CN109451571B - Joint resource allocation method in NOMA relay system - Google Patents

Joint resource allocation method in NOMA relay system Download PDF

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CN109451571B
CN109451571B CN201811213118.7A CN201811213118A CN109451571B CN 109451571 B CN109451571 B CN 109451571B CN 201811213118 A CN201811213118 A CN 201811213118A CN 109451571 B CN109451571 B CN 109451571B
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power allocation
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CN109451571A (en
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朱琦
梁广俊
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Nanjing University of Posts and Telecommunications
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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
    • H04W52/30—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
    • 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
    • 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
    • H04W52/38—TPC being performed in particular situations
    • H04W52/46—TPC being performed in particular situations in multi hop networks, e.g. wireless relay networks

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Abstract

The invention discloses a joint resource allocation method in a NOMA relay system, which aims at maximizing the average user transmission rate, constructs an optimization model of joint user channel assignment and power allocation, then proves that the optimization problem is NP-hard problem, and adopts a decoupling method to decompose the original problem into two sub-problems: on the basis of respectively solving the two sub-problems, an iterative-based joint resource optimization algorithm is further provided. In order to access users as much as possible on the premise of meeting the requirement of the lowest transmission rate, the invention introduces the NOMA technology into the relay system, so that a plurality of users can be accessed to one channel of the relay station, and particularly, when the number of the users is always larger than that of the channels of the relay station and the base station, the satisfaction degree of the users can be improved.

Description

Joint resource allocation method in NOMA relay system
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a game theory-based NOMA relay system joint resource allocation method.
Background
With the demand of rapid development of future cellular networks, the next generation mobile communication services are urgently needed to provide smaller time delay and greater connectivity under limited spectrum resources. The conventional ofdma technology is difficult to cope with the explosive growth of mobile terminals and data services, and therefore, a new ofdma technology is urgently needed to meet the requirements of low delay and higher spectrum efficiency of future wireless communication networks. In recent years, the non-orthogonal multiple access technology provides a feasible scheme to improve the performance of a wireless communication network with limited frequency spectrum, compared with OFDMA, NOMA can accommodate multiple users simultaneously on the same frequency spectrum by using the difference of different terminals and adopting a power domain multiplexing or coding domain multiplexing scheme.
Unlike OFDMA systems, NOMA systems allow multiple users to occupy the same spectral resources to achieve multiplexing gain, but also inevitably cause interference among multiple users. In recent years, some scholars combine NOMA with relay technology to generate some representative heuristic articles, however, most of the attempts aim at the performance analysis of the multi-user NOMA relay system, and few articles study the resource allocation problem of the NOMA relay system. In the resource allocation algorithm of the existing NOMA relay system, the continuous interference elimination technology is applied more commonly, the signals received and decoded at the user terminal can reduce the inter-channel interference, the average throughput is maximized as an optimization target, a combined power allocation and user assignment optimization problem is provided, and a decoupling method is used for solving to obtain a suboptimal solution with low complexity.
Consider the optimization problem of a NOMA-based multi-user relay system in a multi-user and scarce spectrum resource scenario. Especially in cooperative cellular networks, the number of users is always larger than the number of channels of relays and base stations, which results in poor user satisfaction. By introducing the NOMA technology into the relay network, partial users are allowed to share the limited channel resources of the relay, and when the users share the same channel resources, the SIC technology is adopted to eliminate the interference among the users. With the goal of maximizing the average user rate, a joint user channel assignment and power allocation optimization problem is proposed. The joint resource allocation problem is non-convex and needs to be converted into a convex form, however, the converted convex problem is an NP-hard problem and needs an exhaustive search algorithm to be obtained, but the algorithm cannot be obtained in a short time and cannot be used for practice.
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 joint resource allocation method in the NOMA relay system, which takes the total power limit of the whole system and the service quality requirement of users into consideration and takes the maximization of the average user rate as the target to solve the problems of joint user channel assignment and power allocation optimization.
