CN111511007A - Power distribution method in multi-cluster NOMA system - Google Patents

Power distribution method in multi-cluster NOMA system Download PDF

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CN111511007A
CN111511007A CN202010234497.9A CN202010234497A CN111511007A CN 111511007 A CN111511007 A CN 111511007A CN 202010234497 A CN202010234497 A CN 202010234497A CN 111511007 A CN111511007 A CN 111511007A
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cluster
power
base station
users
user
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田心记
李晓静
张丹青
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/24—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters
    • H04W52/241—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters taking into account channel quality metrics, e.g. SIR, SNR, CIR, Eb/lo
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/24—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters
    • H04W52/243—TPC being performed according to specific parameters using SIR [Signal to Interference Ratio] or other wireless path parameters taking into account interferences
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/26—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service]
    • H04W52/267—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service] taking into account the information rate
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/30—TPC using constraints in the total amount of available transmission power
    • H04W52/34—TPC management, i.e. sharing limited amount of power among users or channels or data types, e.g. cell loading
    • H04W52/346—TPC management, i.e. sharing limited amount of power among users or channels or data types, e.g. cell loading distributing total power among users or channels

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Abstract

The invention discloses a power distribution method in a multi-cluster NOMA system, which is suitable for a system comprising 1 base station andMKthe downlink NOMA system of each user, and the base station and the users are both configured with a single antenna. The base station calculates the minimum power required by each user and the minimum power required by each cluster according to the channel condition and the minimum rate requirement of each user, establishes a power distribution optimization problem of maximizing the system weight and the rate by taking the total power of the base station and the minimum rate requirement of the user as constraint conditions, firstly solves the power distribution of maximizing the user weight and the rate in a single cluster to obtain the relation between the maximum value of the single cluster weight and the rate and the total power of the cluster, converts the power distribution among the users in the optimization problem into the power distribution among the clusters based on the result, solves the power distribution among the clusters and distributes the power to each user according to the result.

Description

Power distribution method in multi-cluster NOMA system
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a power distribution method in a multi-cluster NOMA system.
Background
With the rapid development of mobile communications, it has been difficult for conventional multiple access techniques to meet the explosive growth of wireless data traffic. Therefore, the fifth generation mobile communication employs a Non-Orthogonal Multiple Access (NOMA) technology with higher system throughput and higher spectral efficiency. Compared with the research of the traditional multiple access technology in time domain, frequency domain and code domain, the NOMA technology introduces a new dimension, namely power domain, distributes different powers for a plurality of users at a base station end, then superposes the signals of the users on the same time-frequency resource, and after receiving the signals, the users adopt the Successive Interference Cancellation (SIC) technology to detect the expected received signals. Power allocation not only relates to the detection order of each user signal, but also affects the reliability and effectiveness of the system, and therefore, power allocation in NOMA is one of the research hotspots in recent years.
Many documents have studied power allocation in single cell downlink NOMA systems, where the targets of power allocation are of three types: maximize sum rate, maximize energy efficiency, and maximize fairness. The maximum fair power allocation scheme uses the total power or the rate of a single user as a constraint condition, and adopts various fairness criteria to derive power allocation which maximizes system fairness. The power allocation scheme that maximizes energy efficiency also derives the power allocated to each user with the goal of maximizing the ratio of the sum rate of users to the total power, with the total power or the rate of individual users as constraints. The document "On-optimal power allocation for downlink non-orthogonal multiple access systems" studies the power allocation scheme for maximizing sum rate in a multi-cluster NOMA system, which however does not take into account the weight of the users and contains only two users per cluster.
Disclosure of Invention
The invention provides a power distribution method in a multi-cluster NOMA system, which is suitable for a downlink NOMA system comprising 1 base station and MK users, wherein the base station and the users are both provided with a single antenna.
The technical idea for realizing the invention is as follows: the base station calculates the minimum power required by each user and the minimum power required by each cluster according to the channel condition and the minimum rate requirement of each user, establishes a power distribution optimization problem of maximizing the system weight and the rate by taking the total power of the base station and the minimum rate requirement of the user as constraint conditions, firstly solves the power distribution of maximizing the user weight and the rate in a single cluster to obtain the relation between the maximum value of the single cluster weight and the rate and the total power of the cluster, converts the power distribution among the users in the optimization problem into the power distribution among the clusters based on the result, solves the power distribution among the clusters and distributes the power to each user according to the result.
