such as space, frequency spectrum and power are comprehensively considered as a main line for multidimensional resource allocation research under the downlink MIMO-NOMA network, network performance is measured by effective capacity, a multidimensional resource allocation model under the downlink MIMO-NOMA network is established, and optimal multidimensional resource allocation is rapidly realized by using the characteristics of convergence and low complexity of an alternative iteration optimization theory.
The method specifically comprises the following steps:
1) clustering users: acquiring channel state information and cell information of users, and performing user clustering on each cell by combining the channel state information of the users, so that the users in the cluster can occupy the same wave beam, share the same time-frequency resource, and determine the optimal user clustering.
Step 11) as shown in fig. 2, the users in cell n are divided into G groups based on the average channel gain of the users, and the G groups are recorded as
Figure BDA0002010896190000091
Wherein
Figure BDA0002010896190000092
Is the set of users in the g-th group in the cell n;
Figure BDA0002010896190000093
inner user
Figure BDA0002010896190000094
The channel gain vector on subcarrier u is noted as
Figure BDA0002010896190000095
Wherein
Figure BDA0002010896190000096
Is the user in antenna m
Figure BDA0002010896190000097
Channel gain on subcarrier u; user' s
Figure BDA0002010896190000098
Is expressed as the average channel gain vector
Figure BDA0002010896190000099
Defining users
Figure BDA00020108961900000910
And the user
Figure BDA00020108961900000911
The average channel gain correlation coefficient between is:
Figure BDA00020108961900000912
wherein
Figure BDA00020108961900000913
And
Figure BDA00020108961900000914
are respectively average channel gain vectors
Figure BDA00020108961900000915
And
Figure BDA00020108961900000916
of (1). The evaluation index of whether the user can be divided into one cluster is defined as the minimum correlation coefficient rho when
Figure BDA00020108961900000917
Greater than rho then user
Figure BDA00020108961900000918
And the user
Figure BDA00020108961900000919
May be divided into a cluster.
Step 12), introducing a variable G as an index for traversing the G group, wherein the initial value of G is 1; from
Figure BDA00020108961900000920
In randomly selecting a user
Figure BDA00020108961900000921
Step 13), g is g + 1; if G > G, go to step 14), otherwise go from
Figure BDA00020108961900000922
Is selected so that
Figure BDA00020108961900000923
Maximum and satisfy
Figure BDA00020108961900000924
To a user
Figure BDA00020108961900000925
If there are users who satisfy the condition
Figure BDA00020108961900000926
Turning to the step 12), otherwise, turning to the step 13 from g';
step 14), g is g + 1; if G > G, go to step 14), otherwise go from
Figure BDA0002010896190000101
Is selected so that
Figure BDA0002010896190000102
Maximum and satisfy
Figure BDA0002010896190000103
To a user
Figure BDA0002010896190000104
If there are users who satisfy the condition
Figure BDA0002010896190000105
Go to step 12), otherwise go to step 13);
and 15) dividing the users obtained by traversing into a cluster, deleting the users from the G group, and repeating the steps 11) to 13) until all the users are divided.
2) Beam allocation: analyzing the beam forming process, and obtaining the optimal cluster distribution beam vector by using a zero-forcing beam forming theory as the step 1).
