CN107509243B - Bandwidth and power combined control method based on downlink non-orthogonal multiple access system - Google Patents

Bandwidth and power combined control method based on downlink non-orthogonal multiple access system Download PDF

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CN107509243B
CN107509243B CN201710679118.5A CN201710679118A CN107509243B CN 107509243 B CN107509243 B CN 107509243B CN 201710679118 A CN201710679118 A CN 201710679118A CN 107509243 B CN107509243 B CN 107509243B
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CN107509243A (en
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吴远
毛浩伟
杨晓维
柴浩涵
钱丽萍
黄亮
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Zhejiang University of Technology ZJUT
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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
    • H04W72/00—Local resource management
    • H04W72/04—Wireless resource allocation
    • H04W72/044—Wireless resource allocation based on the type of the allocated resource
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/04—Wireless resource allocation
    • H04W72/044—Wireless resource allocation based on the type of the allocated resource
    • H04W72/0473—Wireless resource allocation based on the type of the allocated resource the resource being transmission power

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Abstract

A bandwidth and power combined control method based on a downlink non-orthogonal multiple access system comprises the following steps: (1) the base station transmits data through a non-orthogonal multiple access technology to provide data traffic service for the mobile user; (2) analyzing system characteristics to perform equivalent transformation on the problems; (3) the problem after conversion is proved to be a feasibility checking problem, so that efficient solution can be realized; (4) and designing a feasible and efficient algorithm solution according to the finally converted problem characteristics, and finally substituting the algorithm output result back to the top layer problem to obtain the optimal bandwidth and power distribution value. The invention provides a feasible and efficient optimization method which not only guarantees the data requirements of mobile users, but also minimizes the total resource consumption of the system, so as to improve the utilization rate of system resources and optimize the configuration of the system resources.

Description

Bandwidth and power combined control method based on downlink non-orthogonal multiple access system
Technical Field
The invention relates to a bandwidth and power joint control method based on a downlink non-orthogonal multiple access (NOMA) system in a wireless network.
Background
In order to achieve high spectrum efficiency and large-scale connection in the 5 th generation mobile communication technology, a Non-Orthogonal Multiple Access (NOMA) technology is proposed, and unlike the conventional OMA (OMA) technology, NOMA can serve more users through Non-Orthogonal resource allocation, and the spectrum efficiency can be obviously improved by enabling a large number of users to simultaneously share the same frequency band channel and eliminating co-channel interference by using a Successive Interference Cancellation (SIC) mechanism. Therefore, NOMA fits well with the ultimate goal of future 5G cellular networks, providing ultra-high throughput and ultra-dense connections.
Disclosure of Invention
The present invention provides a bandwidth and power joint control method based on a downlink non-orthogonal multiple access system, which aims to overcome the defects of the prior art.
The invention applies NOMA technology to transmit data in the wireless cellular network, considers the bandwidth and the power jointly, and realizes the minimization of the resource consumption in the system on the premise of meeting the data flow requirements of all MUs.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a bandwidth and power combined control method based on a downlink non-orthogonal multiple access (NOMA) system in a wireless network comprises the following steps:
(1) there are a total of T Mobile Users (MUs) under the coverage of the mBS, in which case the mBS transmits data using NOMA technology. In consideration of technical characteristics of NOMA, index set is introduced
Figure BDA0001375050390000021
Representing T MUs. First, since the successive interference cancellation mechanism (SIC) orders the channel gains from the mBS to all MUs from large to small, there is the following order:
gB1>gB2>…>gBj>gBi>…>gBT(1)
wherein g isBiRepresents the channel gain of the mBS to the ith MU,
Figure BDA0001375050390000022
the ith MU (or jth MU) mentioned in the following description is in the index set
Figure BDA0001375050390000023
The method of (1).