In summary, the power allocation method in the multi-cluster NOMA systems is applicable to a downlink NOMA system including 1 base station and MK users, and the base station and the users are both configured with a single antenna, and includes the following steps:
a, a base station clusters users according to channels from the base station to MK users, each cluster comprises M users, the M users are divided into K clusters, and u is usedkmDenotes the mth user in the kth cluster, K1, 2, …, K, M1, 2, …, M, base station to ukmIs hkm，|hk1|2≤|hk2|2≤…≤|hkM|2The base station allocates a sub-band for each cluster, and the sub-bands among the clusters are orthogonal;
b, the base station calculates the minimum power required by a single user and the minimum power required by a single cluster;
c, the base station establishes a power distribution optimization problem for maximizing the system weight and the rate, and decomposes the optimization problem into a plurality of power distribution optimization sub-problems for maximizing the user weight and the rate in a single cluster;
d, the base station solves the optimization sub-problem in the step C, and converts the power distribution among users in the power distribution optimization problem into inter-cluster power distribution according to the result;
and E, the base station firstly solves the optimization problem in the step D to obtain the total power distributed to each cluster, and then distributes power to each user.
Further, the step B specifically includes the steps of:
b1, base station u is pkmkmAllocated power, pk1≥pk2≥…≥pkM，
Figure BDA0002429899740000021
pkIs the total power allocated by the base station for the kth cluster, using r0To representThe lowest unit bandwidth rate requirement of a single user is calculated by the base station to obtain pkmIs taken to satisfy
Figure BDA0002429899740000022
Wherein the content of the first and second substances,
Figure BDA0002429899740000023
c is the minimum requirement for SINR when the minimum unit bandwidth rate requirement of the user is met, sigma2Is the variance of the noise received by the user, and therefore ukmThe minimum power required is
Figure BDA0002429899740000024
K1, 2, …, K, M1, 2, M, K being the total number of clusters, M being the total number of users in each cluster;
b2, the base station obtains p according to the step B1kmSatisfied condition and
Figure BDA0002429899740000025
calculating to obtain the lowest power p required by the kth clusterk0，
Figure BDA0002429899740000026
K1, 2, …, K, M1, 2, M, K being the total number of clusters and M being the total number of users in each cluster.
Further, the step C specifically includes the steps of:
c1, setting the total power of the base station
Figure BDA0002429899740000031
The lowest unit bandwidth rate requirement of all users is taken as a constraint condition, a power distribution optimization problem of maximizing the system weight and the rate is established,
Figure BDA0002429899740000032
Figure BDA0002429899740000033
Figure BDA0002429899740000034
wherein, wkmIs ukmThe weight of (a) is determined,
Figure BDA0002429899740000035
represents ukmPer unit bandwidth rate of r0Represents ukmMinimum required rate per unit bandwidth, constraint Rkm≥r0Represents ukmHas a unit bandwidth rate of not less than r0Constraint conditions
Figure BDA0002429899740000036
Representing the total power of the base station as PmaxConstraint conditions
Figure BDA0002429899740000037
To ensure proper performance of SIC, K1, 2, …, K, M1, 2, M, K is the total number of clusters, M is the total number of users in each cluster;
c2, decomposing the optimization problem in the step C1 into K optimization sub-problems, and establishing the total power p of the kth clusterkA power allocation optimization sub-problem that maximizes the cluster user weights and rates,
Figure BDA0002429899740000038
Figure BDA0002429899740000039
Figure BDA00024298997400000310
wherein, wkmIs ukmThe weight of (a) is determined,
Figure BDA0002429899740000041
represents ukmPer unit bandwidth rate of r0To representukmMinimum required rate per unit bandwidth, constraint Rkm≥r0Represents ukmHas a unit bandwidth rate of not less than r0Constraint conditions
Figure BDA0002429899740000042
Denotes the total power of the cluster as pkConstraint conditions
Figure BDA0002429899740000043
To ensure proper performance of SIC, K1, 2, …, K, M1, 2, M, K is the total number of clusters, M is the total number of users in each cluster;
c3, defining variables
Figure BDA0002429899740000044
And q isk(M+1)0, M1, 2, M, then pkmThe relationship with this variable can be expressed as pkm＝qkm-qk(m+1)，ukmPer unit bandwidth rate RkmThe relationship with the variable can be expressed as
Figure BDA0002429899740000045
The optimization sub-problem in step C2 is equivalently expressed as,
Figure BDA0002429899740000046
Figure BDA0002429899740000047
Figure BDA0002429899740000048
wherein, βkm＝cαkm，fk1(qk1)＝wk1log2(αk1+qk1)-wkMlog2(αkM) Constraint conditions
Figure BDA0002429899740000049
Denotes the total power of the kth cluster as qk1Constraint conditions
Figure BDA00024298997400000410
Indicates that u is satisfiedkmQ at the lowest unit bandwidth rate requirementkmA condition to be satisfied, the condition consisting of
Figure BDA00024298997400000411
As derived, K is 1,2, …, K, M is 1,2, …, M, K is the total number of clusters, and M is the total number of users in each cluster.
