CN112469128B - User maximum sum rate optimization method in environment backscattering access NOMA system - Google Patents

User maximum sum rate optimization method in environment backscattering access NOMA system Download PDF

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CN112469128B
CN112469128B CN202011366997.4A CN202011366997A CN112469128B CN 112469128 B CN112469128 B CN 112469128B CN 202011366997 A CN202011366997 A CN 202011366997A CN 112469128 B CN112469128 B CN 112469128B
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李兴旺
乔大伟
孙江峰
郑一珂
谢珍
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Henan University of Technology
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Abstract

The invention discloses a user maximum sum rate optimization method in an environment backscatter access NOMA system, which is suitable for a system comprising a base station, two users and a backscatter, wherein all equipment is provided with a single antenna. The base station distributes power to two users according to a power distribution principle, backscattering scatters the two users under the condition that a scattering coefficient is larger than 0 and smaller than 1, a joint optimization problem for realizing the optimal sum rate of the two users is established, the optimization problem is a double-target optimization problem about the power distribution coefficient and the backscattering coefficient of the base station, a scattering coefficient is fixed, a Lagrange function is established by utilizing a KKT condition to obtain an optimal value of the power distribution coefficient, the optimal value of the power distribution coefficient is substituted into an original objective function, the optimal value of the scattering coefficient is solved according to the same method, and finally the two solved optimal values are substituted into a sum rate formula to obtain the optimized sum rate.

Description

User maximum sum rate optimization method in environment backscattering access NOMA system
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a user maximum sum rate optimization method in an environment backscattering access NOMA system.
Background
Future 6G technologies promise to support low power wireless connections for large-scale deployments, with high data rates and minimal latency. The power domain NOMA provides hyper-spectral and energy efficient communication with an ambient backscatter communication system in a large-scale internet of things (IoT) network. More specifically, NOMA, which is a technique utilizing superposition coding and Successive Interference Cancellation (SIC), allows multiple cellular devices to communicate over the same frequency spectrum or time resource using different levels of transmission power, and NOMA also ensures fairness between different cellular devices over the same frequency spectrum or time resource. On the other hand, environmental backscatter communication has received great attention because of its ultra-low power consumption communication characteristics.
Over the last few years, academic and industrial communities have shown great research interest in backscatter communications based on non-orthogonal multiple access environments and investigated different aspects of these networks, mainly security and reliability, power joint optimization aspects. However, in the prior art, the SIC decoding is considered to be performed well at the receiving end, but in an actual system, an error may occur in the SIC decoding process. Thus, in this case, the receiver cannot completely correctly remove interference from weak cellular devices that would significantly degrade system performance. And in the existing maximum sum rate optimization, joint optimization of base station power distribution and scattering coefficients in the case of i-SIC is not considered.
