CN114124172B - Intelligent reflector wave beam shaping and phase shift design method based on alternate direction - Google Patents

Abstract

The invention belongs to the technical field of wireless communication, and in particular relates to an intelligent reflective surface beam forming and phase shifting design method based on alternating directions. The solution of the present invention is mainly to optimize the design of the phase matrix Θ without considering the beamforming vector w, so as to achieve the goal of maximizing the lower bound of the overall receiving signal-to-noise ratio. The present invention is based on a RIS-assisted MIMO transmission communication system, A low-complexity alternating direction smart reflector beamforming and phase shifting design scheme is proposed. In the LAD scheme, unlike the AD scheme, it is only solved by optimizing the phase shift without considering the beamforming vector problem, greatly reducing the complexity and increasing the convergence speed.

Description

Beamforming and phase shifting design method for smart reflectors based on alternating directions

technical field

The invention belongs to the technical field of wireless communication, and in particular relates to an intelligent reflective surface beam forming and phase shifting design method based on alternating directions.

Background technique

Smart Reflective Surface (RIS) technology is a new revolutionary technology, which can intelligently reconfigure the wireless propagation environment by integrating a large number of low-cost passive reflective elements on a plane, thereby significantly improving the performance of wireless communication networks.

By utilizing the RIS controller to change the reflection coefficient, each element can independently adjust the phase shift of the wireless signal by optimizing the beamforming and phase shift, and synergistically provide multipath diversity gain, which has attracted extensive research

However, in order to solve the non-convex problem of joint optimization of beamforming and phase shift design in MIMO systems, the conventional RIS technology solution often results in performance loss and high complexity.

Contents of the invention

In view of the above problems, the present invention proposes a low-complexity alternating direction (LAD, Low-complexity Alternating Direction) scheme, and proposes a low-complexity alternating direction (LAD) scheme, which is different from the AD scheme in maximizing the overall receiving signal-to-noise ratio , LAD greatly reduces computational complexity and improves convergence speed by maximizing the lower bound of the overall received SNR.

与

分别表示BS-RIS链路的信道、RIS-Receiver链路的信道和BS-Receiver链路的信道，其中

表示复数域。The technical solution adopted by the present invention is based on low-complexity alternating direction intelligent reflector beamforming and phase shift design: the system model is shown in Figure 1, considering a RIS-assisted MIMO transmission communication system, the sender is BS, and the receiver is For Receiver. The BS of the sender is deployed with N _t antennas, the RIS is deployed with N reflection units, and the Receiver is deployed with N _r antennas. The sender communicates with the receiver through RIS. Each reflection unit in the RIS can independently use the reflection coefficient to adjust the phase shift (Phase Shift, PS) of the incident signal.

and

respectively represent the channel of the BS-RIS link, the channel of the RIS-Receiver link and the channel of the BS-Receiver link, where

Represents a complex field.

进行预编码，接收机整体信号可建模为The working principle of the beamforming and phase shifting design of smart reflectors based on alternating directions is: define the baseband transmit signal as s, and its power constraint satisfies s ^H s = E _s , and the beamforming vector

For precoding, the overall signal of the receiver can be modeled as

为复加性高斯白噪声，σ²表示方差，I表示单位矩阵，H＝RΘT+D为信道；Among them, y is the received signal, Θ is the phase shift matrix of RIS,

For complex additive Gaussian white noise, σ ² represents the variance, I represents the identity matrix, and H=RΘT+D is the channel;

Therefore, the problem can be formulated as:

st||w|| ² = 1,

θ _i ∈ [0,2π), i=1,2,…,N

Where R is the objective function, θ _i is the i-th element of the phase shift matrix Θ, according to the expression of the received signal, the objective function of the problem is

R=log(1+γ _SNR )

where γ _SNR is the received signal-to-noise ratio, expressed as:

可以转换为：then question

can be converted to:

st||w|| ² = 1,

θ _i ∈ [0,2π), i=1,2,…,N

Due to the high coupling of w and Θ, conventional methods are difficult to solve this problem. Therefore, the present invention designs a low-complexity alternating direction-based intelligent reflector beamforming and phase shifting design scheme, specifically:

