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CN112291841A - User cooperation method based on backscattering under power domain non-orthogonal multiple access - Google Patents

User cooperation method based on backscattering under power domain non-orthogonal multiple access Download PDF

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CN112291841A
CN112291841A CN202011150460.4A CN202011150460A CN112291841A CN 112291841 A CN112291841 A CN 112291841A CN 202011150460 A CN202011150460 A CN 202011150460A CN 112291841 A CN112291841 A CN 112291841A
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user
power
base station
users
received signal
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陈炜宇
丁海洋
王世练
李海鹏
王昊
辛可为
胡礼
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National University of Defense Technology
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W52/00Power management, e.g. Transmission Power Control [TPC] or power classes
    • H04W52/04Transmission power control [TPC]
    • H04W52/30Transmission power control [TPC] using constraints in the total amount of available transmission power
    • H04W52/34TPC management, i.e. sharing limited amount of power among users or channels or data types, e.g. cell loading
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W52/00Power management, e.g. Transmission Power Control [TPC] or power classes
    • H04W52/04Transmission power control [TPC]
    • H04W52/30Transmission power control [TPC] using constraints in the total amount of available transmission power
    • H04W52/34TPC management, i.e. sharing limited amount of power among users or channels or data types, e.g. cell loading
    • H04W52/346TPC 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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  • Computer Networks & Wireless Communication (AREA)
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Abstract

本发明属于无线通信领域,公开了一种功率域非正交多址下基于反向散射的用户协作方法。本发明通过:基站基于功率域非正交多址接入技术向用户广播下行信号;瞬时信道条件较好的用户基于反向散射技术,将一部分接收信号功率用于译码,将其余接收信号反射至瞬时信道条件较差的用户以增强瞬时信道条件较差的用户处的信干噪比;以达到信息速率要求为前提,调整基站功率分配和各用户用于反向散射协作的功率占其总接收信号功率的百分比,达到最小化基站总功耗的目的。本发明能够有效提高基于功率域非正交多址接入的蜂窝网下行通信系统的传输可靠性和传输有效性,且相较于现有的转发协作方法进一步降低了功耗。

Figure 202011150460

The invention belongs to the field of wireless communication, and discloses a user cooperation method based on backscattering under non-orthogonal multiple access in the power domain. The invention adopts: the base station broadcasts downlink signals to users based on the power domain non-orthogonal multiple access technology; the users with better instantaneous channel conditions use a part of the received signal power for decoding based on the backscattering technology, and reflect the rest of the received signals To users with poor instantaneous channel conditions, the signal-to-interference noise ratio at users with poor instantaneous channel conditions is enhanced; on the premise of meeting the information rate requirement, the power allocation of the base station and the power used for backscatter cooperation by each user are adjusted to account for their total power. The percentage of received signal power to minimize the total power consumption of the base station. The invention can effectively improve the transmission reliability and transmission effectiveness of the cellular network downlink communication system based on the power domain non-orthogonal multiple access, and further reduces the power consumption compared with the existing forwarding cooperation method.

Figure 202011150460

Description

User cooperation method based on backscattering under power domain non-orthogonal multiple access
Technical Field
The invention belongs to the technical field of wireless communication, relates to a user cooperation method based on backscattering and a corresponding optimal resource allocation method, and is suitable for a cellular network downlink communication system based on power domain non-orthogonal multiple access.
Background
The non-orthogonal multiple access technology realizes high-spectrum-efficiency communication by bearing information of different users on the same frequency time resource, and is considered to be a multiple access mode with great application prospect in the 5G and later 5G times. The non-orthogonal multiple access technology of the power domain distributes different powers for different users on the basis of superposition coding on the transmitting end, and adopts the continuous interference elimination technology to realize interference elimination and information recovery on the receiving end. The comparison document "Concept and positive requirements of non-orthogonal multiple access (NOMA) for future radio access" published on the International Symposium on Intelligent Signal Processing and Communication Systems indicates that non-orthogonal multiple access techniques in the power domain can achieve a system level performance gain of 30% over orthogonal multiple access techniques.