Step 21) assume that users of cell n are divided into LnA cluster of
Figure BDA0002010896190000106
Wherein C isnlIs the user set of the ith cluster in the cell n and is recorded as
Figure BDA0002010896190000107
|CnlIs | CnlThe number of users. The transmitted signal vector of cell n on channel u is
Figure BDA0002010896190000108
Wherein
Figure BDA0002010896190000109
Is CnlThe superposition coded signal transmitted on channel u,
Figure BDA00020108961900001010
is allocated on channel u
Figure BDA00020108961900001011
Power ratio of (A) to (B)
Figure BDA00020108961900001012
Figure BDA00020108961900001013
Is that
Figure BDA00020108961900001014
The signal is transmitted on channel u. The beamforming matrix for cell n on channel u is
Figure BDA00020108961900001015
Wherein
Figure BDA00020108961900001016
Is CnlA beam vector on channel u. The transmitted signal of cell n on channel u is:
Figure BDA00020108961900001017
step 22) Beam vector
Figure BDA00020108961900001018
The functions of (1) are as follows: 1) eliminating inter-cluster interference; 2) determine the power allocation between clusters and therefore
Figure BDA00020108961900001019
Is shown as
Figure BDA00020108961900001020
Wherein
Figure BDA00020108961900001021
For eliminating CnlInter-cluster interference experienced by the inner user on channel u,
Figure BDA00020108961900001022
for determining C on channel unlThe allocated power. Defining users
Figure BDA00020108961900001023
The channel gain vector on channel u is
Figure BDA00020108961900001024
The number of transmitting antennas is assumed to be greater than or equal to the number of receiving antennas, so that inter-cluster interference can be completely eliminated. CnlInter-cluster interference experienced by an inner user on channel u is divided by C in cell nnlUser generation, definition of other clusters
Figure BDA00020108961900001025
Is dividing C in cell nnlChannel gain matrix on channel u for users in other clusters, wherein
Figure BDA00020108961900001026
Is CnlA channel gain matrix for the inner user on channel u;
step 23) pair
Figure BDA00020108961900001027
Singular value decomposition to obtain
Figure BDA00020108961900001028
Wherein
Figure BDA00020108961900001029
Is that
Figure BDA00020108961900001030
Front K ofn-|CnlL left singular vectors, corresponding
Figure BDA00020108961900001031
A non-zero singular value of;
Figure BDA00020108961900001032
is that
Figure BDA00020108961900001033
Rear M ofn-Kn+|CnlL left singular vectors, corresponding
Figure BDA00020108961900001034
And zero singular value of
Figure BDA00020108961900001035
Order to
Figure BDA00020108961900001036
Is equal to
Figure BDA00020108961900001037
Sum of medium anisotropy
Figure BDA0002010896190000111
By using
Figure BDA0002010896190000112
Can eliminate CnlInter-cluster interference experienced by the inner user on channel u.
3) Problems are formed: and introducing EC as an index for measuring network performance, and establishing an optimization problem by taking the EC of the maximized user as a target.
Step 31) utilizing
Figure BDA0002010896190000113
Elimination of CnlAfter inter-cluster interference experienced by the inner user on channel u,
Figure BDA0002010896190000114
the received signal of the terminal on channel u is:
Figure BDA0002010896190000115
wherein the first term is
Figure BDA0002010896190000116
The second term is intra-cluster interference, the third term is inter-zone interference,
Figure BDA0002010896190000117
is noise that follows a complex gaussian distribution;
step 32), because the users in the cluster occupy the same wave beam and share the same time-frequency resource, the SIC technology is utilized to decode the user signals step by step according to the ascending sequence of the channel gain. Hypothesis CnlThe channel gain vector of the inner user on the channel u satisfies
Figure BDA0002010896190000118
The decoding order of SIC is
Figure BDA0002010896190000119
Figure BDA00020108961900001110
The terminal decodes the user by SIC technology
Figure BDA00020108961900001111
After the signal of (2), the user
Figure BDA00020108961900001112
The signal to interference plus noise ratio on channel u is:
Figure BDA00020108961900001113
step 33) obtaining the user by utilizing the Shannon formula
Figure BDA00020108961900001114
The transmission rate on channel u is:
Figure BDA00020108961900001115
step 34) because the 5G service has different requirements for bandwidth, delay and packet loss rate, and the network capacity can only reflect the requirements for bandwidth, EC is introduced as an index for measuring network performance.
