CN115865148A - De-cellular MIMO robust beamforming method under non-ideal channel - Google Patents

De-cellular MIMO robust beamforming method under non-ideal channel Download PDF

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CN115865148A
CN115865148A CN202310134418.0A CN202310134418A CN115865148A CN 115865148 A CN115865148 A CN 115865148A CN 202310134418 A CN202310134418 A CN 202310134418A CN 115865148 A CN115865148 A CN 115865148A
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CN115865148B (en
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高文奂
张余
张治中
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Nanjing University of Information Science and Technology
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Abstract

本发明公开了一种非理想信道下的去蜂窝MIMO鲁棒性波束赋形方法，步骤为：构建去蜂窝分布式大规模MIMO的框架；获取框架所需参数；对参数误差，加入误差约束，构建误差信道模型；构建可达速率与误差信道模型的信道误差约束下功率最小化模型，提升模型鲁棒性；将功率最小化模型的目标函数从

Figure ZY_1
范数最小化问题近似成一个凸的加权的
Figure ZY_2
范数问题，并通过迭代获取足够的稀疏性；将可达速率约束条件转化为线性矩阵不等式模型；将信道误差约束转化为线性矩阵不等式模型；将得到的模型转化为SDP问题，通过凸优化工具箱求解，得到最优的波束赋形向量。本发明实现了在存在信道误差的情况下，保证用户可达速率，满足服务质量的同时将系统传输功率最小化。

Figure 202310134418

The invention discloses a robust beamforming method for de-cellular MIMO under non-ideal channels. The steps are: constructing a framework for de-cellular distributed large-scale MIMO; obtaining parameters required by the framework; adding error constraints to parameter errors, Construct the error channel model; construct the power minimization model under the channel error constraint of the reachable rate and error channel model, and improve the robustness of the model; the objective function of the power minimization model is changed from

Figure ZY_1
The norm minimization problem is approximated as a convex weighted
Figure ZY_2
Norm problem, and obtain enough sparsity through iteration; transform the attainable rate constraint into a linear matrix inequality model; transform the channel error constraint into a linear matrix inequality model; transform the obtained model into an SDP problem, and use a convex optimization tool Box solution to obtain the optimal beamforming vector. The present invention realizes that under the condition of channel error, the attainable rate of the user is ensured, the system transmission power is minimized while satisfying the quality of service.

Figure 202310134418

Description

一种非理想信道下的去蜂窝MIMO鲁棒性波束赋形方法A robust beamforming method for decellularized MIMO in non-ideal channels

技术领域Technical Field

本发明涉及具有鲁棒性的波束赋形设计方法，特别是涉及一种非理想信道下的去蜂窝MIMO鲁棒性波束赋形方法。The invention relates to a robust beamforming design method, in particular to a decellularized MIMO robust beamforming method under a non-ideal channel.

背景技术Background Art

蜂窝网络架构通过频率复用和小区分裂技术，大大提高了频谱效率，为移动通信的快速发展提供了有力的支撑，但是蜂窝小区面积的不断减小也渐渐增加了小区间的干扰和越区切换的复杂度，这使得移动通信系统性能的提升遇到了瓶颈，为了解决这些问题，去蜂窝网络架构成为未来变革蜂窝网络架构的可行技术方案之一。The cellular network architecture has greatly improved the spectrum efficiency through frequency reuse and cell splitting technology, providing strong support for the rapid development of mobile communications. However, the continuous reduction in the area of cellular cells has gradually increased the interference between cells and the complexity of inter-cell switching, which has caused the improvement of mobile communication system performance to encounter bottlenecks. In order to solve these problems, de-cellularizing the network architecture has become one of the feasible technical solutions for the future transformation of the cellular network architecture.

去蜂窝大规模分布式MIMO（Multiple-Input Multiple-Output）去除了传统的小区的概念，引入了“以用户为中心”的思想，通过部署大量分布式接入点(Access Point，AP)，缩短了用户与接入点之间的距离，获得了空间宏分集增益，从而使全区域均匀覆盖，并且利用大量接入点带来的有利传播(Favorable Propagation)，减少了用户之间的干扰。但是现有技术中，针对大规模分布式MIMO的研究主要为传统理论且基于理想信道状态信息，基于此进行去蜂窝大规模MIMO系统信息理论分析并不十分准确。在去蜂窝大规模分布式MIMO系统中，由于AP的计算能力有限，传统的线性最小均方误差尽管能获得较好的估计性能，对AP来说复杂度仍然较高。而能否使用低复杂度的深度学习算法去提高去蜂窝大规模MIMO系统信道准确度仍然有待解决。并且随着移动通信网络的逐步应用与发展，移动用户和移动设备数量的急剧增加势必带来AP的大量部署，在AP采用的高精度硬件的射频电路会耗费巨大能量，能耗问题将一直存在并且日益严峻，如何在存在信道误差的情况下，在保证用户可达速率，满足服务质量的需求的同时，将系统传输功率最小化显得十分重要。Decellularized massive distributed MIMO (Multiple-Input Multiple-Output) removes the concept of traditional cells and introduces the idea of "user-centricity". By deploying a large number of distributed access points (AP), the distance between users and access points is shortened, and spatial macro-diversity gain is obtained, so that the entire area is evenly covered, and the favorable propagation brought by a large number of access points is utilized to reduce interference between users. However, in the prior art, the research on massive distributed MIMO is mainly based on traditional theory and ideal channel state information. The information theory analysis of decellularized massive MIMO system based on this is not very accurate. In the decellularized massive distributed MIMO system, due to the limited computing power of AP, the traditional linear minimum mean square error can obtain better estimation performance, but the complexity is still high for AP. Whether low-complexity deep learning algorithms can be used to improve the channel accuracy of decellularized massive MIMO system remains to be solved. And with the gradual application and development of mobile communication networks, the sharp increase in the number of mobile users and mobile devices will inevitably lead to the deployment of a large number of APs. The high-precision hardware RF circuits used in APs will consume huge energy. The energy consumption problem will always exist and become increasingly serious. How to minimize the system transmission power while ensuring the user's achievable rate and meeting the service quality requirements in the presence of channel errors is very important.

发明内容Summary of the invention

发明目的：本发明的目的是提供一种在非理想信道的环境下实现系统传输功率最小化的非理想信道下的去蜂窝MIMO鲁棒性波束赋形方法。Purpose of the invention: The purpose of the present invention is to provide a de-cellularized MIMO robust beamforming method under non-ideal channels to minimize system transmission power under non-ideal channel environments.