Cooperative communication has received much attention in a power domain non-orthogonal multiple access scenario as a means to improve the reliability of a communication system. A comparison document, "Cooperative non-orthogonal multiple access in 5G systems", published on IEEE Communication Letters, indicates that half-duplex forwarding between users in a cellular downlink Communication system based on power domain non-orthogonal multiple access can achieve K-order diversity gain at all K users. However, this forwarding cooperation method needs to consume additional time resources, and is a method for improving transmission reliability at the expense of transmission effectiveness. To this end, the reference document "Full-Duplex Device-to-Device-air cooperative non-orthogonal multiple access" published on IEEE Transactions on Vehicular Technology proposes to adopt a Full-Duplex architecture at the user, thereby achieving user cooperation without additional time resources. However, user cooperation based on full-duplex forwarding may introduce self-interference, causing the user to degrade the quality of its own received signal while assisting other users. In addition, no matter half-duplex forwarding or full-duplex forwarding, a user serving as a forwarding node needs to generate a local carrier first and then modulate information onto the carrier to be forwarded, so that energy consumption is high. Therefore, a user cooperation mechanism that does not occupy additional time resources, does not introduce self-interference, and has low energy consumption is needed.
Disclosure of Invention
The purpose of the present invention is to overcome the deficiencies of the prior art, and provide a user cooperation mechanism for a cellular network downlink communication system based on power domain non-orthogonal multiple access, so as to achieve user cooperation without occupying additional time resources, introducing self-interference, and consuming less energy. Meanwhile, the invention provides a corresponding optimal resource allocation method, thereby simultaneously improving the transmission reliability and the transmission effectiveness of the system.
The technical scheme adopted by the invention is as follows:
the user cooperation method based on backscattering under the power domain non-orthogonal multiple access comprises the following steps:
1) the downlink communication process between the base station and the multiple users is divided in time into successive time blocks, each time block,
the base station broadcasts the information of all users through superposition coding based on a power domain non-orthogonal multiple access technology: based on two-user scenario, for each time block, the user with better instantaneous channel condition is denoted as user 1, the user with worse instantaneous channel condition is denoted as user 2, and the power allocated to user 1 and user 2 by the base station is denoted as P respectively1And P2The base station broadcasts the information of all users through superposition coding based on the power domain non-orthogonal multiple access technology, and the received signal at the user 1 is represented as
Figure BDA0002741039210000021
Wherein x1And x2Respectively representing the normalized signals (E { | x) transmitted by the base station to user 1 and user 21|2}=E{|x2|2}=1),h1Representing the channel coefficient, n, from the base station to user 11Representing additive white gaussian noise at user 1, with power expressed as
Figure BDA0002741039210000022
2) Based on the backscattering technology, the user with better channel condition uses a part of received signal power for decoding by adjusting local load impedance, and reflects the rest received signals to the user with poorer channel condition, thereby achieving the purpose of enhancing the received signal-to-interference-and-noise ratio of the user with poorer channel condition:
based on the two-user scenario, the power used for backscatter coordination at user 1 as a percentage of its total received signal power is expressed as β1User 1 first attempts to recover x2Expressing the corresponding SINR as
Figure BDA0002741039210000023
User 1 successfully recovers x according to shannon's formula2Under the condition that
Figure BDA0002741039210000024
Wherein R is2Indicates the data rate transmitted by the base station to user 2; user 1 then attempts to recover x1The corresponding signal-to-noise ratio is expressed as
Figure BDA0002741039210000025
User 1 successfully recovers x according to shannon's formula1Under the condition that
Figure BDA0002741039210000026
Wherein R is1Represents the data rate transmitted by the base station to user 1;
3) users with poor channel conditions use all the received signal power for decoding:
based on the two-user scenario, the received signal at user 2 is represented as
Figure BDA0002741039210000027
Wherein h is2Representing the channel coefficients from the base station to user 2, g representing the channel coefficients from user 1 to user 2, n2Representing additive white gaussian noise at user 2, with power expressed as
Figure BDA0002741039210000028
User 2 uses all received signal power for decoding, attempting to recover x2Expressing the corresponding SINR as
Figure BDA0002741039210000029
User 2 successfully recovers x2Under the condition that
Figure BDA00027410392100000210
And the inequality sign in equation (5) is achieved by subscriber 1 adjusting the local load impedance so that the backscatter signal arriving at subscriber 2 is in phase with the direct transmission channel;
4) on the premise of meeting the requirement of a given information rate, the power distribution of the base station and the percentage of the power used by each user for backscattering cooperation in the total received signal power are adjusted, so that the aim of minimizing the total power consumption of the base station is achieved:
based on two-user scenario, the power P allocated to user 1 and user 2 by the base station is adjusted1And P2And adjusting the power used for backscatter coordination at user 1 as a percentage of its total received signal power, beta1Eventually with minimum total base station power consumption (P)1+P2) Achieving information transmission rates R corresponding to user 1 and user 21And R2(ii) a Based on gamma in formula (5)22Strict lower bound ofγ′22To approximate the signal to interference and noise ratio at user 2 to determine the effective minimum total power consumption P1+P2The resource allocation scheme of (2) representing the corresponding optimization problem as
Figure BDA0002741039210000031
And (6) solving through algebraic operation, and determining a minimum resource allocation scheme as follows:
Figure BDA0002741039210000032
Figure BDA0002741039210000033
Figure BDA0002741039210000034
wherein
Figure BDA0002741039210000035
Figure BDA0002741039210000036
Compared with the user cooperation mechanism in the existing power domain non-orthogonal multiple access cellular network downlink communication system, the invention has the beneficial effects that:
(1) improving transmission reliability without sacrificing transmission effectiveness
The present invention reduces the total power required to achieve the transmission rate, and thus the outage rate (when the total power required is greater than the total power allowed, an outage occurs), through a backscatter coordination mechanism and optimal resource allocation. The backscattering cooperation mechanism provided by the invention does not cause transmission rate loss because no additional time slot is needed. Conventional half-duplex forwarding cooperation can also achieve the purpose of reducing the outage rate by reducing the total power required, but it creates a rate penalty because additional forwarding slots are required.
(2) No self-interference and low power consumption
User cooperation based on full-duplex forwarding can improve transmission reliability without sacrificing transmission effectiveness. Compared with a user cooperation mechanism based on full-duplex forwarding, the backscattering user cooperation mechanism provided by the invention does not introduce self-interference. Meanwhile, the backscattering cooperation does not need a user to generate a local carrier, so that the power consumption of the user can be reduced compared with the full-duplex forwarding user cooperation and the half-duplex forwarding user cooperation.
Drawings
Fig. 1 is a schematic diagram of a backscatter user cooperation mechanism in a downlink communication system of a power domain non-orthogonal multiple access cellular network in the case of an embodiment of two users;
fig. 2 is a graph comparing the interruption rate of the backscattering cooperation method proposed by the present invention with the interruption rate of the existing cooperation method under the optimal resource allocation for the downlink communication system of the power domain non-orthogonal multiple access cellular network under the rayleigh channel;
fig. 3 is a graph comparing expected rates under optimal resource allocation (the expected rate is defined as the sum of the rates reached by the users) by using the backscattering cooperation method proposed by the present invention and the existing cooperation method for a downlink communication system of a power domain non-orthogonal multiple access cellular network under a rayleigh channel.
Detailed Description
The invention is described in further detail below with reference to the figures and specific examples.
