CN113795051B - Antenna-by-antenna power robust optimization method based on NOMA system - Google Patents

Antenna-by-antenna power robust optimization method based on NOMA system Download PDF

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CN113795051B
CN113795051B CN202110939683.7A CN202110939683A CN113795051B CN 113795051 B CN113795051 B CN 113795051B CN 202110939683 A CN202110939683 A CN 202110939683A CN 113795051 B CN113795051 B CN 113795051B
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林泽帆
黄永伟
杨文政
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Guangdong University of Technology
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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
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    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W24/00—Supervisory, monitoring or testing arrangements
    • H04W24/02—Arrangements for optimising operational condition
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
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    • H04W24/06—Testing, supervising or monitoring using simulated traffic
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/26—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service]

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Abstract

The invention relates to a method for optimizing power robustness of antenna by antenna based on NOMA system, comprising the following steps: s1: establishing a constraint optimization target problem of the NOMA system, wherein the constraint optimization target problem comprises a per-antenna power minimization model and quality constraint of robust user service; s2: converting robust user service quality constraints into quadratic matrix inequalities and converting a constraint optimization target problem into a semi-definite programming problem; s3: and solving the semi-positive definite programming problem to obtain the optimal solution or suboptimal solution of the semi-positive definite programming problem. In the scheme, an antenna-by-antenna power model is established, quality constraints of robust user services are given, then S lemma and semi-definite technology are applied to convert the optimization problem into a semi-definite planning problem, and finally the semi-definite planning problem is solved, so that the optimal solution or suboptimal solution of the original problem is quickly solved, the robustness of the system is improved, and the system is closer to practical application.