技术方案：为实现上述目的，本发明所述的一种非理想信道下的去蜂窝MIMO鲁棒性波束赋形方法，包括以下步骤：Technical solution: To achieve the above purpose, the present invention provides a method for robust beamforming of decellularized MIMO in a non-ideal channel, comprising the following steps:

S1：构建去蜂窝分布式大规模MIMO的框架；S1: Building a framework for decellularized distributed massive MIMO;

S2：获取框架所需参数；S2: Get the parameters required by the framework;

S3：对获取的参数误差，加入误差约束，构建误差信道模型；S3: Add error constraints to the obtained parameter errors and construct an error channel model;

S4：构建用户可达速率与误差信道模型的信道误差约束下功率最小化模型，提升模型鲁棒性；S4: Construct a power minimization model under channel error constraints for the user achievable rate and error channel model to improve the model robustness;

S5：将功率最小化模型的目标函数从

Figure SMS_1
范数最小化问题近似成一个凸的加权的
Figure SMS_2
范数问题，并通过迭代获取足够的稀疏性；S5: Change the objective function of the power minimization model from
Figure SMS_1
The norm minimization problem is approximated as a convex weighted
Figure SMS_2
norm problem and obtain sufficient sparsity through iteration;

S6：将可达速率约束条件转化为线性矩阵不等式模型；S6: Convert the achievable rate constraint into a linear matrix inequality model;

S7：将信道误差约束转化为线性矩阵不等式模型；S7: Convert the channel error constraint into a linear matrix inequality model;

S8：将步骤S5至S7所得的模型转化为SDP问题，通过凸优化工具箱进行求解，得到最优的波束赋形向量。S8: Convert the model obtained in steps S5 to S7 into an SDP problem, solve it using a convex optimization toolbox, and obtain an optimal beamforming vector.

步骤S1所述的构建去蜂窝分布式大规模MIMO的框架具体为：部署一个装有M根发射天线、L个接入点用于服务K个单天线用户的去蜂窝大规模分布式MIMO系统，接入点负责数据的传输，中央处理器负责数据的处理，其中N为发射天线数量，L为接入点数量，K为单天线用户数量。The framework for constructing de-cellularized distributed large-scale MIMO described in step S1 is specifically: deploying a de-cellularized large-scale distributed MIMO system equipped with M transmitting antennas and L access points to serve K single-antenna users, the access points are responsible for data transmission, and the central processor is responsible for data processing, where N is the number of transmitting antennas, L is the number of access points, and K is the number of single-antenna users.

步骤S3所述的对获取的参数误差，加入误差约束，构建误差信道模型具体为：The step S3 of adding error constraints to the acquired parameter errors and constructing the error channel model is specifically as follows:

信道误差模型为：

Figure SMS_4
，其中，
Figure SMS_7
表示用户，
Figure SMS_9
表示所有接入点到用户
Figure SMS_5
的真实信道，
Figure SMS_6
为估计信道，
Figure SMS_8
为误差向量，约束关系为：
Figure SMS_10
，
Figure SMS_3
为误差约束；The channel error model is:
Figure SMS_4
,in,
Figure SMS_7
Represents the user,
Figure SMS_9
Indicates all access points to users
Figure SMS_5
The true channel,
Figure SMS_6
To estimate the channel,
Figure SMS_8
is the error vector, and the constraint relationship is:
Figure SMS_10
,
Figure SMS_3
is the error constraint;

估计信道

Figure SMS_11
和大尺度衰落在估计信道上是已知的，因此总体功率以估计信道为标准进行计算，用户
Figure SMS_12
的接收信号
Figure SMS_13
为：
Figure SMS_14
；Estimated Channel
Figure SMS_11
The large-scale fading is known on the estimated channel, so the overall power is calculated based on the estimated channel.
Figure SMS_12
The received signal
Figure SMS_13
for:
Figure SMS_14
;

式中，

Figure SMS_16
为所有AP对用户
Figure SMS_19
的传输波束赋形向量，
Figure SMS_21
表示矩阵h的共轭转置，
Figure SMS_17
表示除用户
Figure SMS_20
外的任一用户，
Figure SMS_22
，
Figure SMS_23
分别表示用户
Figure SMS_15
的预期信号服从期望为0，标准差为1的高斯分布和接收噪声服从期望为0，标准差为
Figure SMS_18
的高斯分布。In the formula,
Figure SMS_16
For all APs to users
Figure SMS_19
The transmit beamforming vector of
Figure SMS_21
represents the conjugate transpose of the matrix h,
Figure SMS_17
Indicates that except user
Figure SMS_20
Any user other than
Figure SMS_22
,
Figure SMS_23
Respectively represent users
Figure SMS_15
The expected signal follows a Gaussian distribution with an expectation of 0 and a standard deviation of 1, and the received noise follows a Gaussian distribution with an expectation of 0 and a standard deviation of
Figure SMS_18
Gaussian distribution.

步骤S4所述的构建用户可达速率与误差信道模型的信道误差约束下功率最小化模型，提升模型鲁棒性，具体为：The power minimization model under the channel error constraint of constructing the user achievable rate and error channel model described in step S4 improves the robustness of the model, specifically:

用户

Figure SMS_24
的信号与干扰的比值SINR为：
Figure SMS_25
，引入香农公式，用户
Figure SMS_26
的可达速率即为：
Figure SMS_27
，其中
Figure SMS_28
为辅助变量；user
Figure SMS_24
The signal-to-interference ratio SINR is:
Figure SMS_25
, introducing Shannon's formula, user
Figure SMS_26
The achievable rate is:
Figure SMS_27
,in
Figure SMS_28
is an auxiliary variable;

AP消耗的功率为：

Figure SMS_29
；
Figure SMS_30
为功率传输效率系数，
Figure SMS_31
为天线发射功率，
Figure SMS_32
为AP活跃时的最小功率，
Figure SMS_33
为AP休眠时消耗的功率；The power consumed by the AP is:
Figure SMS_29
;
Figure SMS_30
is the power transmission efficiency coefficient,
Figure SMS_31
is the antenna transmission power,
Figure SMS_32
is the minimum power when the AP is active,
Figure SMS_33
The power consumed by the AP when it is in sleep mode.

用户

Figure SMS_34
可达速率与信道误差约束下的系统总功率最小化模型表示为：user
Figure SMS_34
The system total power minimization model under the constraints of achievable rate and channel error is expressed as:

Figure SMS_35
；
Figure SMS_35
;

式中，

Figure SMS_41
为所有AP对用户
Figure SMS_38
的传输波束赋形向量，
Figure SMS_43
为其中一个接入点，
Figure SMS_39
为从接入点
Figure SMS_42
发射到用户
Figure SMS_46
的波束赋形向量，若第
Figure SMS_50
个AP不为用户
Figure SMS_44
服务，那么
Figure SMS_48
，
Figure SMS_36
表示非零
Figure SMS_40
的数量，
Figure SMS_45
为AP活跃时与休眠时的功率差，
Figure SMS_49
，
Figure SMS_47
为对所有用户的最小信干比约束，
Figure SMS_51
为用户可达速率约束，
Figure SMS_37
为非理想信道约束。In the formula,
Figure SMS_41
For all APs to users
Figure SMS_38
The transmit beamforming vector of
Figure SMS_43
For one of the access points,
Figure SMS_39
From the access point
Figure SMS_42
Transmit to user
Figure SMS_46
The beamforming vector of
Figure SMS_50
AP is not for users
Figure SMS_44
Service, then
Figure SMS_48
,
Figure SMS_36
Indicates non-zero
Figure SMS_40
The number of
Figure SMS_45
is the power difference between when the AP is active and when it is asleep.
Figure SMS_49
,
Figure SMS_47
is the minimum signal-to-interference ratio constraint for all users,
Figure SMS_51
is the user achievable rate constraint,
Figure SMS_37
is a non-ideal channel constraint.