Disclosure of Invention
In summary, the method for user maximization and rate optimization in an environmental backscatter access NOMA system proposed in the present invention is applicable to a system including 1 base station, two users, and one backscatter, and all devices are configured with a single antenna, and includes the following steps:
A. base station by S, R i And R j Representing two users, F representing back-scattering,
Figure BDA0002804366460000021
and
Figure BDA0002804366460000022
and H SF Representing base station to user R i And R j And the channel gain of the backscatter F,
Figure BDA0002804366460000023
and
Figure BDA0002804366460000024
representing back-scattering F to the user R i And R j Channel gain of (P) s Is the transmit power of the base station;
B. maximizing the sum rate of an environmental backscatter NOMA system by jointly optimizing the base station power and the backscattering coefficient on the basis of i-SIC decoding, and mathematically expressing the optimization problem considered as
Figure BDA0002804366460000025
s.t.P s ξ≤P s (1-ξ)
0≤ζ≤1
Where ξ represents the base station power distribution coefficient, ζ represents the scattering coefficient of the backscattering, and a constraint bar P s ξ≤P s (1- ξ) represents that the base station transmission power distribution needs to meet the NOMA principle, and the constraint condition of 0 ≦ ζ ≦ 1 represents that the scattering coefficient of the back scattering is between 0 and 1;
user R i And R j The signal-to-interference-and-noise ratio of the received signal is expressed as
Figure BDA0002804366460000026
Figure BDA0002804366460000031
Figure BDA0002804366460000032
Wherein sigma 2 Representing the variance of Gaussian white noise, and alpha represents an i-SIC parameter;
C. solving the optimization problem in the step B to obtain an optimized power distribution parameter xi * And scattering coefficient of backscattering ζ * ；
D. The xi obtained after optimization * And ζ * Substituting the SINR formula to obtain an optimized SINR, and substituting the optimized SINR into the optimization problem in the step B to obtain an optimized sum rate, wherein the optimized sum rate is not the optimal sum rate;
further, the step C specifically comprises
C1, because the objective function has interference item and two variables, it is difficult to get the optimal solution directly, in order to solve the problem effectively, the invention first calculates the effective power distribution coefficient at S according to the fixed value of the scattering coefficient at F, then the calculated power distribution coefficient is substituted into the original formula to get the optimized scattering coefficient,
fixed zeta is zeta * Reduce the optimization problem in B to
Figure BDA0002804366460000033
s.t.P s ξ≤P s (1-ξ)
Constraint P s ξ≤P s (1- ξ) represents that base station transmission power allocation needs to satisfy the PD-NOMA principle;
using the KKT condition to find an effective solution, the Lagrangian function can be expressed as
Figure BDA0002804366460000041
Wherein
Figure BDA00028043664600000411
Represents the Lagrangian multiplier;
partial derivative is obtained on xi by the Lagrange function, and the optimized value xi of xi can be solved *
Figure BDA0002804366460000042
Wherein [ a ]] + Is represented by [ a ]] + ＝max(0,a)，
A, B and C are obtained by calculation
Figure BDA0002804366460000043
Figure BDA0002804366460000044
Figure BDA0002804366460000045
Figure BDA0002804366460000046
Iterative update using a sub-gradient approach
Figure BDA0002804366460000047
Where β represents the step size and c is the iteration index.
Figure BDA0002804366460000048
First, updating through xi, the updated
Figure BDA0002804366460000049
Used to calculate the optimized ξ * ；
C2, mixing xi * Optimization of calculated ζ into original optimization formula can be obtained
Figure BDA00028043664600000410
The constraint implies that the backscattering coefficient is between 0 and 1,
corresponding Lagrangian function of
Figure BDA0002804366460000051
Where lambda represents the lagrangian multiplier,
partial derivative of Zeta is calculated by the Lagrange function, and the optimized value Zeta of Zeta can be solved *
Figure BDA0002804366460000052
Wherein [ a ]] + Is represented by [ a ]] + ＝max(0,a)，
D, E and F are obtained by calculation
Figure BDA0002804366460000053
Figure BDA0002804366460000054
Figure BDA0002804366460000055
Lambda can be iteratively updated using a sub-gradient method
λ(1+c)＝λ(c)+β(c)(ζ-1)
λ is first updated by ζ, the updated λ * For calculating the optimum ζ * 。
Advantageous effects
Compared with the maximization and rate optimization scheme in the existing environment backscattering NOMA system, the method has more practical significance in solving the optimal sum rate of the user under the conditions that the power distribution principle is satisfied, the scattering coefficient is larger than zero and smaller than one, and the method is suitable for i-SIC.
Drawings
FIG. 1 is an environmental backscatter NOMA system model of the present invention;
fig. 2 is a flow chart of the present invention.
Detailed Description
An embodiment of the present invention is given below, and the present invention will be described in further detail.