(2) At the mBS end, instantaneous channel gain per MU
Figure BDA0001375050390000024
Are known. Based on NOMA, the mBS will transmit all data to each MU superimposed on the same frequency band. At the MU end, partial identity between MUs is eliminated by using SICAnd (4) frequency interference. By MUi、MUkAnd MUjTo illustrate the working principle of SIC, for MUiDecoding MU first in received datak(k>i, i.e. MU in particularkArranged at MUiLater) and then removes the decoded data from the received data (the specific order of operation is k-T, T-1, T-2, …, i +1) while the MU is being operated onj(j<i, i.e. MU in particularjArranged at MUiThe preceding) data signal is considered as noise, MUjIndicates that the MU is arranged at the jth MU; MU (Multi-user)iIndicating that the MU is ranked at the ith MU; MU (Multi-user)kIndicating that the MU is ranked at the kth. From mBS to MU according to the above decoding mechanismiThe throughput of (a) is:
Figure BDA0001375050390000025
wherein the relevant parameters are defined as follows:
pBi: mBS to MUiThe transmit power of (a);
pBi: mBS to MUiData throughput of (d);
WB: an amount of bandwidth allocated to service the group of mobile users;
n0: power spectral density of background noise.
(3) In this patent, considering the situation of a single mBS, the data requirements of all mobile users are met simultaneously while minimizing the total resource consumption of the system, and the following constraints are set:
Figure BDA0001375050390000031
wherein
Figure BDA0001375050390000032
Represents MUiThe data requirements of (1).
In a wireless network, a macro cell base station (mBS) transmits data through non-orthogonal multiple access (NOMA), and applies Successive Interference Cancellation (SIC) to cancel part of co-channel interference generated by the mBS during transmission of data using the same channel, minimizing system resource consumption (TCM) while ensuring that each MU data requirement is met, while describing this optimization problem as follows:
Figure BDA0001375050390000033
Figure BDA0001375050390000034
Figure BDA0001375050390000035
Figure BDA0001375050390000036
Figure BDA0001375050390000037
wherein the relevant parameters are defined as follows:
Figure BDA0001375050390000038
total power of the mBS;
Figure BDA0001375050390000039
total bandwidth owned by mBS;
this is a problem of jointly considering bandwidth and power allocation, and the optimal solution of the problem is the minimum consumption of system resources in the case of meeting the data requirements of mobile users.
Note that α and β involved in the TCM problem represent the price factor of power and the price factor of bandwidth, respectively, that is, the cost incurred using a unit of power is α and the cost incurred using a unit of bandwidth is β.
(4) The problem (TCM) is caused by the power pBiSum bandwidth WBCo-determined, analytical problem characterizationEquivalent translates to the bandwidth allocation problem we introduce βBiTo represent mBS to MUiSignal to interference plus Noise Ratio (SINR), i.e.:
Figure BDA00013750503900000310
it is assumed here that
Figure BDA0001375050390000041
Given, mBS to MU can be recursively calculated by the above formulaiIs expressed as follows:
Figure BDA0001375050390000042
the minimum total transmit power that can be obtained from this equation to all mobile users is expressed as follows:
Figure BDA0001375050390000043
wherein the assumption is gB0Is a sufficiently large value, so
Figure BDA0001375050390000044
(5) W is to beBConsidering as variables, applying the minimum total power expression, the TCM problem can be equivalently converted into a Bandwidth-Allocation (BA) problem as follows:
Figure BDA0001375050390000045
Figure BDA0001375050390000046
Figure BDA0001375050390000047
variables:WB>0.
through the step of equivalence transformation, the problem BA only has one decision variable W compared with the problem TCMBIt becomes easier to solve.
Although BA has only one decision variable, it is still difficult to solve the problem directly, so a variable substitution is introduced as follows:
Figure BDA0001375050390000048
when the substitution formula is available, the problem BA can be equivalently converted by combining the minimum total transmitting power expression, the English letter E is added after the BA to obtain BA-E, and the BA-E is converted to obtain the problem BA-E
Figure BDA0001375050390000049
Figure BDA00013750503900000410
Figure BDA0001375050390000051
The problem BA-E is still non-convex due to the non-convexity of the objective function and the constraints (13), but can be solved effectively through the algorithm steps designed by the invention.