Description

Antenna-by-antenna power robust optimization method based on NOMA system
Technical Field
The invention relates to the field of signal processing, in particular to a method for optimizing power robustness of antenna by antenna based on a NOMA system.
Background
Currently, non-orthogonal multiple access (NOMA) is an important radio access technology, and is suitable for fifth-generation wireless networks. In recent years, in a multi-user system, the application of the beam forming of the non-orthogonal multiple access becomes more and more popular due to the characteristics of improving the fairness of users, the throughput of the system and the like of the beam forming. NOMA beamforming typically assumes perfect channel state information known at the base station, allowing the base station to apply superposition coding using spatial degrees of freedom, and the receiver to do continuous interference cancellation at manageable cost, while applying continuous interference cancellation techniques can effectively cancel interference caused by weak users. For multi-beam scenarios, advanced beamforming may be applied to mitigate inter-beam or inter-user interference, which may further serve to improve the achievable performance of NOMA-based networks. Generally, the conventional NOMA system only considers the problem of minimizing the total power and only considers perfect channel state information, but in practical application, the perfect channel state information cannot be always obtained, so that the robustness for solving the original problem is low.
In the prior art, chinese invention patent CN111917444a discloses "a resource allocation method suitable for a millimeter wave MIMO-NOMA system", which is disclosed as 11, 10 and 11 months in 2020, and acquires channel state information from a base station to all clients; dividing all users into M groups according to the channel state information; randomly generating a power distribution matrix according to the decoding sequence of the users in each group; calculating the signal-to-leakage-noise ratio of each user according to the power distribution matrix, and optimizing the power distribution matrix by taking the minimum signal-to-leakage-noise ratio in all the maximized users as a target function to obtain an optimal power distribution matrix; allocating transmitting power to each user according to the optimal power allocation matrix; the method is suitable for a millimeter wave MIMO-NOMA system, and the method takes the minimum value of the signal-to-leakage-noise ratio of the user as a target by finishing the power distribution after considering the user grouping, can improve the fairness of the user, and adopts convex optimization to design an optimal power distribution matrix, but the NOMA system only considers the problem of total power minimization and perfect channel state information, and has low robustness.
Disclosure of Invention
The invention provides an antenna-by-antenna power robust optimization method based on a NOMA system, aiming at solving the technical defect of low robustness of solving the original problem in the traditional NOMA system.
In order to realize the purpose of the invention, the technical scheme is as follows:
an antenna-by-antenna power robust optimization method based on a NOMA system comprises the following steps:
s1: establishing a constraint optimization target problem of the NOMA system, wherein the constraint optimization target problem comprises a per-antenna power minimization model and quality constraint of robust user service;
s2: converting robust user service quality constraints into quadratic matrix inequalities and converting a constraint optimization target problem into a semi-definite planning problem;
s3: and solving the semi-definite programming problem to obtain the optimal solution or suboptimal solution of the semi-definite programming problem.
In the scheme, an antenna-by-antenna power model is established, quality constraints of robust user services are given, then S lemma and semi-definite technology are applied to convert the optimization problem into a semi-definite planning problem, and finally the semi-definite planning problem is solved, so that the optimal solution or suboptimal solution of the original problem is quickly solved, the robustness of the system is improved, and the system is closer to practical application.
Preferably, in step S1, the antenna-by-antenna power model is:
Figure BDA0003214343410000021
Figure BDA0003214343410000022
Figure BDA0003214343410000023
{w m the NOMA transmission under multi-user multi-input single-output system in the model, the beam former weight vector of the down link, a is the proportionality coefficient in the power constraint by antenna, e k Is the k-th column of the identity matrix, P k Is an upper bound on the power value given by each antenna constraint; r is n Is user u n The target transmission rate of.
Preferably, the thresholds for the signal to interference and noise ratio of the user and the quality constraint of the robust user service are:
Figure BDA0003214343410000024
Figure BDA0003214343410000025
wherein
Figure BDA0003214343410000026
Is the SINR, h, of the nth user of the mth channel m Is the m-th channel, γ n Is a threshold value, σ, of a user quality of service constraint m Is white gaussian noise for the mth channel.
Preferably, the actual channel h m Involving estimating the channel
Figure BDA0003214343410000027
And an error amount delta m And adding an ellipsoid constraint to the error amount:
Figure BDA0003214343410000028
ε m is an upper bound on the mth channel error quantity, C n Refers to an n-dimensional vector in the complex domain space, and | | · | | | represents a 2-norm of the vector.
Preferably, in step S2, the quality constraint of the robust user service is:
Figure BDA0003214343410000031
Figure BDA0003214343410000032
Figure BDA0003214343410000033
wherein
Figure BDA0003214343410000034
Is the SINR, h, of the nth user of the mth channel m Is the m-th channel, γ n Is a threshold value, σ, of a user quality of service constraint m Is gaussian white noise for the mth channel.
Preferably, in step S2, the actual sir of the users in the qos constraint of the robust user is extracted, and the algorithm formula of the qos constraint of the robust user is changed into a quadratic matrix inequality by using the S theorem.
Preferably, the actual sir of the users is as follows:
Figure BDA0003214343410000035
the above formula translates to:
Figure BDA0003214343410000036
the following optimization problems are obtained by expanding the above formula and combining an antenna-by-antenna power model:
Figure BDA0003214343410000037
Figure BDA0003214343410000038
Figure BDA0003214343410000039
Figure BDA00032143434100000310
Figure BDA00032143434100000311
rank(W j )＝1，1≤j≤M
it is still non-convex to the optimization problem described above, where rank () is the rank of the matrix,
Figure BDA0003214343410000041
and (3) converting the optimization problem into a quadratic matrix inequality by adopting an S theorem to obtain a target problem:
Figure BDA0003214343410000042
Figure BDA0003214343410000043
Figure BDA0003214343410000044
Figure BDA0003214343410000045
μ m,n ≥0,1≤n≤m≤M
Figure BDA00032143434100000413
rank(W j )＝1，1≤j≤M。
in the above scheme, the theorem of S is for any b 1 ∈C n×1 ,b 2 ∈C n×1 ,c 1 ∈R,c 2 E R and for an arbitrary Hermite matrix, the conjugate transpose of the Hermite matrix is equal to itself, A 1 ∈C n×n ,A 2 ∈C n×n Definition of f 1 (x),f 2 (x) The following were used:
Figure BDA0003214343410000046
Figure BDA0003214343410000047
if and only if mu is greater than or equal to 0,
Figure BDA0003214343410000048
the following is true:
Figure BDA0003214343410000049
preferably, in step S3, the non-convex rank-one constraint in the target problem is removed, and the target problem is converted into a semi-positive definite programming problem:
Figure BDA00032143434100000410