Referring to the attached figure 1, the invention provides a backscattering-based user cooperation method under power domain non-orthogonal multiple access, which is specifically realized by the following steps:
step 1, dividing the downlink communication process between a base station and multiple users into continuous time blocks in time, wherein in each time block, the base station broadcasts the information of all users through superposition coding based on a power domain non-orthogonal multiple access technology:
based on two-user scenario, for each time block, the user with better instantaneous channel condition is denoted as user 1, the user with worse instantaneous channel condition is denoted as user 2, and the power allocated to user 1 and user 2 by the base station is denoted as P respectively1And P2The base station broadcasts the information of all users through superposition coding based on the power domain non-orthogonal multiple access technology, and the received signal at the user 1 is represented as
Figure BDA0002741039210000041
Wherein x1And x2Respectively representing the normalized signals (E { | x) transmitted by the base station to user 1 and user 21|2}=E{|x2|2}=1),h1Representing the channel coefficient, n, from the base station to user 11Representing additive white gaussian noise at user 1, with power expressed as
Figure BDA0002741039210000042
Step 2, the user with better channel condition uses a part of received signal power for decoding by adjusting local load impedance based on backscattering technology, and reflects the rest received signals to the user with worse channel condition, so as to achieve the purpose of enhancing the received signal-to-interference-and-noise ratio of the user with worse channel condition:
based on the two-user scenario, the power used for backscatter coordination at user 1 as a percentage of its total received signal power is expressed as β1User 1 first attempts to recover x2Expressing the corresponding SINR as
Figure BDA0002741039210000043
User 1 successfully recovers x according to shannon's formula2Under the condition that
Figure BDA0002741039210000044
Wherein R is2Indicates the data rate transmitted by the base station to user 2; user 1 then attempts to recover x1The corresponding signal-to-noise ratio is expressed as
Figure BDA0002741039210000045
User 1 successfully recovers x according to shannon's formula1Under the condition that
Figure BDA0002741039210000046
Wherein R is1Represents the data rate transmitted by the base station to user 1;
step 3, the users with poor channel conditions use all received signal powers for decoding:
based on the two-user scenario, the received signal at user 2 is represented as
Figure BDA0002741039210000047
Wherein h is2Representing the channel coefficients from the base station to user 2, g representing the channel coefficients from user 1 to user 2, n2Representing additive white gaussian noise at user 2, with power expressed as
Figure BDA0002741039210000048
User 2 uses all received signal power for decoding, attempting to recover x2Expressing the corresponding SINR as
Figure BDA0002741039210000049
User 2 successfully recovers x2Under the condition that
Figure BDA00027410392100000410
And the unequal sign in equation (5) adjusts the local load impedance by subscriber 1 so that the reverse direction to subscriber 2 is reachedThe scattering signal and the direct transmission channel are in phase;
and 4, on the premise of meeting the requirement of a given information rate, adjusting the power distribution of the base station and the percentage of the power used by each user for backscattering cooperation in the total received signal power of the users, so as to achieve the purpose of minimizing the total power consumption of the base station:
based on two-user scenario, the power P allocated to user 1 and user 2 by the base station is adjusted1And P2And adjusting the power used for backscatter coordination at user 1 as a percentage of its total received signal power, beta1Eventually with minimum total base station power consumption (P)1+P2) Achieving information transmission rates R corresponding to user 1 and user 21And R2(ii) a Based on gamma in formula (5)22Of strict lower bound of γ'22To approximate the signal to interference and noise ratio at user 2 to determine the effective minimum total power consumption P1+P2The resource allocation scheme of (2) representing the corresponding optimization problem as
Figure BDA0002741039210000051
And (6) solving through algebraic operation, and determining a minimum resource allocation scheme as follows:
Figure BDA0002741039210000052
Figure BDA0002741039210000053
Figure BDA0002741039210000054
wherein
Figure BDA0002741039210000055
Figure BDA0002741039210000056
To verify the effectiveness of the present invention, a comparison of the performance of the prior art method and the present invention in the case of two users is given below with reference to fig. 2 and 3. The existing methods involved include:
1. no cooperation: the basic power domain non-orthogonal multiple access cellular network downlink communication system is that users do not cooperate with each other.
2. Traditional forwarding: the base station occupies a time slot resource with a certain length each time to complete downlink transmission, and the user 1 consumes the time slot resource with the same length to forward the information of the user 2 to the user 2.
3. Adaptive forwarding: only when the user 1 forwards the information of the user 2 to the user 2, which can help the user 2 to successfully recover the information from the occurrence of the information interruption, the user 1 consumes the equal-length time slot resources after the base station completes the downlink transmission and forwards the information of the user 2 to the user 2. Otherwise, the users do not cooperate with each other.
The number of simulation time blocks is set to 107The time length of the time block is set to be equal time length 1s, the average power gain of the channels from the base station to the two users is set to be 1 and 0.5 respectively, the average power gain of the channels between the users is 0.5, and the target rates of the two users are 1bit/s/Hz and 0.5bit/s/Hz respectively. The additive white gaussian noise power at both users is normalized to 1, and the ratio of the total power allowed to be consumed by the base station (in both conventional and adaptive forwarding, also including the user) to the normalized noise power is taken as the signal-to-noise ratio (in dB). For the existing cooperative methods such as no cooperation, traditional forwarding, adaptive forwarding and the like and the backscattering cooperative method provided by the invention, the resource allocation is optimized in each time block respectively, so that the total power required to be consumed is minimum.