Further, the step D specifically includes the steps of:
d1, the base station solves the optimization sub-problem in the step C3 to obtain the total power q of the kth clusterk1The power allocation that maximizes the cluster user weights and rates,
Figure BDA00024298997400000412
wherein the content of the first and second substances,
Figure BDA0002429899740000051
Figure BDA0002429899740000052
Figure BDA0002429899740000053
k1., K, M2., M, K is the total number of clusters, M is the total number of users in each cluster;
d2, according to the step D1, simplifying the optimization problem in the step C1 if wkm≥wk(m-1)And a is1B is less than or equal to infinity, the optimization problem in the step C1 is simplified into,
Figure BDA0002429899740000054
Figure BDA0002429899740000055
if wkm＜wk(m-1)And a is2≤b＜a1The optimization problem in step C1 is simplified to,
Figure BDA0002429899740000056
Figure BDA0002429899740000057
if wkm＜wk(m-1)And b is more than or equal to 0 and less than a2The optimization problem in step C1 is simplified to,
Figure BDA0002429899740000061
Figure BDA0002429899740000062
wherein the content of the first and second substances,
Figure BDA0002429899740000063
constraint conditions under three conditions of the step
Figure BDA0002429899740000064
All represent the total power of the base station as PmaxConstraint q in three cases of this stepk1≥pk0All represent the total power q of a single cluster when the cluster meets the user's lowest unit bandwidth rate requirement in that clusterk1The conditions to be satisfied are K1, 2, …, K, M2, …, M, K being the total number of clusters and M being the total number of users in each cluster.
Further, the step E specifically includes the steps of:
e1, the base station solves the optimization problem in the step D2, when the obtained system weight and the rate are maximum, the total power of the kth cluster is,
Figure BDA0002429899740000065
wherein, λ is Lagrange multiplier, and the value of λ satisfies
Figure BDA0002429899740000066
If w iskm≥wk(m-1)、a1B is less than infinity
Figure BDA0002429899740000067
Then
Figure BDA0002429899740000068
Otherwise
Figure BDA0002429899740000069
If w iskm＜wk(m-1)、a2≤b＜a1And is
Figure BDA00024298997400000610
Then
Figure BDA00024298997400000611
Otherwise
Figure BDA00024298997400000612
If w iskm＜wk(m-1)、0≤b＜a2And y- αk1≥pk0Then, then
Figure BDA00024298997400000613
Otherwise
Figure BDA00024298997400000614
Figure BDA00024298997400000615
a＝-λln2，
Figure BDA0002429899740000071
Figure BDA0002429899740000072
d＝wk1Λk1Λk2，
Figure BDA0002429899740000073
Figure BDA0002429899740000074
E2, determined according to step E1
Figure BDA0002429899740000075
Is allocated power for the user if wkm≥wk(m-1)And a is1≤b＜∞，ukmHas a power of
Figure BDA0002429899740000076
uk1Has a power of
Figure BDA0002429899740000077
If wkm＜wk(m-1)And a is2≤b＜a1，ukmHas a power of
Figure BDA0002429899740000078
uk1Has a power of
Figure BDA0002429899740000079
If wkm＜wk(m-1)And b is more than or equal to 0 and less than a2，ukmHas a power of
Figure BDA00024298997400000710
uk1Has a power of
Figure BDA00024298997400000711
Where K in this step is 1,2, …, K, M is 2, …, M, K being the total number of clusters, M being the total number of users in each cluster.
Has the advantages that:
the invention extends the power allocation scheme of maximum sum rate in NOMA system to the scene that each cluster contains a plurality of users, also considers the weight and the lowest rate requirement of each user, and under the condition of meeting the lowest rate requirement of all users, the system weight and the rate under different weights are maximized, which is more applicable than the existing scheme.
Drawings
FIG. 1 is a system model of an embodiment of the invention;
fig. 2 is a flow chart of the present invention.
Detailed Description
An embodiment of the present invention is given below, and the present invention will be explained in further detail:
as shown in fig. 1, in the power allocation method in the multi-cluster NOMA system, a single-cell downlink NOMA system including 1 base station and MK users is considered, and both the base station and the users are configured with a single antenna. The users are divided into K clusters, each cluster containing M users, ukmDenotes the mth user in the kth cluster, K being 1,2, …, K, M being 1,2, …, M. Base station to ukmIs hkm，|hk1|2≤|hk2|2≤…≤|hkM|2. The base station allocates the total power p for the kth clusterkWherein u iskmHas a power of pkm，pk1≥pk2≥…≥pkM，
Figure BDA0002429899740000081
The base station allocates a sub-band for each cluster, and the sub-bands among the clusters are orthogonal.