Figure BDA00020108961900001116
EC of (a) may be expressed as:
Figure BDA00020108961900001117
wherein
Figure BDA00020108961900001118
Is a user
Figure BDA00020108961900001119
QoS index of (E [. cndot.)]Representing the expectation. In view of
Figure BDA00020108961900001120
Time of flight
Figure BDA00020108961900001121
The above equation is therefore Taylor expanded at 1 as:
Figure BDA00020108961900001122
ignoring the higher order terms of the above, the simplified EC expression is:
Figure BDA0002010896190000121
since the above formula is only
Figure BDA0002010896190000122
Is a random variable, so it would be desirable to develop:
Figure BDA0002010896190000123
wherein
Figure BDA0002010896190000124
Is the sub-carrier indicator, if CnlOccupying sub-carrier u then
Figure BDA0002010896190000125
Otherwise, the reverse is carried out
Figure BDA0002010896190000126
Will be provided with
Figure BDA0002010896190000127
Substituting the expression to obtain:
Figure BDA0002010896190000128
wherein
Figure BDA0002010896190000129
Step 35) indicating factor by joint optimization of subcarriers
Figure BDA00020108961900001210
Inter-cluster power allocation
Figure BDA00020108961900001211
Power distribution ratio between users in cluster
Figure BDA00020108961900001212
Obtaining an optimization problem aiming at maximizing EC of users in a downlink multi-cell MIMO-NOMA network:
Figure BDA00020108961900001213
Figure BDA00020108961900001214
Figure BDA00020108961900001215
Figure BDA00020108961900001216
Figure BDA00020108961900001217
Figure BDA00020108961900001218
wherein C1 ensures that the different requirements of the user on bandwidth, delay and packet loss rate are met,
Figure BDA0002010896190000131
is a user
Figure BDA0002010896190000132
Minimum EC requirements of (a); equations C2 and C3 ensure that the sum of the transmit powers allocated by the cell to the users does not exceed the maximum transmit power of the cell,
Figure BDA0002010896190000133
is the maximum transmit power of cell n; equation C4 ensures
Figure BDA0002010896190000134
Is a binary variable; equation C5 ensures that one subcarrier corresponds to one cluster. Variables in the objective function due to the optimization problem P1
Figure BDA0002010896190000135
And
Figure BDA0002010896190000136
all occur as products, thus defining variables
Figure BDA0002010896190000137
Using variables
Figure BDA0002010896190000138
Replacing variables
Figure BDA0002010896190000139
And
Figure BDA00020108961900001310
a simplified optimization problem P2 is obtained:
Figure BDA00020108961900001311
Figure BDA00020108961900001312
Figure BDA00020108961900001313
Figure BDA00020108961900001314
Figure BDA00020108961900001315
4) channel allocation: under the condition of given transmitting power, the optimization problem P2 is converted into an equivalent maximum weighted bipartite matching problem, and the optimal channel allocation is obtained by utilizing the Hungarian algorithm to solve.
Step 41) assuming that the transmit power is evenly distributed to the users, the optimization problem P2 can be simplified as:
Figure BDA00020108961900001316
Figure BDA00020108961900001317
Figure BDA00020108961900001318
Figure BDA00020108961900001319
construct weighted bipartite graph G ═ VC×VSE), in which VCAnd VSSet of vertices, V, representing clusters and subcarriers, respectivelyCVertex v in (1)C(n, l) represents Cnl，VSVertex v in (1)SAnd (u) represents a subcarrier u. E represents a connection VCAnd VSE (n, l, u) in E represents a connecting vertex vC(n, l) and vertex vS(u) the weight defining the edge e (n, l, u) is
Figure BDA0002010896190000141
A match of graph G is defined as a set of pairs of non-adjacent edges, i.e., any two edges in a match cannot share the same vertex. According to the above definition, the optimization problem P3 can be converted into a maximum weighted bipartite graph matching problem, i.e. finding a match E in graph G*So that E*The sum of the weights of the middle edges is the largest, and the classical Hungarian algorithm can be used for directly solving.