As shown in FIG. 1, consider a 1 base station, two users and a backscatter ambient backscatter access NOMA system, and all devices are configured with a single antenna, denoted S for base station, R i And R j Representing two users, F representing back-scattering,
Figure BDA0002804366460000061
and
Figure BDA0002804366460000062
and H SF Representing base station to user R i And R j And the channel gain of the backscatter F,
Figure BDA0002804366460000063
and
Figure BDA0002804366460000064
representing backscattering F to user R i And R j Channel gain of (P) s Is the transmit power of the base station.
The maximum user rate and the constraint are expressed as follows
Figure BDA0002804366460000065
s.t.P s ξ≤P s (1-ξ)
0≤ζ≤1
Where ξ represents the base station power distribution coefficient, ζ represents the backscattering scattering coefficient, and the constraint bar P s ξ≤P s (1-xi) indicates that the base station transmission power distribution needs to meet the NOMA principle, and the constraint condition of 0 ≦ ζ ≦ 1 indicates that the scattering coefficient of the backscattering is between 0 and 1. The SINR is expressed as
Figure BDA0002804366460000071
Figure BDA0002804366460000072
Figure BDA0002804366460000073
Wherein sigma 2 Represents the variance of gaussian white noise and alpha represents the i-SIC parameter.
Fixed zeta is zeta * Simplifying the optimization problem in B to
Figure BDA0002804366460000074
s.t.P s ξ≤P s (1-ξ)
Constraint P s ξ≤P s (1- ξ) indicates that the base station transmit power allocation needs to satisfy the NOMA principle.
Using the KKT condition to find an effective solution, the Lagrangian function can be expressed as
Figure BDA0002804366460000075
Wherein
Figure BDA0002804366460000076
Representing the lagrange multiplier.
Partial derivative is obtained on xi by the Lagrange function, and the optimized value xi of xi can be solved *
Figure BDA0002804366460000077
Wherein [ a ]] + Is represented by [ a ]] + ＝max(0，a)。
A, B and C are obtained by calculation
Figure BDA0002804366460000081
Figure BDA0002804366460000082
Figure BDA0002804366460000083
Figure BDA0002804366460000084
Iterative updating using a sub-gradient method
Figure BDA0002804366460000085
Where β represents the step size and c is the iteration index.
Figure BDA0002804366460000086
First, updating through xi, updated
Figure BDA0002804366460000087
Xi used to calculate the optimization * 。
Xi will be * Optimization of calculated ζ into original optimization formula can be obtained
Figure BDA0002804366460000088
The constraint indicates that the backscattering has a scattering coefficient between 0 and 1.
The corresponding Lagrangian function is
Figure BDA0002804366460000089
Where λ represents the lagrangian multiplier.
Partial derivative of Zeta is calculated by the Lagrange function, and the optimized value Zeta of Zeta can be solved *
Figure BDA0002804366460000091
Wherein [ a ]] + Is represented by [ a ]] + ＝max(0,a)。
D, E and F are obtained by calculation
Figure BDA0002804366460000092
Figure BDA0002804366460000093
Figure BDA0002804366460000094
Lambda can be iteratively updated using a sub-gradient method
λ(1+c)＝λ(c)+β(c)(ζ-1)
λ is first updated by ζ, the updated λ * For calculating the optimum ζ * 。
The xi obtained after optimization * And ζ * And substituting the optimized SINR into the SINR formula to obtain an optimized SINR, and substituting the optimized SINR into the optimization problem in B to obtain an optimized sum rate, wherein the optimized sum rate is not the optimal sum rate.