The technical scheme is as follows: in order to achieve the above object, the present invention provides a method for allocating joint resources in a NOMA relay system, including the following steps:
1) initializing the external circulation parameters:
setting maximum external circulation times
Figure GDA0001891354990000021
Initial power allocation and setting outer loop iteration factor
Figure GDA0001891354990000022
2) User channel assignment for fixed power allocation:
performing a fixed power allocation user channel assignment algorithm to obtain a user channel assignment phik,mThe result is;
3) power allocation for fixed user channel assignment:
3.1) initializing internal circulation parameters and setting maximum internal circulation times
Figure GDA0001891354990000023
Setting the Lagrangian factor mukω, ξ and ηmAnd sets an initial inner loop iteration factor
Figure GDA0001891354990000024
3.2) according to
Figure GDA0001891354990000025
And phik,mAnd the Lagrangian factor mu in the present cyclek,ω,ξ,ηmCalculate Pk,m；
3.3) according to the sub-gradient method, andk,mand Pk,mUpdating a Lagrange multiplier;
3.4) by
Figure GDA0001891354990000026
Updating an inner loop iteration factor;
3.5) judging the end condition of the inner loop body if the inner loop converges or
Figure GDA0001891354990000027
The power distribution process is ended, the step 4 is skipped, otherwise, the step 3.2 is skipped, and the inner loop iterative algorithm is continued;
4) user channel assignment for fixed power allocation:
4.1) performing a user channel assignment algorithm for fixed power allocation to obtain a user channel assignment φk,mThe result is;
4.2) by
Figure GDA0001891354990000028
Updating an outer loop iteration factor;
5) judging the outer loop body end condition if the outer loop converges or
Figure GDA0001891354990000029
And (4) ending the iterative resource allocation process, outputting the optimal user channel assignment power allocation result, otherwise jumping to the step 3, and continuing the inner loop iterative algorithm.
Further, the user channel assignment algorithm of fixed power allocation in step 2 and step 4.1 comprises the following steps:
2.1) initializing the network and signals, collecting CSI for two time slots of the NOMA Relay System, at a given Pk,mAccording to
Figure GDA00018913549900000210
Computing
Figure GDA00018913549900000211
At a given Pk,mAccording to
Figure GDA00018913549900000212
Computing
Figure GDA00018913549900000213
2.2) many-to-many matching game initialization, each user m constructs a preference list according to the utility function of the user m, each channel k constructs a preference list according to the utility function of the user m, each m selects the best access channel according to the preference, each channel k sorts the application users of the channels, and the number of users on the channels is determined
Figure GDA0001891354990000031
And XmaxMake a comparison if
Figure GDA0001891354990000032
The channel k accepts the best application user, rejects other application users, if
Figure GDA0001891354990000033
The channel k refuses all the users applying for the application, and all the users are accepted and added into a unified waiting list;
2.3) in the process of many-to-many matching game, all users are rejected and re-apply for their suboptimal selection, each channel k accepts or rejects his applicant by using the same method, and adds the accepted users into a waiting list, and the process of matching game is finished after iteration is circulated until all users are in the waiting list;
2.4) initializing the alliance game with the transfer rule, and setting the maximum iteration times;
2.5) league gaming procedure with transfer rules, selecting a channel k and selecting from the user league AkSelects one user m, searches the next channel k', if
Figure GDA0001891354990000034
m∈AkChannel k transfers user m to channel k', otherwise not, one channel k is selected and from user association akSelects one user m, searches another channel k' and from the user association Ak'If one user m' is selected
Figure GDA0001891354990000035
m∈Ak,m'∈Ak'From federation AkUser m exchange alliance Ak'If not, the user m' in the game is not transferred, and the iteration is circulated until the transfer rule does not meet or the maximum iteration times is reached, and then the alliance game is ended;
2.6) outputting the optimal user channel assignment result.
Further, the step 3.3 secondary gradient method comprises the following steps:
a) for a given Pk,mSo that:
Figure GDA0001891354990000036
wherein mukω, ξ and ηmIs the lagrangian factor of the signal,
Figure GDA0001891354990000037
b) using the KKT conditions, one can obtain:
Figure GDA0001891354990000041
Figure GDA0001891354990000042
Figure GDA0001891354990000043
Figure GDA0001891354990000044
Figure GDA0001891354990000045
c) by passingWater filling algorithm pair Pk,mIs allocated, expressed as:
Figure GDA0001891354990000046
wherein x+＝max(0,x)；
f) Lagrange factor mukω, ξ and ηmThe iterative equation of (a) is as follows:
Figure GDA0001891354990000047
Figure GDA0001891354990000048
Figure GDA0001891354990000049
Figure GDA00018913549900000410
where n denotes the iteration index, τμ(n)，τω(n)，τξ(n) and τη(n) represents the value of a dual variable μkω, ξ and ηmIn the iterative method of the secondary gradient, the step size is iterated for the nth time.