By ykmRepresents ukmOf the received signal, ykmIs expressed in the form of
Figure BDA0002429899740000082
Wherein x iskmIs ukmDesired received signal of nkmIs ukmReceived white Gaussian noise with mean value of zero and variance of sigma2。
According to the principles of SIC technology, user ukmIn decoding the desired received signal x itselfkmIn the former, weak users u are decoded in turnki(i<m) desired received signal xkiAnd from ykmMiddle warmer (Xiao)Except for xkiThe resulting interference.
ukmDetecting xkiThe Signal to Interference and Noise Ratio (SINR) is expressed as
Figure BDA0002429899740000083
Suppose a0Is ukmCorrect detection of xkiMinimum requirement for SINR, u in order to perform SICkmDetecting xkiThe SINR must not be less than a0. Therefore, the following equation is required to be satisfied
Figure BDA0002429899740000084
Is derived from formula (3) uki(i<m) power pkiHas a value range satisfying
Figure BDA0002429899740000085
After correct SIC, ukmSubject to strong user u onlykjDesired received signal xkjj-M + 1. Therefore, ukmPer unit bandwidth rate RkmIs expressed in the form of
Figure BDA0002429899740000086
The sum of the unit bandwidth rates of all users in the kth cluster is
Figure BDA0002429899740000087
The sum of the unit bandwidth rates of MK users in the system is
Figure BDA0002429899740000091
By r0Represents ukmThe minimum required unit bandwidth rate, where K is 1,2, …, K, M is 1,2, …, M. By P0Represents the minimum total power, P, required to meet the minimum rate requirements of all usersmaxRepresenting the total power of the base station. Pmax≥P0And in time, the total power of the base station can meet the requirement of the lowest unit bandwidth rate of all users. The proposed solution aims at: under the condition of meeting the minimum unit bandwidth rate requirement of each user and ensuring SIC, the weight and the rate of the system are maximized by distributing proper power.
According to the above, Pmax≥P0The target of the power allocation is formulated as
Figure BDA0002429899740000092
Wherein, wkmIs ukmWeight of r0Represents ukmMinimum required unit bandwidth rate, constraint
Figure BDA0002429899740000093
Representing the total power of the base station as PmaxConstraint Rkm≥r0Represents ukmHas a unit bandwidth rate of not less than r0Constraint conditions
Figure BDA0002429899740000094
To ensure proper execution of the SIC.
The minimum power required for each cluster is first derived. When M is M, derived from C2 in formula (5) and formula (8), pkMHas a value range of
pkM≥cαkM(9)
Wherein the content of the first and second substances,
Figure BDA0002429899740000095
m＝1,2,...,M，
Figure BDA0002429899740000096
c is the SINR when the lowest unit bandwidth rate requirement of the user is metThe minimum requirement of (2). When M is M-1, pk(M-1)Has a value range of
pk(M-1)≥c(pkM+αk(M-1))＝c[cαkM+αk(M-1)](10)
When M is M-2, pk(M-2)Has a value range of
pk(M-2)≥c(pkM+pk(M-1)+αk(M-2))＝c[c(1+c)αkM+cαk(M-1)+αk(M-2)](11)
When M is M-3, pk(M-3)Has a value range of
Figure BDA0002429899740000101
When M is M-4, pk(M-4)Has a value range of
Figure BDA0002429899740000102
Obtained by induction method, pkmSatisfies the following formula
Figure BDA0002429899740000103
Due to a0Is ukmCorrect decoding of xkiMinimum requirement for SINR, so a0C may be sufficient. When C2 in the immediate expression (8) of the expression (14) is satisfied, C3 in the expression (8) is necessarily satisfied. By pkm0Indicates that u is satisfiedkmU is the lowest unit bandwidth rate requirementkmMinimum power required, pkm0Is taken as
Figure BDA0002429899740000104
By pk0Represents the minimum power required for the k-th cluster, pk0Is composed of
Figure BDA0002429899740000105
Considering that each cluster has the lowest power requirement, the lowest total power required to satisfy the lowest unit bandwidth rate requirement of all users is
Figure BDA0002429899740000106
The documents "On-optimal power allocation for downlink non-orthogonal multiple access systems" and "Dynamic power allocation for downlink multi-carrier NOMA systems" both study power allocation schemes in NOMA systems with multiple clusters each containing two users, and both derive the relation between the sum rate of a single cluster and the total power of the cluster and then perform inter-cluster power allocation. Therefore, the optimization problem in equation (8) is converted into a plurality of sub-problems by methods similar to those of the two documents, and the total power p of the kth cluster is solvedkAnd then, maximizing the power distribution of the weight and the speed of the cluster user, and the weight and the speed of the cluster user at the moment, then simplifying the formula (8) into an inter-cluster power distribution optimization problem of maximizing the system weight and the speed, solving the problem, and finally distributing power for a single user according to the result of the inter-cluster power distribution.
Total power of kth cluster is pkThe power allocation equation that maximizes the cluster user weight and rate is expressed as
Figure BDA0002429899740000111
Wherein the constraint condition
Figure BDA0002429899740000112
Denotes the total power of the cluster as pkConstraint Rkm≥r0Represents ukmHas a unit bandwidth rate of not less than r0Constraint conditions
Figure BDA0002429899740000113
To ensure proper execution of the SIC.