Step 42) construct weighted bipartite graph G ═ VC×VSE), in which VCSet of vertices, V, representing all clustersSVertex set representing all subcarriers, E represents connection VCAnd VSUsing Hungarian algorithm to solve to obtain a matching E*；
Step 43) determines whether P3 is satisfied (C1), and if not, reconstructs weighted bipartite graph G '═ V'C×V'SAnd E '), wherein V'CRepresents a set of vertices, V ', of clusters that do not satisfy P3 (C1)'SRepresents a vertex set of unmatched subcarriers, E 'represents a connection V'CAnd V'SThe edge set is solved by using Hungarian algorithm to obtain a matching E'*. Repeating step 42) until P3(C1) is satisfied;
step 44) judging whether unmatched subcarriers exist or not, and if the unmatched subcarriers exist, reconstructing a weighted bipartite graph G ″ (V)C×V'SE') in which VCSet of vertices, V ', representing all clusters'SVertex set representing unmatched subcarriers, E' representing connection VCAnd V'SThe edge set is solved by using Hungarian algorithm to obtain a matching E'*. Repeating step 43) until the sub-carriers are allocated.
5) Power distribution: under the condition of channel allocation, converting the optimization problem P2 into an equivalent Lagrangian dual problem, and solving by using a sub-gradient algorithm to obtain optimal transmission power allocation.
Step 51) after allocating the sub-carriers according to step 4), the optimization problem P2 can be simplified as:
Figure BDA0002010896190000142
Figure BDA0002010896190000143
Figure BDA0002010896190000144
step 52) obtaining the lagrangian function of the optimization problem P4 according to the lagrangian theory is:
Figure BDA0002010896190000151
where μ and v are lagrange multiplier vectors introduced according to the optimization problems P4(C1) and P4(C2), respectively,
Figure BDA0002010896190000152
and vnAre the elements in μ and v, respectively. Its dual function is
Figure BDA0002010896190000153
Where sup {. is the supremum, the lagrange dual problem from which the optimization problem P4 is derived is:
Figure BDA0002010896190000154
s.t.C1:μ≥0,v≥0
step 53) Simultaneous update with a sub-gradient Algorithm
Figure BDA0002010896190000155
And vnTo minimize L (μ, v). L (. mu.v) about variables
Figure BDA0002010896190000156
And vnThe sub-gradients of (a) are:
Figure BDA0002010896190000157
Figure BDA0002010896190000158
Figure BDA0002010896190000159
and vnThe update formulas of (a) are respectively:
Figure BDA00020108961900001510
Figure BDA00020108961900001511
where s is the number of iterations, phi(s)And
Figure BDA00020108961900001512
the update step sizes of mu and v in the s-th iteration process, {. cndot. }+＝max{·,0}。φ(s)And
Figure BDA00020108961900001513
the choice of (b) influences the convergence of the sub-gradient algorithm, if phi(s)And
Figure BDA00020108961900001514
if the choice is too large, the algorithm may fail to converge, if φ(s)And
Figure BDA00020108961900001515
if chosen too small, the algorithm may converge too slowly. The use of a decreasing step update scheme therefore ensures that the algorithm can converge quickly:
Figure BDA00020108961900001516
where a, b are constants, phi, with increasing s(s)And
Figure BDA0002010896190000161
gradually decrease;
step 54) suppose
Figure BDA0002010896190000162
Is the optimal solution of the optimization problem P4, and obtains mu by iteration of a sub-gradient algorithm*And v*After-utilization of
Figure BDA0002010896190000163
To pair
Figure BDA0002010896190000164
Is equal to 0 to obtain
Figure BDA0002010896190000165
6) Alternate iterative optimization: and alternately iterating the step 4) and the step 5) until the effective capacity of the user tends to converge.
Step 61) obtaining the optimal channel allocation under the fixed transmitting power according to the step 4);
step 62) obtaining the optimal transmission power distribution under the fixed channel according to the step 5);
step 63) repeats steps 61) and 62) until the effective capacity of the user tends to converge.