The simulation obtains the variation curve of the interruption rate with the signal-to-noise ratio of the downlink communication system of the non-orthogonal multiple access cellular network under the rayleigh channel condition by using the three existing methods and by using the backscattering cooperation method proposed by the present invention, as shown in fig. 2. Compared with a non-cooperation method, the backscattering cooperation method provided by the invention can effectively reduce the interruption rate of the system and improve the transmission reliability of the system.
The simulation results in the curve of the expected rate of the non-orthogonal multiple access cellular network downlink communication system along with the signal-to-noise ratio under the rayleigh channel condition by using the three existing methods and by using the backscattering cooperation method proposed by the present invention, as shown in fig. 3. It can be seen that the backscattering cooperation method proposed by the present invention has the highest expected rate compared with other existing methods, i.e. the transmission efficiency of the system can be improved.
While the above description shows and describes embodiments of the invention in its application, it is to be understood that the invention is not limited to the precise form disclosed herein and that the invention is not to be considered as limited to the disclosed embodiments, but is capable of use in various other combinations, modifications, and environments and is capable of modifications within the scope of the inventive concept as described herein, by the teachings set forth above, or by the techniques of the related art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (1)

1.功率域非正交多址下基于反向散射的用户协作方法,其特征在于,包含以下步骤:1. The user collaboration method based on backscattering under non-orthogonal multiple access in power domain, is characterized in that, comprises the following steps: 1)将基站与多用户间的下行通信过程在时间上分割为连续的时间块,每个时间块内,1) The downlink communication process between the base station and the multi-users is divided into continuous time blocks in time, and in each time block, 基站基于功率域非正交多址接入技术,将所有用户的信息通过叠加编码进行广播:Based on the power domain non-orthogonal multiple access technology, the base station broadcasts the information of all users through superposition coding: 基于两用户场景,对于每个时间块,将瞬时信道条件较好的用户表示为用户1,将瞬时信道条件较差的用户表示为用户2,将基站分配给用户1和用户2的功率分别表示为P1和P2,基站基于功率域非正交多址接入技术,将所有用户的信息通过叠加编码进行广播,将用户1处的接收信号表示为Based on the two-user scenario, for each time block, the user with better instantaneous channel condition is denoted as user 1, the user with poor instantaneous channel condition is denoted as user 2, and the powers allocated by the base station to user 1 and user 2 are denoted respectively For P 1 and P 2 , the base station broadcasts the information of all users through superposition coding based on the power domain non-orthogonal multiple access technology, and the received signal at user 1 is expressed as
Figure FDA0002741039200000011
Figure FDA0002741039200000011
其中x1和x2分别表示基站传输给用户1和用户2的归一化信号(E{|x1|2}=E{|x2|2}=1),h1表示基站到用户1的信道系数,n1表示用户1处的加性高斯白噪声,其功率表示为
Figure FDA0002741039200000012
where x 1 and x 2 represent the normalized signals transmitted by the base station to user 1 and user 2 respectively (E{|x 1 | 2 }=E{|x 2 | 2 }=1), h 1 represents the base station to user 1 The channel coefficient of , n 1 represents the additive white Gaussian noise at user 1, and its power is expressed as
Figure FDA0002741039200000012
2)信道条件较好的用户基于反向散射技术,通过调整本地负载阻抗,将一部分接收信号功率用于译码,将其余接收信号反射至信道条件较差的用户,达到增强信道条件较差的用户处的接收信干噪比的目的:2) Based on the backscattering technology, users with better channel conditions use part of the received signal power for decoding by adjusting the local load impedance, and reflect the rest of the received signals to users with poor channel conditions, so as to enhance the performance of users with poor channel conditions. The purpose of the received signal-to-interference-noise ratio at the user: 基于两用户场景,将用户1处用于反向散射协作的功率占其总接收信号功率的百分比表示为β1,用户1首先尝试恢复x2,将相应的信干噪比表示为Based on the two-user scenario, the percentage of the power used for backscatter cooperation at user 1 to its total received signal power is expressed as β 1 , and user 1 first tries to recover x 2 , and the corresponding signal-to-interference-noise ratio is expressed as
