CN113660022B - Transceiver and IRS Optimization Design Method of Over-the-Air Computing System under Nonideal CSI - Google Patents
Transceiver and IRS Optimization Design Method of Over-the-Air Computing System under Nonideal CSI Download PDFInfo
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Abstract
本发明公开了一种非理想CSI下空中计算系统的收发机及IRS优化设计方法,包括以下步骤:(1)根据CSI的不确定域,求解接收端MSE最恶劣情况下CSI的误差
并计算接收端MSE;(2)去除IRS相位的恒模约束,以最小化接收端MSE为目标,固定各个传感器的发射功率tk和接收端的合并系数m,优化IRS的反射相位向量vk;(3)固定IRS的反射相位向量vk,优化各个传感器发射功率tk和接收端的合并系数m;(4)重复步骤(2)‑(3),直至接收端的MSE迭代收敛;(5)对IRS的反射相位向量vk进行恒模约束。本发明能够在发射总功率受限的条件下,降低系统在非理想CSI条件下的接收误差。The invention discloses a transceiver and an IRS optimization design method of an over-the-air computing system under non-ideal CSI, comprising the following steps: (1) According to the uncertainty domain of CSI, solve the error of CSI under the worst case of MSE at the receiving end
And calculate the MSE of the receiving end; (2) remove the constant modulus constraint of the IRS phase, take the minimum MSE of the receiving end as the goal, fix the transmit power t k of each sensor and the combining coefficient m of the receiving end, and optimize the reflection phase vector v k of the IRS; (3) Fix the reflection phase vector v k of the IRS, and optimize the transmit power t k of each sensor and the combining coefficient m of the receiving end; (4) Repeat steps (2)-(3) until the MSE iteratively converges at the receiving end; (5) pair The reflection phase vector v k of the IRS carries out constant modulus constraint. The invention can reduce the receiving error of the system under the condition of non-ideal CSI under the condition that the total transmit power is limited.Description
技术领域technical field
本发明涉及通信领域,涉及非理想CSI下空中计算系统的收发机及IRS优化设计方法。The invention relates to the field of communication, and relates to a transceiver and an IRS optimization design method of an over-the-air computing system under non-ideal CSI.
背景技术Background technique
物联网(IoT)服务发展如火如荼,涉及到人们生活的方方面面。作为当前信息高速时代最突出的特征,海量数据的惊人增长对物联网具有至关重要的意义。一方面,物联网智能设备数量不断增加,数据收集变得更加困难。另一方面,海量数据的信息融合,或者我们称之为数据聚合,对于数十亿传感器带来的低频谱效率和高延迟更具挑战性。The Internet of Things (IoT) services are in full swing and touch every aspect of people's lives. As the most prominent feature of the current era of high-speed information, the astonishing growth of massive data is of vital significance to the Internet of Things. On the one hand, the growing number of IoT smart devices makes data collection more difficult. On the other hand, information fusion of massive data, or what we call data aggregation, is more challenging with the low spectral efficiency and high latency brought about by billions of sensors.
为了解决这个问题,研究人员提出了一种有前途的解决方案,即利用无线多址信道(MAC)的叠加特性的空中计算(AirComp)。通过传感器的并发传输和系统中分布式本地计算的加权平均函数,可以在接收端直接获得所需的数据。AirComp在信息论、信号处理、收发器设计等诸多方面都备受关注,研究发现AirComp可以提高通信效率并降低所需带宽。但是,上述技术的优点是有前提的,即MAC不被阻塞。To address this problem, researchers propose a promising solution, Over-the-Air Computation (AirComp) that exploits the superposition properties of wireless multiple-access channels (MACs). Through the concurrent transmission of sensors and the weighted average function of distributed local computation in the system, the required data can be obtained directly at the receiving end. AirComp has attracted much attention in many aspects such as information theory, signal processing, transceiver design, etc. The study found that AirComp can improve communication efficiency and reduce the required bandwidth. However, the advantage of the above technique is premised that the MAC is not blocked.