For a single cluster NOMA system involving arbitrary users, the document "a novel low-level power allocation algorithm for downlink NOMA networks" gives a power allocation scheme that maximizes weight and rate. The conclusions in this document can be directly quoted when deriving the relationship between maximum weight and rate within a single cluster and the total power of that cluster. To this end, the optimization problem in equation (18) is transformed into a form similar to equation (8) in this document. Therefore defining a variable
Figure BDA0002429899740000114
And q isk(M+1)0, M1, 2, M, then pkmThe relationship with this variable can be expressed as pkm＝qkm-qk(m+1)Total power p of kth clusterkThe relationship with this variable can be expressed as pk＝qk1，ukmPer unit bandwidth rate RkmThe relationship with the variable can be expressed as
Figure BDA0002429899740000115
Therefore, the formula (18) can be equivalently expressed as
Figure BDA0002429899740000116
Wherein, βkm＝cαkm，fk1(qk1)＝wk1log2(αk1+qk1)-wkMlog2(αkM)，
fkm(qkm)＝wkmlog2(αkm+qkm)-wk(m-1)log2(αk(m-1)+qkm) (20)
Where M in the formula (20) is 2, …, M, the constraint
Figure BDA0002429899740000117
Denotes the total power of the kth cluster as qk1Constraint conditions
Figure BDA0002429899740000118
Indicates that u is satisfiedkmQ at the lowest unit bandwidth rate requirementkmA condition to be satisfied, the condition consisting of
Figure BDA0002429899740000119
Derived by derivation.
According to this document, in wkm≥wk(m-1)And wkm＜wk(m-1)When the weight and the rate of the user in the cluster are maximum qkmIs taken as
Figure BDA0002429899740000121
Wherein M is 2., M,
Figure BDA0002429899740000122
Figure BDA0002429899740000123
the total power of the kth cluster is q according to the derivationk1The power allocation that maximizes the cluster user weight and rate is
Figure BDA0002429899740000124
Wherein q iskmIs represented by the formula (21).
It is deduced so far that the total power of the kth cluster is qk1Then, the power allocation of the cluster user weight and rate is maximized, and the inter-cluster power allocation of the system weight and rate is maximized in the three cases shown in equation (21).
Case1:wkm≥wk(m-1),a1≤b＜∞
When q iskm＝qkmminWhen is, pkm＝qkm-qk(m+1)＝pkm0M2, M, the power allocation being such that u in the kth cluster isk1，uk2，…，uk(M-1)Just reaching their minimum unit bandwidth rate requirements and then will remainAll the residual power is allocated to ukM. At this time, the weights and rates of all users in the cluster are
Figure BDA0002429899740000125
In this case, the formula (8) can be simplified to
Figure BDA0002429899740000126
Wherein the content of the first and second substances,
Figure BDA0002429899740000127
constraint conditions
Figure BDA0002429899740000128
Representing the total power of the base station as PmaxConstraint qk1≥pk0Representing the total power q of a single cluster at which the cluster meets the user's lowest unit bandwidth rate requirementk1The conditions to be met are required.
A Lagrangian function G1 (q) is constructed according to equation (23)k1,k＝1,2,…K,λ)，
Figure BDA0002429899740000131
Where λ is the lagrange multiplier. Separately, G1 (q)k1K1, 2, … K, λ) with respect to qk1And the partial derivative of λ and making it equal to zero, the following system of equations is obtained
Figure BDA0002429899740000132
The optimum cluster power is obtained from equation (25)
Figure BDA0002429899740000133
Is taken as
Figure BDA0002429899740000134
Wherein the value of λ satisfies
Figure BDA0002429899740000135
In the formula (26), if
Figure BDA0002429899740000136
Then
Figure BDA0002429899740000137
Otherwise
Figure BDA0002429899740000138
pk0Indicating the lowest power required for the kth cluster.
In formula (26)
Figure BDA0002429899740000139
Is the optimal solution of equation (23). The power allocation that maximizes the system weight and rate at this time is: p is a radical ofkm＝pkm0，m＝2,...,M，
Figure BDA00024298997400001310
Case2：wkm＜wk(m-1),a2≤b＜a1
Q under the condition of C4 in formula (21)kmAnd the optimization problem (19) can be found to be the weight and rate of the cluster wk1log2(αk1+qk1)-wkMlog2(αkM) + U (k), wherein,
Figure BDA00024298997400001311
thus, the formula (8) can be converted into
Figure BDA00024298997400001312
Wherein the constraint condition
Figure BDA00024298997400001313
Representing the total power of the base station as PmaxAboutBundle condition qk1≥pk0Representing the total power q of a single cluster at which the cluster meets the user's lowest unit bandwidth rate requirementk1The conditions to be met are required.
