阅读说明：本技术 一种基于noma系统下的逐天线功率鲁棒优化方法 (Antenna-by-antenna power robust optimization method based on NOMA system ) 是由 林泽帆 黄永伟 杨文政 于 2021-08-16 设计创作，主要内容包括：本发明涉及一种基于NOMA系统下的逐天线功率鲁棒优化方法,包括以下步骤：S1：建立NOMA系统的约束优化目标问题,约束优化目标问题包括逐天线功率最小化模型及鲁棒用户服务的质量约束；S2：将鲁棒用户服务质量约束转化为二次矩阵不等式,将约束优化目标问题转化为半正定规划问题；S3：求解半正定规划问题,得到半正定规划问题的最优解或次优解。上述方案中,建立逐天线功率模型,并给出鲁棒用户服务的质量约束,紧接着应用S引理和半正定技术将该优化问题转化为半正定规划问题,最后求解该半正定规划问题,实现了快速求解原问题的最优解或次优解,这样做提高了系统的鲁棒性,使系统更贴近实际应用。(The invention relates to a method for optimizing antenna-by-antenna power robustness based on a NOMA system, which 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 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.)

1. A method for optimizing antenna-by-antenna power robustness 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 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.

2. The method of claim 1, wherein in step S1, the antenna-by-antenna power minimization model is

{w_mThe 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, a is the proportionality coefficient in the power constraint of antenna by antenna, e_kIs the k-th column of the identity matrix, P_kIs an upper bound on the power value given by each antenna constraint; r_nIs user u_nThe target transmission rate of.

3. The antenna-by-antenna power robust optimization method based on the NOMA system as claimed in claim 2, wherein the SINR of the user and the quality constraint threshold of the robust user service are both:

whereinIs the SINR, h, of the nth user of the mth channel_mIs the m-th channel, γ_nIs a threshold value, σ, of a user quality of service constraint_mIs gaussian white noise for the mth channel.

4. The method of claim 3, wherein the actual channel h is an antenna-by-antenna power robust optimization method based on the NOMA system_mInvolving estimating the channelAnd error quantity delta_mAnd adding an ellipsoid constraint to the error amount:

ε_mis an upper bound on the mth channel error quantity, CⁿRefers to an n-dimensional vector in the complex domain space, and | | · | | | represents a 2-norm of the vector.

5. The method of claim 4, wherein in step S2, the quality constraint of robust user service is:

whereinIs the SINR, h, of the nth user of the mth channel_mIs the m-th channel, γ_nIs a threshold value, σ, of a user quality of service constraint_mIs gaussian white noise for the mth channel.

6. The method of claim 5, wherein in step S2, the actual SINR of the users in the robust user QoS constraint is extracted, and the algorithmic formula of the robust user QoS constraint is changed into a quadratic matrix inequality by using S theorem.

7. The method of claim 6, wherein the actual SINR of the user is as follows:

the above formula translates to:

the following optimization problems are obtained by expanding the above formula and combining an antenna-by-antenna power model:

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,

and (3) converting the optimization problem into a quadratic matrix inequality by adopting an S theorem to obtain a target problem:

μ_m,n≥0,1≤n≤m≤M

rank(W_j)＝1，1≤j≤M。

8. the antenna-by-antenna power robust optimization method based on the NOMA system of claim 7, wherein in step S3, the non-convex rank-one constraint in the target problem is removed, and the target problem is transformed into a semi-positive definite programming problem:

μ_m,n≥0,1≤n≤m≤M

9. the method of claim 8, wherein the semi-positive definite programming problem is a convex problem.

10. The method of claim 9, wherein in step S3, a CVX toolkit is applied to solve a semi-definite programming problem to obtain an optimal solution or a sub-optimal solution.

Technical Field

The invention relates to the field of signal processing, in particular to a method for optimizing antenna-by-antenna power robustness 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 is becoming 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 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 user terminals; 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; distributing transmitting power for each user according to the optimal power distribution 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 conventional NOMA system.

In order to realize the purpose, 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 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.