步骤S5所述的将功率最小化模型的目标函数从

Figure SMS_52
范数最小化问题近似成一个凸的加权的
Figure SMS_53
范数问题，并通过迭代获取足够的稀疏性，包括以下子步骤：Step S5 changes the objective function of the power minimization model from
Figure SMS_52
The norm minimization problem is approximated as a convex weighted
Figure SMS_53
norm problem and obtain sufficient sparsity through iteration, including the following sub-steps:

S501：由于AP休眠功率为常数，对优化结果没有影响，将其去除，对目标函数进行变形，若用

Figure SMS_54
范数的平方来替换
Figure SMS_55
范数，
Figure SMS_56
范数的个数总量保持不变，AP活跃与休眠模式功率差表述为：
Figure SMS_57
；S501: Since the AP sleep power is a constant and has no effect on the optimization result, it is removed and the objective function is deformed.
Figure SMS_54
The square of the norm is used to replace
Figure SMS_55
norm,
Figure SMS_56
The total number of norms remains unchanged, and the power difference between AP active and sleep modes is expressed as:
Figure SMS_57
;

S502：根据压缩感知理论，

Figure SMS_58
范数最小化问题能够近似成一个凸的加权的
Figure SMS_59
范数问题，则用户
Figure SMS_60
可达速率与信道误差约束下的系统总功率最小化优化问题可近似表述为：S502: According to the theory of compressed sensing,
Figure SMS_58
The norm minimization problem can be approximated as a convex weighted
Figure SMS_59
norm problem, then the user
Figure SMS_60
The optimization problem of minimizing the total system power under the constraints of achievable rate and channel error can be approximately expressed as:

Figure SMS_61
，
Figure SMS_62
为接入点
Figure SMS_63
对用户
Figure SMS_64
所占的权重；
Figure SMS_61
,
Figure SMS_62
For access point
Figure SMS_63
For users
Figure SMS_64
The weight it occupies;

S503：将

Figure SMS_65
合并同类项后，得到下式：
Figure SMS_66
；S503:
Figure SMS_65
After combining like terms, we get the following formula:
Figure SMS_66
;

S504：不断迭代权重

Figure SMS_67
，并用迭代后的权重不断地对步骤S503的公式进行求解，最终得到一个最优解，对
Figure SMS_68
进行迭代的重加权公式为：
Figure SMS_69
，其中，
Figure SMS_70
为一个正指数，
Figure SMS_71
，
Figure SMS_72
为一个极小的防止分母为0正数。S504: Continuously iterate weights
Figure SMS_67
, and use the iterated weights to continuously solve the formula in step S503, and finally obtain an optimal solution.
Figure SMS_68
The iterative reweighting formula is:
Figure SMS_69
,in,
Figure SMS_70
is a positive index,
Figure SMS_71
,
Figure SMS_72
is a very small positive number that prevents the denominator from being zero.

步骤S6所述的将可达速率约束条件转化为线性矩阵不等式，包括以下子步骤：The step S6 of converting the achievable rate constraint condition into a linear matrix inequality comprises the following sub-steps:

S601：对约束条件进行处理，用户

Figure SMS_73
可达速率约束和信道误差约束分别为：S601: Process the constraints.
Figure SMS_73
The achievable rate constraint and channel error constraint are:

Figure SMS_74
(1) ，
Figure SMS_74
(1) ,

Figure SMS_75
(2)；
Figure SMS_75
(2);

S602：处理用户

Figure SMS_76
可达速率约束，不等式左边用一阶泰勒公式逼近为一个如下的下界：S602: Processing users
Figure SMS_76
The achievable rate constraint, the left side of the inequality is approximated by the first-order Taylor formula as a lower bound as follows:

设

Figure SMS_77
为迭代
Figure SMS_78
次后的最优解，那么
Figure SMS_79
的线性下界为：
Figure SMS_80
，其中
Figure SMS_81
，处理用户
Figure SMS_82
可达速率约束为：set up
Figure SMS_77
For iteration
Figure SMS_78
The optimal solution after that,
Figure SMS_79
The linear lower bound of is:
Figure SMS_80
,in
Figure SMS_81
, handle user
Figure SMS_82
The achievable rate constraint is:

Figure SMS_83
；
Figure SMS_83
;

S603：引入S-引理，将约束转化为如下线性矩阵不等式模型：S603: Introduce the S-lemma and transform the constraints into the following linear matrix inequality model:

Figure SMS_84
；(3)
Figure SMS_84
; (3)

式中，I为单位矩阵，IM为M×M的单位矩阵，

Figure SMS_85
表示
Figure SMS_86
的估计值，
Figure SMS_87
为稀疏变量。Where I is the identity matrix, IM is the M×M identity matrix,
Figure SMS_85
express
Figure SMS_86
The estimated value of
Figure SMS_87
is a sparse variable.

步骤S7所述的将信道误差约束转化为线性矩阵不等式，包括以下子步骤：The step S7 of converting the channel error constraint into a linear matrix inequality comprises the following sub-steps:

S701：用舒尔补将信道误差约束公式写为：S701: Use Schur complement to write the channel error constraint formula as:

Figure SMS_88
，其中
Figure SMS_89
；
Figure SMS_88
,in
Figure SMS_89
;

S702：根据涅米罗夫斯基引理，并引入稀疏变量

Figure SMS_90
，将S701中的公式转换为线性矩阵不等式模型：S702: Based on Nemirovsky's lemma, and introducing sparse variables
Figure SMS_90
, convert the formula in S701 into a linear matrix inequality model:

Figure SMS_91
(4)。
Figure SMS_91
(4).

步骤S8所述的将步骤S5至S7所得的模型转化为SDP问题，通过凸优化工具箱进行求解，得到最优的波束赋形向量，包括以下子步骤：Step S8 converts the model obtained in steps S5 to S7 into an SDP problem, solves it using a convex optimization toolbox, and obtains an optimal beamforming vector, including the following sub-steps:

S801：将步骤S5至S7所得的模型转化为SDP问题：

Figure SMS_92
；S801: Convert the model obtained from steps S5 to S7 into an SDP problem:
Figure SMS_92
;

S802：根据

Figure SMS_93
得到
Figure SMS_94
为本SDP问题的最优波束赋形向量。S802: According to
Figure SMS_93
get
Figure SMS_94
is the optimal beamforming vector for this SDP problem.