Figure BDA00032143434100000411
Figure BDA00032143434100000412
Figure BDA0003214343410000051
μ m,n ≥0,1≤n≤m≤M
Figure BDA0003214343410000052
preferably, the semi-positive definite planning problem is a convex problem.
Preferably, in step S3, a CVX toolkit is used to solve the semi-definite programming problem to obtain an optimal solution or a suboptimal solution.
In the above scheme, the conventional NOMA system only considers the problem of minimizing the total power and only considers perfect channel state information, but in practical application, perfect channel state information cannot always be acquired. Therefore, on the basis, considering imperfect channel state information, a minimization problem of establishing antenna-by-antenna power under the NOMA system is provided, and robust user service quality constraint is given, so that the robustness of the system can be improved, the method is closer to practical application, generally the signal-to-interference-and-noise ratio of a user and the sum of the antenna-by-antenna power are used as evaluation performance, and the smaller the sum of the antenna-by-antenna power is, the better the evaluation performance is.
Compared with the prior art, the invention has the beneficial effects that:
the antenna-by-antenna power robust optimization method based on the NOMA system, provided by the invention, comprises the steps of establishing an antenna-by-antenna power model, providing quality constraints of robust user services, converting the optimization problem into a semi-definite programming problem by applying S lemma and semi-definite technology, and finally solving the semi-definite programming problem, so that the optimal solution or the suboptimal solution of the original problem is quickly solved, the robustness of the system is improved, and the system is closer to practical application.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a model diagram of the NOMA system of the present invention.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
the invention is further illustrated below with reference to the figures and examples.
Example 1
As shown in fig. 1, a method for robust optimization of antenna-by-antenna power based on NOMA system includes the following steps:
s1: establishing a constraint optimization target problem of the NOMA system, wherein the constraint optimization target problem comprises a per-antenna power minimization model and quality constraint of robust user service;
s2: converting robust user service quality constraints into quadratic matrix inequalities and converting a constraint optimization target problem into a semi-definite planning problem;
s3: and solving the semi-positive definite programming problem to obtain the optimal solution or suboptimal solution of the semi-positive definite programming problem.
In the scheme, an antenna-by-antenna power model is established, quality constraints of robust user services are given, the optimization problem is converted into a semi-definite planning problem by applying S lemma and semi-definite technology, and the semi-definite planning problem is solved finally, so that the optimal solution or suboptimal solution of the original problem is solved quickly, the robustness of the system is improved, and the system is closer to practical application.
Preferably, in step S1, the antenna-by-antenna power model is
Figure BDA0003214343410000061
Figure BDA0003214343410000062
Figure BDA0003214343410000063
{w m The NOMA transmission under multi-user multi-input single-output system in the model, the beam former weight vector of the down link, a is the proportionality coefficient in the power constraint by antenna, e k Is the k-th column of the identity matrix, P k Is an upper bound on the power value given by each antenna constraint; r is n Is user u n The target transmission rate of (2).
Preferably, the thresholds for the signal to interference and noise ratio of the user and the quality constraint of the robust user service are:
Figure BDA0003214343410000064
Figure BDA0003214343410000065
wherein
Figure BDA0003214343410000066
Is the SINR, h, of the nth user of the mth channel m Is the m-th channel, γ n Is a threshold, σ, of a user quality of service constraint m Is m atWhite gaussian noise for each channel.
Preferably, the actual channel h m Involving estimating the channel
Figure BDA0003214343410000067
And an error amount delta m And adding an ellipsoid constraint to the error amount:
Figure BDA0003214343410000068
ε m is an upper bound, C, on the mth channel error amount n Refers to an n-dimensional vector in a complex domain space, and | | · | | |, which represents a 2-norm of the vector.
Preferably, in step S2, the quality constraint of the robust user service is:
Figure BDA0003214343410000071
Figure BDA0003214343410000072
Figure BDA0003214343410000073
wherein
Figure BDA0003214343410000074
Is the SINR, h, of the nth user of the mth channel m Is the m-th channel, γ n Is a threshold, σ, of a user quality of service constraint m Is gaussian white noise for the mth channel.
Preferably, in step S3, the actual sir of the users in the qos constraint of the robust user is extracted, and the algorithm formula of the qos constraint of the robust user is changed into a quadratic matrix inequality by using the S theorem.
Preferably, the actual sir of the users is as follows:
Figure BDA0003214343410000075
the above formula translates to:
Figure BDA0003214343410000076
the following optimization problems are obtained by expanding the above formula and combining an antenna-by-antenna power model:
Figure BDA0003214343410000077
Figure BDA0003214343410000078
Figure BDA0003214343410000079
Figure BDA00032143434100000710
Figure BDA00032143434100000712
rank(W j )＝1，1≤j≤M
it remains non-convex for the optimization problem described above, where rank () is the rank of the matrix,
Figure BDA00032143434100000711
and (3) converting the optimization problem into a quadratic matrix inequality by adopting an S theorem to obtain a target problem:
Figure BDA0003214343410000081
Figure BDA0003214343410000082
Figure BDA0003214343410000083
Figure BDA0003214343410000084
μ m,n ≥0,1≤n≤m≤M
Figure BDA00032143434100000813
rank(W j )＝1，1≤j≤M。
in the above scheme, the theorem of S is for any b 1 ∈C n×1 ,b 2 ∈C n×1 ,c 1 ∈R,c 2 E R and for an arbitrary Hermite matrix, the conjugate transpose of the Hermite matrix is equal to itself, A 1 ∈C n×n ,A 2 ∈C n×n Definition of f 1 (x),f 2 (x) The following were used:
Figure BDA0003214343410000085
Figure BDA0003214343410000086
if and only if μ ≧ 0,
Figure BDA0003214343410000087
it holds true for the following:
Figure BDA0003214343410000088
preferably, in step S4, the non-convex rank-one constraint in the target problem is removed, and the target problem is converted into a semi-positive definite programming problem:
Figure BDA0003214343410000089
Figure BDA00032143434100000810
Figure BDA00032143434100000811
Figure BDA00032143434100000812
μ m,n ≥0,1≤n≤m≤M
Figure BDA0003214343410000091
preferably, the semi-positive definite planning problem is a convex problem.
Preferably, in step S5, the CVX toolkit is used to solve the semi-definite programming problem to obtain an optimal solution or a suboptimal solution.
Example 2
As shown in fig. 2, the stronger the channel condition (the smaller the distance between the base station and the user), the larger the subscript. User service quality constraint, that is, the power ratio (signal to interference plus noise ratio) of the signal to interference plus noise of each user is greater than a threshold, and the information of the strong user affects the weak user, in other words, the information of the strong user becomes the interference of the information of the weak user; but conversely, the information of the weak user does not affect the strong user.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. This need not be, nor should it be exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (3)