Figure FDA0002741039200000013
Figure FDA0002741039200000013
根据香农公式,用户1成功恢复x2的条件为
Figure FDA0002741039200000014
其中R2表示基站传输给用户2的数据速率;随后用户1尝试恢复x1,将相应的信噪比表示为
According to Shannon's formula, the condition for user 1 to successfully recover x 2 is
Figure FDA0002741039200000014
where R 2 represents the data rate transmitted by the base station to user 2; then user 1 attempts to recover x 1 , and the corresponding signal-to-noise ratio is expressed as
Figure FDA0002741039200000015
Figure FDA0002741039200000015
根据香农公式,用户1成功恢复x1的条件为
Figure FDA0002741039200000016
其中R1表示基站传输给用户1的数据速率;
According to Shannon's formula, the condition for user 1 to successfully recover x 1 is
Figure FDA0002741039200000016
where R 1 represents the data rate that the base station transmits to user 1;
3)信道条件较差的用户将所有接收信号功率用于译码:3) Users with poor channel conditions use all received signal power for decoding: 基于两用户场景,将用户2处的接收信号表示为Based on the two-user scenario, the received signal at user 2 is expressed as
Figure FDA0002741039200000017
Figure FDA0002741039200000017
其中h2表示基站到用户2的信道系数,g表示用户1到用户2的信道系数,n2表示用户2处的加性高斯白噪声,其功率表示为
Figure FDA0002741039200000018
用户2将所有接收信号功率用于译码,尝试恢复x2,将相应的信干噪比表示为
where h 2 represents the channel coefficient from the base station to user 2, g represents the channel coefficient from user 1 to user 2, n 2 represents the additive white Gaussian noise at user 2, and its power is expressed as
Figure FDA0002741039200000018
User 2 uses all received signal power for decoding, tries to recover x 2 , and expresses the corresponding signal-to-interference-noise ratio as
Figure FDA0002741039200000019
Figure FDA0002741039200000019
用户2成功恢复x2的条件为
Figure FDA00027410392000000110
且式(5)中的不等号通过用户1调整本地负载阻抗使得到达用户2的反向散射信号与直传信道同相而实现;
The condition for user 2 to successfully recover x 2 is
Figure FDA00027410392000000110
And the inequality sign in formula (5) is realized by user 1 adjusting the local load impedance so that the backscattered signal reaching user 2 is in phase with the direct transmission channel;
4)以达到给定的信息速率要求为前提,调整基站功率分配和各用户用于反向散射协作的功率占其总接收信号功率的百分比,达到最小化基站总功耗的目的:4) On the premise of achieving a given information rate requirement, adjust the power allocation of the base station and the percentage of the power used by each user for backscatter cooperation to the total received signal power to minimize the total power consumption of the base station: 基于两用户场景,通过调整基站分配给用户1和用户2的功率P1和P2,以及调整用户1处用于反向散射协作的功率占其总接收信号功率的百分比β1,最终以最小的基站总功耗(P1+P2)达到对应于用户1和用户2的信息传输速率R1和R2;基于式(5)中γ22的严格下界γ′22来近似用户2处的信干噪比,以确定有效的最小化总功耗P1+P2的资源分配方案,将对应的优化问题表示为Based on the two-user scenario, by adjusting the powers P 1 and P 2 allocated by the base station to user 1 and user 2, and adjusting the percentage β 1 of the power used for backscatter cooperation at user 1 to its total received signal power, the minimum The total power consumption of the base station (P 1 +P 2 ) reaches the information transmission rates R 1 and R 2 corresponding to user 1 and user 2 ; based on the strict lower bound γ′ 22 of γ 22 in Eq. Signal-to-interference-noise ratio to determine an effective resource allocation scheme that minimizes the total power consumption P 1 +P 2 , and the corresponding optimization problem is expressed as
Figure FDA0002741039200000021
Figure FDA0002741039200000021
通过代数运算求解(6),确定最小资源分配方案为:Solve (6) through algebraic operations, and determine the minimum resource allocation scheme as:
Figure FDA0002741039200000022
Figure FDA0002741039200000022
Figure FDA0002741039200000023
Figure FDA0002741039200000023
Figure FDA0002741039200000024
Figure FDA0002741039200000024
其中in
Figure FDA0002741039200000025
Figure FDA0002741039200000025
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