The invention considers the total power limit of the whole system and the service quality requirement of the user, and constructs an optimization model combining user channel assignment and power allocation by taking the maximum average user transmission rate as a target; then, it is proved that the optimization problem is an NP-hard problem, and the original problem is decomposed into two sub-problems by adopting a decoupling method: user channel assignment problem under fixed power allocation and power allocation problem under fixed user channel assignment; providing a alliance game method with transfer rules to solve the channel assignment problem under fixed power, and solving the power distribution problem under fixed user channel assignment by applying a Lagrange dual theory and a sub-gradient method; and finally, further providing a joint resource optimization algorithm based on iteration on the basis of respectively solving the two subproblems. Has the advantages that: compared with the prior art, the invention has the following advantages:
1. in order to access users as much as possible on the premise of meeting the requirement of the lowest transmission rate, the invention introduces the NOMA technology into the relay system, so that a plurality of users can be accessed to one channel of the relay station, and particularly, when the number of the users is always larger than that of the channels of the relay station and the base station, the satisfaction degree of the users can be improved.
2. The invention provides a combined resource optimization algorithm of user channel assignment and power allocation for a downlink NOMA relay network. Since the optimization problem proved to be an NP-hard problem, the original problem was decomposed into two sub-problems using a decoupling method: the user channel assignment problem under the fixed power allocation and the power allocation problem under the fixed user channel assignment greatly simplify the calculation complexity of the solution.
3. The invention provides a alliance game method with transfer rules for solving a channel assignment problem under fixed power, and solves a power distribution problem under fixed user channel assignment by applying a Lagrangian dual theory and a sub-gradient method, thereby further reducing the operation complexity.
Drawings
Fig. 1 is a model diagram of a NOMA-based DF relay system;
FIG. 2 is a flowchart of the joint resource allocation algorithm of the present invention.
Detailed Description
The invention is further elucidated with reference to the drawings and the embodiments.
As shown in fig. 1, this embodiment considers a NOMA-based relay system, which includes a base station, a DF relay R and M users, wherein the relay uses DF protocol to decode and forward signals from the base station and addressed to all users, and the user set is denoted as { U }1,U2,...,UMB, available bandwidth of the systemTDivided into K mutually orthogonal channels, denoted by { SC }1,SC2,...,SCKIn this embodiment, a scenario in which the number of users is much larger than the number of channels is considered, that is, M > K.
As shown in fig. 2, the present embodiment provides a method for allocating joint resources in a NOMA relay system, including the following steps:
1) initializing the external circulation parameters:
setting maximum external circulation times
Figure GDA0001891354990000051
Initial power allocation and setting outer loop iteration factor
Figure GDA0001891354990000052
2) User channel assignment for fixed power allocation:
performing a fixed power allocation user channel assignment algorithm to obtain a user channel assignment phik,mThe result is;
3) power allocation for fixed user channel assignment:
3.1) initializing internal circulation parameters and setting maximum internal circulation times
Figure GDA0001891354990000061
Setting the Lagrangian factor mukω, ξ and ηmAnd sets an initial inner loop iteration factor
Figure GDA0001891354990000062
3.2) according to
Figure GDA0001891354990000063
And phik,mAnd the Lagrangian factor mu in the present cyclek,ω,ξ,ηmCalculate Pk,m；
3.3) according to the sub-gradient method, andk,mand Pk,mUpdating a Lagrange multiplier;
3.4) by
Figure GDA0001891354990000064
Updating an inner loop iteration factor;
3.5) judging the end condition of the inner loop body if the inner loop converges or
Figure GDA0001891354990000065
The power distribution process is ended, the step 4 is skipped, otherwise, the step 3.2 is skipped, and the inner loop iterative algorithm is continued;
4) user channel assignment for fixed power allocation:
4.1) performing a user channel assignment algorithm for fixed power allocation to obtain a user channel assignment φk,mThe result is;
4.2) by
Figure GDA0001891354990000066
Updating an outer loop iteration factor;
5) judging the outer loop body end condition if the outer loop converges or
Figure GDA0001891354990000067
And (4) ending the iterative resource allocation process, outputting the optimal user channel assignment power allocation result, otherwise jumping to the step 3, and continuing the inner loop iterative algorithm.
The above method is described and demonstrated in detail below with reference to FIGS. 1 and 2
Non-orthogonal multiple access (NOMA) is widely used in wireless communication scenarios with resource shortage, and due to its highly spectrally efficient nature, the employment of NOMA technology may allow multiple users to multiplex the same channel. In the first time slot, the base station sends signals to the relay R on all K channels, and since M is larger than K, the NOMA mechanism is adopted and M users are divided into K groups, each group independently occupies one channel and users in the same group use the same channel, which is respectively denoted as A1,A2,...,AK. For example, AkIs indicated in the channel SCkA subset of users. Assuming that all instantaneous channel information is available at the relay R, the base station transmission in the first time slot and the relay transmission in the second time slot take the same user channel assignment, i.e., the relay R decodes the forwarding base station in the second time slotAnd all signals are transmitted to the users in the same channel through the NOMA mode, and the user channel assignment strategy adopted by the second time slot is the same as that adopted by the first time slot.