(6) An additional variable v is introduced in this step, where
Figure BDA0001375050390000052
Figure BDA0001375050390000053
Representing a system resource consumption value. Further transformation of the problem BA-E gives a problem BA-EV which is expressed as follows:
(BA-EV):min v
Figure BDA0001375050390000054
Figure BDA0001375050390000055
Figure BDA0001375050390000056
note that the problem BA-EV is equivalent to the problem BA-E, and the optimal solution v of the problem corresponds to the minimum value of the system resource consumption.
Observing the problem BA-EV finds that if the v value is fixed, the problem BA-EV can be converted into a feasible domain inspection problem with convexity, so that the following optimization problem can be obtained under the given v value, and is marked as BA-EVsub:
(BA-EVsub):
Figure BDA0001375050390000057
Figure BDA0001375050390000058
in which inputting a v value can obtain a
Figure BDA0001375050390000059
The value is obtained. For problem output
Figure BDA00013750503900000510
A value if
Figure BDA00013750503900000511
It indicates that the problem BA-EV is feasible given v and that the v value can be further reduced. If it is not
Figure BDA00013750503900000512
It indicates that the problem BA-EV is not feasible and the input v value needs to be increased. When in use
Figure BDA00013750503900000513
When the value reaches the set accuracy, the algorithm is ended, and the calculated v is output*And x*。
(7) In conjunction with the description of the above steps, two conclusions are drawn about the problem BA-EVsub: 71) given the value of v, the problem BA-EVsub is a convex optimization problem with respect to x; 72) optimal solution of problem BA-EVsub
Figure BDA0001375050390000061
Is a non-increasing function with respect to v; an algorithm is designed and solved based on the two conclusions, and the algorithm is specifically described as follows, wherein the algorithm is marked as Sol-BA:
algorithm step S1: input upper limit value vmaxLower limit value vminEnding the threshold tol of the cycle;
algorithm step S2: according to the condition | vmax-vmin| ≧ tol, determine whether to enter a loop, that is, | vmax-vminIf | ≧ tol, entering a loop, executing the algorithm step S3, | vmax-vmin|<tol does not enter a loop, and an algorithm step S7 is executed;
algorithm step S3: setting the value of v to
Figure BDA0001375050390000062
Namely, it is
Figure BDA0001375050390000063
Algorithm step S4: obtaining an optimal value according to a set v value to solve the problem BA-EVsub
Figure BDA0001375050390000064
To correspond to
Figure BDA0001375050390000065
Algorithm step S5: the optimal value obtained according to algorithm step S4
Figure BDA0001375050390000066
Make a determination if
Figure BDA0001375050390000067
The upper limit value v is updatedmaxV; otherwise, the lower limit value v is updatedminReturning to algorithm step S2;
algorithm step S6: ending the circulation;
algorithm step S7: output optimum value
Figure BDA0001375050390000068
v*＝v；
(8) The original problem TCM can be solved by using the output value of the algorithm Sol-BA, and the optimal bandwidth allocation is obtained as follows:
Figure BDA0001375050390000069
obtaining MU of each mobile user through recursive calculationiThe optimal power allocation of (c) is:
Figure BDA00013750503900000610
the technical conception of the invention is as follows: first, in a wireless network, 1 macro base station (mBS) transmits data to T Mobile Users (MUs) through non-orthogonal multiple access (NOMA), and the use of NOMA can improve the system spectrum efficiency. Then, a Successive Interference Cancellation (SIC) mechanism is applied to eliminate partial co-channel interference so as to improve the transmission quality of system data. System resource consumption is then minimized while meeting all Mobile User (MU) data traffic requirements. The problem is a non-convex optimization problem, and therefore it is difficult to solve the problem directly. The original problem is subjected to characteristic analysis, the problem is converted into a convex bandwidth allocation problem, and finally an algorithm can be designed for efficient solution.
The invention has the advantages that 1, for the whole system, the introduction of the NOMA technology not only conforms to the development requirement of the fifth generation mobile communication technology (5G) in the future, but also improves the frequency spectrum use efficiency; 2. two different problems of bandwidth allocation and power allocation are considered jointly, and the overall resource consumption of the system is minimized.