Preferably, in step S1, the antenna-by-antenna power model is:

{w_mthe 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, a is the proportionality coefficient in the power constraint of antenna by antenna, e_kIs the k-th column of the identity matrix, P_kIs an upper bound on the power value given by each antenna constraint; r_nIs user u_nThe 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:

whereinIs the SINR, h, of the nth user of the mth channel_mIs the m-th channel, γ_nIs a threshold value, σ, of a user quality of service constraint_mIs gaussian white noise for the mth channel.

Preferably, the actual channel h_mInvolving estimating the channelAnd error quantity delta_mAnd adding an ellipsoid constraint to the error amount:

ε_mis an upper bound on the mth channel error quantity, CⁿRefers 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:

whereinIs the SINR, h, of the nth user of the mth channel_mIs the m-th channel, γ_nIs a threshold value, σ, of a user quality of service constraint_mIs gaussian white noise for the mth channel.

Preferably, in step S2, the actual sir of the user 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 signal to interference plus noise ratio of the user is as follows:

the above formula translates to:

the following optimization problems are obtained by expanding the above formula and combining an antenna-by-antenna power model:

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,

and (3) converting the optimization problem into a quadratic matrix inequality by adopting an S theorem to obtain a target problem:

μ_m,n≥0,1≤n≤m≤M

rank(W_j)＝1，1≤j≤M。

in the above scheme, the theorem of S is for any b₁∈C^n×1,b₂∈C^n×1,c₁∈R,c₂E R and for an arbitrary Hermite matrix, the conjugate transpose of the Hermite matrix is equal to itself, A₁∈C^n×n,A₂∈C^n×nDefinition of f₁(x),f₂(x) The following were used:

if and only if μ ≧ 0,it holds true for the following:

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:

μ_m,n≥0,1≤n≤m≤M

preferably, the semi-positive definite planning problem is a convex problem.

Preferably, in step S3, the CVX toolkit is used to solve the semi-definite programming problem, so as to obtain an optimal solution or a sub-optimal 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 antenna-by-antenna power robust optimization based on a 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 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.

Preferably, in step S1, the antenna-by-antenna power model is

{w_mThe NOMA transmission under the multi-user multi-input single-output system in the model, the weight vector of the beam former of the downlink, and a is the ratio of the antenna-by-antenna power constraintExample coefficient of e_kIs the k-th column of the identity matrix, P_kIs an upper bound on the power value given by each antenna constraint; r_nIs user u_nThe 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:

whereinIs the SINR, h, of the nth user of the mth channel_mIs the m-th channel, γ_nIs a threshold value, σ, of a user quality of service constraint_mIs gaussian white noise for the mth channel.

Preferably, the actual channel h_mInvolving estimating the channelAnd error quantity delta_mAnd adding an ellipsoid constraint to the error amount:

ε_mis an upper bound on the mth channel error quantity, CⁿRefers 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:

whereinIs the SINR, h, of the nth user of the mth channel_mIs the m-th channel, γ_nIs a threshold value, σ, of a user quality of service constraint_mIs gaussian white noise for the mth channel.

Preferably, in step S3, the actual sir of the user 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 signal to interference plus noise ratio of the user is as follows:

the above formula translates to:

the following optimization problems are obtained by expanding the above formula and combining an antenna-by-antenna power model:

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,

and (3) converting the optimization problem into a quadratic matrix inequality by adopting an S theorem to obtain a target problem:

μ_m,n≥0,1≤n≤m≤M

rank(W_j)＝1，1≤j≤M。

in the above scheme, the theorem of S is for any b₁∈C^n×1,b₂∈C^n×1,c₁∈R,c₂E R and for an arbitrary Hermite matrix, the conjugate transpose of the Hermite matrix is equal to itself, A₁∈C^n×n,A₂∈C^n×nDefinition of f₁(x),f₂(x) The following were used:

if and only if μ ≧ 0,it holds true for the following:

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:

μ_m,n≥0,1≤n≤m≤M

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, so as to obtain an optimal solution or a sub-optimal 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. And are neither required nor 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.