In the first time slot, the relay R is in the sub-channel SCkThe composite signal from the base station to user m is received, denoted as:
Figure GDA0001891354990000068
wherein
Figure GDA0001891354990000071
The noise signal of the relay end is subjected to the mean value of 0 and the variance of
Figure GDA0001891354990000072
Is a Gaussian distribution of
Figure GDA0001891354990000073
Figure GDA0001891354990000074
xk,lAnd pk,lRespectively transmitted symbol information and on channel SCkThe power of the upper base station for transmitting the information of the user l, wherein l belongs to Ak. In the first time slot, it is sent by the base station to the relay R, and the user m is in the channel SCkThe channel gain on is expressed as
Figure GDA0001891354990000075
Wherein
Figure GDA0001891354990000076
Is from the base station to the relay R on the channel SCkThe small-scale fading follows a complex gaussian distribution, and the small-scale fading is assumed to be kept unchanged in the same time slot and changed in different time slots.
Figure GDA0001891354990000077
And alpha are the base station to relay distance and the path loss factor respectively,
Figure GDA0001891354990000078
is a large scale fading that remains the same at different time slots, assuming that the large scale fading is only related to the base station and relay distance. Considering that the first time slot has a direct link, the mth user receives the channel SCkThe superimposed signal above is represented as:
Figure GDA0001891354990000079
wherein
Figure GDA00018913549900000710
The noise signal of the first time slot user terminal is subject to mean value of 0 and variance of
Figure GDA00018913549900000711
Is a Gaussian distribution of
Figure GDA00018913549900000712
Figure GDA00018913549900000713
On-channel SC from base station to user m in first time slotkThe channel gain on is expressed as
Figure GDA00018913549900000714
Wherein
Figure GDA00018913549900000715
Is from the base station to the user m on the channel SCkThe small-scale fading follows a complex gaussian distribution, and the small-scale fading is assumed to be kept unchanged in the same time slot and changed in different time slots.
Figure GDA00018913549900000716
And alpha are the base station to user m distance and the path loss factor respectively,
Figure GDA00018913549900000717
is a large rulerDegree fading, assuming that large scale fading is only related to base station and user distance, remains the same at different time slots.
And in the second path time slot, the relay decodes and forwards the data from the base station to the user. User m is on channel SCkThe received superimposed signal from the relay is represented as:
Figure GDA00018913549900000718
wherein
Figure GDA00018913549900000719
The noise signal of the second time slot user terminal is subjected to mean value of 0 and variance of
Figure GDA00018913549900000720
Is a Gaussian distribution of
Figure GDA00018913549900000721
Figure GDA00018913549900000722
qk,lIs at the channel SCkThe power of the upper relay R for transmitting the information of the user l, wherein l belongs to Ak. On-channel SC from relay R to user m in the second time slotkIs expressed as
Figure GDA00018913549900000723
Wherein
Figure GDA00018913549900000724
Is a channel SC from a relay R to a user mkThe small-scale fading follows a complex gaussian distribution, and the small-scale fading is assumed to be kept unchanged in the same time slot and changed in different time slots.
Figure GDA00018913549900000725
And alpha is the distance of the relay R to the user m and the path loss factor respectively,
Figure GDA00018913549900000726
is a large scale fading that is assumed to be dependent only on relay and user distance and remains the same at different time slots.
By analyzing equations (1) - (3), the received interference at relay R and user m is represented as:
Figure GDA00018913549900000727
Figure GDA0001891354990000081
Figure GDA0001891354990000082
due to consideration of the NOMA transmission mechanism and the SIC technology, the interference among users can be effectively reduced. For example, consider the channel gain in equation (3)
Figure GDA0001891354990000083
Wherein K is equal to K and Ui,Uj∈Ak. When in use
Figure GDA0001891354990000084
While, user UiCan eliminate the U from the user during decodingjThe interference of (2).