Drawings
Fig. 1 is a schematic diagram of a system model including a macrocell base station (mBS) and a plurality of Mobile Users (MUs) in a wireless network to which the method of the present invention is applied.
Detailed Description
The present invention is described in further detail below with reference to the attached drawing figures.
Referring to fig. 1, a bandwidth and power joint control method based on a downlink non-orthogonal multiple access (NOMA) system in a wireless network can minimize the total resource consumption of the system and improve the spectrum utilization efficiency while satisfying the data requirements of all MUs. The invention is applied to a wireless cellular network (as shown in figure 1), the mBS uses NOMA to send data, SIC is introduced to eliminate partial co-channel interference, and simultaneously, the requirement of meeting the data flow of all MUs is considered. The joint control method proposed for the problem has the following steps:
(1) there are a total of T Mobile Users (MUs) under the coverage of the mBS, in which case the mBS transmits data using NOMA technology. In consideration of technical characteristics of NOMA, index set is introduced
Figure BDA0001375050390000081
Representing T MUs. First, since the successive interference cancellation mechanism (SIC) orders the channel gains from the mBS to all MUs from large to small, there is the following order:
gB1>gB2>…>gBj>gBi>…>gBT(1)
wherein g isBiRepresents the channel gain of the mBS to the ith MU,
Figure BDA0001375050390000082
the ith MU (or jth MU) mentioned in the following description is in the index set
Figure BDA0001375050390000083
The method of (1).
(2) At the mBS end, instantaneous channel gain per MU
Figure BDA0001375050390000084
Are known. Based on NOMA, the mBS will transmit all data to each MU superimposed on the same frequency band. At the MU end, SIC is used for eliminating mutual interference between MUs. By MUi、MUkAnd MUjTo illustrate the working principle of SIC, for MUiDecoding MU first in received datak(k>i, i.e. MU in particularkArranged at MUiLater) and then removes the decoded data from the received data (the specific order of operation is k-T, T-1, T-2, …, i +1) while the MU is being operated onj(j<i, i.e. MU in particularjArranged at MUiThe preceding) data signal is considered as noise, MUjIndicates that the MU is arranged at the jth MU; MU (Multi-user)iIndicating that the MU is ranked at the ith MU; MU (Multi-user)kIndicating that the MU is ranked at the kth. From mBS to MU according to the above decoding mechanismiThe throughput of (a) is:
Figure BDA0001375050390000085
wherein the relevant parameters are defined as follows:
pBi: mBS to MUiThe transmit power of (a);
RBi: mBS to MUiData throughput of (d);
WB: an amount of bandwidth allocated to service the group of mobile users;
n0: power spectral density of background noise.
(3) In this patent, considering the situation of a single mBS, the data requirements of all mobile users are met simultaneously while minimizing the total resource consumption of the system, and the following constraints are set:
Figure BDA0001375050390000091
wherein
Figure BDA0001375050390000092
Represents MUiThe data traffic demand of (1).
In a wireless network, a macro cellular base station (mBS) transmits data through non-orthogonal multiple access (NOMA), and applies Successive Interference Cancellation (SIC) to cancel part of the interference generated by the mBS during transmission of data using the same channel, minimizing system resource consumption (TCM) while ensuring that each MU data requirement is met, and describing this optimization problem as follows:
Figure BDA0001375050390000093
Figure BDA0001375050390000094
Figure BDA0001375050390000095
Figure BDA0001375050390000096
Figure BDA0001375050390000097
wherein the relevant parameters are defined as follows:
Figure BDA0001375050390000098
total power of the mBS;
Figure BDA0001375050390000099
total bandwidth possessed by the mBS;
this is a joint consideration of bandwidth and power allocation problems, the optimal solution to the problem is to minimize the system resource consumption value while meeting the mobile user data requirements.