为了解决这个问题,智能反射面(IRS)被认为可以通过利用无源反射元件以理想角度反射入射信号来改善信号传播条件,这是一种新兴的补充技术。它可以很容易地连附着到建筑物的外部,并且成本低。鉴于IRS的实时重构特性,其应用得到了广泛的发展,如物联网中的安全通信、同步无线信息和电力传输系统(SWIPT)、边缘计算(MEC)等。因此,利用IRS对AirComp系统进行辅助,可以通过优化收发器和相移来降低AirComp的MSE。然而,上述所有研究都高度依赖于完美的CSI,这在应用中很难获得。因此,也有必要引入随机和确定性鲁棒性以减轻CSI不准确度方面的性能下降。此外,AirComp系统的无线传感器通常由功率有限的信标供电,总功率约束也是一大挑战。To address this issue, intelligent reflective surfaces (IRS) are considered to improve signal propagation conditions by utilizing passive reflective elements to reflect incident signals at ideal angles, an emerging complementary technology. It can be easily attached to the exterior of a building and is inexpensive. In view of the real-time reconfiguration characteristics of IRS, its applications have been widely developed, such as secure communication in the Internet of Things, synchronous wireless information and power transmission system (SWIPT), edge computing (MEC), etc. Therefore, using the IRS to assist the AirComp system can reduce the MSE of AirComp by optimizing the transceiver and phase shift. However, all the above studies are highly dependent on perfect CSI, which is difficult to obtain in applications. Therefore, it is also necessary to introduce stochastic and deterministic robustness to mitigate performance degradation in terms of CSI inaccuracy. In addition, the wireless sensors of AirComp systems are often powered by power-limited beacons, and overall power constraints are also a challenge.
发明内容SUMMARY OF THE INVENTION
本发明的目的是提供一种非理想CSI下空中计算系统的收发机及IRS优化设计方法,通过设计IRS辅助AirComp系统的系统发射端各个传感器的发射功率、接收端的合并系数和IRS相位,从而最小化接收端的接收MSE。The purpose of the present invention is to provide a transceiver and an IRS optimization design method of an air computing system under non-ideal CSI. Receive MSE at the receiving end.
为了解决复杂的非凸问题,本发明通过利用高效的交替优化算法和KKT条件获得鲁棒问题的闭式解和各个传感器的发射功率、接收端的合并系数和IRS相位的联合设计。In order to solve the complex non-convex problem, the present invention obtains the closed-form solution of the robust problem and the joint design of the transmitting power of each sensor, the combining coefficient of the receiving end and the IRS phase by using an efficient alternating optimization algorithm and KKT conditions.
为了达到上述目的,本发明提供如下技术方案:In order to achieve the above object, the present invention provides the following technical solutions:
一种非理想CSI下空中计算系统的收发机及IRS优化设计方法,包括以下步骤:A transceiver and an IRS optimization design method for an over-the-air computing system under non-ideal CSI, comprising the following steps:
(1)根据CSI的不确定域,求解接收端MSE最恶劣情况下CSI的误差并计算接收端MSE,其中,k∈{1,2,…,K},K表示空中计算系统中发射端传感器数量;(1) According to the uncertainty domain of CSI, solve the error of CSI in the worst case of MSE at the receiving end And calculate the receiver MSE, where k∈{1,2,…,K}, K represents the number of transmitter sensors in the air computing system;
(2)去除IRS相位的恒模约束,以最小化接收端MSE为目标,固定各个传感器的发射功率tk和接收端的合并系数m,优化IRS的反射相位向量vk;(2) remove the constant modulus constraint of the IRS phase, take minimizing the MSE of the receiving end as the goal, fix the transmit power t k of each sensor and the combining coefficient m of the receiving end, and optimize the reflection phase vector v k of the IRS;
(3)固定IRS的反射相位向量vk,优化各个传感器发射功率tk和接收端的合并系数m;(3) The reflection phase vector v k of the IRS is fixed, and the transmit power t k of each sensor and the combining coefficient m of the receiving end are optimized;
(4)重复步骤(2)-(3),直至接收端的MSE迭代收敛;(4) Repeat steps (2)-(3) until the MSE iteratively converges at the receiving end;
(5)对IRS的反射相位向量vk进行恒模约束。(5) Constrain the constant modulus of the reflection phase vector v k of the IRS.