The relay network adopting the NOMA strategy may reach the performance upper bound, and decodes the user signal according to the increasing order of the channel gain, and the system SINR under two transmission time slots can be expressed as:
Figure GDA0001891354990000085
Figure GDA0001891354990000086
Figure GDA0001891354990000087
according to the DF Relay protocol, user m is on the channel SCkThe data rate of the two slots above can be expressed as:
Figure GDA0001891354990000088
for ease of understanding, a binary K × M user-channel allocation factor Φ is defined as { Φ ═ fk,mIn which phik,m1 denotes that channel k is allocated to user m, whereas phik,m0 means that no k is allocated to user m. Since the scenario assumed is that the number of users is greater than the number of channels, it is specified that each user can only occupy one channel, but that channel k can be allocated to at most
Figure GDA0001891354990000089
The following conditions are satisfied for each user:
φk,m∈{0,1} (11)
Figure GDA00018913549900000810
Figure GDA00018913549900000811
in addition, the maximum transmission power of the base station and the relay are respectively defined as
Figure GDA00018913549900000812
And
Figure GDA00018913549900000813
the minimum service rate of user m is
Figure GDA00018913549900000814
Then base station, inThe constraints of the relay, the sub-channel k and the user m satisfy the following conditions:
Figure GDA00018913549900000815
Figure GDA0001891354990000091
Figure GDA0001891354990000092
Figure GDA0001891354990000093
therefore, the joint resource allocation problem [ phi ] aimed at maximizing system and ratek,m,pk,m,qk,mIt can be formulated as:
Figure GDA0001891354990000094
to further solve the joint resource allocation problem P1, some necessary description is first needed, for the user set akDefining channels SCkThe number of elements of (1) is SkChannel SCkUser set a ofkIs defined as
Figure GDA0001891354990000095
In a downlink NOMA network, a first time slot base station broadcasts and sends M pieces of user information to a relay and a user on all K channels. And in the second time slot, after the user information is relay-decoded, the user information is forwarded on the same channel, all the user terminals receive the information of the two time slots at the maximum ratio, and the SIC technology is adopted for decoding to eliminate interference. For convenience and simplicity, it is specified that the channel gains are ordered from small to large as 1,2k-1,SkAnd describe the set A as a subscriptkA user.
To channel SCkThe sum power of the user m in two time slots is defined as Pk,m，Pk,m＝pk,m+qk,m. Given channel SCkSum power P of upper user mk,mSum rate R of joint resource optimization problem P1k,mCan be converted into:
Figure GDA0001891354990000101
theorem 1: given sum power P in joint resource optimization problem P1k,mChannel SCkThe equivalent channel gain of the upper user m can be expressed as:
Figure GDA0001891354990000102
wherein
Figure GDA0001891354990000103
Proof of theorem 1: consider a downlink NOMA relay system where the user with the worst channel gain experiences the most interference, and conversely, the user with the strongest channel gain can cancel the interference due to the SIC technique. Therefore, when
Figure GDA0001891354990000104
When, first, the user is solved
Figure GDA0001891354990000105
The transmission power of two time slots can be obtained:
Figure GDA0001891354990000106
user' s
Figure GDA0001891354990000107
The transmission power of the two time slots is:
Figure GDA0001891354990000108
Figure GDA0001891354990000109
then, it is solved out
Figure GDA00018913549900001010
And
Figure GDA00018913549900001011
time user
Figure GDA00018913549900001012
The transmit power of two time slots. It should be noted that the user is
Figure GDA00018913549900001013
Can be derived by recursion, since the user is not aware of the power of the transmission
Figure GDA00018913549900001014
The interference of (2) is known. Thereby, it is possible to obtain:
Figure GDA00018913549900001015
user' s
Figure GDA00018913549900001016
The two-slot transmit power of (a) is:
Figure GDA00018913549900001017
Figure GDA00018913549900001018
in the same way, we can solve the user
Figure GDA00018913549900001019
Up to
Figure GDA00018913549900001020
The two time slots transmit power, and finally, the channel SC is obtained by adopting a induction methodkThe equivalent channel gain expression for user m is:
Figure GDA0001891354990000111
in summary, the theorem 1 is based on the induction method.
Thus, by conversion, equations (14) - (15) and (17) can be converted into:
Figure GDA0001891354990000112
Figure GDA0001891354990000113
Figure GDA0001891354990000114
by derived equivalent channel gain gammak,mThe optimized resource allocation problem P1 may be converted into:
Figure GDA0001891354990000115
wherein gamma isk,m＝αk,mβk,mRespectively define αk,mAnd betak,mComprises the following steps:
Figure GDA0001891354990000116
Figure GDA0001891354990000117
as can be seen from the joint resource optimization problem P2, the present embodiment proposes a joint user-channel allocation and power allocation problem, aiming to solve the system power limitation and maximize the average sum rate of users under the user QoS guarantee; however, the joint resource allocation problem P2 is an NP-hard problem, and solving the NP-hard problem generally requires exhaustive search and has a high computational complexity, and the following embodiment provides an iterative optimization algorithm to attempt to solve the joint resource allocation problem with a low computational complexity.