有益效果：本发明具有如下优点：1、本发明所述的去蜂窝大规模分布式MIMO中的AP的发射功率可由具有鲁棒性的波束赋形设计，在非理想信道的环境下实现最小化，能够应用于5G，6G移动通信等领域；Beneficial effects: The present invention has the following advantages: 1. The transmit power of the AP in the decellularized massive distributed MIMO of the present invention can be minimized by a robust beamforming design in a non-ideal channel environment, and can be applied to 5G, 6G mobile communications and other fields;

2、本发明在确保模型鲁棒性的同时，还兼具运算复杂度低，收敛次数少的特点，能够减少系统运算量，提高系统对模型求解的速度，达到最短时间内求得问题最优解的效果，实现了发射功率最小化的目的。2. While ensuring the robustness of the model, the present invention also has the characteristics of low computational complexity and few convergence times, which can reduce the amount of system calculations and increase the speed at which the system solves the model, so as to achieve the effect of obtaining the optimal solution to the problem in the shortest time and realize the purpose of minimizing the transmission power.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1是本发明的方法流程图；Fig. 1 is a flow chart of the method of the present invention;

图2是本发明的去蜂窝分布式大规模MIMO的示意图；FIG2 is a schematic diagram of a decellularized distributed massive MIMO according to the present invention;

图3是本发明的迭代算法伪代码图。FIG. 3 is a pseudo code diagram of the iterative algorithm of the present invention.

实施方式Implementation

下面结合实施例和附图对本发明的技术方案作详细说明。The technical solution of the present invention is described in detail below in conjunction with the embodiments and drawings.

如图1所示，本发明所述的一种非理想信道下的去蜂窝MIMO鲁棒性波束赋形方法，包括以下步骤：As shown in FIG1 , a method for robust beamforming for decellularized MIMO in a non-ideal channel according to the present invention comprises the following steps:

S1：构建去蜂窝分布式大规模MIMO的框架；S1: Building a framework for decellularized distributed massive MIMO;

S2：获取框架所需参数；S2: Get the parameters required by the framework;

S3：对获取的参数误差，加入误差约束，构建误差信道模型；S3: Add error constraints to the obtained parameter errors and construct an error channel model;

S4：构建用户可达速率与误差信道模型的信道误差约束下功率最小化模型，提升模型鲁棒性；S4: Construct a power minimization model under channel error constraints for the user achievable rate and error channel model to improve the model robustness;

S5：将功率最小化模型的目标函数从

Figure SMS_95
范数最小化问题近似成一个凸的加权的
Figure SMS_96
范数问题，并通过迭代获取足够的稀疏性；S5: Change the objective function of the power minimization model from
Figure SMS_95
The norm minimization problem is approximated as a convex weighted
Figure SMS_96
norm problem and obtain sufficient sparsity through iteration;

S6：将可达速率约束条件转化为线性矩阵不等式模型；S6: Convert the achievable rate constraint into a linear matrix inequality model;

S7：将信道误差约束转化为线性矩阵不等式模型；S7: Convert the channel error constraint into a linear matrix inequality model;

S8：将步骤S5至S7所得的模型转化为SDP问题，通过凸优化工具箱进行求解，得到最优的波束赋形向量。S8: Convert the model obtained in steps S5 to S7 into an SDP problem, solve it using a convex optimization toolbox, and obtain an optimal beamforming vector.

如图2所示，步骤S1所述的构建去蜂窝分布式大规模MIMO的框架具体为：部署一个装有M根发射天线、L个接入点用于服务K个单天线用户的去蜂窝大规模分布式MIMO系统，接入点负责数据的传输，中央处理器负责数据的处理，其中N为发射天线数量，L为接入点数量，K为单天线用户数量。As shown in FIG2 , the framework for constructing a de-cellularized distributed large-scale MIMO described in step S1 is specifically as follows: deploying a de-cellularized large-scale distributed MIMO system equipped with M transmitting antennas and L access points for serving K single-antenna users, wherein the access points are responsible for data transmission and the central processor is responsible for data processing, where N is the number of transmitting antennas, L is the number of access points, and K is the number of single-antenna users.

步骤S3所述的对获取的参数误差，加入误差约束，构建误差信道模型具体为：The step S3 of adding error constraints to the acquired parameter errors and constructing the error channel model is specifically as follows:

信道误差模型为：

Figure SMS_98
，其中，
Figure SMS_101
表示用户，
Figure SMS_103
表示所有接入点到用户
Figure SMS_99
的真实信道，
Figure SMS_100
为估计信道，
Figure SMS_102
为误差向量，约束关系为：
Figure SMS_104
，
Figure SMS_97
为误差约束；The channel error model is:
Figure SMS_98
,in,
Figure SMS_101
Represents the user,
Figure SMS_103
Indicates all access points to users
Figure SMS_99
The true channel,
Figure SMS_100
To estimate the channel,
Figure SMS_102
is the error vector, and the constraint relationship is:
Figure SMS_104
,
Figure SMS_97
is the error constraint;

估计信道

Figure SMS_105
和大尺度衰落在估计信道上是已知的，因此总体功率以估计信道为标准进行计算，用户
Figure SMS_106
的接收信号
Figure SMS_107
为：
Figure SMS_108
；Estimated Channel
Figure SMS_105
The large-scale fading is known on the estimated channel, so the overall power is calculated based on the estimated channel.
Figure SMS_106
The received signal
Figure SMS_107
for:
Figure SMS_108
;

式中，

Figure SMS_111
为所有AP对用户
Figure SMS_114
的传输波束赋形向量，
Figure SMS_116
表示矩阵h的共轭转置，
Figure SMS_109
表示除用户
Figure SMS_113
外的任一用户，
Figure SMS_115
，
Figure SMS_117
分别表示用户
Figure SMS_110
的预期信号服从期望为0，标准差为1的高斯分布和接收噪声服从期望为0，标准差为
Figure SMS_112
的高斯分布。In the formula,
Figure SMS_111
For all APs to users
Figure SMS_114
The transmit beamforming vector of
Figure SMS_116
represents the conjugate transpose of the matrix h,
Figure SMS_109
Indicates that except user
Figure SMS_113
Any user other than
Figure SMS_115
,
Figure SMS_117
Respectively represent users
Figure SMS_110
The expected signal follows a Gaussian distribution with an expectation of 0 and a standard deviation of 1, and the received noise follows a Gaussian distribution with an expectation of 0 and a standard deviation of
Figure SMS_112
Gaussian distribution.