A Lagrangian function G2 (q) is constructed according to equation (28)k1,k＝1,2,…K,λ)，
Figure BDA00024298997400001314
Where λ is the lagrange multiplier. Separately, G2 (q)k1K1, 2, … K, λ) with respect to qk1And the partial derivative of λ and making it equal to zero, the following system of equations is obtained
Figure BDA0002429899740000141
The optimum cluster power is obtained from equation (30)
Figure BDA0002429899740000142
Is taken as
Figure BDA0002429899740000143
Wherein the value of λ satisfies
Figure BDA0002429899740000144
In the formula (31), if
Figure BDA0002429899740000145
Then
Figure BDA0002429899740000146
Otherwise
Figure BDA0002429899740000147
pk0Indicating the lowest power required for the kth cluster.
In formula (31)
Figure BDA0002429899740000148
Is of the formula (28)And (5) optimal solution. Q under the condition of C4 in formula (21)kmAnd in formula (31)
Figure BDA0002429899740000149
By substituting equation (22), the power allocated to each user in this case to maximize the system weight and rate can be obtained.
Case3:wkm＜wk(m-1),0≤b＜a2
By
Figure BDA00024298997400001410
When m is 2, q isk2Is taken as
Figure BDA00024298997400001411
When m is 3, qk3Is taken as
Figure BDA00024298997400001412
When m is 4, qk4Is taken as
Figure BDA00024298997400001413
When m is 5, qk5Is taken as
Figure BDA00024298997400001414
Obtained by the induction method, qkmIs taken as
Figure BDA00024298997400001415
Q in formula (36)kmIs substituted for f in formula (20)km(qkm) Can obtain the product
Figure BDA00024298997400001416
Wherein M is 2., M,
Figure BDA0002429899740000151
the cluster user weight and rate can be obtained from equation (37) as
Figure BDA0002429899740000152
Thus, the formula (8) can be converted into
Figure BDA0002429899740000153
Wherein the constraint condition
Figure BDA0002429899740000154
Representing the total power of the base station as PmaxConstraint qk1≥pk0Representing the total power q of a single cluster at which the cluster meets the user's lowest unit bandwidth rate requirementk1The conditions to be met are required.
A Lagrangian function G3 (q) is constructed according to equation (38)k1,k＝1,2,…K,λ)，
Figure BDA0002429899740000155
Where λ is the lagrange multiplier. Separately, G3 (q)k1K1, 2, … K, λ) with respect to qk1And the partial derivative of λ and making it equal to zero, the following system of equations is obtained
Figure BDA0002429899740000156
To pair
Figure BDA0002429899740000157
Simple and easy to obtain
Figure BDA0002429899740000158
Wherein, y is αk1+qk1，
Figure BDA0002429899740000159
Figure BDA00024298997400001510
By converting formula (41) to the standard one-dimensional cubic equation
ay3+by2+cy+d＝0 (42)
Wherein a ═ λ ln2,
Figure BDA0002429899740000161
Figure BDA0002429899740000162
d＝wk1Λk1Λk2。
order to
Figure BDA0002429899740000163
Then equation (42) may be converted to
z3+pz+q＝0 (43)
Wherein the content of the first and second substances,
Figure BDA0002429899740000164
according to the Kadan equation, the solution of equation (43) is
Figure BDA0002429899740000165
So that the value of y can be obtained as,
Figure BDA0002429899740000166
by y- αk1+qk1Available, optimal cluster power
Figure BDA0002429899740000167
Is taken as
Figure BDA0002429899740000168
Wherein the value of λ satisfies
Figure BDA0002429899740000169
In formula (45), if y- αk1≥pk0Then, then
Figure BDA00024298997400001610
Otherwise
Figure BDA00024298997400001611
pk0Indicating the lowest power required for the kth cluster.
In formula (45)
Figure BDA00024298997400001612
Is the optimal solution for equation (38). Q under the condition of C5 in formula (21)kmAnd in formula (45)
Figure BDA00024298997400001613
The power per user at which the system weight and rate are maximized in this case can be obtained by substitution in equation (22).
With reference to the flowchart of the present invention, i.e. fig. 2, the specific steps of the power allocation method for maximizing weight and rate in a multi-cluster NOMA system are as follows:
a, a base station clusters users according to channels from the base station to MK users, each cluster comprises M users, the M users are divided into K clusters, and u is usedkmDenotes the mth user in the kth cluster, K1, 2, …, K, M1, 2, …, M, base station to ukmIs hkm，|hk1|2≤|hk2|2≤…≤|hkM|2The base station allocates a sub-band for each cluster, and the sub-bands among the clusters are orthogonal;
b, the base station calculates the minimum power required by a single user and the minimum power required by a single cluster;
c, the base station establishes a power distribution optimization problem for maximizing the system weight and the rate, and decomposes the optimization problem into a plurality of power distribution optimization sub-problems for maximizing the user weight and the rate in a single cluster;
d, the base station solves the optimization sub-problem in the step C, and converts the power distribution among users in the power distribution optimization problem into power distribution among clusters according to the result;
and E, the base station firstly solves the optimization problem in the step D to obtain the total power distributed to each cluster, and then distributes power to each user.