Note that α and β involved in the TCM problem represent the price factor of power and the price factor of bandwidth, respectively, that is, the cost incurred using a unit of power is α and the cost incurred using a unit of bandwidth is β.
(4) Problem TCM is that power pBiSum bandwidth WBCo-determined, equivalent transformation into bandwidth allocation problem by analysis of problem characteristics introduction βBiTo represent mBS to MUiSignal to Interference plus noise Ratio (SINR), i.e.:
Figure BDA0001375050390000101
it is assumed here that
Figure BDA0001375050390000102
Given, mBS to MU can be recursively calculated by the above formulaiIs expressed as follows:
Figure BDA0001375050390000103
observation (8) of MUiPower distribution of (2) with βBj}j≤iIs increased, in combination with (6), it is concluded that: when each MUiIs provided with
Figure BDA0001375050390000104
A globally optimal solution for the problem TCM is obtained.
The minimum total transmit power from the resulting mBS to all mobile users is expressed as follows:
Figure BDA0001375050390000105
wherein the assumption is gB0Is a sufficiently large value and is therefore
Figure BDA0001375050390000106
For the above conclusions, the demonstration was carried out by mathematical induction (forward-reduction), and the following demonstration procedure was followed:
step 4.1: when T is 1, the conclusion can be drawn
Figure BDA0001375050390000107
With mBS to MUiThe minimum transmit power expressions of (a) are consistent;
step 4.2: when T >1, it is assumed that all are true for the conclusion;
step 4.3: we further add the i +1 MU while guaranteeing gBT>gBT+1. When the following formula is proved to be established, the proposed conclusion can be proved to be correct;
Figure BDA0001375050390000108
step 4.4: proof of step 4.3;
a. for T +1 have
Figure BDA0001375050390000109
b. Thus, it is possible to obtain
Figure BDA0001375050390000111
And (5) finishing the certification.
(5) W is to beBConsidering as variables, applying the minimum total power expression, the TCM problem can be equivalently converted into a Bandwidth-Allocation (BA) problem as follows:
Figure BDA0001375050390000112
Figure BDA0001375050390000113
Figure BDA0001375050390000114
variables:WB>0.
through the step of equivalence transformation, the problem BA only has one decision variable W compared with the problem TCMBIt becomes easier to solve.
Nevertheless, it is difficult to solve the problem directly, and a variable substitution is introduced as follows:
Figure BDA0001375050390000115
when the substitution formula is available, the problem BA can be equivalently converted by combining the minimum total transmitting power expression, the English letter E is added after the BA to obtain BA-E, and the BA-E is converted to obtain the problem BA-E
Figure BDA0001375050390000121
Figure BDA0001375050390000122
Figure BDA0001375050390000123
The problem BA-E is still non-convex due to the non-convexity of the objective function and the constraint (13), but the algorithm steps designed by the invention can be effectively solved, and the algorithm is specifically explained in (7).
(6) An additional variable v is introduced in this step, where
Figure BDA0001375050390000124
Figure BDA0001375050390000125
Representing a system resource consumption value. Further transformation of the problem BA-E gives a problem BA-EV which is expressed as follows:
(BA-EV):min v
Figure BDA0001375050390000126
Figure BDA0001375050390000127
Figure BDA0001375050390000128
note that the problem BA-EV is substantially equivalent to the problem BA-E, the optimal solution v to the problem*What corresponds to this is the minimum value of system resource consumption.
Observing the problem BA-EV finds that if the v value is fixed, the problem BA-EV can be transformed into a feasible domain inspection problem with convexity, so that the following optimization problem can be obtained by giving the v value.