The invention carries out user clustering based on the analysis of the channel state information of the user, takes multidimensional resource allocation research under the downlink MIMO-NOMA network as a main line, comprehensively considers multidimensional resources such as space, frequency spectrum and power, and the like, measures the network performance by effective capacity, establishes a multidimensional resource allocation model under the downlink MIMO-NOMA network, and quickly realizes optimal multidimensional resource allocation by using the characteristics of convergence and low complexity of the alternating iterative optimization theory. The invention fully considers the characteristics of beam directivity, service diversity and the like, meets the beam directivity by user clustering, meets the service diversity by effective capacity, and realizes the multi-dimensional resource allocation under the downlink MIMO-NOMA network.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (3)

1. A resource allocation method under a downlink MIMO-NOMA network is characterized by comprising the following steps:
step 1), clustering users: acquiring channel state information and cell information of users, and performing user clustering on each cell by combining the channel state information of the users, so that the users in the clusters occupy the same wave beam, share the same time-frequency resource, and determine the optimal user clustering;
the specific steps of the step 1) are as follows:
step 11), dividing users of the cell n into G groups based on the average channel gain of the users, and recording the G groups as the G groups
Figure FDA0003298420020000011
Wherein
Figure FDA0003298420020000012
Is the set of users in the G-th group in cell n, G ═ 1, 2.
Figure FDA0003298420020000013
Inner user
Figure FDA0003298420020000014
The channel gain vector on subcarrier u is noted as
Figure FDA0003298420020000015
Wherein the content of the first and second substances,
Figure FDA0003298420020000016
is the user in antenna m
Figure FDA0003298420020000017
Channel gain, M, over subcarrier unRepresents the number of antennas in cell n; user' s
Figure FDA0003298420020000018
Is expressed as the average channel gain vector
Figure FDA0003298420020000019
Defining users
Figure FDA00032984200200000110
And the user
Figure FDA00032984200200000111
The average channel gain correlation coefficient between is:
Figure FDA00032984200200000112
wherein the content of the first and second substances,
Figure FDA00032984200200000113
and
Figure FDA00032984200200000114
are respectively average channel gain vectors
Figure FDA00032984200200000115
And
Figure FDA00032984200200000116
the evaluation index of whether the user can be divided into a cluster is defined as the minimum correlation coefficient rho when
Figure FDA00032984200200000117
Then the user
Figure FDA00032984200200000118
And the user
Figure FDA00032984200200000119
Dividing the data into a cluster;
step 12), introducing a variable G as an index for traversing the G group, wherein the initial value of G is 1; from
Figure FDA00032984200200000120
In randomly selecting a user
Figure FDA00032984200200000121
Step 13), g is g + 1; if G > G, go to step 14), otherwise go from
Figure FDA00032984200200000122
Is selected so that
Figure FDA00032984200200000123
Maximum and satisfy
Figure FDA00032984200200000124
To a user
Figure FDA00032984200200000125
If there are users who satisfy the condition
Figure FDA00032984200200000126
Turning to the step 12), otherwise, turning to the step 13 from g';
step 14), g is g + 1; if G > G, go to step 14), otherwise go from
Figure FDA00032984200200000127
Is selected so that
Figure FDA00032984200200000128
Maximum and satisfy
Figure FDA00032984200200000129
To a user
Figure FDA00032984200200000130
If there are users who satisfy the condition
Figure FDA00032984200200000131
Go to step 12), otherwise go to step 13);
step 15), dividing the users obtained by traversing into a cluster, deleting the users from the G group, and repeating the steps 11) to 13) until all the users are dividedFinishing; the users who get cell n are divided into LnCluster, denoted as Cn1,Cn2,...,CnLnIn which C isnlIs the user set of the ith cluster in the cell n and is recorded as