步骤S4所述的构建用户可达速率与误差信道模型的信道误差约束下功率最小化模型，提升模型鲁棒性，具体为：The power minimization model under the channel error constraint of constructing the user achievable rate and error channel model described in step S4 improves the robustness of the model, specifically:

用户

Figure SMS_118
的信号与干扰的比值SINR为：
Figure SMS_119
，引入香农公式，用户
Figure SMS_120
的可达速率即为：
Figure SMS_121
，其中
Figure SMS_122
为辅助变量；user
Figure SMS_118
The signal-to-interference ratio SINR is:
Figure SMS_119
, introducing Shannon's formula, user
Figure SMS_120
The achievable rate is:
Figure SMS_121
,in
Figure SMS_122
is an auxiliary variable;

AP消耗的功率为：

Figure SMS_123
；
Figure SMS_124
为功率传输效率系数，
Figure SMS_125
为天线发射功率，
Figure SMS_126
为AP活跃时的最小功率，
Figure SMS_127
为AP休眠时消耗的功率；The power consumed by the AP is:
Figure SMS_123
;
Figure SMS_124
is the power transmission efficiency coefficient,
Figure SMS_125
is the antenna transmission power,
Figure SMS_126
is the minimum power when the AP is active,
Figure SMS_127
The power consumed by the AP when it is in sleep mode.

用户

Figure SMS_128
可达速率与信道误差约束下的系统总功率最小化模型表示为：user
Figure SMS_128
The system total power minimization model under the constraints of achievable rate and channel error is expressed as:

Figure SMS_129
；
Figure SMS_129
;

式中，

Figure SMS_141
为所有AP对用户
Figure SMS_132
的传输波束赋形向量，
Figure SMS_137
为其中一个接入点，
Figure SMS_138
为从接入点
Figure SMS_142
发射到用户
Figure SMS_143
的波束赋形向量，若第
Figure SMS_145
个AP不为用户
Figure SMS_135
服务，那么
Figure SMS_139
，
Figure SMS_130
表示非零
Figure SMS_134
的数量，
Figure SMS_133
为AP活跃时与休眠时的功率差，
Figure SMS_136
，
Figure SMS_140
为对所有用户的最小信干比约束，
Figure SMS_144
为用户可达速率约束，
Figure SMS_131
为非理想信道约束。In the formula,
Figure SMS_141
For all APs to users
Figure SMS_132
The transmit beamforming vector of
Figure SMS_137
For one of the access points,
Figure SMS_138
From the access point
Figure SMS_142
Transmit to user
Figure SMS_143
The beamforming vector of
Figure SMS_145
AP is not for users
Figure SMS_135
Service, then
Figure SMS_139
,
Figure SMS_130
Indicates non-zero
Figure SMS_134
The number of
Figure SMS_133
is the power difference between when the AP is active and when it is asleep.
Figure SMS_136
,
Figure SMS_140
is the minimum signal-to-interference ratio constraint for all users,
Figure SMS_144
is the user achievable rate constraint,
Figure SMS_131
is a non-ideal channel constraint.

步骤S5所述的将功率最小化模型的目标函数从

Figure SMS_146
范数最小化问题近似成一个凸的加权的
Figure SMS_147
范数问题，并通过迭代获取足够的稀疏性，包括以下子步骤：Step S5 changes the objective function of the power minimization model from
Figure SMS_146
The norm minimization problem is approximated as a convex weighted
Figure SMS_147
norm problem and obtain sufficient sparsity through iteration, including the following sub-steps:

S501：由于AP休眠功率为常数，对优化结果没有影响，将其去除，对目标函数进行变形，若用

Figure SMS_148
范数的平方来替换
Figure SMS_149
范数，
Figure SMS_150
范数的个数总量保持不变，AP活跃与休眠模式功率差表述为：
Figure SMS_151
；S501: Since the AP sleep power is a constant and has no effect on the optimization result, it is removed and the objective function is deformed.
Figure SMS_148
The square of the norm is used to replace
Figure SMS_149
norm,
Figure SMS_150
The total number of norms remains unchanged, and the power difference between AP active and sleep modes is expressed as:
Figure SMS_151
;

S502：根据压缩感知理论，

Figure SMS_152
范数最小化问题能够近似成一个凸的加权的
Figure SMS_153
范数问题，则用户
Figure SMS_154
可达速率与信道误差约束下的系统总功率最小化优化问题可近似表述为：S502: According to the theory of compressed sensing,
Figure SMS_152
The norm minimization problem can be approximated as a convex weighted
Figure SMS_153
norm problem, then the user
Figure SMS_154
The optimization problem of minimizing the total system power under the constraints of achievable rate and channel error can be approximately expressed as:

Figure SMS_155
，
Figure SMS_156
为接入点
Figure SMS_157
对用户
Figure SMS_158
所占的权重；
Figure SMS_155
,
Figure SMS_156
For access point
Figure SMS_157
For users
Figure SMS_158
The weight it occupies;

S503：将

Figure SMS_159
合并同类项后，得到下式：
Figure SMS_160
；S503:
Figure SMS_159
After combining like terms, we get the following formula:
Figure SMS_160
;

S504：如图3所示，不断迭代权重

Figure SMS_161
，并用迭代后的权重不断地对步骤S503的公式进行求解，最终得到一个最优解，对
Figure SMS_162
进行迭代的重加权公式为：
Figure SMS_163
，其中，
Figure SMS_164
为一个正指数，
Figure SMS_165
，
Figure SMS_166
为一个极小的防止分母为0正数。S504: As shown in FIG3, the weights are continuously iterated
Figure SMS_161
, and use the iterated weights to continuously solve the formula in step S503, and finally obtain an optimal solution.
Figure SMS_162
The iterative reweighting formula is:
Figure SMS_163
,in,
Figure SMS_164
is a positive index,
Figure SMS_165
,
Figure SMS_166
is a very small positive number that prevents the denominator from being zero.

步骤S6所述的将可达速率约束条件转化为线性矩阵不等式，包括以下子步骤：The step S6 of converting the achievable rate constraint condition into a linear matrix inequality comprises the following sub-steps:

S601：对约束条件进行处理，用户

Figure SMS_167
可达速率约束和信道误差约束分别为：S601: Process the constraints.
Figure SMS_167
The achievable rate constraint and channel error constraint are:

Figure SMS_168
(1) ，
Figure SMS_168
(1) ,

Figure SMS_169
(2)；
Figure SMS_169
(2);

S602：处理用户

Figure SMS_170
可达速率约束，不等式左边用一阶泰勒公式逼近为一个如下的下界：S602: Processing users
Figure SMS_170
The achievable rate constraint, the left side of the inequality is approximated by the first-order Taylor formula as a lower bound as follows:

设

Figure SMS_171
为迭代
Figure SMS_172
次后的最优解，那么
Figure SMS_173
的线性下界为：
Figure SMS_174
，其中
Figure SMS_175
，处理用户
Figure SMS_176
可达速率约束为：
Figure SMS_177
；set up
Figure SMS_171
For iteration
Figure SMS_172
The optimal solution after that,
Figure SMS_173
The linear lower bound of is:
Figure SMS_174
,in
Figure SMS_175
, handle user
Figure SMS_176
The achievable rate constraint is:
Figure SMS_177
;

S603：引入S-引理，将约束转化为如下线性矩阵不等式模型：S603: Introduce the S-lemma and transform the constraints into the following linear matrix inequality model:

Figure SMS_178
；(3)
Figure SMS_178
; (3)

式中，I为单位矩阵，IM为M×M的单位矩阵，

Figure SMS_179
表示
Figure SMS_180
的估计值，
Figure SMS_181
为稀疏变量。Where I is the identity matrix, IM is the M×M identity matrix,
Figure SMS_179
express
Figure SMS_180
The estimated value of
Figure SMS_181
is a sparse variable.