The above embodiments are merely illustrative of the present invention, and those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (2)

1. A user maximum and rate optimization method in an environment backscatter access NOMA system is suitable for a system comprising 1 base station, two users and one backscatter, and all devices are configured with a single antenna, and is characterized in that: the method comprises the following steps:
A. base station by S, R i And R j Representing two users, F representing backscatter,
Figure FDA0003705881440000011
and
Figure FDA0003705881440000012
and H SF Representing base station to user R i And R j And the channel gain of the backscatter F,
Figure FDA0003705881440000013
and
Figure FDA0003705881440000014
representing backscatter F to user R i And R j Channel gain of (P) s Is the transmit power of the base station;
B. maximization of sum rate of ambient backscatter NOMA system is achieved by joint optimization of base station power and backscatter coefficients on the basis of non-ideal successive interference cancellation i-SIC decoding, the optimization problem considered being mathematically expressed as
Figure FDA0003705881440000015
s.t.P s ξ≤P s (1-ξ)
0≤ζ≤1
Where ξ denotes the base station power distribution coefficient, ζ denotes the backscattering coefficient, the constraint bar P s ξ≤P s (1-xi) represents that the base station transmission power distribution needs to meet the NOMA principle, the constraint condition of 0 to 1 represents that the scattering coefficient of the directional scattering is between 0 and 1,
user R i And R j The signal-to-interference-and-noise ratio of the received signal is expressed as
Figure FDA0003705881440000016
Figure FDA0003705881440000017
Figure FDA0003705881440000021
Wherein sigma 2 Representing the variance of Gaussian white noise, and alpha represents an i-SIC parameter;
C. solving the optimization problem in the step B to obtain an optimized power distribution parameter xi * And scattering coefficient of backscattering ζ * ；
D is to optimize the obtained xi * And ζ * And substituting the optimized signal to interference plus noise ratio into a signal to interference plus noise ratio formula to obtain an optimized signal to interference plus noise ratio, and substituting the optimized signal to interference plus noise ratio into the optimization problem in the step B to obtain an optimized sum rate.
2. The method for optimizing user maximum sum rate in an environmental backscatter access NOMA system as claimed in claim 1, wherein the optimization problem in step C is solved to obtain the optimization sum rate, and the specific process is as follows:
c1, in order to effectively obtain the optimal solution of the objective function, the optimization method firstly calculates the effective power distribution coefficient at S according to the fixed value of the scattering coefficient at F, then the calculated power distribution coefficient is substituted into the original formula to obtain the optimized scattering coefficient,
fixed zeta is zeta * Simplifying the optimization problem in B to
Figure FDA0003705881440000022
s.t.P s ξ≤P s (1-ξ)
Constraint P s ξ≤P s (1- ξ) indicates that the base station transmit power allocation needs to satisfy the NOMA principle,
the KKT condition is used to find an effective solution, and the Lagrangian function is expressed as
Figure FDA0003705881440000031
Wherein
Figure FDA0003705881440000032
The lagrange multiplier is represented by a number of words,
the Lagrange function calculates partial derivative of xi, and solves the optimized value xi of xi *
Figure FDA0003705881440000033
Wherein [ a ]] + Is represented by [ a ]] + ＝max(0，a)，
A, B and C are obtained by calculation
Figure FDA0003705881440000034
Figure FDA0003705881440000035
Figure FDA0003705881440000036
Figure FDA0003705881440000037
Iterative update using sub-gradient method
Figure FDA0003705881440000038
Wherein beta represents the step length, and c is an iteration index;
Figure FDA0003705881440000039
first, updating through xi, the updated
Figure FDA00037058814400000310
Used to calculate the optimized ξ * ，
C2 converts xi * Optimization of the calculated zeta into the original optimization formula, resulting in
Figure FDA00037058814400000311
s.t.0≤ζ≤1
The constraint condition means that the backscattering scattering coefficient is between 0 and 1, and the corresponding Lagrangian function is
Figure FDA0003705881440000041
Where lambda represents the lagrangian multiplier,
solving partial derivative of zeta by Lagrange function, and solving zeta optimized value *
Figure FDA0003705881440000042
Wherein [ a ]] + Is represented by [ a ]] + ＝max(0，a)，
D, E and F are obtained by calculation
Figure FDA0003705881440000043
Figure FDA0003705881440000044
Figure FDA0003705881440000045
Lambda is iteratively updated using a sub-gradient method
λ(1+c)＝λ(c)+β(c)(ζ-1)
λ is first updated by ζ, the updated λ * For calculating the optimum ζ * 。
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