Theorem 2: the user averaging and rate maximization problem in the joint resource allocation problem P2 is the NP-hard problem. Proof of theorem 2: the certification process is divided into two cases,
Figure GDA0001891354990000118
and
Figure GDA0001891354990000119
when in use
Figure GDA00018913549900001110
The optimization problem P2 translates into a joint user channel assignment and power allocation problem that has proven to be an NP-hard problem in conventional OFDMA systems.
When in use
Figure GDA00018913549900001111
We need to demonstrate that the optimization problem P2 is still a NP-hard problem even though the power allocation at each channel is a fixed value. However, the three-dimensional matching problem with fixed power allocation has proven to be an NP-complete problem in the prior art, and thus, the optimization problem P2 is a special case of the fixed power allocation problem, which is an NP-hard problem.
Finally, averageUser and rate maximization problem P2, including
Figure GDA0001891354990000121
And
Figure GDA0001891354990000122
two cases, an NP-hard problem.
In conclusion, theorem 2 proves.
It has been demonstrated that the optimization problem P2 is an NP-hard problem, and then the convex optimization theory is used to decouple the resource allocation problem P2 into two sub-problems, namely the user channel assignment problem under fixed power allocation and the power allocation problem under fixed user-channel assignment.
To solve the user channel assignment problem, the utility functions of the user and channel are first defined, respectively denoted as
Figure GDA0001891354990000123
And
Figure GDA0001891354990000124
the following can be obtained:
Figure GDA0001891354990000125
Figure GDA0001891354990000126
wherein
Figure GDA0001891354990000127
Is the average sum rate of user m over all channels, and
Figure GDA0001891354990000128
representing the average sum rate of all users over channel k. Given user m is on channel SCkIs fixed and power Pk,m(pk,m,qk,m) The optimization problem P2 may be transformedComprises the following steps:
Figure GDA0001891354990000129
applying matching game theory[169]The optimization problem of user channel assignment P3 can be equivalent to a many-to-one matching gambling problem with external effects.
Definition 1: a user-channel pair is represented by a matching mu, where
Figure GDA00018913549900001210
Then the user set is M {1, 2., M }, and the channel set K is K {1, 2., K }, which satisfy | μ (M) | 1, | μ (K) | q |kWhere μ (M) — { M ∈ M }, μ (K) — { K ∈ M },
Figure GDA00018913549900001211
defined as a set of element matches.
| represents the number of elements of the matching set; mu (m) | 1 indicates that to avoid more interference among users, one user is allocated only one channel; mu (k) | qkRepresenting the maximum number of users, q, that each channel can accommodatekIs the maximum number of users (quota) that can be served by channel k.
The embodiment adopts a rational matching game method, and assumes that all users and channels are rational, or that all users and channels respectively pursue maximization of self benefits.
Definition 2: the preference list is an ordered set of participants i (i ∈ M @), which includes a subset of all cases. Given B1,B2,...,BnIs a subset of participant i, participant i's preference list p (i) ═ B1,B2,...,BnMeans for B1,B2,...,BnIs a potentially matching pair of participants i, and B1 fi B2 fi...fi Bn。
The preference list set of users and channels is defined as
P＝{P(D1),P(D2),...,P(DM),P(SC1),P(SC2),...,P(SCK) In which P (D)m) And P (SC)k) Are each DmAnd SCkA preference list of (a). It is assumed that the preferences of the user and channel are transitive, i.e. if Lf is presentmL 'and L' fmL', then LfmL ", where m is one participant in the matching game, and L, L' and L" are subsets of participant m.
Definition 3: if one of the following two conditions exists:
(1) for user m,. mu.m.noteq.k and
Figure GDA00018913549900001311
(2) for channel k, μ (k) ≠ m and
Figure GDA00018913549900001312
then the matching μ is said to be blocked by the user channel pair (m, μ (m)) or (μ (k), k).
Definition 4: if there is no blocking for a matching μ, the matching μ is said to be stable.
In particular, users select different channels by establishing their preferences with utility functions, both matching for any user m and for any two channels K, K' e K, K ≠ K
Figure GDA0001891354990000131
And m is equal to mu (k) and m is equal to mu' (k), and the following properties are satisfied:
Figure GDA0001891354990000132
”
similarly, for any channel k and any two users M, M belongs to M, M is not equal to M, and the two kinds of matching are carried out
Figure GDA0001891354990000133
And m ═ μ (k), m ═ μ' (k), and the following properties are satisfied:
Figure GDA0001891354990000134
definition 5: transfer matching
Figure GDA0001891354990000135
Or
Figure GDA0001891354990000136
Wherein:
Figure GDA0001891354990000137
Figure GDA0001891354990000138
note that, here, "transition" includes two forms,
Figure GDA0001891354990000139
or
Figure GDA00018913549900001310
That is, two users of different access channels are swapped, or one user is swapped from one access channel to another.