Figure FDA00032984200200000132
|CnlIs | CnlThe number of users;
step 2), beam allocation: analyzing the beam forming process, and determining the optimal beam distribution quantity by utilizing the zero forcing beam forming theory as the user clustering distribution beam direction obtained in the step 1);
the specific steps of the step 2) are as follows:
step 21), the users of the cell n obtained according to step 1 are divided into LnAn individual cluster Cn1,Cn2,...,CnLnIn which C isnlIs the user set of the l-th cluster in the cell n
Figure FDA0003298420020000021
Let the vector of the transmitted signal of cell n on channel u be
Figure FDA0003298420020000022
Wherein
Figure FDA0003298420020000023
Is CnlThe superposition coded signal transmitted on channel u,
Figure FDA0003298420020000024
is allocated on channel u
Figure FDA0003298420020000025
Power ratio of (A) to (B)
Figure FDA0003298420020000026
Figure FDA0003298420020000027
Is that
Figure FDA0003298420020000028
A transmit signal on channel u; the beamforming matrix for cell n on channel u is
Figure FDA0003298420020000029
Wherein
Figure FDA00032984200200000210
Is CnlA beam vector on channel u; the transmitted signal of cell n on channel u is:
Figure FDA00032984200200000211
step 22), mixing
Figure FDA00032984200200000212
Is shown as
Figure FDA00032984200200000213
Wherein
Figure FDA00032984200200000214
For eliminating CnlInter-cluster interference experienced by the inner user on channel u,
Figure FDA00032984200200000215
for determining C on channel unlAllocated power, defining users
Figure FDA00032984200200000216
The channel gain vector on channel u is
Figure FDA00032984200200000217
Assuming that the number of transmitting antennas is greater than or equal to the number of receiving antennas, the inter-cluster interference is completely eliminated, CnlCluster of inner users experienced on channel uInter-interference by dividing C within cell nnlUser generation, definition of other clusters
Figure FDA00032984200200000218
Is dividing C in cell nnlChannel gain matrix on channel u for users in other clusters, wherein
Figure FDA00032984200200000219
Is CnlA channel gain matrix for the inner user on channel u;
step 23), for
Figure FDA00032984200200000220
Singular value decomposition to obtain
Figure FDA00032984200200000221
Wherein
Figure FDA00032984200200000222
Is that
Figure FDA00032984200200000223
Front K ofn-|CnlL left singular vectors, corresponding
Figure FDA00032984200200000224
A non-zero singular value of;
Figure FDA00032984200200000225
is that
Figure FDA00032984200200000226
Rear M ofn-Kn+|CnlL left singular vectors, corresponding
Figure FDA00032984200200000227
And zero singular value of
Figure FDA00032984200200000228
Order to
Figure FDA00032984200200000229
Is equal to
Figure FDA00032984200200000230
Sum of medium anisotropy
Figure FDA00032984200200000231
By using
Figure FDA00032984200200000232
Elimination of CnlInter-cluster interference experienced by the inner user on channel u,
Figure FDA00032984200200000233
is formed by
Figure FDA00032984200200000234
Is used to form a matrix of singular values of,
Figure FDA00032984200200000235
is that
Figure FDA00032984200200000236
Right singular matrix of (d);
step 3), problem formation: introducing EC as an index for measuring network performance, and establishing an optimization problem by taking the EC of the maximized user as a target;
the specific steps of the step 3) are as follows:
step 31) utilizing
Figure FDA00032984200200000237
Elimination of CnlAfter inter-cluster interference experienced by the inner user on channel u,
Figure FDA00032984200200000238
is received by the terminal on channel uThe numbers are:
Figure FDA0003298420020000031
wherein the first term is
Figure FDA0003298420020000032
The second term is intra-cluster interference, the third term is inter-zone interference,
Figure FDA0003298420020000033
is noise that follows a complex gaussian distribution;
step 32), because the users in the cluster occupy the same wave beam and share the same time-frequency resource, the SIC technology is utilized to decode the user signals step by step according to the sequence of increasing the channel gain; hypothesis CnlThe channel gain vector of the inner user on the channel u satisfies