变换为：Regardless of the information of the beamforming vector w, the problem

Transforms to:

stθ _i ∈ [0,2π), i=1,2,…,N

According to theorem

的下界，其中||·||₂表示矩阵的2-范数，||·||_F表示矩阵的F-范数，将问题转换为maximize

, where ||·|| ₂ represents the 2-norm of the matrix, and ||·|| _F represents the F-norm of the matrix, transforming the problem into

stθ _i ∈ [0,2π), i=1,2,…,N

分解为N个子问题，每个子问题用于优化一个反射单元：Will

Decomposed into N sub-problems, each sub-problem is used to optimize a reflective unit:

stθ _n ∈ [0,2π)

为第n个子问题，定义

其中in

For the nth subproblem, define

in

方程

有两个根，表示为：make

equation

has two roots, expressed as:

in

和

中哪个能使

的目标函数

变大来确定其解，为了得到整体解，必须从θ₁重复到θ_n，直到所有元素收敛，得到最优的Θ后，利用得到的Θ再通过问题

得到最优的w，最后得到最优的Θ和w。by judgment

with

Which of the

The objective function of

become larger to determine its solution. In order to obtain the overall solution, it is necessary to repeat from θ ₁ to θ _n until all elements converge. After obtaining the optimal Θ, use the obtained Θ to pass the problem

Get the optimal w, and finally get the optimal Θ and w.

The beneficial effect of the present invention is that, based on a RIS-assisted MIMO transmission communication system, a low-complexity alternating direction intelligent reflector beamforming and phase shift design scheme is proposed. In the LAD scheme, different from the AD scheme, The problem is solved only by optimizing the phase shift without considering the beamforming vector, which greatly reduces the complexity and improves the convergence speed.

Description of drawings

Fig. 1 is a schematic diagram of the logical structure of the system of the present invention.

Figure 2 shows the comparison between the simulation results of the LAD algorithm and the theoretical boundary.

目标函数随θ_n变化图。Figure 3 is

A plot of the objective function as a function of θ _n .

Figure 4 is a comparison of the convergence of the AD algorithm and the LAD algorithm.

Figure 5 shows the performance comparison between the AD algorithm and the LAD algorithm.

Detailed ways

The specific implementation manners of the present invention will be further described in detail below in conjunction with the accompanying drawings.

Due to the two-layer iteration, the AD algorithm has a high computational complexity. More specifically, when w is updated, the inner Θ must be iteratively updated again. Furthermore, the updated Θ requires w to be updated again in the outer iteration. Therefore, cross-iteration brings too much complexity, which is not good for practical scenarios. LAD only optimizes the design phase matrix Θ without considering the beamforming vector w. The specific plan is as follows.

可以变换为Regardless of the information of the beamforming vector w, the problem

can be converted to

stθ _i ∈ [0,2π), i=1,2,…,N

的难度非常大，因此根据定理direct solution

The difficulty of is very large, so according to theorem

的下界，则问题转换为can be maximized

The lower bound of , then the problem is transformed into

stθ _i ∈ [0,2π), i=1,2,…,N

可以分解为N个子问题Likewise, a closed-form solution for θ _n can be derived when other variables are held constant. therefore,

can be decomposed into N sub-problems

stθ _n ∈ [0,2π)

其中Similarly, define

in

该方程有两个根，表示为：make

The equation has two roots, expressed as:

in

和

中哪个能使

的目标函数

变大来确定其解。by judgment

with

Which of the

The objective function of

becomes larger to determine its solution.

In order to illustrate the superiority of the solution in terms of power performance, the beneficial effect of the present invention is verified through simulation below.