1. An antenna-by-antenna power robust optimization method based on a NOMA system is characterized by comprising the following steps:
s1: establishing a constraint optimization target problem of the NOMA system, wherein the constraint optimization target problem comprises an antenna-by-antenna power minimization model and quality constraint of robust user service;
s2: converting robust user service quality constraints into quadratic matrix inequalities and converting a constraint optimization target problem into a semi-definite programming problem;
s3: solving the semi-positive definite programming problem to obtain the optimal solution or suboptimal solution of the semi-positive definite programming problem;
in step S1, the antenna-by-antenna power minimization model is
Figure FDA0003855933190000011
Figure FDA0003855933190000012
Figure FDA0003855933190000013
{w m The NOMA transmission under the multi-user multi-input single-output system in the model, the weight vector of the beam former of the down link, and a is the work of antenna by antennaProportionality coefficient in rate constraint, e k Is the k-th column of the identity matrix, P k Is an upper bound on the power value given by each antenna constraint; r is n Is user u n The target transmission rate of (c);
the signal-to-interference-and-noise ratio of the user and the quality constraint threshold of the robust user service are both:
Figure FDA0003855933190000014
Figure FDA0003855933190000015
wherein
Figure FDA0003855933190000016
Is the SINR, h, of the nth user of the mth channel m Is the m-th channel, γ n Is a threshold value, σ, of a user quality of service constraint m Is gaussian white noise of the mth channel;
actual channel h m Involving estimating the channel
Figure FDA0003855933190000017
And error quantity delta m And adding an ellipsoid constraint for the error amount:
Figure FDA0003855933190000018
ε m is an upper bound on the mth channel error quantity, C n The vector is an n-dimensional vector in a complex field space, and | l | · | |, which represents a 2-norm of the vector;
in step S1, the quality constraint of the robust user service is:
Figure FDA0003855933190000021
Figure FDA0003855933190000022
Figure FDA0003855933190000023
wherein
Figure FDA0003855933190000024
Is the SINR, h, of the nth user of the mth channel m Is the m-th channel, γ n Is a threshold, σ, of a user quality of service constraint m Is gaussian white noise for the mth channel;
in step S2, extracting the actual signal to interference plus noise ratio of the user in the robust user service quality constraint, and changing the algorithm formula of the robust user service quality constraint into a quadratic matrix inequality by adopting an S theorem;
the actual signal to interference and noise ratio of the user is as follows:
Figure FDA0003855933190000025
the above formula translates to:
Figure FDA0003855933190000026
the following optimization problems are obtained by expanding the above formula and combining an antenna-by-antenna power model:
Figure FDA0003855933190000027
Figure FDA0003855933190000028
Figure FDA0003855933190000029
Figure FDA00038559331900000210
Figure FDA00038559331900000211
rank(W j )＝1，1≤j≤M
it is still non-convex to the optimization problem described above, where rank () is the rank of the matrix,
Figure FDA0003855933190000031
and (3) converting the optimization problem into a quadratic matrix inequality by adopting an S theorem to obtain a target problem:
Figure FDA0003855933190000032
Figure FDA0003855933190000033
Figure FDA0003855933190000034
Figure FDA0003855933190000035
μ m,n ≥0,1≤n≤m≤M
Figure FDA0003855933190000036
rank(W j )＝1，1≤j≤M；
in step S2, the non-convex rank-one constraint in the target problem is removed, and the target problem is converted into a semi-positive definite programming problem:
Figure FDA0003855933190000037
Figure FDA0003855933190000038
Figure FDA0003855933190000039
Figure FDA00038559331900000310
μ m,n ≥0,1≤n≤m≤M
Figure FDA00038559331900000311
2. the antenna-by-antenna power robust optimization method based on the NOMA system as claimed in claim 1, wherein the semi-positive definite programming problem is a convex problem.
3. The antenna-by-antenna power robust optimization method based on the NOMA system as claimed in claim 2, wherein in step S3, a CVX tool kit is applied to solve a semi-definite programming problem to obtain an optimal solution or a sub-optimal solution.
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