进一步的,所述步骤(1)中,CSI的不确定域为即CSI的不确定域被限制在以ε为半径的区域内。Further, in the step (1), the uncertainty domain of CSI is That is, the uncertainty region of CSI is limited to the region with ε as the radius.
其中,表示信道反馈的CSI误差,表示第k个传感器经由第k个IRS阵面反射到达接收基站的真实的等效级联信道,表示第k个传感器经由第k个IRS阵面反射到达接收基站的估计的等效级联信道。其中,N表示IRS反射单元数目,k∈{1,2,…,K},K表示空中计算系统中发射端传感器数量,‖‖2表示向量Frobenius范数,()H表示矩阵共轭转置;in, represents the CSI error of the channel feedback, represents the real equivalent concatenated channel of the kth sensor reaching the receiving base station through the kth IRS front reflection, represents the estimated equivalent concatenated channel of the kth sensor arriving at the receiving base station via the kth IRS front reflection. Among them, N represents the number of IRS reflection units, k∈{1,2,…,K}, K represents the number of transmitter sensors in the air computing system, ‖‖2 represents the vector Frobenius norm, () H represents the matrix conjugate transpose ;
接收端的最恶劣情况的MSE问题表述为The worst-case MSE problem at the receiver is formulated as
约束条件为其中,m为接收端的合并系数,vk为第k个IRS的反射向量,tk表示第k个传感器的发射功率,σ2为加性高斯白噪声功率,||2表示复数的模的平方;Constraints are Among them, m is the combining coefficient of the receiving end, v k is the reflection vector of the kth IRS, tk is the transmit power of the kth sensor, σ 2 is the additive white Gaussian noise power, and || 2 is the square of the modulus of the complex number ;
由于每个传感器的级联等效信道相互独立,最恶劣情况的MSE问题转换为Since the cascaded equivalent channels of each sensor are independent of each other, the worst-case MSE problem is transformed into
进一步的,所述步骤(1)中,接收端MSE最恶劣情况下CSI的误差为Further, in the step (1), the error of the CSI in the worst case of the receiving end MSE is:
其中,()*表示复数的共轭,为中间变量,λk表示对于第k个传感器的等效级联信道误差优化时的KKT(Karush-Kuhn-Tucker)乘子,且where () * denotes the conjugate of complex numbers, is an intermediate variable, λ k represents the KKT (Karush-Kuhn-Tucker) multiplier when optimizing the equivalent cascaded channel error for the kth sensor, and
此时为CSI最恶劣情况,且接收端的接收MSE为At this time, it is the worst case of CSI, and the receiving MSE of the receiving end is
进一步的,所述步骤(2)中,通过固定各个传感器的发射功率tk和接收端的合并系数m,构建如下优化问题优化IRS的反射相位向量vk:Further, in the step (2), by fixing the transmit power t k of each sensor and the combining coefficient m of the receiving end, the following optimization problem is constructed to optimize the reflection phase vector v k of the IRS:
优化目标为: The optimization objective is:
约束条件为:|vk(n)|2=1,n∈{1,…,N}The constraints are: |v k (n)| 2 = 1, n∈{1,…,N}
其中,vk(n)表示第k个IRS的反射向量中第n个元素;由于各个传感器之间相互独立,求和优化问题可以分解为K个子优化问题,k∈{1,2,…,K},K表示空中计算系统中发射端传感器数量;要使问题可解,先暂时去除IRS相位的恒模约束,优化目标变为Among them, v k (n) represents the n-th element in the reflection vector of the k-th IRS; since each sensor is independent of each other, the summation optimization problem can be decomposed into K sub-optimization problems, k∈{1,2,…, K}, K represents the number of transmitter sensors in the air computing system; to make the problem solvable, first temporarily remove the constant modulus constraint of the IRS phase, and the optimization objective becomes
其中,为中间变量,表示空中计算系统里K个传感器的总功率限制。in, is an intermediate variable, Represents the total power limit of the K sensors in the air computing system.
进一步的,所述步骤(2)中,最优IRS的反射相位向量为Further, in the step (2), the reflection phase vector of the optimal IRS is
其中,表示计算矩阵的Moore-Penrose逆。in, Represents computing the Moore-Penrose inverse of a matrix.