Definition 6: a two-way stable matching transition match, mu, is stable if and only if there is no transition below.
(1)
Figure GDA0001891354990000141
And is
(2)
Figure GDA0001891354990000142
Introduction 1: match for arbitrary transitions
Figure GDA0001891354990000143
If so:
(1)
Figure GDA0001891354990000144
and is
(2)
Figure GDA0001891354990000145
Then there is
Figure GDA0001891354990000146
For the proof of lemma 1: without loss of generality, the reference function is chosen to be the utility function, as in formula (39) and formula (40) in definition 5, there are two different possible transmission modes,
Figure GDA0001891354990000147
and
Figure GDA0001891354990000148
thus, the attestation process of lemma 1 needs to be divided into two cases.
A solving algorithm based on the game idea is given below for the optimization problem P3, and the detailed user channel assignment process is described in table 1.
Table 1 user channel assignment algorithm (USAA)
Figure GDA0001891354990000149
Figure GDA0001891354990000151
Given a user m on the channel SCkThe following user-channel assignment, optimization problem P2, may be transformed into:
Figure GDA0001891354990000152
when the number of users increases to be large enough, the performance gap caused by the dual method of the optimization problem P4 can be ignored, and the progressive optimization solution can be obtained by the dual method[34]。
For a given Pk,mSo that:
Figure GDA0001891354990000161
wherein mukω, ξ and ηmIs the lagrangian factor of the signal,
Figure GDA0001891354990000162
obviously, L is Pk,mFor an optimization problem P4, when Pk,mNot less than 0, and by using the KKT condition, the following can be obtained:
Figure GDA0001891354990000163
Figure GDA0001891354990000164
Figure GDA0001891354990000165
Figure GDA0001891354990000166
Figure GDA0001891354990000167
p pair by water filling algorithmk,mIs allocated, expressed as:
Figure GDA0001891354990000168
wherein x+Max (0, x), applying a sub-gradient iterative algorithm, setting the lagrange factor μkInitial values of ω, ξ and η m, and then iteratively solving the Lagrangian dual function L (P)k,m,μk,ω,ξ,ηm). Lagrange factor mukω, ξ and ηmThe iterative equation of (a) is as follows:
Figure GDA0001891354990000171
Figure GDA0001891354990000172
Figure GDA0001891354990000173
Figure GDA0001891354990000174
where n denotes the iteration index, τμ(n)，τω(n)，τξ(n) and τη(n) represents the value of a dual variable μkω, ξ and ηmIn the nth iteration step length in the sub-gradient iteration method, a decreasing step length strategy is adopted to ensure that the optimal dual variable can be reached, and the details of the iteration distribution algorithm can be referred to documents.
The joint resource allocation problem P2 is decomposed into two sub-problems, the user channel assignment problem under fixed power allocation, and the power allocation problem for fixed user channel assignment. With the maximum average user rate as the optimization goal, a joint resource optimization algorithm based on iterative thought within the affordable time is given in table 2.
Table 2 joint user channel assignment power allocation algorithm (JUSAPAA)
Figure GDA0001891354990000175
Figure GDA0001891354990000181
The embodiment considers a multi-user relay scenario with scarce spectrum resources, and improves the system performance by introducing the NOMA strategy. Firstly, the current research situation and the limitation of a resource optimization algorithm in a NOMA cooperative communication network are researched, on the basis, all users are allowed to share limited channel resources provided by a relay, a problem of channel assignment and power allocation optimization of a combined user is provided, and the aim is to maximize the sum rate of all users; then, the optimization problem is proved to be an NP-hard problem, and the original problem is decomposed into two sub-problems by adopting a decoupling method: user channel assignment problem under fixed power allocation and power allocation problem under fixed user channel assignment; after the two sub-problems are solved respectively, a joint resource allocation algorithm based on an iterative idea is provided, and the system performance is further improved.