Figure FDA0003298420020000034
The decoding order of SIC is
Figure FDA0003298420020000035
Figure FDA0003298420020000036
The terminal decodes the user by SIC technology
Figure FDA0003298420020000037
After the signal of (2), the user
Figure FDA0003298420020000038
The signal to interference plus noise ratio on channel u is:
Figure FDA0003298420020000039
step 33) using the shannon formulaGet user
Figure FDA00032984200200000310
The transmission rate on channel u is:
Figure FDA00032984200200000311
step 34), introducing EC as an index for measuring network performance,
Figure FDA00032984200200000312
EC of (a) is expressed as:
Figure FDA00032984200200000313
wherein the content of the first and second substances,
Figure FDA00032984200200000314
is a user
Figure FDA00032984200200000315
QoS index of (E [. cndot.)]Represents expectation in view of
Figure FDA00032984200200000316
Time of flight
Figure FDA00032984200200000317
The above equation is therefore Taylor expanded at 1 as:
Figure FDA00032984200200000318
ignoring the higher order terms of the above, the simplified EC expression is:
Figure FDA00032984200200000319
since the above formula is only
Figure FDA00032984200200000320
Is a random variable, so it would be desirable to develop:
Figure FDA0003298420020000041
wherein
Figure FDA0003298420020000042
Is the sub-carrier indicator, if CnlOccupying sub-carrier u then
Figure FDA0003298420020000043
Otherwise, the reverse is carried out
Figure FDA0003298420020000044
Will be provided with
Figure FDA0003298420020000045
Substituting the expression to obtain:
Figure FDA0003298420020000046
wherein
Figure FDA0003298420020000047
Step 35) of jointly optimizing the subcarrier indication factors
Figure FDA0003298420020000048
Inter-cluster power allocation
Figure FDA0003298420020000049
Power distribution ratio between users in cluster
Figure FDA00032984200200000410
Obtaining an optimization problem aiming at maximizing EC of users in a downlink multi-cell MIMO-NOMA network:
P1:
Figure FDA00032984200200000411
Figure FDA00032984200200000412
Figure FDA00032984200200000413
Figure FDA00032984200200000414
Figure FDA00032984200200000415
Figure FDA00032984200200000416
wherein the content of the first and second substances,
Figure FDA00032984200200000417
is a user
Figure FDA00032984200200000418
Minimum EC requirements of (a);
Figure FDA00032984200200000419
is the maximum transmit power of cell n; defining variables
Figure FDA00032984200200000420
Using variables
Figure FDA00032984200200000421
Replacing variables
Figure FDA00032984200200000422
And
Figure FDA00032984200200000423
a simplified optimization problem P2 is obtained:
P2:
Figure FDA00032984200200000424
Figure FDA0003298420020000051
Figure FDA0003298420020000052
Figure FDA0003298420020000053
Figure FDA0003298420020000054
step 4), channel allocation: under the given condition of power distribution, converting the optimization problem obtained in the step 3) into an equivalent maximum weighted bipartite graph matching problem, and solving by using a Hungarian algorithm to obtain optimal channel distribution;
the specific steps of the step 4) are as follows:
step 41) assuming that the transmission power is evenly distributed to the users, the optimization problem P2 is simplified as follows:
P3:
Figure FDA0003298420020000055
Figure FDA0003298420020000056
Figure FDA0003298420020000057
Figure FDA0003298420020000058
construct weighted bipartite graph F ═ VC×VSE), in which VCAnd VSSet of vertices, V, representing clusters and subcarriers, respectivelyCVertex v in (1)C(n, l) represents Cnl，VSVertex v in (1)S(u) denotes the subcarrier u, E denotes the connection VCAnd VSE (n, l, u) in E represents a connecting vertex vC(n, l) and vertex vS(u) the weight defining the edge e (n, l, u) is
Figure FDA0003298420020000059
A match definition for graph F is a set of pairs of non-adjacent edges, i.e., any two edges in a match cannot share the same vertex, and according to the definition, the optimization problem P3 is transformed into a maximum weighted bipartite graph matching problem, i.e., a match E is found in graph F*So that E*The sum of the weights of the middle edges is maximum, the classical Hungarian algorithm is utilized to directly solve,