步骤S7所述的将信道误差约束转化为线性矩阵不等式，包括以下子步骤：The step S7 of converting the channel error constraint into a linear matrix inequality comprises the following sub-steps:

S701：用舒尔补将信道误差约束公式写为：S701: Use Schur complement to write the channel error constraint formula as:

Figure SMS_182
，其中
Figure SMS_183
；
Figure SMS_182
,in
Figure SMS_183
;

S702：根据涅米罗夫斯基引理，并引入稀疏变量

Figure SMS_184
，将S701中的公式转换为线性矩阵不等式模型：S702: Based on Nemirovsky's lemma, and introducing sparse variables
Figure SMS_184
, convert the formula in S701 into a linear matrix inequality model:

Figure SMS_185
(4)。
Figure SMS_185
(4).

步骤S8所述的将步骤S5至S7所得的模型转化为SDP问题，通过凸优化工具箱进行求解，得到最优的波束赋形向量，包括以下子步骤：Step S8 converts the model obtained in steps S5 to S7 into an SDP problem, solves it using a convex optimization toolbox, and obtains an optimal beamforming vector, including the following sub-steps:

S801：将步骤S5至S7所得的模型转化为SDP问题：

Figure SMS_186
；S801: Convert the model obtained from steps S5 to S7 into an SDP problem:
Figure SMS_186
;

S802：根据

Figure SMS_187
得到
Figure SMS_188
为本SDP问题的最优波束赋形向量。S802: According to
Figure SMS_187
get
Figure SMS_188
is the optimal beamforming vector for this SDP problem.

本发明设计了一种具有鲁棒性的波束赋形，由于目标函数波束赋形变量为二次型，约束条件中可达速率限制与信道误差的不确定性，这个问题是非凸的，为了解决这个问题，对目标函数进行连续凸逼近，将其从

Figure SMS_189
范数最小化问题近似成一个凸的加权的
Figure SMS_190
范数问题，并通过迭代算法进行求解。而为了解决可达速率限制与信道误差的不确定性，先通过连续凸逼近将约束条件线性化近似，然后利用S-引理将其转化为线性矩阵不等式，整个问题转化为一个凸的半正定规划（SDP，Semidefinite Program）问题，最后由凸优化工具箱求解，得到最优的波束赋形向量。The present invention designs a robust beamforming. Since the objective function beamforming variable is a quadratic form, the uncertainty of the achievable rate limit and the channel error in the constraint conditions makes this problem non-convex. In order to solve this problem, a continuous convex approximation is performed on the objective function, which is converted from
Figure SMS_189
The norm minimization problem is approximated as a convex weighted
Figure SMS_190
norm problem and solve it through an iterative algorithm. In order to solve the uncertainty of the achievable rate limit and channel error, the constraints are first linearized and approximated through continuous convex approximation, and then converted into linear matrix inequalities using the S-lemma. The entire problem is converted into a convex semidefinite program (SDP) problem, and finally solved by the convex optimization toolbox to obtain the optimal beamforming vector.

Claims (8)