进一步的,所述步骤(3)中,通过固定IRS的反射相位向量vk,构建如下优化问题优化优化各个传感器发射功率tk和接收端的合并系数m:Further, in the step (3), by fixing the reflection phase vector v k of the IRS, the following optimization problem is constructed to optimize the transmission power t k of each sensor and the combining coefficient m of the receiving end:
优化目标为: The optimization objective is:
通过求导,得到最优中间变量Obtain the optimal intermediate variable by derivation
且and
其中,表示计算矩阵的Moore-Penrose逆。in, Represents computing the Moore-Penrose inverse of a matrix.
进一步的,所述步骤(5)中,对IRS的反射相位向量vk进行恒模约束为Further, in the step (5), the constant modulus constraint is performed on the reflection phase vector v k of the IRS as
其中,‖‖2表示向量Frobenius范数。where ‖‖ 2 represents the Frobenius norm of the vector.
有益效果:本发明通过设计IRS辅助AirComp系统的系统发射端各个传感器的发射功率、接收端的合并系数和IRS相位,从而最小化接收端的接收MSE。为了解决复杂的非凸问题,我们通过利用高效的交替优化算法和KKT条件获得鲁棒问题的闭式解和各个传感器的发射功率、接收端的合并系数和IRS相位的联合设计。采用交替优化算法解决原本非凸且耦合度非常高的复杂优化问题,并且通过中间变量将非凸问题转化为凸问题,并得到了闭式解,相比其他发明的非闭式解具有绝对优势。此外,本发明能够在发射总功率受限的条件下,有效降低系统在非理想CSI条件下的接收误差。Beneficial effects: The present invention minimizes the receiving MSE at the receiving end by designing the transmit power of each sensor at the transmitting end of the IRS-assisted AirComp system, the combining coefficient at the receiving end and the IRS phase. To solve the complex non-convex problem, we obtain the closed-form solution of the robust problem and the joint design of the transmit power of each sensor, the combining coefficient at the receiver and the IRS phase by utilizing an efficient alternating optimization algorithm and KKT conditions. The alternating optimization algorithm is used to solve the original non-convex and highly coupled complex optimization problem, and the non-convex problem is transformed into a convex problem through intermediate variables, and a closed-form solution is obtained, which has absolute advantages compared with other invented non-closed-form solutions. . In addition, the present invention can effectively reduce the reception error of the system under the condition of non-ideal CSI under the condition that the total transmit power is limited.
附图说明Description of drawings
图1是本发明实际应用场景示意图;1 is a schematic diagram of a practical application scenario of the present invention;
图2是本发明的流程图;Fig. 2 is the flow chart of the present invention;
图3是采用本发明的优化方法的接收NMSE随IRS反射单元数N的曲线图。FIG. 3 is a graph of the received NMSE versus the number N of IRS reflection units using the optimization method of the present invention.
具体实施方式Detailed ways
以下将结合具体实施例对本发明提供的技术方案进行详细说明,应理解下述具体实施方式仅用于说明本发明而不用于限制本发明的范围。The technical solutions provided by the present invention will be described in detail below with reference to specific embodiments, and it should be understood that the following specific embodiments are only used to illustrate the present invention and not to limit the scope of the present invention.
本发明所涉及的技术术语解释如下:The technical terms involved in the present invention are explained as follows:
CSI:信道状态信息;CSI: channel state information;
AirComp:空中计算系统;AirComp: air computing system;
IRS:智能反射面;IRS: Intelligent Reflector;
MSE:最小均方误差。MSE: Minimum Mean Squared Error.
本发明的一种非理想信道状态信息(CSI)下空中计算系统(AirComp)的收发机及智能反射面(IRS)优化设计方法,其中,发射端为K个单天线传感器发送IoT系统所需的环境信息,经由K个具有N个反射单元的IRS的发射,到达接收端,接收端为单天线且接收所需量为K个单天线传感器发送的信息量的和。A transceiver and intelligent reflector (IRS) optimization design method of an air computing system (AirComp) under non-ideal channel state information (CSI) of the present invention, wherein, the transmitting end is K single-antenna sensors to transmit the required information of the IoT system. The environmental information reaches the receiving end through the transmission of K IRSs with N reflecting units. The receiving end is a single antenna and the required amount of reception is the sum of the information sent by the K single-antenna sensors.