(BA-EVsub):
Figure BDA0001375050390000131
Figure BDA0001375050390000132
In which inputting a v value can obtain a
Figure BDA0001375050390000133
The value is obtained. For problem output
Figure BDA0001375050390000134
A value if
Figure BDA0001375050390000135
It indicates that the problem BA-EV is feasible given v and that the v value can be further reduced. If it is not
Figure BDA0001375050390000136
It indicates that the problem BA-EV is not feasibleThe value of v of the input is increased. When in use
Figure BDA0001375050390000137
When the value meets the set accuracy condition and is small enough, the algorithm is ended, and the calculated v is output*And x*。
(7) In conjunction with the description of the above steps, two conclusions are drawn about the problem (BA-EVsub): 71) given the value of v, the problem (BA-EVsub) is a convex optimization problem with respect to x; 72) optimal solution of problem (BA-EVsub)
Figure BDA0001375050390000138
Is a non-increasing function with respect to v. An algorithm (Sol-BA) is designed to solve based on the two conclusions, and the specific description is as follows:
algorithm step S1: input upper limit value vmaxLower limit value vminEnding the threshold tol of the cycle;
algorithm step S2: according to the condition | vmax-vmin| ≧ tol, determine whether to enter a loop, that is, | vmax-vminIf | ≧ tol, entering a loop, executing the algorithm step S3, | vmax-vmin|<tol does not enter a loop, and an algorithm step S7 is executed;
algorithm step S3: setting the value of v to
Figure BDA0001375050390000139
Namely, it is
Figure BDA00013750503900001310
Algorithm step S4: obtaining an optimal value according to a set v value solution problem (BA-EVsub)
Figure BDA00013750503900001311
To correspond to
Figure BDA00013750503900001312
Algorithm step S5: the optimal value obtained according to algorithm step S4
Figure BDA00013750503900001313
Make a determination if
Figure BDA00013750503900001314
The upper limit value v is updatedmaxV; otherwise, the lower limit value v is updatedminReturning to algorithm step S2;
algorithm step S6: ending the circulation;
algorithm step S7: output optimum value
Figure BDA00013750503900001315
v*＝v。
(8) The original problem (TCM) can be solved by using the output values of the algorithm (Sol-BA), obtaining an optimal bandwidth allocation as:
Figure BDA0001375050390000141
obtaining MU of each mobile user through recursive calculationiThe optimal power allocation of (c) is:
Figure BDA0001375050390000142
the problem is thus successfully solved by the algorithm of the present invention.
In this example, fig. 1 is a system model diagram of a macrocell base station (mBS) and T Mobile Users (MUs) in a cellular data network contemplated by the present invention. In this system, the main technical points considered include the following: 1) the mBS sends data through NOMA; 2) because the mBS transmits data for all the MUs on the same frequency band, SIC is introduced to eliminate partial co-channel interference; 3) and the data flow requirement of each MU is met. According to the technical points, the invention provides an optimization problem of the total resource consumption of the system, but the optimization problem is a non-convex optimization problem. In order to overcome the problem, the invention analyzes the problem characteristics, performs equivalent transformation on the provided optimization problem, the transformed problem is a strict convex optimization problem, and most importantly, the invention provides an efficient algorithm for solving the problem and has good effect.
The embodiment aims to minimize the total resource consumption cost of the system and improve the spectrum efficiency of the system on the premise of simultaneously meeting the data traffic demand of the Mobile User (MU). The invention can make the mobile user in the wireless cellular network obtain the service with better quality and lower price, and further realize the more optimized power and spectrum resource allocation of the whole system and higher utilization rate.