The above embodiments are merely illustrative of the present invention, and those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (5)

1. A power distribution method in a multi-cluster NOMA system is suitable for a downlink NOMA system comprising 1 base station and MK users, and the base station and the users are both provided with a single antenna, and the method is characterized in that: the method comprises the following steps:
a, a base station clusters users according to channels from the base station to MK users, each cluster comprises M users, the M users are divided into K clusters, and u is usedkmDenotes the mth user in the kth cluster, K1, 2, …, K, M1, 2, …, M, base station to ukmIs hkm，|hk1|2≤|hk2|2≤…≤|hkM|2The base station allocates a sub-band for each cluster, and the sub-bands among the clusters are orthogonal;
a, a base station clusters users according to channels from the base station to MK users, each cluster comprises M users, the M users are divided into K clusters, and u is usedkmDenotes the mth user in the kth cluster, K1, 2, …, K, M1, 2, …, M, base station to ukmIs hkm，|hk1|2≤|hk2|2≤…≤|hkM|2The base station allocates a sub-band for each cluster, and the sub-bands among the clusters are orthogonal;
b, the base station calculates the minimum power required by a single user and the minimum power required by a single cluster;
c, the base station establishes a power distribution optimization problem for maximizing the system weight and the rate, and decomposes the optimization problem into a plurality of power distribution optimization sub-problems for maximizing the user weight and the rate in a single cluster;
d, the base station solves the optimization sub-problem in the step C, and converts the power distribution among users in the power distribution optimization problem into inter-cluster power distribution according to the result;
and E, the base station firstly solves the optimization problem in the step D to obtain the total power distributed to each cluster, and then distributes power to each user.
2. The method of power allocation in a multi-cluster NOMA system as in claim 1, wherein said step B comprises the steps of:
b1, with pkmIndicating a base station as ukmAllocated power, pk1≥pk2≥…≥pkM，
Figure FDA0002429899730000011
pkIs the total power allocated by the base station for the kth cluster, using r0Representing the lowest unit bandwidth rate requirement of a single user, and the base station calculates pkmIs taken to satisfy
Figure FDA0002429899730000012
Wherein the content of the first and second substances,
Figure FDA0002429899730000013
Figure FDA0002429899730000015
c is the minimum requirement for SINR when the minimum unit bandwidth rate requirement of the user is met, sigma2Is the variance of the noise received by the user, and therefore ukmThe minimum power required is
Figure FDA0002429899730000014
K1, 2, …, K, M1, 2Number, M is the total number of users in each cluster;
b2, the base station obtains p according to the step B1kmSatisfied condition and
Figure FDA0002429899730000021
calculating to obtain the lowest power p required by the kth clusterk0，
Figure FDA0002429899730000022
K1, 2, …, K, M1, 2, M, K being the total number of clusters and M being the total number of users in each cluster.
3. The method of power allocation in a multi-cluster NOMA system as in claim 1, wherein said step C comprises the steps of:
c1, setting the total power of the base station
Figure FDA0002429899730000023
The lowest unit bandwidth rate requirement of all users is taken as a constraint condition, a power distribution optimization problem of maximizing the system weight and the rate is established,
Figure FDA0002429899730000024
Figure FDA0002429899730000025
Figure FDA0002429899730000026
wherein, wkmIs ukmThe weight of (a) is determined,
Figure FDA0002429899730000027
represents ukmPer unit bandwidth rate of r0Represents ukmMinimum required rate per unit bandwidth, constraint Rkm≥r0Represents ukmHas a unit bandwidth rate of not less than r0Constraint conditions
Figure FDA0002429899730000028
Representing the total power of the base station as PmaxConstraint conditions
Figure FDA0002429899730000029
To ensure proper performance of SIC, K1, 2, …, K, M1, 2, M, K is the total number of clusters, M is the total number of users in each cluster;
c2, decomposing the optimization problem in the step C1 into K optimization sub-problems, and establishing the total power p of the kth clusterkA power allocation optimization sub-problem that maximizes the cluster user weights and rates,
Figure FDA0002429899730000031
Figure FDA0002429899730000032
Figure FDA0002429899730000033
wherein, wkmIs ukmThe weight of (a) is determined,
Figure FDA0002429899730000034
represents ukmPer unit bandwidth rate of r0Represents ukmMinimum required rate per unit bandwidth, constraint Rkm≥r0Represents ukmHas a unit bandwidth rate of not less than r0Constraint conditions
Figure FDA0002429899730000035
Denotes the total power of the cluster as pkConstraint conditions
Figure FDA0002429899730000036
To ensure proper performance of SIC, K1, 2, …, K, M1, 2, M, K is the total number of clusters, M is the total number of users in each cluster;
c3, defining variables
Figure FDA0002429899730000037
And q isk(M+1)0, M1, 2, M, then pkmThe relationship with this variable can be expressed as pkm＝qkm-qk(m+1)，ukmPer unit bandwidth rate RkmThe relationship with the variable can be expressed as
Figure FDA0002429899730000038
The optimization sub-problem in step C2 is equivalently expressed as,
Figure FDA0002429899730000039
Figure FDA00024298997300000310
Figure FDA00024298997300000311
wherein, βkm＝cαkm，fk1(qk1)＝wk1log2(αk1+qk1)-wkMlog2(αkM) Constraint conditions
Figure FDA00024298997300000312
Denotes the total power of the kth cluster as qk1Constraint conditions
Figure FDA00024298997300000313
Indicates that u is satisfiedkmQ at the lowest unit bandwidth rate requirementkmA condition to be satisfied, the condition consisting of
Figure FDA00024298997300000314
As derived, K is 1,2, …, K, M is 1,2, …, M, K is the total number of clusters, and M is the total number of users in each cluster.