1.一种非理想信道下的去蜂窝MIMO鲁棒性波束赋形方法，其特征在于：包括以下步骤：1. A method for robust beamforming of decellularized MIMO in non-ideal channels, characterized in that it comprises the following steps: S1：构建去蜂窝分布式大规模MIMO的框架；S1: Building a framework for decellularized distributed massive MIMO; S2：获取框架所需参数；S2: Get the parameters required by the framework; S3：对获取的参数误差，加入误差约束，构建误差信道模型；S3: Add error constraints to the obtained parameter errors and construct an error channel model; S4：构建用户可达速率与误差信道模型的信道误差约束下功率最小化模型，提升模型鲁棒性；S4: Construct a power minimization model under channel error constraints for the user achievable rate and error channel model to improve the model robustness; S5：将功率最小化模型的目标函数从
Figure QLYQS_1
范数最小化问题近似成一个凸的加权的
Figure QLYQS_2
范数问题，并通过迭代获取足够的稀疏性；S5: Change the objective function of the power minimization model from
Figure QLYQS_1
The norm minimization problem is approximated as a convex weighted
Figure QLYQS_2
norm problem and obtain sufficient sparsity through iteration; S6：将可达速率约束条件转化为线性矩阵不等式模型；S6: Convert the achievable rate constraint into a linear matrix inequality model; S7：将信道误差约束转化为线性矩阵不等式模型；S7: Convert the channel error constraint into a linear matrix inequality model; S8：将步骤S5至S7所得的模型转化为SDP问题，通过凸优化工具箱进行求解，得到最优的波束赋形向量。S8: Convert the model obtained in steps S5 to S7 into an SDP problem, solve it using a convex optimization toolbox, and obtain an optimal beamforming vector. 2.根据权利要求1所述的非理想信道下的去蜂窝MIMO鲁棒性波束赋形方法，其特征在于：步骤S1所述的构建去蜂窝分布式大规模MIMO的框架具体为：部署一个装有M根发射天线、L个接入点用于服务K个单天线用户的去蜂窝大规模分布式MIMO系统，接入点负责数据的传输，中央处理器负责数据的处理，其中N为发射天线数量，L为接入点数量，K为单天线用户数量。2. According to the de-cellularized MIMO robust beamforming method under non-ideal channels described in claim 1, it is characterized in that: the framework for constructing de-cellularized distributed large-scale MIMO described in step S1 is specifically: deploying a de-cellularized large-scale distributed MIMO system equipped with M transmitting antennas and L access points to serve K single-antenna users, the access points are responsible for data transmission, and the central processing unit is responsible for data processing, wherein N is the number of transmitting antennas, L is the number of access points, and K is the number of single-antenna users. 3.根据权利要求1所述的非理想信道下的去蜂窝MIMO鲁棒性波束赋形方法，其特征在于：步骤S3所述的对获取的参数误差，加入误差约束，构建误差信道模型具体为：3. The method for robust beamforming of decellularized MIMO in non-ideal channels according to claim 1, characterized in that: the step S3 of adding error constraints to the acquired parameter errors to construct the error channel model is specifically: 信道误差模型为：
Figure QLYQS_5
，其中，
Figure QLYQS_6
表示用户，
Figure QLYQS_8
表示所有接入点到用户
Figure QLYQS_4
的真实信道，
Figure QLYQS_7
为估计信道，
Figure QLYQS_9
为误差向量，约束关系为：
Figure QLYQS_10
，
Figure QLYQS_3
为误差约束；The channel error model is:
Figure QLYQS_5
,in,
Figure QLYQS_6
Represents the user,
Figure QLYQS_8
Indicates all access points to users
Figure QLYQS_4
The true channel,
Figure QLYQS_7
To estimate the channel,
Figure QLYQS_9
is the error vector, and the constraint relationship is:
Figure QLYQS_10
,
Figure QLYQS_3
is the error constraint; 估计信道
Figure QLYQS_11
和大尺度衰落在估计信道上是已知的，因此总体功率以估计信道为标准进行计算，用户
Figure QLYQS_12
的接收信号
Figure QLYQS_13
为：
Figure QLYQS_14
；Estimated Channel
Figure QLYQS_11
The large-scale fading is known on the estimated channel, so the overall power is calculated based on the estimated channel.
Figure QLYQS_12
The received signal
Figure QLYQS_13
for:
Figure QLYQS_14
; 式中，
Figure QLYQS_15
为所有AP对用户
Figure QLYQS_19
的传输波束赋形向量，
Figure QLYQS_21
表示矩阵h的共轭转置，
Figure QLYQS_17
表示除用户
Figure QLYQS_20
外的任一用户，
Figure QLYQS_22
，
Figure QLYQS_23
分别表示用户
Figure QLYQS_16
的预期信号服从期望为0，标准差为1的高斯分布和接收噪声服从期望为0，标准差为
Figure QLYQS_18
的高斯分布。In the formula,
Figure QLYQS_15
For all APs to users
Figure QLYQS_19
The transmit beamforming vector of
Figure QLYQS_21
represents the conjugate transpose of the matrix h,
Figure QLYQS_17
Indicates that except user
Figure QLYQS_20
Any user other than
Figure QLYQS_22
,
Figure QLYQS_23
Respectively represent users
Figure QLYQS_16
The expected signal follows a Gaussian distribution with an expectation of 0 and a standard deviation of 1, and the received noise follows a Gaussian distribution with an expectation of 0 and a standard deviation of
Figure QLYQS_18
Gaussian distribution. 4.根据权利要求1所述的非理想信道下的去蜂窝MIMO鲁棒性波束赋形方法，其特征在于：步骤S4所述的构建用户可达速率与误差信道模型的信道误差约束下功率最小化模型，提升模型鲁棒性，具体为：4. The method for robust beamforming of decellularized MIMO in non-ideal channels according to claim 1, characterized in that: the power minimization model under channel error constraint of constructing the user achievable rate and error channel model in step S4 improves the robustness of the model, specifically: 用户
Figure QLYQS_24
的信号与干扰的比值SINR为：
Figure QLYQS_25
，引入香农公式，用户
Figure QLYQS_26
的可达速率即为：
Figure QLYQS_27
，其中
Figure QLYQS_28
为辅助变量；user
Figure QLYQS_24
The signal-to-interference ratio SINR is:
Figure QLYQS_25
, introducing Shannon's formula, user
Figure QLYQS_26
The achievable rate is:
Figure QLYQS_27
,in
Figure QLYQS_28
is an auxiliary variable; AP消耗的功率为：
Figure QLYQS_29
；The power consumed by the AP is:
Figure QLYQS_29
;
Figure QLYQS_30
为功率传输效率系数，
Figure QLYQS_31
为天线发射功率，
Figure QLYQS_32
为AP活跃时的最小功率，
Figure QLYQS_33
为AP休眠时消耗的功率；
Figure QLYQS_30
is the power transmission efficiency coefficient,
Figure QLYQS_31
is the antenna transmission power,
Figure QLYQS_32
is the minimum power when the AP is active,
Figure QLYQS_33
The power consumed by the AP when it is in sleep mode. 用户
Figure QLYQS_34
可达速率与信道误差约束下的系统总功率最小化模型表示为：user
Figure QLYQS_34
The system total power minimization model under the constraints of achievable rate and channel error is expressed as:
Figure QLYQS_35
；
Figure QLYQS_35
; 式中，
Figure QLYQS_40
为所有AP对用户
Figure QLYQS_37
的传输波束赋形向量，
Figure QLYQS_41
为其中一个接入点，
Figure QLYQS_36
为从接入点
Figure QLYQS_43
发射到用户
Figure QLYQS_46
的波束赋形向量，若第
Figure QLYQS_50
个AP不为用户
Figure QLYQS_45
服务，那么
Figure QLYQS_49
，
Figure QLYQS_39
表示非零
Figure QLYQS_42
的数量，
Figure QLYQS_44
为AP活跃时与休眠时的功率差，
Figure QLYQS_48
，
Figure QLYQS_47
为对所有用户的最小信干比约束，
Figure QLYQS_51
为用户可达速率约束，
Figure QLYQS_38
为非理想信道约束。In the formula,
Figure QLYQS_40
For all APs to users
Figure QLYQS_37
The transmit beamforming vector of
Figure QLYQS_41
For one of the access points,
Figure QLYQS_36