Claims (1)

1. A bandwidth and power combined control method based on a downlink non-orthogonal multiple access system comprises the following steps:
(1) there are a total of T mobile users MU under the coverage of the macrocell base station mBS, in which case the mBS transmits data using a non-orthogonal multiple access technique NOMA; in consideration of technical characteristics of NOMA, index set is introduced
Figure FDA0002455123430000011
Represents T MU; firstly, because the successive interference cancellation mechanism SIC orders the channel gains from the mBS to all MUs from large to small, there is the following order:
gB1＞gB2＞…＞gBj＞gBi＞…＞gBT(1)
wherein g isBiRepresents the channel gain of the mBS to the ith MU,
Figure FDA0002455123430000012
mBS denotes a macro cellular base station; MU represents a mobile user; NOMA denotes a non-orthogonal multiple access technique; SIC denotes a successive interference cancellation mechanism,
(2) at the mBS end, instantaneous channel gain per MU
Figure FDA0002455123430000013
The section is known; based on NOMA, the mBS can superpose all data on the same frequency band and send the data to each MU; at MU end, SIC is used for eliminating mutual interference between MUs(ii) a For MUiDecoding MU first in received datakK > i refers to MUkArranged at MUiAnd then deleting the decoded data from the received data, wherein the specific operation sequence is k-T, T-1, T-2, i +1, and the MU is simultaneously deletedjThe data signal is regarded as noise, j < i means that MU is specifiedjArranged at MUiFront, MUjIndicates that the MU is arranged at the jth MU; MU (Multi-user)iIndicating that the MU is ranked at the ith MU; MU (Multi-user)kIndicating that the MU is ranked at the k-th MU, from mBS to MU according to the above decoding schemeiThe throughput of (a) is:
Figure FDA0002455123430000014
wherein the relevant parameters are defined as follows:
pBi: mBS to MUiThe transmit power of (a);
RBi: mBS to MUiData throughput of (d);
WB: an amount of bandwidth allocated to service the group of mobile users;
nn: power spectral density of background noise;
(3) considering the case of a single mBS, the following constraints are set to satisfy the data requirements of all mobile users simultaneously while minimizing the total resource consumption of the system:
Figure FDA0002455123430000015
wherein
Figure FDA0002455123430000016
Represents MUiThe data traffic demand of (1);
in a wireless network, an mBS transmits data through NOMA, and SIC is applied to eliminate partial interference generated by the mBS during transmission of data using the same channel, so as to minimize system resource consumption while ensuring that data requirements of each MU are met, the optimization problem is described as follows, denoted as TCM:
TCM：min
Figure FDA0002455123430000021
subjectto：
Figure FDA0002455123430000022
Figure FDA0002455123430000023
Figure FDA0002455123430000024
variables：pBi＞0，
Figure FDA0002455123430000025
and WB＞0.
wherein the relevant parameters are defined as follows:
Figure FDA0002455123430000026
total power of the mBS;
Figure FDA0002455123430000027
total bandwidth possessed by the mBS;
α and β involved in the TCM problem represent the price factor of power and the price factor of bandwidth, respectively, that is, the cost of using a unit of power is α and the cost of using a unit of bandwidth is β;
(4) problem TCM is that power pBiSum bandwidth WBCo-determined, equivalent transformation into bandwidth allocation problem by analysis of problem characteristics, introduction βBiTo represent mBS to MUiThe signal to interference plus noise ratio SINR, i.e.:
Figure FDA0002455123430000028
it is assumed here that
Figure FDA0002455123430000029
Given, mBS to MU can be recursively calculated by the above formulaiIs expressed as follows:
Figure FDA00024551234300000210
observation of mBS to MUiDiscovery of MU by minimum transmit power expressioniPower distribution of (2) with βBj}j≤iIs increased with MU, andithe data flow demand limiting conditions are combined to draw a conclusion that: when each MUiIs provided with
Figure FDA00024551234300000211
Is the global optimal solution of the problem TCM;
the minimum total transmit power from the resulting mBS to all mobile users is expressed as follows:
Figure FDA00024551234300000212
wherein the assumption is gB0Is a sufficiently large value and is therefore
Figure FDA00024551234300000213
For the above conclusions, as demonstrated by mathematical induction, the procedure was as follows:
step 4.1: when T is 1, the conclusion can be drawn
Figure FDA0002455123430000031
With mBS to MUiThe minimum transmit power expressions of (a) are consistent;
step 4.2: at T >1, it is assumed that all are true for the conclusion;
step 4.3: we further add the i +1 MU while guaranteeing gBT＞gBT+1；
When the following formula is proved to be established, the proposed conclusion can be proved to be correct;
Figure FDA0002455123430000032
step 4.4: proof of step 4.3;
a. for T +1 have
Figure FDA0002455123430000033
b. Thus, it is possible to obtain
Figure FDA0002455123430000034
Finishing the certification;
(5) w is to beBConsidering as a variable, and applying the minimum total power expression, the TCM problem can be equivalently converted into the following bandwidth allocation BA problem, which is denoted as BA:
BA：min
Figure FDA0002455123430000035
subject to：
Figure FDA0002455123430000036
Figure FDA0002455123430000037
variables：WB＞0.