本发明以发射总功率受限为约束条件,研究接收端MSE最恶劣CSI情况下的接收端MSE和CSI的误差并联合优化系统发射端各个传感器的发射功率tk、接收端的合并系数m和IRS相位vk,从而最小化接收端的接收最小均方误差(MSE)。The invention takes the limitation of the total transmission power as the constraint condition, and studies the error of the MSE and CSI of the receiving end under the worst CSI condition of the receiving end MSE And jointly optimize the transmit power t k of each sensor at the transmitter end, the combining coefficient m and the IRS phase v k at the receiver end, so as to minimize the minimum mean square error (MSE) of the receiver end.
为了降低接收端的接收MSE,本发明通过设计IRS辅助AirComp系统的系统发射端各个传感器的发射功率、接收端的合并系数和IRS相位,从而最小化接收端的接收MSE。为了解决复杂的非凸问题,本发明通过利用高效的交替优化算法和KKT条件获得鲁棒问题的闭式解和各个传感器的发射功率、接收端的合并系数和IRS相位的联合设计。采用交替优化算法解决原本非凸且耦合度非常高的复杂优化问题,并且通过中间变量将非凸问题转化为凸问题,并得到了闭式解,相比其他发明的非闭式解具有绝对优势。In order to reduce the receiving MSE at the receiving end, the present invention minimizes the receiving MSE at the receiving end by designing the transmit power of each sensor at the transmitting end of the IRS-assisted AirComp system, the combining coefficient and the IRS phase at the receiving end. In order to solve the complex non-convex problem, the present invention obtains the closed-form solution of the robust problem and the joint design of the transmitting power of each sensor, the combining coefficient of the receiving end and the IRS phase by using an efficient alternating optimization algorithm and KKT conditions. The alternating optimization algorithm is used to solve the original non-convex and highly coupled complex optimization problem, and the non-convex problem is transformed into a convex problem through intermediate variables, and a closed-form solution is obtained, which has absolute advantages compared with other invented non-closed-form solutions. .
如图1所示,发射端为K个单天线传感器发送IoT系统所需的环境信息,为了增强接收端的接收信号,采用K个IRS进行传播环境重构。主要优化设计思路是首先根据CSI的不确定域,分析接收端MSE最恶劣情况下接收MSE和此时CSI的误差;然后在该最恶劣情况的MSE下,先去除IRS相位的恒模约束,固定各个传感器的发射功率和接收端的合并系数,优化IRS的反射相位向量,然后固定IRS的反射相位向量,优化固定各个传感器的发射功率和接收端的合并系数,重复IRS的反射相位向量和系统的收发端系数的交替优化步骤直至系统的接收MSE收敛;对IRS的反射相位向量的优化结果进行恒模限制。本发明能够在发射总功率受限的条件下,有效降低系统在非理想CSI条件下的接收误差。As shown in Figure 1, the transmitter sends the environmental information required by the IoT system for K single-antenna sensors. In order to enhance the received signal at the receiver, K IRSs are used to reconstruct the propagation environment. The main optimization design idea is to first analyze the error of the receiving MSE and the CSI in the worst case of the receiver MSE according to the uncertainty field of CSI; then, under the worst case MSE, first remove the constant modulus constraint of the IRS phase, and fix The transmit power of each sensor and the combining coefficient of the receiving end, optimize the reflection phase vector of the IRS, then fix the reflected phase vector of the IRS, optimize and fix the transmitting power of each sensor and the combining coefficient of the receiving end, repeat the reflected phase vector of the IRS and the transmitting and receiving end of the system Alternate optimization steps of the coefficients until the received MSE of the system converges; the optimization result of the reflected phase vector of the IRS is limited by constant modulus. The invention can effectively reduce the reception error of the system under the condition of non-ideal CSI under the condition that the total transmit power is limited.