4. The method of power allocation in a multi-cluster NOMA system as in claim 1, wherein said step D comprises the steps of:
d1, the base station solves the optimization sub-problem in the step C3 to obtain the total power q of the kth clusterk1The power allocation that maximizes the cluster user weights and rates,
Figure FDA0002429899730000041
wherein the content of the first and second substances,
Figure FDA0002429899730000042
Figure FDA0002429899730000043
k1., K, M2., M, K is the total number of clusters, M is the total number of users in each cluster;
d2, according to the step D1, simplifying the optimization problem in the step C1 if wkm≥wk(m-1)And a is1B is less than or equal to infinity, the optimization problem in the step C1 is simplified into,
Figure FDA0002429899730000044
Figure FDA0002429899730000045
if wkm＜wk(m-1)And a is2≤b＜a1The optimization problem in step C1 is simplified to,
Figure FDA0002429899730000046
Figure FDA0002429899730000047
if wkm＜wk(m-1)And b is more than or equal to 0 and less than a2The optimization problem in step C1 is simplified to,
Figure FDA0002429899730000051
Figure FDA0002429899730000052
wherein the content of the first and second substances,
Figure FDA0002429899730000053
constraint conditions under three conditions of the step
Figure FDA0002429899730000054
All represent the total power of the base station as PmaxConstraint q in three cases of this stepk1≥pk0All represent the total power q of a single cluster when the cluster meets the user's lowest unit bandwidth rate requirement in that clusterk1The conditions to be satisfied are K1, 2, …, K, M2, …, M, K being the total number of clusters and M being the total number of users in each cluster.
5. The method of power allocation in a multi-cluster NOMA system as claimed in claim 1, wherein said step E comprises the steps of:
e1, the base station solves the optimization problem in the step D2, when the obtained system weight and the rate are maximum, the total power of the kth cluster is,
Figure FDA0002429899730000055
wherein the content of the first and second substances,λ is Lagrange multiplier, and the value of λ satisfies
Figure FDA0002429899730000056
If w iskm≥wk(m-1)、a1B is less than infinity
Figure FDA0002429899730000057
Then
Figure FDA0002429899730000058
Otherwise
Figure FDA0002429899730000059
If w iskm＜wk(m-1)、a2≤b＜a1And is
Figure FDA00024298997300000510
Then
Figure FDA00024298997300000511
Otherwise
Figure FDA00024298997300000512
If w iskm＜wk(m-1)、0≤b＜a2And y- αk1≥pk0Then, then
Figure FDA0002429899730000061
Otherwise
Figure FDA0002429899730000062
Figure FDA0002429899730000063
a＝-λln2，
Figure FDA0002429899730000064
Figure FDA0002429899730000065
d＝wk1Λk1Λk2，
Figure FDA0002429899730000066
E2, determined according to step E1
Figure FDA0002429899730000067
Is allocated power for the user if wkm≥wk(m-1)And a is1≤b＜∞，ukmHas a power of
Figure FDA0002429899730000068
uk1Has a power of
Figure FDA0002429899730000069
If wkm＜wk(m-1)And a is2≤b＜a1，ukmHas a power of
Figure FDA00024298997300000610
uk1Has a power of
Figure FDA00024298997300000611
If wkm＜wk(m-1)And b is more than or equal to 0 and less than a2，ukmHas a power of
Figure FDA00024298997300000612
uk1Has a power of
Figure FDA00024298997300000613
Where K in this step is 1,2, …, K, M is 2, …, M, K being the total number of clusters, M being the total number of users in each cluster.
CN202010234497.9A 2020-03-28 2020-03-28 Power distribution method in multi-cluster NOMA system Withdrawn CN111511007A (en)

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CN112261713A (en) * 2020-10-22 2021-01-22 岭南师范学院 Multi-input single-output NOMA system power distribution method based on matched filtering precoding

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112261713A (en) * 2020-10-22 2021-01-22 岭南师范学院 Multi-input single-output NOMA system power distribution method based on matched filtering precoding
CN112261713B (en) * 2020-10-22 2022-05-17 岭南师范学院 Multi-input single-output NOMA system power distribution method based on matched filtering precoding

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