step 42), construct weighted bipartite graph F ═ VC×VSE), in which VCSet of vertices, V, representing all clustersSVertex set representing all subcarriers, E represents connection VCAnd VSUsing Hungarian algorithm to solve to obtain a matching E*；
Step 43), judging whether P3 is satisfied (C1), and if not, reconstructing a weighted bipartite graph F '((V)'C×V′SAnd E '), wherein V'CRepresents a set of vertices, V ', of clusters that do not satisfy P3 (C1)'SRepresents a vertex set of unmatched subcarriers, E 'represents a connection V'CAnd V'SThe edge set is solved by using Hungarian algorithm to obtain a matching E'*Repeating step 42) until P3(C1) is satisfied;
step 44), judging whether unmatched subcarriers exist or not, and if the unmatched subcarriers exist, reconstructing a weighted bipartite graph F ″ (V)C×V′SE "), wherein VCSet of vertices, V ', representing all clusters'SVertex set representing unmatched subcarriers, E' representing connection VCAnd V'SThe edge set is solved by using Hungarian algorithm to obtain a matching E ″)*Repeating the step 43) until the sub-carriers are distributed;
step 5), power distribution: under the condition of assuming given channel allocation, converting the optimization problem obtained in the step 3) into an equivalent Lagrange dual problem, and solving by utilizing a sub-gradient algorithm to obtain optimal transmission power allocation;
the specific steps of the step 5) are as follows:
step 51), after the sub-carriers are allocated according to the step 4), the optimization problem P2 is simplified into:
P4:
Figure FDA0003298420020000061
Figure FDA0003298420020000062
Figure FDA0003298420020000063
step 52), obtaining the Lagrangian function of the optimization problem P4 according to the Lagrangian theory as follows:
Figure FDA0003298420020000064
where μ and v are lagrange multiplier vectors introduced according to the optimization problems P4(C1) and P4(C2), respectively,
Figure FDA0003298420020000065
and vnElements in μ and v, respectively, whose dual function is
Figure FDA0003298420020000066
Wherein sup {. is a supremum, and the lagrangian dual problem from which the optimization problem P4 is derived is:
P5:
Figure FDA0003298420020000067
s.t.C1:μ≥0,v≥0
step 53), updating simultaneously with a sub-gradient algorithm
Figure FDA0003298420020000071
And vnTo minimize L (μ, v); l (. mu.v) about variables
Figure FDA0003298420020000072
And vnThe sub-gradients of (a) are:
Figure FDA0003298420020000073
Figure FDA0003298420020000074
Figure FDA0003298420020000075
and vnThe update formulas of (a) are respectively:
Figure FDA0003298420020000076
Figure FDA0003298420020000077
where s is the number of iterations, phi(s)And
Figure FDA00032984200200000714
the update step sizes of mu and v in the s-th iteration process, {. cndot. }+＝max{·,0}；
Step 54), assume
Figure FDA0003298420020000078
Is the optimal solution of the optimization problem P4, and obtains mu by iteration of a sub-gradient algorithm*And v*After-utilization of
Figure FDA0003298420020000079
To pair
Figure FDA00032984200200000710
Is equal to 0 to obtain
Figure FDA00032984200200000711
Step 6), alternately and iteratively optimizing: and alternately iterating the step 4) and the step 5) until the effective capacity of the user tends to converge, so as to obtain the optimal channel allocation and power allocation.
2. The method for allocating resources in a downlink MIMO-NOMA network according to claim 1, wherein: the specific steps of the step 6) are as follows:
step 61) obtaining the optimal channel allocation under the fixed transmitting power according to the step 4);
step 62) obtaining the optimal transmission power distribution under the fixed channel according to the step 5);
step 63) repeats steps 61) and 62) until the effective capacity of the user tends to converge.
3. The method for allocating resources in a downlink MIMO-NOMA network according to claim 2, wherein: the use of a decreasing step update method ensures that convergence is fast:
Figure FDA00032984200200000712
where a, b are constants, phi, with increasing s(s)And
Figure FDA00032984200200000713
gradually decreases.
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