本发明的非理想CSI下AirComp系统的收发机及IRS的优化设计方法,包括如下步骤:The optimal design method of the transceiver of the AirComp system and the IRS under the non-ideal CSI of the present invention comprises the following steps:
(1)根据CSI的不确定域,求解接收端MSE最恶劣情况下CSI的误差 (1) According to the uncertainty domain of CSI, solve the error of CSI in the worst case of MSE at the receiving end
其中,CSI的不确定域为即CSI的不确定域被限制在以ε为半径的区域内;Among them, the uncertainty domain of CSI is That is, the uncertainty domain of CSI is limited to the area with ε as the radius;
其中,表示信道反馈的CSI误差,表示第k个传感器经由第k个IRS阵面反射到达接收基站的真实的等效级联信道,表示第k个传感器经由第k个IRS阵面反射到达接收基站的估计的等效级联信道。其中,N表示IRS反射单元数目,k∈{1,2,…,K},K表示AirComp系统中发射端传感器数量,‖‖2表示向量Frobenius范数,()H表示矩阵共轭转置;in, represents the CSI error of the channel feedback, represents the real equivalent concatenated channel of the kth sensor reaching the receiving base station through the kth IRS front reflection, represents the estimated equivalent concatenated channel of the kth sensor arriving at the receiving base station via the kth IRS front reflection. Among them, N represents the number of IRS reflection units, k∈{1,2,…,K}, K represents the number of transmitter sensors in the AirComp system, ‖‖2 represents the vector Frobenius norm, () H represents the matrix conjugate transpose;
此时,接收端的最恶劣情况的MSE问题表述为At this point, the worst-case MSE problem at the receiver is formulated as
约束条件为其中,m为接收端的合并系数,vk为第k个IRS的反射向量,tk表示第k个传感器的发射功率,σ2为加性高斯白噪声功率,||2表示复数的模的平方;Constraints are Among them, m is the combining coefficient of the receiving end, v k is the reflection vector of the kth IRS, tk is the transmit power of the kth sensor, σ 2 is the additive white Gaussian noise power, and || 2 is the square of the modulus of the complex number ;
由于每个传感器的级联等效信道相互独立,上述最恶劣情况的MSE问题转换为Since the cascaded equivalent channels of each sensor are independent of each other, the above worst-case MSE problem transforms into
其中,k∈{1,2,…,K},K表示AirComp系统中发射端传感器数量;Among them, k∈{1,2,…,K}, K represents the number of transmitter sensors in the AirComp system;
上述最恶劣情况下CSI的误差为The error of the CSI in the worst case above is
其中,()*表示复数的共轭,为中间变量,λk表示对于第k个传感器的等效级联信道误差优化时的KKT(Karush-Kuhn-Tucker)乘子,且where () * denotes the conjugate of complex numbers, is an intermediate variable, λ k represents the KKT (Karush-Kuhn-Tucker) multiplier when optimizing the equivalent cascaded channel error for the kth sensor, and
此时为CSI最恶劣情况,且接收端的接收MSE为At this time, it is the worst case of CSI, and the receiving MSE of the receiving end is
(2)去除IRS相位的恒模约束,以最小化接收端MSE为目标,固定各个传感器的发射功率tk和接收端的合并系数m,优化IRS的反射相位向量vk。通过固定各个传感器的发射功率tk和接收端的合并系数m,构建如下优化问题优化IRS的反射相位向量vk:(2) Removing the constant modulus constraint of the IRS phase, aiming at minimizing the MSE of the receiving end, fixing the transmit power t k of each sensor and the combining coefficient m of the receiving end, and optimizing the reflection phase vector v k of the IRS. By fixing the transmit power t k of each sensor and the combining coefficient m of the receiving end, the following optimization problem is constructed to optimize the reflection phase vector v k of the IRS:
优化目标为: The optimization objective is:
约束条件为:|vk(n)|2=1,n∈{1,…,N}The constraints are: |v k (n)| 2 = 1, n∈{1,…,N}
其中,vk(n)表示第k个IRS的反射向量中第n个元素;由于各个传感器之间相互独立,求和优化问题分解为K个子优化问题,k∈{1,2,…,K},K表示空中计算系统中发射端传感器数量;要使问题可解,先暂时去除IRS相位的恒模约束,优化目标变为Among them, v k (n) represents the n-th element in the reflection vector of the k-th IRS; since each sensor is independent of each other, the summation optimization problem is decomposed into K sub-optimization problems, k∈{1,2,…,K }, K represents the number of transmitter sensors in the air computing system; to make the problem solvable, first temporarily remove the constant modulus constraint of the IRS phase, and the optimization objective becomes
其中,为中间变量,表示AirComp系统里K个传感器的总功率限制;in, is an intermediate variable, Indicates the total power limit of the K sensors in the AirComp system;
其中,最优IRS的反射相位向量为Among them, the reflection phase vector of the optimal IRS is
其中,表示计算矩阵的Moore-Penrose逆。in, Represents computing the Moore-Penrose inverse of a matrix.