First, the theoretical bounds are compared with the simulation results, and the accuracy of the theoretical results is verified by Monte Carlo simulations. Combined with Monte Carlo simulation, Figure 2 reveals the impact of the number N _t of BS antennas and the number N of RIS units on the bit error rate of the LAD scheme. The solid and dotted lines represent computer simulation results and theoretical analysis results, respectively. According to the results shown in Figure 1, the larger the number of BS antennas, the better the bit error rate performance, and increasing the number of RIS units can also obtain better bit error rate performance. For example, at BER=10 ^-3 , the SNR loss of N _t =2 compared to N _t =4 is about 3dB, while the SNR gain of N=32 compared to N=16 is about 5dB.

为目标函数，

和

中的一个达到最大值，而另一个达到最小值。证明了方案的最优性。Figure 3 depicts the value of the objective function as a function of the specific RIS unit θ _n in [0,2π] for a single channel. The results in Figure 3 show that the

is the objective function,

with

One of them reaches a maximum value, while the other reaches a minimum value. The optimality of the scheme is proved.

In Fig. 4, the convergence of the AD algorithm and the LAD algorithm is evaluated and compared. Wherein, the simulation parameters are set as N _t =4, N _r =4. The maximum number of iterations of the AD algorithm is set to I=1. It can be seen that: 1) After many iterations, the performance of AD and LAD is almost the same. 2) LAD is better than AD in terms of convergence speed, because the boundary of LAD is always higher than the boundary of AD.

Fig. 5 compares the information accessibility performance of the AD algorithm and the LAD algorithm under the conditions of N _t =4, N _r =2,4 and N=16×1˜16×8. As expected, the performance of AD and LAD is the same. In addition, a larger number of RIS units helps to increase information reachability, while a larger number of receive antennas also provides performance gains. Therefore, compared with AD, LAD has lower complexity and almost the same performance.

Claims (1)

1. The design method of intelligent reflector beamforming and phase shift based on low-complexity alternating directions is used in a communication system for RIS-assisted MIMO transmission. In the system, the sender BS is deployed with N _t antennas, and the RIS is deployed with N reflection units , the receiver is deployed with N _r antennas, the sender communicates with the receiver through RIS, and each reflection unit in RIS can independently adjust the phase shift of the incident signal by using the reflection coefficient; define

and

respectively represent the channel of the BS-RIS link, the channel of the RIS-Receiver link and the channel of the BS-Receiver link, where

Represents the complex domain, define the baseband transmit signal as s, its power constraint satisfies s ^H s=E _s , and the beamforming vector

Precoding; the receiver signal model is:

Among them, y is the received signal, Θ is the phase shift matrix of RIS,

For complex additive Gaussian white noise, σ ² represents the variance, I represents the identity matrix, and H=RΘT+D is the channel; It is characterized in that, the beamforming and phase shift design method is, firstly, an optimization model is established:

st||w|| ² = 1, θ _i ∈ [0,2π), i=1,2,…,N Where R is the objective function, θ _i is the i-th element of the phase shift matrix Θ, according to the expression of the received signal, the objective function of the problem is expressed as: R=log(1+γ _SNR ) where γ _SNR is the received signal-to-noise ratio, expressed as:

then question

can be converted to:

st||w|| ² = 1, θ _i ∈ [0,2π), i=1,2,…,N Due to the high coupling of w and Θ, it is difficult to solve this problem by conventional methods. Therefore, a low-complexity alternating direction-based smart reflector beamforming and phase shifting design method is adopted, specifically: Regardless of the information of the beamforming vector w, the problem

Transforms to:

stθ _i ∈ [0,2π), i=1,2,…,N According to theorem

maximize

, where ||·|| ₂ represents the 2-norm of the matrix, and ||·|| _F represents the F-norm of the matrix, transforming the problem into

stθ _i ∈ [0,2π), i=1,2,…,N Will

Decomposed into N sub-problems, each sub-problem is used to optimize a reflective unit:

stθ _n ∈ [0,2π) in

For the nth subproblem, define

in

make

equation

has two roots, expressed as:

in

by judgment

with

Which of the

The objective function of

become larger to determine its solution. In order to obtain the overall solution, it is necessary to repeat from θ ₁ to θ _n until all elements converge. After obtaining the optimal Θ, use the obtained Θ to pass the problem

Get the optimal w, and finally get the optimal Θ and w.

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