From the access point
Figure QLYQS_43
Transmit to user
Figure QLYQS_46
The beamforming vector of
Figure QLYQS_50
AP is not for users
Figure QLYQS_45
Service, then
Figure QLYQS_49
,
Figure QLYQS_39
Indicates non-zero
Figure QLYQS_42
The number of
Figure QLYQS_44
is the power difference between when the AP is active and when it is asleep.
Figure QLYQS_48
,
Figure QLYQS_47
is the minimum signal-to-interference ratio constraint for all users,
Figure QLYQS_51
is the user achievable rate constraint,
Figure QLYQS_38
is a non-ideal channel constraint. 5.根据权利要求1所述的非理想信道下的去蜂窝MIMO鲁棒性波束赋形方法，其特征在于：步骤S5所述的将功率最小化模型的目标函数从
Figure QLYQS_52
范数最小化问题近似成一个凸的加权的
Figure QLYQS_53
范数问题，并通过迭代获取足够的稀疏性，包括以下子步骤：5. The method for robust beamforming of decellularized MIMO in non-ideal channels according to claim 1, characterized in that: the objective function of the power minimization model in step S5 is changed from
Figure QLYQS_52
The norm minimization problem is approximated as a convex weighted
Figure QLYQS_53
norm problem and obtain sufficient sparsity through iteration, including the following sub-steps: S501：由于AP休眠功率为常数，对优化结果没有影响，将其去除，对目标函数进行变形，若用
Figure QLYQS_54
范数的平方来替换
Figure QLYQS_55
范数，
Figure QLYQS_56
范数的个数总量保持不变，AP活跃与休眠模式功率差表述为：
Figure QLYQS_57
；S501: Since the AP sleep power is a constant and has no effect on the optimization result, it is removed and the objective function is deformed.
Figure QLYQS_54
The square of the norm is used to replace
Figure QLYQS_55
norm,
Figure QLYQS_56
The total number of norms remains unchanged, and the power difference between AP active and sleep modes is expressed as:
Figure QLYQS_57
; S502：根据压缩感知理论，
Figure QLYQS_58
范数最小化问题能够近似成一个凸的加权的
Figure QLYQS_59
范数问题，则用户
Figure QLYQS_60
可达速率与信道误差约束下的系统总功率最小化优化问题可近似表述为：S502: According to the theory of compressed sensing,
Figure QLYQS_58
The norm minimization problem can be approximated as a convex weighted
Figure QLYQS_59
norm problem, then the user
Figure QLYQS_60
The optimization problem of minimizing the total system power under the constraints of achievable rate and channel error can be approximately expressed as:
Figure QLYQS_61
，
Figure QLYQS_62
为接入点
Figure QLYQS_63
对用户
Figure QLYQS_64
所占的权重；
Figure QLYQS_61
,
Figure QLYQS_62
For access point
Figure QLYQS_63
For users
Figure QLYQS_64
The weight it occupies; S503：将
Figure QLYQS_65
合并同类项后，得到下式：S503:
Figure QLYQS_65
After combining like terms, we get the following formula:
Figure QLYQS_66
；
Figure QLYQS_66
; S504：不断迭代权重
Figure QLYQS_67
，并用迭代后的权重不断地对步骤S503的公式进行求解，最终得到一个最优解，对
Figure QLYQS_68
进行迭代的重加权公式为：
Figure QLYQS_69
，其中，
Figure QLYQS_70
为一个正指数，
Figure QLYQS_71
，
Figure QLYQS_72
为一个极小的防止分母为0正数。S504: Continuously iterate weights
Figure QLYQS_67
, and use the iterated weights to continuously solve the formula in step S503, and finally obtain an optimal solution.
Figure QLYQS_68
The iterative reweighting formula is:
Figure QLYQS_69
,in,
Figure QLYQS_70
is a positive index,
Figure QLYQS_71
,
Figure QLYQS_72
is a very small positive number that prevents the denominator from being zero. 6.根据权利要求1所述的非理想信道下的去蜂窝MIMO鲁棒性波束赋形方法，其特征在于：步骤S6所述的将可达速率约束条件转化为线性矩阵不等式，包括以下子步骤：6. The method for robust beamforming of decellularized MIMO in non-ideal channels according to claim 1, characterized in that: the step S6 of converting the achievable rate constraint condition into a linear matrix inequality comprises the following sub-steps: S601：对约束条件进行处理，用户
Figure QLYQS_73
可达速率约束和信道误差约束分别为：S601: Process the constraints.
Figure QLYQS_73
The achievable rate constraint and channel error constraint are:
Figure QLYQS_74
(1)
Figure QLYQS_74
(1)
Figure QLYQS_75
(2)；
Figure QLYQS_75
(2); S602：处理用户
Figure QLYQS_76
可达速率约束，不等式左边用一阶泰勒公式逼近为一个如下的下界：S602: Processing users
Figure QLYQS_76
The achievable rate constraint, the left side of the inequality is approximated by the first-order Taylor formula as a lower bound as follows: 设
Figure QLYQS_77
为迭代
Figure QLYQS_78
次后的最优解，那么
Figure QLYQS_79
的线性下界为：
Figure QLYQS_80
，其中
Figure QLYQS_81
，处理用户
Figure QLYQS_82
可达速率约束为：set up
Figure QLYQS_77
For iteration
Figure QLYQS_78
The optimal solution after that,
Figure QLYQS_79
The linear lower bound of is:
Figure QLYQS_80
,in
Figure QLYQS_81
, handle user
Figure QLYQS_82
The achievable rate constraint is:
Figure QLYQS_83
；
Figure QLYQS_83
; S603：引入S-引理，将约束转化为如下线性矩阵不等式模型：S603: Introduce the S-lemma and transform the constraints into the following linear matrix inequality model:
Figure QLYQS_84
；(3)
Figure QLYQS_84
; (3) 式中，I为单位矩阵，IM为M×M的单位矩阵，
Figure QLYQS_85
表示
Figure QLYQS_86
的估计值，
Figure QLYQS_87
为稀疏变量。Where I is the identity matrix, IM is the M×M identity matrix,
Figure QLYQS_85
express
Figure QLYQS_86
The estimated value of
Figure QLYQS_87
is a sparse variable. 7.根据权利要求1所述的非理想信道下的去蜂窝MIMO鲁棒性波束赋形方法，其特征在于：步骤S7所述的将信道误差约束转化为线性矩阵不等式，包括以下子步骤：7. The method for robust beamforming of decellularized MIMO in non-ideal channels according to claim 1, characterized in that: the step S7 of converting the channel error constraint into a linear matrix inequality comprises the following sub-steps: S701：用舒尔补将信道误差约束公式写为：S701: Use Schur complement to write the channel error constraint formula as:
Figure QLYQS_88
，其中
Figure QLYQS_89
；
Figure QLYQS_88
,in
Figure QLYQS_89
; S702：根据涅米罗夫斯基引理，并引入稀疏变量
Figure QLYQS_90
，将S701中的公式转换为线性矩阵不等式模型：S702: Based on Nemirovsky's lemma, and introducing sparse variables
Figure QLYQS_90
, convert the formula in S701 into a linear matrix inequality model:
Figure QLYQS_91
(4)。
Figure QLYQS_91
(4). 8.根据权利要求1所述的非理想信道下的去蜂窝MIMO鲁棒性波束赋形方法，其特征在于：所述步骤S8将步骤S5至S7所得的模型转化为SDP问题，通过凸优化工具箱进行求解，得到最优的波束赋形向量，包括以下子步骤：8. The method for robust beamforming of decellularized MIMO in non-ideal channels according to claim 1, characterized in that: the step S8 converts the model obtained in steps S5 to S7 into an SDP problem, solves it by a convex optimization toolbox, and obtains an optimal beamforming vector, comprising the following sub-steps: S801：将步骤S5至S7所得的模型转化为SDP问题：S801: Convert the model obtained from steps S5 to S7 into an SDP problem:
Figure QLYQS_92
；
Figure QLYQS_92
; S802：根据
Figure QLYQS_93
得到
Figure QLYQS_94
为本SDP问题的最优波束赋形向量。S802: According to
Figure QLYQS_93
get
Figure QLYQS_94
is the optimal beamforming vector for this SDP problem.
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