(3)固定IRS的反射相位向量vk,优化各个传感器发射功率tk和接收端的合并系数m;通过固定IRS的反射相位向量vk,构建如下优化问题优化优化各个传感器发射功率tk和接收端的合并系数m:(3) Fix the reflection phase vector v k of the IRS, and optimize the transmission power t k of each sensor and the combining coefficient m of the receiving end; by fixing the reflection phase vector v k of the IRS, the following optimization problem is constructed to optimize the transmission power t k and the receiving end of each sensor. Merging factor m at the end:
优化目标为: The optimization objective is:
通过求导,得到最优中间变量Obtain the optimal intermediate variable by derivation
且and
其中,表示计算矩阵的Moore-Penrose逆。in, Represents computing the Moore-Penrose inverse of a matrix.
(4)重复步骤(2)-(3),直至接收端的MSE迭代收敛。(4) Repeat steps (2)-(3) until the MSE at the receiving end is iteratively converged.
(5)对IRS的反射相位向量vk进行恒模约束,即(5) Constrain the constant modulus of the reflection phase vector v k of the IRS, namely
其中,‖‖2表示向量Frobenius范数。where ‖‖ 2 represents the Frobenius norm of the vector.
如图2所示,本发明的主要流程是首先根据CSI的不确定域,分析接收端MSE最恶劣情况下接收MSE和此时CSI的误差;然后在该最恶劣情况的MSE下,先去除IRS相位的恒模约束,固定各个传感器的发射功率和接收端的合并系数,优化IRS的反射相位向量,然后固定IRS的反射相位向量,优化固定各个传感器的发射功率和接收端的合并系数,重复IRS的反射相位向量和系统的收发端系数的交替优化步骤直至系统的接收MSE收敛;对IRS的反射相位向量的优化结果进行恒模限制。As shown in Figure 2, the main process of the present invention is to first analyze the error between the receiving MSE and the CSI in the worst case of the MSE at the receiving end according to the uncertainty field of the CSI; then, in the worst case of the MSE, first remove the IRS The constant modulus constraint of the phase, fix the transmit power of each sensor and the combining coefficient of the receiving end, optimize the reflection phase vector of the IRS, then fix the reflection phase vector of the IRS, optimize and fix the transmitting power of each sensor and the combining coefficient of the receiving end, repeat the reflection of the IRS Alternate optimization steps of the phase vector and the coefficients of the transceiver end of the system until the receiving MSE of the system converges; the optimization result of the reflected phase vector of the IRS is limited by constant modulus.
如图3所示,本发明提出的优化设计方案能在发射总功率受限的条件下,有效地降低系统在非理想CSI条件下的接收误差。和传统方案不考虑鲁棒性设计相比,具有性能优势。As shown in FIG. 3 , the optimized design scheme proposed by the present invention can effectively reduce the reception error of the system under the condition of non-ideal CSI under the condition that the total transmit power is limited. Compared with the traditional scheme without considering the robustness design, it has performance advantages.
本发明方案所公开的技术手段不仅限于上述实施方式所公开的技术手段,还包括由以上技术特征任意组合所组成的技术方案。应当指出,对于本技术领域的普通技术人员来说,在不脱离本发明原理的前提下,还可以做出若干改进和润饰,这些改进和润饰也视为本发明的保护范围。The technical means disclosed in the solution of the present invention are not limited to the technical means disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features. It should be pointed out that for those skilled in the art, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications are also regarded as the protection scope of the present invention.
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