Claims (2)

1. A joint resource allocation method in a NOMA relay system is characterized in that: the method comprises the following steps:
1) initializing the external circulation parameters:
setting maximum external circulation times
Figure FDA0003011456960000011
Initial power allocation and setting outer loop iteration factor
Figure FDA0003011456960000012
2) User channel assignment for fixed power allocation:
performing a fixed power allocation user channel assignment algorithm to obtain a user channel assignment phik,mThe result is;
3) power allocation for fixed user channel assignment:
3.1) initializing internal circulation parameters and setting maximum internal circulation times
Figure FDA0003011456960000013
Setting the Lagrangian factor mukω, ξ and ηmAnd sets an initial inner loop iteration factor
Figure FDA0003011456960000014
3.2) according to
Figure FDA0003011456960000015
And phik,mAnd the Lagrangian factor mu in the present cyclek,ω,ξ,ηmCalculate Pk,m；
3.3) according to the sub-gradient method, andk,mand Pk,mUpdating a Lagrange multiplier;
3.4) by
Figure FDA0003011456960000016
Updating an inner loop iteration factor;
3.5) judging the end condition of the inner loop body if the inner loop converges or
Figure FDA0003011456960000017
The power distribution process is ended, the step 4 is skipped, otherwise, the step 3.2 is skipped, and the inner loop iterative algorithm is continued;
4) user channel assignment for fixed power allocation:
4.1) performing a user channel assignment algorithm for fixed power allocation to obtain a user channel assignment φk,mThe result is;
4.2) by
Figure FDA0003011456960000018
Updating an outer loop iteration factor;
5) judging the end condition of the external circulation body, if notThe circulation converges or
Figure FDA0003011456960000019
Ending the iterative resource allocation process, outputting the optimal user channel assignment power allocation result, otherwise jumping to the step 3, and continuing the inner loop iterative algorithm;
the user channel assignment algorithm for fixed power allocation in step 2 and step 4.1 comprises the following steps:
2.1) initializing the network and signals, collecting CSI for two time slots of the NOMA Relay System, at a given Pk,mAccording to
Figure FDA00030114569600000110
Computing
Figure FDA00030114569600000111
At a given Pk,mAccording to
Figure FDA00030114569600000112
Computing
Figure FDA00030114569600000113
2.2) many-to-many matching game initialization, each user m constructs a preference list according to the utility function of the user m, each channel k constructs a preference list according to the utility function of the user m, each m selects the best access channel according to the preference, each channel k sorts the application users of the channels, and the number of users on the channels is determined
Figure FDA00030114569600000114
And XmaxMake a comparison if
Figure FDA0003011456960000021
The channel k accepts the best application user, rejects other application users, if
Figure FDA0003011456960000022
The channel k refuses all the users applying for the application, and all the users are accepted and added into a unified waiting list;
2.3) in the process of many-to-many matching game, all users are rejected and re-apply for their suboptimal selection, each channel k accepts or rejects his applicant by using the same method, and adds the accepted users into a waiting list, and the process of matching game is finished after iteration is circulated until all users are in the waiting list;
2.4) initializing the alliance game with the transfer rule, and setting the maximum iteration times;
2.5) league gaming procedure with transfer rules, selecting a channel k and selecting from the user league AkSelects one user m, searches the next channel k', if
Figure FDA0003011456960000023
Channel k transfers user m to channel k', otherwise not transfer, selects one channel k and from user alliance AkSelects one user m, searches another channel k' and from the user association Ak'If one user m' is selected
Figure FDA0003011456960000024
By federation AkUser m exchange alliance Ak'If not, the user m' in the game is not transferred, and the iteration is circulated until the transfer rule does not meet or the maximum iteration times is reached, and then the alliance game is ended;
2.6) outputting the optimal user channel assignment result.
2. The method of claim 1 for joint resource allocation in a NOMA relay system, wherein: the step 3.3 secondary gradient method comprises the following steps:
a) for a given Pk,mSo that:
Figure FDA0003011456960000025
wherein mukω, ξ and ηmIs the lagrangian factor of the signal,
Figure FDA0003011456960000026
b) using the KKT conditions, one can obtain:
Figure FDA0003011456960000027
Figure FDA0003011456960000031
Figure FDA0003011456960000032
Figure FDA0003011456960000033
Figure FDA0003011456960000034
c) p pair by water filling algorithmk,mIs allocated, expressed as:
Figure FDA0003011456960000035
wherein x+＝max(0,x)；
f) Lagrange factor mukω, ξ and ηmThe iterative equation of (a) is as follows:
Figure FDA0003011456960000036
Figure FDA0003011456960000037
Figure FDA0003011456960000038
Figure FDA0003011456960000039
where n denotes the iteration index, τμ(n)，τω(n)，τξ(n) and τη(n) represents the value of a dual variable μkω, ξ and ηmIn the iterative method of the secondary gradient, the step size is iterated for the nth time.
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