through the step of equivalence transformation, the problem BA only has one decision variable W compared with the problem TCMBIt becomes easier to solve;
introducing an auxiliary variable as follows:
Figure FDA0002455123430000041
when the substitution formula is available, the problem BA can be equivalently converted by combining the minimum total transmitting power expression, the English letter E is added after the BA to obtain BA-E, and the BA-E is converted to obtain the problem BA-E
BA-E：min
Figure FDA0002455123430000042
subject to：
Figure FDA0002455123430000043
variables：
Figure FDA0002455123430000044
(6) An additional variable v is introduced in this step, where
Figure FDA0002455123430000045
Representing a system resource consumption value; further transformation of the problem BA-E gives a problem BA-EV which is expressed as follows:
BA-EV：min v
subject to：
Figure FDA0002455123430000046
Figure FDA0002455123430000047
variables：
Figure FDA0002455123430000048
and v≥0.
note that the problem BA-EV is substantially equivalent to the problem BA-E, the optimal solution v to the problem*The corresponding is the minimum value of system resource consumption;
observing the problem BA-EV, finding that if the v value is fixed, the problem BA-EV can be converted into a feasible domain inspection problem with convexity, and therefore the following optimization problem can be obtained by giving the v value and is marked as BA-EVsub;
BA-EVsub：
Figure FDA0002455123430000049
variables：
Figure FDA00024551234300000410
in which inputting a v value can obtain a
Figure FDA00024551234300000411
A value; for problem output
Figure FDA00024551234300000412
A value if
Figure FDA00024551234300000413
It indicates that the problem BA-EV is feasible given v, and that the v value can be further reduced; if it is not
Figure FDA00024551234300000414
It indicates that the problem BA-EV is not feasible and requires an increase in the input v value; when in use
Figure FDA0002455123430000051
When the value reaches the set accuracy, the algorithm is ended, and the calculated v is output*And x*；
(7) In conjunction with the description of the above steps, two conclusions are drawn about the problem BA-EVsub: 71) given the value of v, the problem BA-EVsub is a convex optimization problem with respect to x; 72) optimal solution of problem BA-EVsub
Figure FDA0002455123430000052
Is a non-increasing function with respect to v; an algorithm is designed and solved based on the two conclusions, and the algorithm is specifically described as follows, wherein the algorithm is marked as Sol-BA:
algorithm step S1: input upper limit value vmaxLower limit value vminEnding the threshold tol of the cycle;
algorithm step S2: according to the condition | vmax-vmin| ≧ tol, determine whether to enter a loop, that is, | vmax-vminIf | ≧ tol, entering a loop, executing the algorithm step S3, | vmax-vminIf the absolute value is less than tol, the loop is not entered, and the algorithm step S7 is executed;
algorithm step S3: setting the value of v to
Figure FDA0002455123430000053
Namely, it is
Figure FDA0002455123430000054
Algorithm step S4: obtaining an optimal value according to a set v value to solve the problem BA-EVsub
Figure FDA0002455123430000055
To correspond to
Figure FDA0002455123430000056
Algorithm step S5: the optimal value obtained according to algorithm step S4
Figure FDA0002455123430000057
Make a determination if
Figure FDA0002455123430000058
The upper limit value v is updatedmaxV; otherwise, the lower limit value v is updatedminReturning to algorithm step S2;
algorithm step S6: ending the circulation;
algorithm step S7: output optimum value
Figure FDA0002455123430000059
v*＝v；
(8) The original problem TCM can be solved by using the output value of the algorithm Sol-BA, and the optimal bandwidth allocation is obtained as follows:
Figure FDA00024551234300000510
obtaining MU of each mobile user through recursive calculationiThe optimal power allocation of (c) is:
Figure FDA00024551234300000511
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